Merge branch 'sofia/async-http-h1' into sofia/async-http-server

This PR verifies the `String.dropWhile` and `String.takeWhile`
functions.

It also includes a refactor of the `PatternModel` class so that the
`not_matches_empty` condition is moved into a separate typeclass
`StrictPatternModel`. This allows string patterns to implement
`LawfulForwardPatternModel` unconditionally, which means that more of
the general theory about patterns directly applies to string patterns
without having to do a case distinction for empty strings.

This PR also includes a study of the `PatternModel` machinery given to
slices `s` and `t` such that `s.copy = t.copy`. From these results, we
deduce statements like `s.copy.startsWith pat = s.startsWith pat` (which
is far from obvious!).

.vscode/tasks.json

@@ -11,6 +11,15 @@
 				"isDefault": true
 			}
 		},
+		{
+			"label": "build stage2",
+			"type": "shell",
+			"command": "make -C build/release stage2 -j$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4)",
+			"problemMatcher": [],
+			"group": {
+				"kind": "build"
+			}
+		},
 		{
 			"label": "build-old",
 			"type": "shell",

CMakeLists.txt

@@ -127,7 +127,8 @@ if(USE_MIMALLOC)
     # Unnecessarily deep directory structure, but it saves us from a complicated
     # stage0 update for now. If we ever update the other dependencies like
     # cadical, it might be worth reorganizing the directory structure.
-    SOURCE_DIR "${CMAKE_BINARY_DIR}/mimalloc/src/mimalloc"
+    SOURCE_DIR
+    "${CMAKE_BINARY_DIR}/mimalloc/src/mimalloc"
   )
   FetchContent_MakeAvailable(mimalloc)
 endif()

src/Init/Data/Order/Lemmas.lean

@@ -243,6 +243,10 @@ public theorem lt_iff_le_and_ne [LE α] [LT α] [LawfulOrderLT α] [IsPartialOrd
     a < b ↔ a ≤ b ∧ a ≠ b := by
   simpa [le_iff_lt_or_eq, or_and_right] using Std.ne_of_lt
 
+public theorem lt_trichotomy [LT α] [Std.Trichotomous (α := α) (· < ·)] (a b : α) :
+    a < b ∨ a = b ∨ b < a :=
+  Trichotomous.rel_or_eq_or_rel_swap
+
 end LT
 end Std
 

src/Init/Data/String/Basic.lean

@@ -1386,6 +1386,11 @@ theorem Slice.copy_eq_copy_sliceTo {s : Slice} {pos : s.Pos} :
   rw [Nat.max_eq_right]
   exact pos.offset_str_le_offset_endExclusive
 
+@[simp]
+theorem Slice.sliceTo_append_sliceFrom {s : Slice} {pos : s.Pos} :
+    (s.sliceTo pos).copy ++ (s.sliceFrom pos).copy = s.copy :=
+  copy_eq_copy_sliceTo.symm
+
 /-- Given a slice `s` and a position on `s.copy`, obtain the corresponding position on `s`. -/
 @[inline]
 def Pos.ofCopy {s : Slice} (pos : s.copy.Pos) : s.Pos where
@@ -1745,6 +1750,31 @@ theorem Slice.Pos.offset_cast {s t : Slice} {pos : s.Pos} {h : s.copy = t.copy}
 theorem Slice.Pos.cast_rfl {s : Slice} {pos : s.Pos} : pos.cast rfl = pos :=
   Slice.Pos.ext (by simp)
 
+@[simp]
+theorem Slice.Pos.cast_cast {s t u : Slice} {hst : s.copy = t.copy} {htu : t.copy = u.copy}
+    {pos : s.Pos} : (pos.cast hst).cast htu = pos.cast (hst.trans htu) :=
+  Slice.Pos.ext (by simp)
+
+@[simp]
+theorem Slice.Pos.cast_inj {s t : Slice} {hst : s.copy = t.copy} {p q : s.Pos} : p.cast hst = q.cast hst ↔ p = q := by
+  simp [Slice.Pos.ext_iff]
+
+@[simp]
+theorem Slice.Pos.cast_startPos {s t : Slice} {hst : s.copy = t.copy} : s.startPos.cast hst = t.startPos :=
+  Slice.Pos.ext (by simp)
+
+@[simp]
+theorem Slice.Pos.cast_eq_startPos {s t : Slice} {p : s.Pos} {hst : s.copy = t.copy} : p.cast hst = t.startPos ↔ p = s.startPos := by
+  rw [← cast_startPos (hst := hst), Pos.cast_inj]
+
+@[simp]
+theorem Slice.Pos.cast_endPos {s t : Slice} {hst : s.copy = t.copy} : s.endPos.cast hst = t.endPos :=
+  Slice.Pos.ext (by simp [← rawEndPos_copy, hst])
+
+@[simp]
+theorem Slice.Pos.cast_eq_endPos {s t : Slice} {p : s.Pos} {hst : s.copy = t.copy} : p.cast hst = t.endPos ↔ p = s.endPos := by
+  rw [← cast_endPos (hst := hst), Pos.cast_inj]
+
 @[simp]
 theorem Slice.Pos.cast_le_cast_iff {s t : Slice} {pos pos' : s.Pos} {h : s.copy = t.copy} :
     pos.cast h ≤ pos'.cast h ↔ pos ≤ pos' := by
@@ -1755,6 +1785,22 @@ theorem Slice.Pos.cast_lt_cast_iff {s t : Slice} {pos pos' : s.Pos} {h : s.copy
     pos.cast h < pos'.cast h ↔ pos < pos' := by
   simp [Slice.Pos.lt_iff]
 
+theorem Slice.Pos.cast_le_iff {s t : Slice} {pos : s.Pos} {pos' : t.Pos} {h : s.copy = t.copy} :
+    pos.cast h ≤ pos' ↔ pos ≤ pos'.cast h.symm := by
+  simp [Slice.Pos.le_iff]
+
+theorem Slice.Pos.le_cast_iff {s t : Slice} {pos : t.Pos} {pos' : s.Pos} {h : s.copy = t.copy} :
+    pos ≤ pos'.cast h ↔ pos.cast h.symm ≤ pos' := by
+  simp [Slice.Pos.le_iff]
+
+theorem Slice.Pos.cast_lt_iff {s t : Slice} {pos : s.Pos} {pos' : t.Pos} {h : s.copy = t.copy} :
+    pos.cast h < pos' ↔ pos < pos'.cast h.symm := by
+  simp [Slice.Pos.lt_iff]
+
+theorem Slice.Pos.lt_cast_iff {s t : Slice} {pos : t.Pos} {pos' : s.Pos} {h : s.copy = t.copy} :
+    pos < pos'.cast h ↔ pos.cast h.symm < pos' := by
+  simp [Slice.Pos.lt_iff]
+
 /-- Constructs a valid position on `t` from a valid position on `s` and a proof that `s = t`. -/
 @[inline]
 def Pos.cast {s t : String} (pos : s.Pos) (h : s = t) : t.Pos where
@@ -1769,6 +1815,31 @@ theorem Pos.offset_cast {s t : String} {pos : s.Pos} {h : s = t} :
 theorem Pos.cast_rfl {s : String} {pos : s.Pos} : pos.cast rfl = pos :=
   Pos.ext (by simp)
 
+@[simp]
+theorem Pos.cast_cast {s t u : String} {hst : s = t} {htu : t = u}
+    {pos : s.Pos} : (pos.cast hst).cast htu = pos.cast (hst.trans htu) :=
+  Pos.ext (by simp)
+
+@[simp]
+theorem Pos.cast_inj {s t : String} {hst : s = t} {p q : s.Pos} : p.cast hst = q.cast hst ↔ p = q := by
+  simp [Pos.ext_iff]
+
+@[simp]
+theorem Pos.cast_startPos {s t : String} {hst : s = t} : s.startPos.cast hst = t.startPos := by
+  subst hst; simp
+
+@[simp]
+theorem Pos.cast_eq_startPos {s t : String} {hst : s = t} {p : s.Pos} : p.cast hst = t.startPos ↔ p = s.startPos := by
+  rw [← Pos.cast_startPos (hst := hst), Pos.cast_inj]
+
+@[simp]
+theorem Pos.cast_endPos {s t : String} {hst : s = t} : s.endPos.cast hst = t.endPos := by
+  subst hst; simp
+
+@[simp]
+theorem Pos.cast_eq_endPos {s t : String} {hst : s = t} {p : s.Pos} : p.cast hst = t.endPos ↔ p = s.endPos := by
+  rw [← Pos.cast_endPos (hst := hst), Pos.cast_inj]
+
 @[simp]
 theorem Pos.cast_le_cast_iff {s t : String} {pos pos' : s.Pos} {h : s = t} :
     pos.cast h ≤ pos'.cast h ↔ pos ≤ pos' := by
@@ -1779,6 +1850,22 @@ theorem Pos.cast_lt_cast_iff {s t : String} {pos pos' : s.Pos} {h : s = t} :
     pos.cast h < pos'.cast h ↔ pos < pos' := by
   cases h; simp
 
+theorem Pos.cast_le_iff {s t : String} {pos : s.Pos} {pos' : t.Pos} {h : s = t} :
+    pos.cast h ≤ pos' ↔ pos ≤ pos'.cast h.symm := by
+  simp [Pos.le_iff]
+
+theorem Pos.le_cast_iff {s t : String} {pos : t.Pos} {pos' : s.Pos} {h : s = t} :
+    pos ≤ pos'.cast h ↔ pos.cast h.symm ≤ pos' := by
+  simp [Pos.le_iff]
+
+theorem Pos.cast_lt_iff {s t : String} {pos : s.Pos} {pos' : t.Pos} {h : s = t} :
+    pos.cast h < pos' ↔ pos < pos'.cast h.symm := by
+  simp [Pos.lt_iff]
+
+theorem Pos.lt_cast_iff {s t : String} {pos : t.Pos} {pos' : s.Pos} {h : s = t} :
+    pos < pos'.cast h ↔ pos.cast h.symm < pos' := by
+  simp [Pos.lt_iff]
+
 theorem Pos.copy_toSlice_eq_cast {s : String} (p : s.Pos) :
     p.toSlice.copy = p.cast copy_toSlice.symm :=
   Pos.ext (by simp)
@@ -2054,6 +2141,10 @@ theorem Pos.le_ofToSlice_iff {s : String} {p : s.Pos} {q : s.toSlice.Pos} :
 theorem Pos.toSlice_lt_toSlice_iff {s : String} {p q : s.Pos} :
     p.toSlice < q.toSlice ↔ p < q := Iff.rfl
 
+@[simp]
+theorem Pos.toSlice_le_toSlice_iff {s : String} {p q : s.Pos} :
+    p.toSlice ≤ q.toSlice ↔ p ≤ q := Iff.rfl
+
 theorem Pos.next_le_of_lt {s : String} {p q : s.Pos} {h} : p < q → p.next h ≤ q := by
   rw [next, Pos.ofToSlice_le_iff, ← Pos.toSlice_lt_toSlice_iff]
   exact Slice.Pos.next_le_of_lt

src/Init/Data/String/Lemmas/Basic.lean

@@ -22,6 +22,10 @@ public section
 
 namespace String
 
+@[simp]
+theorem singleton_inj {c d : Char} : singleton c = singleton d ↔ c = d := by
+  simp [← toList_inj]
+
 @[simp]
 theorem singleton_append_inj : singleton c ++ s = singleton d ++ t ↔ c = d ∧ s = t := by
   simp [← toList_inj]
@@ -191,18 +195,74 @@ theorem sliceTo_slice {s : String} {p₁ p₂ h p} :
 theorem Slice.sliceFrom_startPos {s : Slice} : s.sliceFrom s.startPos = s := by
   ext <;> simp
 
+@[simp]
+theorem Slice.sliceFrom_eq_self_iff {s : Slice} {p : s.Pos} : s.sliceFrom p = s ↔ p = s.startPos := by
+  refine ⟨?_, by rintro rfl; simp⟩
+  rcases s with ⟨str, startInclusive, endExclusive, h⟩
+  simp [sliceFrom, Slice.startPos, String.Pos.ext_iff, Pos.Raw.ext_iff, Slice.Pos.ext_iff]
+
 @[simp]
 theorem Slice.sliceTo_endPos {s : Slice} : s.sliceTo s.endPos = s := by
   ext <;> simp
 
+@[simp]
+theorem Slice.sliceTo_eq_self_iff {s : Slice} {p : s.Pos} : s.sliceTo p = s ↔ p = s.endPos := by
+  refine ⟨?_, by rintro rfl; simp⟩
+  rcases s with ⟨str, startInclusive, endExclusive, h⟩
+  simp [sliceTo, Slice.endPos, String.Pos.ext_iff, Pos.Raw.ext_iff, Slice.Pos.ext_iff,
+    utf8ByteSize_eq]
+  omega
+
+@[simp]
+theorem Slice.slice_startPos {s : Slice} {p : s.Pos} :
+    s.slice s.startPos p (Pos.startPos_le _) = s.sliceTo p := by
+  ext <;> simp
+
+@[simp]
+theorem Slice.slice_eq_self_iff {s : Slice} {p₁ p₂ : s.Pos} {h} :
+    s.slice p₁ p₂ h = s ↔ p₁ = s.startPos ∧ p₂ = s.endPos := by
+  refine ⟨?_, by rintro ⟨rfl, rfl⟩; simp⟩
+  rcases s with ⟨str, startInclusive, endExclusive, h⟩
+  simp [slice, Slice.endPos, String.Pos.ext_iff, Pos.Raw.ext_iff, Slice.Pos.ext_iff,
+    utf8ByteSize_eq]
+  omega
+
+@[simp]
+theorem Slice.slice_endPos {s : Slice} {p : s.Pos} :
+    s.slice p s.endPos (Pos.le_endPos _) = s.sliceFrom p := by
+  ext <;> simp
+
 @[simp]
 theorem sliceFrom_startPos {s : String} : s.sliceFrom s.startPos = s := by
   ext <;> simp
 
+@[simp]
+theorem sliceFrom_eq_toSlice_iff {s : String} {p : s.Pos} : s.sliceFrom p = s.toSlice ↔ p = s.startPos := by
+  simp [← sliceFrom_toSlice]
+
 @[simp]
 theorem sliceTo_endPos {s : String} : s.sliceTo s.endPos = s := by
   ext <;> simp
 
+@[simp]
+theorem sliceTo_eq_toSlice_iff {s : String} {p : s.Pos} : s.sliceTo p = s.toSlice ↔ p = s.endPos := by
+  simp [← sliceTo_toSlice]
+
+@[simp]
+theorem slice_startPos {s : String} {p : s.Pos} :
+    s.slice s.startPos p (Pos.startPos_le _) = s.sliceTo p := by
+  ext <;> simp
+
+@[simp]
+theorem slice_endPos {s : String} {p : s.Pos} :
+    s.slice p s.endPos (Pos.le_endPos _) = s.sliceFrom p := by
+  ext <;> simp
+
+@[simp]
+theorem slice_eq_toSlice_iff {s : String} {p₁ p₂ : s.Pos} {h} :
+    s.slice p₁ p₂ h = s.toSlice ↔ p₁ = s.startPos ∧ p₂ = s.endPos := by
+  simp [← slice_toSlice]
+
 end Iterate
 
 theorem Slice.copy_eq_copy_slice {s : Slice} {pos₁ pos₂ : s.Pos} {h} :
@@ -292,4 +352,39 @@ theorem nextn_endPos {s : String} : s.endPos.nextn n = s.endPos := by
 
 end Pos
 
+@[simp]
+theorem Slice.Pos.cast_toSlice_copy {s : Slice} {pos : s.Pos} :
+    pos.copy.toSlice.cast (by simp) = pos := by
+  ext; simp
+
+@[simp]
+theorem Slice.Pos.sliceFrom_eq_startPos {s : Slice} {p : s.Pos} :
+    (Pos.sliceFrom p p (Pos.le_refl _)) = Slice.startPos _ := by
+  simp [← Pos.ofSliceFrom_inj]
+
+@[simp]
+theorem Slice.Pos.sliceFrom_endPos {s : Slice} {p : s.Pos} :
+    (Pos.sliceFrom p s.endPos (Pos.le_endPos _)) = Slice.endPos _ := by
+  simp [← Pos.ofSliceFrom_inj]
+
+@[simp]
+theorem Slice.Pos.sliceTo_startPos {s : Slice} {p : s.Pos} :
+    (Pos.sliceTo p s.startPos (Pos.startPos_le _)) = Slice.startPos _ := by
+  simp [← Pos.ofSliceTo_inj]
+
+@[simp]
+theorem Slice.Pos.sliceTo_eq_endPos {s : Slice} {p : s.Pos} :
+    (Pos.sliceTo p p (Pos.le_refl _)) = Slice.endPos _ := by
+  simp [← Pos.ofSliceTo_inj]
+
+@[simp]
+theorem Slice.Pos.slice_eq_startPos {s : Slice} {p₀ p₁ : s.Pos} {h} :
+    (Pos.slice p₀ p₀ p₁ (Pos.le_refl _) h) = Slice.startPos _ := by
+  simp [← Pos.ofSlice_inj]
+
+@[simp]
+theorem Slice.Pos.slice_eq_endPos {s : Slice} {p₀ p₁ : s.Pos} {h} :
+    (Pos.slice p₁ p₀ p₁ h (Pos.le_refl _)) = Slice.endPos _ := by
+  simp [← Pos.ofSlice_inj]
+
 end String

src/Init/Data/String/Lemmas/Intercalate.lean

@@ -77,6 +77,15 @@ theorem join_cons : join (s :: l) = s ++ join l := by
 theorem toList_join {l : List String} : (String.join l).toList = l.flatMap String.toList := by
   induction l <;> simp_all
 
+@[simp]
+theorem join_append {l m : List String} : String.join (l ++ m) = String.join l ++ String.join m := by
+  simp [← toList_inj]
+
+@[simp]
+theorem length_join {l : List String} : (String.join l).length = (l.map String.length).sum := by
+  simp only [← length_toList, toList_join, List.length_flatMap]
+  simp
+
 namespace Slice
 
 @[simp]

src/Init/Data/String/Lemmas/Order.lean

@@ -368,21 +368,41 @@ theorem Slice.Pos.ofSliceTo_ne_endPos {s : Slice} {p₀ : s.Pos} {p : (s.sliceTo
   refine (lt_endPos_iff _).1 (Std.lt_of_lt_of_le ?_ (le_endPos p₀))
   simpa [← lt_endPos_iff, ← ofSliceTo_lt_ofSliceTo_iff] using h
 
+theorem Slice.Pos.ne_endPos_of_sliceTo_ne_endPos {s : Slice} {p p₀ : s.Pos} {h₀}
+    (h : Pos.sliceTo p₀ p h₀ ≠ Slice.endPos _) : p ≠ s.endPos := by
+  rw [← Pos.ofSliceTo_sliceTo (h := h₀)]
+  apply Pos.ofSliceTo_ne_endPos h
+
 theorem Slice.Pos.ofSliceFrom_ne_startPos {s : Slice} {p₀ : s.Pos} {p : (s.sliceFrom p₀).Pos}
     (h : p ≠ (s.sliceFrom p₀).startPos) : Pos.ofSliceFrom p ≠ s.startPos := by
   refine (startPos_lt_iff _).1 (Std.lt_of_le_of_lt (startPos_le p₀) ?_)
   simpa [← startPos_lt_iff, ← ofSliceFrom_lt_ofSliceFrom_iff] using h
 
+theorem Slice.Pos.ne_startPos_of_sliceFrom_ne_startPos {s : Slice} {p p₀ : s.Pos} {h₀}
+    (h : Pos.sliceFrom p₀ p h₀ ≠ Slice.startPos _) : p ≠ s.startPos := by
+  rw [← Pos.ofSliceFrom_sliceFrom (h := h₀)]
+  apply Pos.ofSliceFrom_ne_startPos h
+
 theorem Pos.ofSliceTo_ne_endPos {s : String} {p₀ : s.Pos} {p : (s.sliceTo p₀).Pos}
     (h : p ≠ (s.sliceTo p₀).endPos) : Pos.ofSliceTo p ≠ s.endPos := by
   refine (lt_endPos_iff _).1 (Std.lt_of_lt_of_le ?_ (le_endPos p₀))
   simpa [← Slice.Pos.lt_endPos_iff, ← ofSliceTo_lt_ofSliceTo_iff] using h
 
+theorem Pos.ne_endPos_of_sliceTo_ne_endPos {s : String} {p p₀ : s.Pos} {h₀}
+    (h : Pos.sliceTo p₀ p h₀ ≠ Slice.endPos _) : p ≠ s.endPos := by
+  rw [← Pos.ofSliceTo_sliceTo (h := h₀)]
+  apply Pos.ofSliceTo_ne_endPos h
+
 theorem Pos.ofSliceFrom_ne_startPos {s : String} {p₀ : s.Pos} {p : (s.sliceFrom p₀).Pos}
     (h : p ≠ (s.sliceFrom p₀).startPos) : Pos.ofSliceFrom p ≠ s.startPos := by
   refine (startPos_lt_iff _).1 (Std.lt_of_le_of_lt (startPos_le p₀) ?_)
   simpa [← Slice.Pos.startPos_lt_iff, ← ofSliceFrom_lt_ofSliceFrom_iff] using h
 
+theorem Pos.ne_startPos_of_sliceFrom_ne_startPos {s : String} {p p₀ : s.Pos} {h₀}
+    (h : Pos.sliceFrom p₀ p h₀ ≠ Slice.startPos _) : p ≠ s.startPos := by
+  rw [← Pos.ofSliceFrom_sliceFrom (h := h₀)]
+  apply Pos.ofSliceFrom_ne_startPos h
+
 theorem Slice.Pos.ofSliceTo_next {s : Slice} {p₀ : s.Pos} {p : (s.sliceTo p₀).Pos} {h} :
     Pos.ofSliceTo (p.next h) = (Pos.ofSliceTo p).next (ofSliceTo_ne_endPos h) := by
   rw [eq_comm, Pos.next_eq_iff]
@@ -514,21 +534,41 @@ theorem Slice.Pos.ofSlice_ne_endPos {s : Slice} {p₀ p₁ : s.Pos} {h} {p : (s.
   refine (lt_endPos_iff _).1 (Std.lt_of_lt_of_le ?_ (le_endPos p₁))
   simpa [← lt_endPos_iff, ← ofSlice_lt_ofSlice_iff] using h
 
+theorem Slice.Pos.ne_endPos_of_slice_ne_endPos {s : Slice} {p p₀ p₁ : s.Pos} {h₁ h₂}
+    (h : Pos.slice p p₀ p₁ h₁ h₂ ≠ Slice.endPos _) : p ≠ s.endPos := by
+  rw [← Pos.ofSlice_slice (h₁ := h₁) (h₂ := h₂)]
+  apply Pos.ofSlice_ne_endPos h
+
 theorem Slice.Pos.ofSlice_ne_startPos {s : Slice} {p₀ p₁ : s.Pos} {h} {p : (s.slice p₀ p₁ h).Pos}
     (h : p ≠ (s.slice p₀ p₁ h).startPos) : Pos.ofSlice p ≠ s.startPos := by
   refine (startPos_lt_iff _).1 (Std.lt_of_le_of_lt (startPos_le p₀) ?_)
   simpa [← startPos_lt_iff, ← ofSlice_lt_ofSlice_iff] using h
 
+theorem Slice.Pos.ne_startPos_of_slice_ne_startPos {s : Slice} {p p₀ p₁ : s.Pos} {h₁ h₂}
+    (h : Pos.slice p p₀ p₁ h₁ h₂ ≠ Slice.startPos _) : p ≠ s.startPos := by
+  rw [← Pos.ofSlice_slice (h₁ := h₁) (h₂ := h₂)]
+  apply Pos.ofSlice_ne_startPos h
+
 theorem Pos.ofSlice_ne_endPos {s : String} {p₀ p₁ : s.Pos} {h} {p : (s.slice p₀ p₁ h).Pos}
     (h : p ≠ (s.slice p₀ p₁ h).endPos) : Pos.ofSlice p ≠ s.endPos := by
   refine (lt_endPos_iff _).1 (Std.lt_of_lt_of_le ?_ (le_endPos p₁))
   simpa [← Slice.Pos.lt_endPos_iff, ← ofSlice_lt_ofSlice_iff] using h
 
+theorem Pos.ne_endPos_of_slice_ne_endPos {s : String} {p p₀ p₁ : s.Pos} {h₁ h₂}
+    (h : Pos.slice p p₀ p₁ h₁ h₂ ≠ Slice.endPos _) : p ≠ s.endPos := by
+  rw [← Pos.ofSlice_slice (h₁ := h₁) (h₂ := h₂)]
+  apply Pos.ofSlice_ne_endPos h
+
 theorem Pos.ofSlice_ne_startPos {s : String} {p₀ p₁ : s.Pos} {h} {p : (s.slice p₀ p₁ h).Pos}
     (h : p ≠ (s.slice p₀ p₁ h).startPos) : Pos.ofSlice p ≠ s.startPos := by
   refine (startPos_lt_iff _).1 (Std.lt_of_le_of_lt (startPos_le p₀) ?_)
   simpa [← Slice.Pos.startPos_lt_iff, ← ofSlice_lt_ofSlice_iff] using h
 
+theorem Pos.ne_startPos_of_slice_ne_startPos {s : String} {p p₀ p₁ : s.Pos} {h₁ h₂}
+    (h : Pos.slice p p₀ p₁ h₁ h₂ ≠ Slice.startPos _) : p ≠ s.startPos := by
+  rw [← Pos.ofSlice_slice (h₁ := h₁) (h₂ := h₂)]
+  apply Pos.ofSlice_ne_startPos h
+
 @[simp]
 theorem Slice.Pos.offset_le_rawEndPos {s : Slice} {p : s.Pos} :
     p.offset ≤ s.rawEndPos :=
@@ -581,21 +621,37 @@ theorem Slice.Pos.get_eq_get_ofSliceTo {s : Slice} {p₀ : s.Pos} {pos : (s.slic
     pos.get h = (ofSliceTo pos).get (ofSliceTo_ne_endPos h) := by
   simp [Slice.Pos.get]
 
+theorem Slice.Pos.get_sliceTo {s : Slice} {p₀ p : s.Pos} {h h'} :
+    (Pos.sliceTo p₀ p h).get h' = p.get (ne_endPos_of_sliceTo_ne_endPos h') := by
+  simp [get_eq_get_ofSliceTo]
+
 theorem Pos.get_eq_get_ofSliceTo {s : String} {p₀ : s.Pos}
     {pos : (s.sliceTo p₀).Pos} {h} :
     pos.get h = (ofSliceTo pos).get (ofSliceTo_ne_endPos h) := by
   simp [Pos.get, Slice.Pos.get]
 
+theorem Pos.get_sliceTo {s : String} {p₀ p : s.Pos} {h h'} :
+    (Pos.sliceTo p₀ p h).get h' = p.get (ne_endPos_of_sliceTo_ne_endPos h') := by
+  simp [get_eq_get_ofSliceTo]
+
 theorem Slice.Pos.get_eq_get_ofSlice {s : Slice} {p₀ p₁ : s.Pos} {h}
     {pos : (s.slice p₀ p₁ h).Pos} {h'} :
     pos.get h' = (ofSlice pos).get (ofSlice_ne_endPos h') := by
   simp [Slice.Pos.get, Nat.add_assoc]
 
+theorem Slice.Pos.get_slice {s : Slice} {p p₀ p₁ : s.Pos} {h₁ h₂ h} :
+    (Pos.slice p p₀ p₁ h₁ h₂).get h = p.get (ne_endPos_of_slice_ne_endPos h) := by
+  simp [get_eq_get_ofSlice]
+
 theorem Pos.get_eq_get_ofSlice {s : String} {p₀ p₁ : s.Pos} {h}
     {pos : (s.slice p₀ p₁ h).Pos} {h'} :
     pos.get h' = (ofSlice pos).get (ofSlice_ne_endPos h') := by
   simp [Pos.get, Slice.Pos.get]
 
+theorem Pos.get_slice {s : String} {p p₀ p₁ : s.Pos} {h₁ h₂ h} :
+    (Pos.slice p p₀ p₁ h₁ h₂).get h = p.get (ne_endPos_of_slice_ne_endPos h) := by
+  simp [get_eq_get_ofSlice]
+
 theorem Slice.Pos.ofSlice_next {s : Slice} {p₀ p₁ : s.Pos} {h}
     {p : (s.slice p₀ p₁ h).Pos} {h'} :
     Pos.ofSlice (p.next h') = (Pos.ofSlice p).next (ofSlice_ne_endPos h') := by

src/Init/Data/String/Lemmas/Pattern/Basic.lean

@@ -12,7 +12,7 @@ public import Init.Data.Iterators.Consumers.Collect
 import all Init.Data.String.Pattern.Basic
 import Init.Data.String.OrderInstances
 import Init.Data.String.Lemmas.IsEmpty
-import Init.Data.String.Lemmas.Basic
+public import Init.Data.String.Lemmas.Basic
 import Init.Data.String.Lemmas.Order
 import Init.Data.String.Termination
 import Init.Data.Order.Lemmas
@@ -52,19 +52,23 @@ The corresponding compatibility typeclasses are
 {name (scope := "Init.Data.String.Lemmas.Pattern.Basic")}`String.Slice.Pattern.Model.LawfulForwardPatternModel`
 and
 {name (scope := "Init.Data.String.Lemmas.Pattern.Basic")}`String.Slice.Pattern.Model.LawfulToForwardSearcherModel`.
-
-We include the condition that the empty string is not a match. This is necessary for the theory to
-work out as there is just no reasonable notion of searching that works for the empty string that is
-still specific enough to yield reasonably strong correctness results for operations based on
-searching.
-
-This means that pattern types that allow searching for the empty string will have to special-case
-the empty string in their correctness statements.
 -/
 class PatternModel {ρ : Type} (pat : ρ) : Type where
   /-- The predicate that says which strings match the pattern. -/
   Matches : String → Prop
-  not_matches_empty : ¬ Matches ""
+
+/--
+Type class for the condition that the empty string is not a match. This is necessary for the theory to
+work out as there is just no reasonable notion of searching that works for the empty string that is
+still specific enough to yield reasonably strong correctness results for operations based on
+searching.
+-/
+class StrictPatternModel {ρ : Type} (pat : ρ) [PatternModel pat] : Prop where
+  not_matches_empty : ¬ PatternModel.Matches pat ""
+
+theorem not_matches_empty {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat] :
+    ¬ PatternModel.Matches pat "" :=
+  StrictPatternModel.not_matches_empty
 
 /--
 Predicate stating that the region between the start of the slice {name}`s` and the position
@@ -74,10 +78,10 @@ Predicate stating that the region between the start of the slice {name}`s` and t
 structure IsMatch (pat : ρ) [PatternModel pat] {s : Slice} (endPos : s.Pos) : Prop where
   matches_copy : PatternModel.Matches pat (s.sliceTo endPos).copy
 
-theorem IsMatch.ne_startPos {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos}
+theorem IsMatch.ne_startPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {pos : s.Pos}
     (h : IsMatch pat pos) : pos ≠ s.startPos := by
   intro hc
-  apply PatternModel.not_matches_empty (pat := pat)
+  apply not_matches_empty (pat := pat)
   simpa [hc] using h.matches_copy
 
 theorem isMatch_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos} :
@@ -90,6 +94,21 @@ theorem isMatch_iff_exists_splits {pat : ρ} [PatternModel pat] {s : Slice} {pos
   refine ⟨fun h => ⟨_, _, pos.splits, h⟩, fun ⟨t₁, t₂, h₁, h₂⟩ => ?_⟩
   rwa [h₁.eq_left pos.splits] at h₂
 
+@[simp]
+theorem isMatch_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (h : s.copy = t.copy) {pos : s.Pos} :
+    IsMatch pat (pos.cast h) ↔ IsMatch pat pos := by
+  simp [isMatch_iff]
+
+@[simp]
+theorem isMatch_sliceTo_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos p : s.Pos} {h} :
+    IsMatch pat (Pos.sliceTo p pos h) ↔ IsMatch pat pos := by
+  simp [isMatch_iff]
+
+@[simp]
+theorem isMatch_ofSliceTo_iff {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos} {pos : (s.sliceTo p).Pos} :
+    IsMatch pat (Pos.ofSliceTo pos) ↔ IsMatch pat pos := by
+  rw [← isMatch_sliceTo_iff (p := p) (h := Pos.ofSliceTo_le), Pos.sliceTo_ofSliceTo]
+
 /--
 Predicate stating that the region between the position {name}`startPos` and the end of the slice
 {name}`s` matches the pattern {name}`pat`. Note that there might be a longer match.
@@ -97,10 +116,10 @@ Predicate stating that the region between the position {name}`startPos` and the
 structure IsRevMatch (pat : ρ) [PatternModel pat] {s : Slice} (startPos : s.Pos) : Prop where
   matches_copy : PatternModel.Matches pat (s.sliceFrom startPos).copy
 
-theorem IsRevMatch.ne_endPos {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos}
+theorem IsRevMatch.ne_endPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {pos : s.Pos}
     (h : IsRevMatch pat pos) : pos ≠ s.endPos := by
   intro hc
-  apply PatternModel.not_matches_empty (pat := pat)
+  apply not_matches_empty (pat := pat)
   simpa [hc] using h.matches_copy
 
 theorem isRevMatch_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos} :
@@ -113,6 +132,21 @@ theorem isRevMatch_iff_exists_splits {pat : ρ} [PatternModel pat] {s : Slice} {
   refine ⟨fun h => ⟨_, _, pos.splits, h⟩, fun ⟨t₁, t₂, h₁, h₂⟩ => ?_⟩
   rwa [h₁.eq_right pos.splits] at h₂
 
+@[simp]
+theorem isRevMatch_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (h : s.copy = t.copy) {pos : s.Pos} :
+    IsRevMatch pat (pos.cast h) ↔ IsRevMatch pat pos := by
+  simp [isRevMatch_iff]
+
+@[simp]
+theorem isRevMatch_sliceFrom_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos p : s.Pos} {h} :
+    IsRevMatch pat (Pos.sliceFrom p pos h) ↔ IsRevMatch pat pos := by
+  simp [isRevMatch_iff]
+
+@[simp]
+theorem isRevMatch_ofSliceFrom_iff {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos} {pos : (s.sliceFrom p).Pos} :
+    IsRevMatch pat (Pos.ofSliceFrom pos) ↔ IsRevMatch pat pos := by
+  rw [← isRevMatch_sliceFrom_iff (p := p) (h := Pos.le_ofSliceFrom), Pos.sliceFrom_ofSliceFrom]
+
 /--
 Predicate stating that the region between the start of the slice {name}`s` and the position
 {name}`pos` matches the pattern {name}`pat`, and that there is no longer match starting at the
@@ -125,10 +159,19 @@ structure IsLongestMatch (pat : ρ) [PatternModel pat] {s : Slice} (pos : s.Pos)
   isMatch : IsMatch pat pos
   not_isMatch : ∀ pos', pos < pos' → ¬ IsMatch pat pos'
 
-theorem IsLongestMatch.ne_startPos {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos}
+theorem isLongestMatch_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos} :
+    IsLongestMatch pat pos ↔ IsMatch pat pos ∧ ∀ pos', pos < pos' → ¬ IsMatch pat pos' :=
+  ⟨fun ⟨h, h'⟩ => ⟨h, h'⟩, fun ⟨h, h'⟩ => ⟨h, h'⟩⟩
+
+theorem IsLongestMatch.ne_startPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {pos : s.Pos}
     (h : IsLongestMatch pat pos) : pos ≠ s.startPos :=
   h.isMatch.ne_startPos
 
+@[simp]
+theorem not_isLongestMatch_startPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} :
+    ¬IsLongestMatch pat s.startPos :=
+  fun h => h.ne_startPos rfl
+
 theorem IsLongestMatch.eq {pat : ρ} [PatternModel pat] {s : Slice} {pos pos' : s.Pos}
     (h : IsLongestMatch pat pos) (h' : IsLongestMatch pat pos') : pos = pos' := by
   apply Std.le_antisymm
@@ -149,6 +192,34 @@ theorem IsLongestMatch.le_of_isMatch {pat : ρ} [PatternModel pat] {s : Slice} {
     (h : IsLongestMatch pat pos) (h' : IsMatch pat pos') : pos' ≤ pos :=
   Std.not_lt.1 (fun hlt => h.not_isMatch _ hlt h')
 
+@[simp]
+theorem isLongestMatch_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice}
+    (hst : s.copy = t.copy) {pos : s.Pos} :
+    IsLongestMatch pat (pos.cast hst) ↔ IsLongestMatch pat pos := by
+  simp only [isLongestMatch_iff, isMatch_cast_iff, and_congr_right_iff]
+  refine fun _ => ⟨fun h p hp => ?_, fun h p hp => ?_⟩
+  · rw [← isMatch_cast_iff hst]
+    exact h _ (by simpa)
+  · have : p = (p.cast hst.symm).cast hst := by simp
+    rw [this, isMatch_cast_iff hst]
+    exact h _ (by rwa [this, Pos.cast_lt_cast_iff] at hp)
+
+theorem IsLongestMatch.of_eq {pat : ρ} [PatternModel pat] {s t : Slice} {pos : s.Pos} {pos' : t.Pos}
+    (h : IsLongestMatch pat pos) (h₁ : s.copy = t.copy) (h₂ : pos.cast h₁ = pos') :
+    IsLongestMatch pat pos' := by
+  subst h₂; simpa
+
+theorem IsLongestMatch.sliceTo {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos}
+    (h : IsLongestMatch pat pos) (p : s.Pos) (hp : pos ≤ p) : IsLongestMatch pat (Pos.sliceTo p pos hp) := by
+  simp [isLongestMatch_iff] at ⊢ h
+  refine ⟨h.1, fun p hp => ?_⟩
+  rw [← isMatch_ofSliceTo_iff]
+  exact h.2 _ (by simpa [Pos.sliceTo_lt_iff] using hp)
+
+theorem isLongestMatch_of_ofSliceTo {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos} {pos : (s.sliceTo p).Pos}
+    (h : IsLongestMatch pat (Pos.ofSliceTo pos)) : IsLongestMatch pat pos := by
+  simpa using h.sliceTo p
+
 /--
 Predicate stating that the region between the start of the slice {name}`s` and the position
 {name}`pos` matches the pattern {name}`pat`, and that there is no longer match starting at the
@@ -161,10 +232,19 @@ structure IsLongestRevMatch (pat : ρ) [PatternModel pat] {s : Slice} (pos : s.P
   isRevMatch : IsRevMatch pat pos
   not_isRevMatch : ∀ pos', pos' < pos → ¬ IsRevMatch pat pos'
 
-theorem IsLongestRevMatch.ne_endPos {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos}
+theorem isLongestRevMatch_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos} :
+    IsLongestRevMatch pat pos ↔ IsRevMatch pat pos ∧ ∀ pos', pos' < pos → ¬ IsRevMatch pat pos' :=
+  ⟨fun ⟨h, h'⟩ => ⟨h, h'⟩, fun ⟨h, h'⟩ => ⟨h, h'⟩⟩
+
+theorem IsLongestRevMatch.ne_endPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {pos : s.Pos}
     (h : IsLongestRevMatch pat pos) : pos ≠ s.endPos :=
   h.isRevMatch.ne_endPos
 
+@[simp]
+theorem not_isLongestRevMatch_endPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} :
+    ¬IsLongestRevMatch pat s.endPos :=
+  fun h => h.ne_endPos rfl
+
 theorem IsLongestRevMatch.eq {pat : ρ} [PatternModel pat] {s : Slice} {pos pos' : s.Pos}
     (h : IsLongestRevMatch pat pos) (h' : IsLongestRevMatch pat pos') : pos = pos' := by
   apply Std.le_antisymm
@@ -185,6 +265,34 @@ theorem IsLongestRevMatch.le_of_isRevMatch {pat : ρ} [PatternModel pat] {s : Sl
     (h : IsLongestRevMatch pat pos) (h' : IsRevMatch pat pos') : pos ≤ pos' :=
   Std.not_lt.1 (fun hlt => h.not_isRevMatch _ hlt h')
 
+@[simp]
+theorem isLongestRevMatch_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice}
+    (hst : s.copy = t.copy) {pos : s.Pos} :
+    IsLongestRevMatch pat (pos.cast hst) ↔ IsLongestRevMatch pat pos := by
+  simp only [isLongestRevMatch_iff, isRevMatch_cast_iff, and_congr_right_iff]
+  refine fun _ => ⟨fun h p hp => ?_, fun h p hp => ?_⟩
+  · rw [← isRevMatch_cast_iff hst]
+    exact h _ (by simpa)
+  · have : p = (p.cast hst.symm).cast hst := by simp
+    rw [this, isRevMatch_cast_iff hst]
+    exact h _ (by rwa [this, Pos.cast_lt_cast_iff] at hp)
+
+theorem IsLongestRevMatch.of_eq {pat : ρ} [PatternModel pat] {s t : Slice} {pos : s.Pos} {pos' : t.Pos}
+    (h : IsLongestRevMatch pat pos) (h₁ : s.copy = t.copy) (h₂ : pos.cast h₁ = pos') :
+    IsLongestRevMatch pat pos' := by
+  subst h₂; simpa
+
+theorem IsLongestRevMatch.sliceFrom {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos}
+    (h : IsLongestRevMatch pat pos) (p : s.Pos) (hp : p ≤ pos) : IsLongestRevMatch pat (Pos.sliceFrom p pos hp) := by
+  simp [isLongestRevMatch_iff] at ⊢ h
+  refine ⟨h.1, fun p' hp' => ?_⟩
+  rw [← isRevMatch_ofSliceFrom_iff]
+  exact h.2 _ (by simpa [Pos.lt_sliceFrom_iff] using hp')
+
+theorem isLongestRevMatch_of_ofSliceFrom {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos} {pos : (s.sliceFrom p).Pos}
+    (h : IsLongestRevMatch pat (Pos.ofSliceFrom pos)) : IsLongestRevMatch pat pos := by
+  simpa using h.sliceFrom p
+
 /--
 Predicate stating that a match for a given pattern is never a proper prefix of another match.
 
@@ -240,12 +348,21 @@ theorem isLongestMatchAt_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos₁ p
       ∃ (h : pos₁ ≤ pos₂), IsLongestMatch pat (Slice.Pos.sliceFrom _ _ h) :=
   ⟨fun ⟨h, h'⟩ => ⟨h, h'⟩, fun ⟨h, h'⟩ => ⟨h, h'⟩⟩
 
-theorem IsLongestMatchAt.lt {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
+theorem IsLongestMatchAt.lt {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {startPos endPos : s.Pos}
     (h : IsLongestMatchAt pat startPos endPos) : startPos < endPos := by
   have := h.isLongestMatch_sliceFrom.ne_startPos
   rw [← Pos.startPos_lt_iff, ← Slice.Pos.ofSliceFrom_lt_ofSliceFrom_iff] at this
   simpa
 
+theorem IsLongestMatchAt.ne {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {startPos endPos : s.Pos}
+    (h : IsLongestMatchAt pat startPos endPos) : startPos ≠ endPos :=
+  Std.ne_of_lt h.lt
+
+@[simp]
+theorem not_isLongestMatchAt_self {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {startPos : s.Pos} :
+    ¬IsLongestMatchAt pat startPos startPos :=
+  fun h => h.ne rfl
+
 theorem IsLongestMatchAt.eq {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos endPos' : s.Pos}
     (h : IsLongestMatchAt pat startPos endPos) (h' : IsLongestMatchAt pat startPos endPos') :
     endPos = endPos' := by
@@ -282,6 +399,77 @@ theorem isLongestMatchAt_startPos_iff {pat : ρ} [PatternModel pat] {s : Slice}
     ⟨fun h => isLongestMatch_of_eq (by simp) (by simp) h,
      fun h => isLongestMatch_of_eq (by simp) (by simp) h⟩
 
+theorem isLongestMatch_iff_isLongestMatchAt_ofSliceFrom {pat : ρ} [PatternModel pat]
+    {s : Slice} {base : s.Pos} (endPos : (s.sliceFrom base).Pos) :
+    IsLongestMatch pat endPos ↔ IsLongestMatchAt pat base (Pos.ofSliceFrom endPos) := by
+  simp [← isLongestMatchAt_startPos_iff, isLongestMatchAt_iff_isLongestMatchAt_ofSliceFrom]
+
+theorem IsLongestMatchAt.matches_slice {pat : ρ} [PatternModel pat] {s : Slice}
+    {startPos endPos : s.Pos} (h : IsLongestMatchAt pat startPos endPos) :
+    PatternModel.Matches pat (s.slice startPos endPos h.le).copy := by
+  simpa using h.isLongestMatch_sliceFrom.isMatch.matches_copy
+
+@[simp]
+theorem isLongestMatchAt_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
+    {startPos endPos : s.Pos} :
+    IsLongestMatchAt pat (startPos.cast hst) (endPos.cast hst) ↔ IsLongestMatchAt pat startPos endPos := by
+  simp [isLongestMatchAt_iff, Pos.sliceFrom_cast]
+
+theorem IsLongestMatchAt.of_eq {pat : ρ} [PatternModel pat] {s t : Slice} {s₁ e₁ : s.Pos} {s₂ e₂ : t.Pos}
+    (h : IsLongestMatchAt pat s₁ e₁) (h₁ : s.copy = t.copy) (h₂ : s₁.cast h₁ = s₂) (h₃ : e₁.cast h₁ = e₂) :
+    IsLongestMatchAt pat s₂ e₂ := by
+  subst h₂ h₃; simpa
+
+theorem IsLongestMatchAt.sliceTo {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
+    (h : IsLongestMatchAt pat startPos endPos) (p : s.Pos) (hp : endPos ≤ p) :
+    IsLongestMatchAt pat (Pos.sliceTo p startPos (by exact Std.le_trans h.le hp)) (Pos.sliceTo p endPos hp) := by
+  simp only [isLongestMatchAt_iff, Pos.sliceTo_le_sliceTo_iff] at ⊢ h
+  obtain ⟨h, hp'⟩ := h
+  exact ⟨h, (hp'.sliceTo (Pos.sliceFrom startPos p (Std.le_trans h hp)) (by simpa)).of_eq (by simp) (by ext; simp)⟩
+
+theorem isLongestMatchAt_of_ofSliceTo {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos} {startPos endPos : (s.sliceTo p).Pos}
+    (h : IsLongestMatchAt pat (Pos.ofSliceTo startPos) (Pos.ofSliceTo endPos)) :
+    IsLongestMatchAt pat startPos endPos := by
+  simpa using h.sliceTo p Pos.ofSliceTo_le
+
+/--
+Predicate stating that the range between two positions of {name}`s` can be covered by longest
+matches of the pattern within {name}`s`.
+-/
+inductive IsLongestMatchAtChain (pat : ρ) [PatternModel pat] {s : Slice} : s.Pos → s.Pos → Prop where
+  | nil (p : s.Pos) : IsLongestMatchAtChain pat p p
+  | cons (startPos middlePos endPos : s.Pos) : IsLongestMatchAt pat startPos middlePos →
+      IsLongestMatchAtChain pat middlePos endPos → IsLongestMatchAtChain pat startPos endPos
+
+attribute [simp] IsLongestMatchAtChain.nil
+
+theorem IsLongestMatchAtChain.eq_of_isLongestMatchAt_self {pat : ρ} [PatternModel pat] {s : Slice}
+    {startPos endPos : s.Pos} (h : IsLongestMatchAtChain pat startPos endPos) (h' : IsLongestMatchAt pat startPos startPos) :
+    startPos = endPos := by
+  induction h with
+  | nil => rfl
+  | cons p₁ p₂ p₃ h₁ h₂ ih =>
+    obtain rfl : p₁ = p₂ := h'.eq h₁
+    exact ih h₁
+
+theorem IsLongestMatchAtChain.le {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
+    (h : IsLongestMatchAtChain pat startPos endPos) : startPos ≤ endPos := by
+  induction h with
+  | nil => exact Std.le_refl _
+  | cons p₁ p₂ p₃ h₁ h₂ ih => exact Std.le_trans h₁.le ih
+
+theorem IsLongestMatchAtChain.sliceTo {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
+    (h : IsLongestMatchAtChain pat startPos endPos) (p : s.Pos) (hp : endPos ≤ p) :
+    IsLongestMatchAtChain pat (Pos.sliceTo p startPos (by exact Std.le_trans h.le hp)) (Pos.sliceTo p endPos hp) := by
+  induction h with
+  | nil => simp
+  | cons p₁ p₂ p₃ h₁ h₂ ih => exact .cons _ _ _ (h₁.sliceTo p (Std.le_trans h₂.le hp)) (ih hp)
+
+theorem isLongestMatchAtChain_of_ofSliceTo {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos}
+    {startPos endPos : (s.sliceTo p).Pos} (h : IsLongestMatchAtChain pat (Pos.ofSliceTo startPos) (Pos.ofSliceTo endPos)) :
+    IsLongestMatchAtChain pat startPos endPos := by
+  simpa using h.sliceTo p Pos.ofSliceTo_le
+
 /--
 Predicate stating that the slice formed by {name}`startPos` and {name}`endPos` contains is a match
 of {name}`pat` in {name}`s` and it is longest among matches ending at {name}`endPos`.
@@ -295,12 +483,21 @@ theorem isLongestRevMatchAt_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos
       ∃ (h : pos₁ ≤ pos₂), IsLongestRevMatch pat (Slice.Pos.sliceTo _ _ h) :=
   ⟨fun ⟨h, h'⟩ => ⟨h, h'⟩, fun ⟨h, h'⟩ => ⟨h, h'⟩⟩
 
-theorem IsLongestRevMatchAt.lt {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
+theorem IsLongestRevMatchAt.lt {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {startPos endPos : s.Pos}
     (h : IsLongestRevMatchAt pat startPos endPos) : startPos < endPos := by
   have := h.isLongestRevMatch_sliceTo.ne_endPos
   rw [← Pos.lt_endPos_iff, ← Slice.Pos.ofSliceTo_lt_ofSliceTo_iff] at this
   simpa
 
+theorem IsLongestRevMatchAt.ne {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {startPos endPos : s.Pos}
+    (h : IsLongestRevMatchAt pat startPos endPos) : startPos ≠ endPos :=
+  Std.ne_of_lt h.lt
+
+@[simp]
+theorem not_isLongestRevMatchAt_self {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {endPos : s.Pos} :
+    ¬IsLongestRevMatchAt pat endPos endPos :=
+  fun h => h.ne rfl
+
 theorem IsLongestRevMatchAt.eq {pat : ρ} [PatternModel pat] {s : Slice} {startPos startPos' endPos : s.Pos}
     (h : IsLongestRevMatchAt pat startPos endPos) (h' : IsLongestRevMatchAt pat startPos' endPos) :
     startPos = startPos' := by
@@ -335,6 +532,77 @@ theorem isLongestRevMatchAt_endPos_iff {pat : ρ} [PatternModel pat] {s : Slice}
     ⟨fun h => isLongestRevMatch_of_eq (by simp) (by simp) h,
      fun h => isLongestRevMatch_of_eq (by simp) (by simp) h⟩
 
+theorem isLongestRevMatch_iff_isLongestRevMatchAt_ofSliceTo {pat : ρ} [PatternModel pat]
+    {s : Slice} {base : s.Pos} (startPos : (s.sliceTo base).Pos) :
+    IsLongestRevMatch pat startPos ↔ IsLongestRevMatchAt pat (Pos.ofSliceTo startPos) base := by
+  simp [← isLongestRevMatchAt_endPos_iff, isLongestRevMatchAt_iff_isLongestRevMatchAt_ofSliceTo]
+
+theorem IsLongestRevMatchAt.matches_slice {pat : ρ} [PatternModel pat] {s : Slice}
+    {startPos endPos : s.Pos} (h : IsLongestRevMatchAt pat startPos endPos) :
+    PatternModel.Matches pat (s.slice startPos endPos h.le).copy := by
+  simpa using h.isLongestRevMatch_sliceTo.isRevMatch.matches_copy
+
+@[simp]
+theorem isLongestRevMatchAt_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
+    {startPos endPos : s.Pos} :
+    IsLongestRevMatchAt pat (startPos.cast hst) (endPos.cast hst) ↔ IsLongestRevMatchAt pat startPos endPos := by
+  simp [isLongestRevMatchAt_iff, Pos.sliceTo_cast]
+
+theorem IsLongestRevMatchAt.of_eq {pat : ρ} [PatternModel pat] {s t : Slice} {s₁ e₁ : s.Pos} {s₂ e₂ : t.Pos}
+    (h : IsLongestRevMatchAt pat s₁ e₁) (h₁ : s.copy = t.copy) (h₂ : s₁.cast h₁ = s₂) (h₃ : e₁.cast h₁ = e₂) :
+    IsLongestRevMatchAt pat s₂ e₂ := by
+  subst h₂ h₃; simpa
+
+theorem IsLongestRevMatchAt.sliceFrom {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
+    (h : IsLongestRevMatchAt pat startPos endPos) (p : s.Pos) (hp : p ≤ startPos) :
+    IsLongestRevMatchAt pat (Pos.sliceFrom p startPos hp) (Pos.sliceFrom p endPos (by exact Std.le_trans hp h.le)) := by
+  simp only [isLongestRevMatchAt_iff, Pos.sliceFrom_le_sliceFrom_iff] at ⊢ h
+  obtain ⟨h, hp'⟩ := h
+  exact ⟨h, (hp'.sliceFrom (Pos.sliceTo endPos p (Std.le_trans hp h)) (by simpa)).of_eq (by simp) (by ext; simp)⟩
+
+theorem isLongestRevMatchAt_of_ofSliceFrom {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos} {startPos endPos : (s.sliceFrom p).Pos}
+    (h : IsLongestRevMatchAt pat (Pos.ofSliceFrom startPos) (Pos.ofSliceFrom endPos)) :
+    IsLongestRevMatchAt pat startPos endPos := by
+  simpa using h.sliceFrom p Pos.le_ofSliceFrom
+
+/--
+Predicate stating that the range between two positions of {name}`s` can be covered by longest
+reverse matches of the pattern within {name}`s`.
+-/
+inductive IsLongestRevMatchAtChain (pat : ρ) [PatternModel pat] {s : Slice} : s.Pos → s.Pos → Prop where
+  | nil (p : s.Pos) : IsLongestRevMatchAtChain pat p p
+  | cons (startPos middlePos endPos : s.Pos) : IsLongestRevMatchAtChain pat startPos middlePos →
+      IsLongestRevMatchAt pat middlePos endPos → IsLongestRevMatchAtChain pat startPos endPos
+
+attribute [simp] IsLongestRevMatchAtChain.nil
+
+theorem IsLongestRevMatchAtChain.eq_of_isLongestRevMatchAt_self {pat : ρ} [PatternModel pat] {s : Slice}
+    {startPos endPos : s.Pos} (h : IsLongestRevMatchAtChain pat startPos endPos) (h' : IsLongestRevMatchAt pat endPos endPos) :
+    startPos = endPos := by
+  induction h with
+  | nil => rfl
+  | cons mid endP hchain hmatch ih =>
+    obtain rfl := hmatch.eq h'
+    exact ih hmatch
+
+theorem IsLongestRevMatchAtChain.le {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
+    (h : IsLongestRevMatchAtChain pat startPos endPos) : startPos ≤ endPos := by
+  induction h with
+  | nil => exact Std.le_refl _
+  | cons mid endP hchain hmatch ih => exact Std.le_trans ih hmatch.le
+
+theorem IsLongestRevMatchAtChain.sliceFrom {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
+    (h : IsLongestRevMatchAtChain pat startPos endPos) (p : s.Pos) (hp : p ≤ startPos) :
+    IsLongestRevMatchAtChain pat (Pos.sliceFrom p startPos hp) (Pos.sliceFrom p endPos (by exact Std.le_trans hp h.le)) := by
+  induction h with
+  | nil => simp
+  | cons mid endP hchain hmatch ih => exact .cons _ _ _ ih (hmatch.sliceFrom p (Std.le_trans hp hchain.le))
+
+theorem isLongestRevMatchAtChain_of_ofSliceFrom {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos}
+    {startPos endPos : (s.sliceFrom p).Pos} (h : IsLongestRevMatchAtChain pat (Pos.ofSliceFrom startPos) (Pos.ofSliceFrom endPos)) :
+    IsLongestRevMatchAtChain pat startPos endPos := by
+  simpa using h.sliceFrom p Pos.le_ofSliceFrom
+
 /--
 Predicate stating that there is a (longest) match starting at the given position.
 -/
@@ -360,7 +628,7 @@ theorem matchesAt_iff_exists_isMatch {pat : ρ} [PatternModel pat] {s : Slice}
      by simpa using hq⟩⟩
 
 @[simp]
-theorem not_matchesAt_endPos {pat : ρ} [PatternModel pat] {s : Slice} :
+theorem not_matchesAt_endPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} :
     ¬ MatchesAt pat s.endPos := by
   simp only [matchesAt_iff_exists_isMatch, Pos.endPos_le, exists_prop_eq]
   intro h
@@ -380,6 +648,14 @@ theorem IsLongestMatchAt.matchesAt {pat : ρ} [PatternModel pat] {s : Slice} {st
     (h : IsLongestMatchAt pat startPos endPos) : MatchesAt pat startPos where
   exists_isLongestMatchAt := ⟨_, h⟩
 
+@[simp]
+theorem matchesAt_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
+    {pos : s.Pos} : MatchesAt pat (pos.cast hst) ↔ MatchesAt pat pos := by
+  simp only [matchesAt_iff_exists_isLongestMatchAt]
+  refine ⟨fun ⟨endPos, h⟩ => ?_, fun ⟨endPos, h⟩ => ?_⟩
+  · exact ⟨endPos.cast hst.symm, by simpa [← isLongestMatchAt_cast_iff hst]⟩
+  · exact ⟨endPos.cast hst, by simpa⟩
+
 /--
 Predicate stating that there is a (longest) match ending at the given position.
 -/
@@ -405,7 +681,7 @@ theorem revMatchesAt_iff_exists_isRevMatch {pat : ρ} [PatternModel pat] {s : Sl
      by simpa using hq⟩⟩
 
 @[simp]
-theorem not_revMatchesAt_startPos {pat : ρ} [PatternModel pat] {s : Slice} :
+theorem not_revMatchesAt_startPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} :
     ¬ RevMatchesAt pat s.startPos := by
   simp only [revMatchesAt_iff_exists_isRevMatch, Pos.le_startPos, exists_prop_eq]
   intro h
@@ -425,6 +701,14 @@ theorem IsLongestRevMatchAt.revMatchesAt {pat : ρ} [PatternModel pat] {s : Slic
     (h : IsLongestRevMatchAt pat startPos endPos) : RevMatchesAt pat endPos where
   exists_isLongestRevMatchAt := ⟨_, h⟩
 
+@[simp]
+theorem revMatchesAt_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
+    {pos : s.Pos} : RevMatchesAt pat (pos.cast hst) ↔ RevMatchesAt pat pos := by
+  simp only [revMatchesAt_iff_exists_isLongestRevMatchAt]
+  refine ⟨fun ⟨endPos, h⟩ => ?_, fun ⟨endPos, h⟩ => ?_⟩
+  · exact ⟨endPos.cast hst.symm, by simpa [← isLongestRevMatchAt_cast_iff hst]⟩
+  · exact ⟨endPos.cast hst, by simpa⟩
+
 open Classical in
 /--
 Noncomputable model function returning the end point of the longest match starting at the given
@@ -450,6 +734,21 @@ theorem matchAt?_eq_none_iff {ρ : Type} {pat : ρ} [PatternModel pat]
   | case1 h => simpa using ⟨h⟩
   | case2 h => simpa using fun ⟨h'⟩ => h h'
 
+theorem lt_of_matchAt?_eq_some {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat]
+    {s : Slice} {startPos endPos : s.Pos} (h : matchAt? pat startPos = some endPos) :
+    startPos < endPos :=
+  (matchAt?_eq_some_iff.1 h).lt
+
+@[simp]
+theorem matchAt?_cast {ρ : Type} (pat : ρ) [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
+    {startPos : s.Pos} :
+    matchAt? pat (startPos.cast hst) = (matchAt? pat startPos).map (Slice.Pos.cast · hst) := by
+  refine Option.ext (fun endPos => ?_)
+  have : endPos = (endPos.cast hst.symm).cast hst := by simp
+  conv => lhs; rw [this, matchAt?_eq_some_iff, isLongestMatchAt_cast_iff]
+  simp only [Option.map_eq_some_iff, matchAt?_eq_some_iff]
+  exact ⟨fun h => ⟨_, ⟨h, by simp⟩⟩, by rintro ⟨pos, h, rfl⟩; simpa⟩
+
 open Classical in
 /--
 Noncomputable model function returning the start point of the longest match ending at the given
@@ -475,6 +774,21 @@ theorem revMatchAt?_eq_none_iff {ρ : Type} {pat : ρ} [PatternModel pat]
   | case1 h => simpa using ⟨h⟩
   | case2 h => simpa using fun ⟨h'⟩ => h h'
 
+theorem lt_of_revMatchAt?_eq_some {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat]
+    {s : Slice} {startPos endPos : s.Pos} (h : revMatchAt? pat endPos = some startPos) :
+    startPos < endPos :=
+  (revMatchAt?_eq_some_iff.1 h).lt
+
+@[simp]
+theorem revMatchAt?_cast {ρ : Type} (pat : ρ) [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
+    {startPos : s.Pos} :
+    revMatchAt? pat (startPos.cast hst) = (revMatchAt? pat startPos).map (Slice.Pos.cast · hst) := by
+  refine Option.ext (fun endPos => ?_)
+  have : endPos = (endPos.cast hst.symm).cast hst := by simp
+  conv => lhs; rw [this, revMatchAt?_eq_some_iff, isLongestRevMatchAt_cast_iff]
+  simp only [Option.map_eq_some_iff, revMatchAt?_eq_some_iff]
+  exact ⟨fun h => ⟨_, ⟨h, by simp⟩⟩, by rintro ⟨pos, h, rfl⟩; simpa⟩
+
 /--
 Predicate stating compatibility between {name}`PatternModel` and {name}`ForwardPattern`.
 
@@ -570,6 +884,24 @@ theorem IsValidSearchFrom.endPos_of_eq {pat : ρ} [PatternModel pat] {s : Slice}
   cases hl
   exact IsValidSearchFrom.endPos
 
+theorem isValidSearchFrom_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
+    {pos : s.Pos} {l : List (SearchStep t)} :
+    IsValidSearchFrom pat (pos.cast hst) l ↔ IsValidSearchFrom pat pos (l.map (·.cast hst.symm)) := by
+  suffices ∀ (s t : Slice) (hst : s.copy = t.copy) (pos : s.Pos) (l : List (SearchStep s)),
+      IsValidSearchFrom pat pos l → IsValidSearchFrom pat (pos.cast hst) (l.map (·.cast hst)) from
+    ⟨fun h => by simpa using this _ _ hst.symm _ _ h, fun h => by
+      have hcomp : (SearchStep.cast hst) ∘ (SearchStep.cast hst.symm) = id := by ext; simp
+      simpa [hcomp] using this _ _ hst _ _ h⟩
+  intro s t hst pos l hl
+  induction hl with
+  | endPos => simpa using IsValidSearchFrom.endPos
+  | matched h₁ h₂ ih =>
+    simpa only [List.map_cons, SearchStep.cast_matched] using IsValidSearchFrom.matched (by simpa) ih
+  | mismatched h₁ h₂ h₃ ih =>
+    simp only [List.map_cons, SearchStep.cast_rejected]
+    refine IsValidSearchFrom.mismatched (by simpa) (fun p hp₁ hp₂ hp₃ => ?_) ih
+    exact h₂ (p.cast hst.symm) (by simpa [Pos.le_cast_iff]) (by simpa [Pos.cast_lt_iff]) (by simpa)
+
 /--
 Predicate stating compatibility between {name}`PatternModel` and {name}`ToForwardSearcher`.
 
@@ -663,6 +995,24 @@ theorem IsValidRevSearchFrom.startPos_of_eq {pat : ρ} [PatternModel pat] {s : S
   cases hl
   exact IsValidRevSearchFrom.startPos
 
+theorem isValidRevSearchFrom_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
+    {pos : s.Pos} {l : List (SearchStep t)} :
+    IsValidRevSearchFrom pat (pos.cast hst) l ↔ IsValidRevSearchFrom pat pos (l.map (·.cast hst.symm)) := by
+  suffices ∀ (s t : Slice) (hst : s.copy = t.copy) (pos : s.Pos) (l : List (SearchStep s)),
+      IsValidRevSearchFrom pat pos l → IsValidRevSearchFrom pat (pos.cast hst) (l.map (·.cast hst)) from
+    ⟨fun h => by simpa using this _ _ hst.symm _ _ h, fun h => by
+      have hcomp : (SearchStep.cast hst) ∘ (SearchStep.cast hst.symm) = id := by ext; simp
+      simpa [hcomp] using this _ _ hst _ _ h⟩
+  intro s t hst pos l hl
+  induction hl with
+  | startPos => simpa using IsValidRevSearchFrom.startPos
+  | matched h₁ h₂ ih =>
+    simpa only [List.map_cons, SearchStep.cast_matched] using IsValidRevSearchFrom.matched (by simpa) ih
+  | mismatched h₁ h₂ h₃ ih =>
+    simp only [List.map_cons, SearchStep.cast_rejected]
+    refine IsValidRevSearchFrom.mismatched (by simpa) (fun p hp₁ hp₂ hp₃ => ?_) ih
+    exact h₂ (p.cast hst.symm) (by simpa [Pos.lt_cast_iff]) (by simpa [Pos.cast_le_iff]) (by simpa)
+
 /--
 Predicate stating compatibility between {name}`PatternModel` and {name}`ToBackwardSearcher`.
 

src/Init/Data/String/Lemmas/Pattern/Char.lean

@@ -28,7 +28,9 @@ namespace String.Slice.Pattern.Model.Char
 
 instance {c : Char} : PatternModel c where
   Matches s := s = String.singleton c
-  not_matches_empty := by simp
+
+instance {c : Char} : StrictPatternModel c where
+  not_matches_empty := by simp [PatternModel.Matches]
 
 instance {c : Char} : NoPrefixPatternModel c :=
   .of_length_eq (by simp +contextual [PatternModel.Matches])
@@ -168,11 +170,61 @@ theorem isLongestMatchAt_iff_isLongestMatchAt_beq {c : Char} {s : Slice}
     IsLongestMatchAt c pos pos' ↔ IsLongestMatchAt (· == c) pos pos' := by
   simp [Model.isLongestMatchAt_iff, isLongestMatch_iff_isLongestMatch_beq]
 
+theorem isLongestMatchAtChain_iff_isLongestMatchAtChain_beq {c : Char} {s : Slice} {pos pos' : s.Pos} :
+    IsLongestMatchAtChain c pos pos' ↔ IsLongestMatchAtChain (· == c) pos pos' := by
+  refine ⟨fun h => ?_, fun h => ?_⟩
+  · induction h with
+    | nil => simp
+    | cons p₁ p₂ p₃ h₁ h₂ ih => exact .cons _ _ _ (isLongestMatchAt_iff_isLongestMatchAt_beq.1 h₁) ih
+  · induction h with
+    | nil => simp
+    | cons p₁ p₂ p₃ h₁ h₂ ih => exact .cons _ _ _ (isLongestMatchAt_iff_isLongestMatchAt_beq.2 h₁) ih
+
+theorem isLongestMatchAtChain_iff {c : Char} {s : Slice} {pos pos' : s.Pos} :
+    IsLongestMatchAtChain c pos pos' ↔ pos ≤ pos' ∧ ∀ pos'', pos ≤ pos'' → (h : pos'' < pos') → pos''.get (Pos.ne_endPos_of_lt h) = c := by
+  simp [isLongestMatchAtChain_iff_isLongestMatchAtChain_beq, CharPred.isLongestMatchAtChain_iff]
+
+theorem isLongestMatchAtChain_iff_toList {c : Char} {s : Slice} {pos pos' : s.Pos} :
+    IsLongestMatchAtChain c pos pos' ↔
+      ∃ (h : pos ≤ pos'), (s.slice pos pos' h).copy.toList = List.replicate (s.slice pos pos' h).copy.length c := by
+  simp [isLongestMatchAtChain_iff_isLongestMatchAtChain_beq, CharPred.isLongestMatchAtChain_iff_toList,
+    List.eq_replicate_iff]
+
+theorem isLongestMatchAtChain_startPos_endPos_iff_toList {c : Char} {s : Slice} :
+    IsLongestMatchAtChain c s.startPos s.endPos ↔ s.copy.toList = List.replicate s.copy.length c := by
+  simp [isLongestMatchAtChain_iff_isLongestMatchAtChain_beq,
+    CharPred.isLongestMatchAtChain_startPos_endPos_iff_toList, List.eq_replicate_iff]
+
 theorem isLongestRevMatchAt_iff_isLongestRevMatchAt_beq {c : Char} {s : Slice}
     {pos pos' : s.Pos} :
     IsLongestRevMatchAt c pos pos' ↔ IsLongestRevMatchAt (· == c) pos pos' := by
   simp [Model.isLongestRevMatchAt_iff, isLongestRevMatch_iff_isLongestRevMatch_beq]
 
+theorem isLongestRevMatchAtChain_iff_isLongestRevMatchAtChain_beq {c : Char} {s : Slice} {pos pos' : s.Pos} :
+    IsLongestRevMatchAtChain c pos pos' ↔ IsLongestRevMatchAtChain (· == c) pos pos' := by
+  refine ⟨fun h => ?_, fun h => ?_⟩
+  · induction h with
+    | nil => simp
+    | cons p₂ p₃ _ hmatch ih => exact .cons _ _ _ ih (isLongestRevMatchAt_iff_isLongestRevMatchAt_beq.1 hmatch)
+  · induction h with
+    | nil => simp
+    | cons p₂ p₃ _ hmatch ih => exact .cons _ _ _ ih (isLongestRevMatchAt_iff_isLongestRevMatchAt_beq.2 hmatch)
+
+theorem isLongestRevMatchAtChain_iff {c : Char} {s : Slice} {pos pos' : s.Pos} :
+    IsLongestRevMatchAtChain c pos pos' ↔ pos ≤ pos' ∧ ∀ pos'', pos ≤ pos'' → (h : pos'' < pos') → pos''.get (Pos.ne_endPos_of_lt h) = c := by
+  simp [isLongestRevMatchAtChain_iff_isLongestRevMatchAtChain_beq, CharPred.isLongestRevMatchAtChain_iff]
+
+theorem isLongestRevMatchAtChain_iff_toList {c : Char} {s : Slice} {pos pos' : s.Pos} :
+    IsLongestRevMatchAtChain c pos pos' ↔
+      ∃ (h : pos ≤ pos'), (s.slice pos pos' h).copy.toList = List.replicate (s.slice pos pos' h).copy.length c := by
+  simp [isLongestRevMatchAtChain_iff_isLongestRevMatchAtChain_beq, CharPred.isLongestRevMatchAtChain_iff_toList,
+    List.eq_replicate_iff]
+
+theorem isLongestRevMatchAtChain_startPos_endPos_iff_toList {c : Char} {s : Slice} :
+    IsLongestRevMatchAtChain c s.startPos s.endPos ↔ s.copy.toList = List.replicate s.copy.length c := by
+  simp [isLongestRevMatchAtChain_iff_isLongestRevMatchAtChain_beq,
+    CharPred.isLongestRevMatchAtChain_startPos_endPos_iff_toList, List.eq_replicate_iff]
+
 theorem matchesAt_iff_matchesAt_beq {c : Char} {s : Slice} {pos : s.Pos} :
     MatchesAt c pos ↔ MatchesAt (· == c) pos := by
   simp [matchesAt_iff_exists_isLongestMatchAt, isLongestMatchAt_iff_isLongestMatchAt_beq]
@@ -242,18 +294,21 @@ theorem skipPrefix?_char_eq_skipPrefix?_beq {c : Char} {s : Slice} :
 theorem Pattern.ForwardPattern.skipPrefix?_char_eq_skipPrefix?_beq {c : Char} {s : Slice} :
     skipPrefix? c s = skipPrefix? (· == c) s := (rfl)
 
+theorem Pos.skip?_char_eq_skip?_beq {c : Char} {s : Slice} {pos : s.Pos} :
+    pos.skip? c = pos.skip? (· == c) := (rfl)
+
 theorem Pos.skipWhile_char_eq_skipWhile_beq {c : Char} {s : Slice} (curr : s.Pos) :
     Pos.skipWhile curr c = Pos.skipWhile curr (· == c) := by
   fun_induction Pos.skipWhile curr c with
   | case1 pos nextCurr h₁ h₂ ih =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pattern.ForwardPattern.skipPrefix?_char_eq_skipPrefix?_beq, h₁, h₂, ih]
+    simp [← Pos.skip?_char_eq_skip?_beq, h₁, h₂, ih]
   | case2 pos nextCurr h ih =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pattern.ForwardPattern.skipPrefix?_char_eq_skipPrefix?_beq, h, ih]
+    simp [← Pos.skip?_char_eq_skip?_beq, h, ih]
   | case3 pos h =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pattern.ForwardPattern.skipPrefix?_char_eq_skipPrefix?_beq]
+    simp [← Pos.skip?_char_eq_skip?_beq, h]
 
 theorem skipPrefixWhile_char_eq_skipPrefixWhile_beq {c : Char} {s : Slice} :
     s.skipPrefixWhile c = s.skipPrefixWhile (· == c) :=
@@ -269,7 +324,7 @@ theorem takeWhile_char_eq_takeWhile_beq {c : Char} {s : Slice} :
 
 theorem all_char_eq_all_beq {c : Char} {s : Slice} :
     s.all c = s.all (· == c) := by
-  simp only [all, dropWhile_char_eq_dropWhile_beq]
+  simp only [all, skipPrefixWhile_char_eq_skipPrefixWhile_beq]
 
 theorem find?_char_eq_find?_beq {c : Char} {s : Slice} :
     s.find? c = s.find? (· == c) :=
@@ -298,18 +353,21 @@ theorem dropSuffix_char_eq_dropSuffix_beq {c : Char} {s : Slice} :
 theorem Pattern.BackwardPattern.skipSuffix?_char_eq_skipSuffix?_beq {c : Char} {s : Slice} :
     skipSuffix? c s = skipSuffix? (· == c) s := (rfl)
 
+theorem Pos.revSkip?_char_eq_revSkip?_beq {c : Char} {s : Slice} {pos : s.Pos} :
+    pos.revSkip? c = pos.revSkip? (· == c) := (rfl)
+
 theorem Pos.revSkipWhile_char_eq_revSkipWhile_beq {c : Char} {s : Slice} (curr : s.Pos) :
     Pos.revSkipWhile curr c = Pos.revSkipWhile curr (· == c) := by
   fun_induction Pos.revSkipWhile curr c with
   | case1 pos nextCurr h₁ h₂ ih =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pattern.BackwardPattern.skipSuffix?_char_eq_skipSuffix?_beq, h₁, h₂, ih]
+    simp [← Pos.revSkip?_char_eq_revSkip?_beq, h₁, h₂, ih]
   | case2 pos nextCurr h ih =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pattern.BackwardPattern.skipSuffix?_char_eq_skipSuffix?_beq, h, ih]
+    simp [← Pos.revSkip?_char_eq_revSkip?_beq, h, ih]
   | case3 pos h =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pattern.BackwardPattern.skipSuffix?_char_eq_skipSuffix?_beq]
+    simp [← Pos.revSkip?_char_eq_revSkip?_beq, h]
 
 theorem skipSuffixWhile_char_eq_skipSuffixWhile_beq {c : Char} {s : Slice} :
     s.skipSuffixWhile c = s.skipSuffixWhile (· == c) :=
@@ -323,4 +381,16 @@ theorem takeEndWhile_char_eq_takeEndWhile_beq {c : Char} {s : Slice} :
     s.takeEndWhile c = s.takeEndWhile (· == c) := by
   simp only [takeEndWhile]; exact congrArg _ skipSuffixWhile_char_eq_skipSuffixWhile_beq
 
+theorem revFind?_char_eq_revFind?_beq {c : Char} {s : Slice} :
+    s.revFind? c = s.revFind? (· == c) :=
+  (rfl)
+
+theorem Pos.revFind?_char_eq_revFind?_beq {c : Char} {s : Slice} {p : s.Pos} :
+    p.revFind? c = p.revFind? (· == c) :=
+  (rfl)
+
+theorem revAll_char_eq_revAll_beq {c : Char} {s : Slice} :
+    s.revAll c = s.revAll (· == c) := by
+  simp [revAll, skipSuffixWhile_char_eq_skipSuffixWhile_beq]
+
 end String.Slice

src/Init/Data/String/Lemmas/Pattern/Find/Basic.lean

@@ -23,8 +23,8 @@ open Std String.Slice Pattern Pattern.Model
 
 namespace String.Slice
 
-theorem Pattern.Model.find?_eq_some_iff {ρ : Type} (pat : ρ) [PatternModel pat] {σ : Slice → Type}
-    [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
+theorem Pattern.Model.find?_eq_some_iff {ρ : Type} (pat : ρ) [PatternModel pat] [StrictPatternModel pat]
+    {σ : Slice → Type} [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
     [∀ s, IteratorLoop (σ s) Id Id] [∀ s, LawfulIteratorLoop (σ s) Id Id]
     [ToForwardSearcher pat σ] [LawfulToForwardSearcherModel pat] {s : Slice} {pos : s.Pos} :
     s.find? pat = some pos ↔ MatchesAt pat pos ∧ (∀ pos', pos' < pos → ¬ MatchesAt pat pos') := by
@@ -40,8 +40,8 @@ theorem Pattern.Model.find?_eq_some_iff {ρ : Type} (pat : ρ) [PatternModel pat
   | matched h₁ _ _ => have := h₁.matchesAt; grind
   | mismatched => grind
 
-theorem Pattern.Model.find?_eq_none_iff {ρ : Type} (pat : ρ) [PatternModel pat] {σ : Slice → Type}
-    [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
+theorem Pattern.Model.find?_eq_none_iff {ρ : Type} (pat : ρ) [PatternModel pat] [StrictPatternModel pat]
+    {σ : Slice → Type} [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
     [∀ s, IteratorLoop (σ s) Id Id] [∀ s, LawfulIteratorLoop (σ s) Id Id]
     [ToForwardSearcher pat σ] [LawfulToForwardSearcherModel pat] {s : Slice} :
     s.find? pat = none ↔ ∀ (pos : s.Pos), ¬ MatchesAt pat pos := by
@@ -65,15 +65,15 @@ theorem find?_eq_none_iff {ρ : Type} (pat : ρ) {σ : Slice → Type}
     [ToForwardSearcher pat σ] {s : Slice} : s.find? pat = none ↔ s.contains pat = false := by
   rw [← Option.isNone_iff_eq_none, ← Option.isSome_eq_false_iff, isSome_find?]
 
-theorem Pattern.Model.contains_eq_false_iff {ρ : Type} (pat : ρ) [PatternModel pat] {σ : Slice → Type}
-    [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
+theorem Pattern.Model.contains_eq_false_iff {ρ : Type} (pat : ρ) [PatternModel pat] [StrictPatternModel pat]
+    {σ : Slice → Type} [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
     [∀ s, IteratorLoop (σ s) Id Id] [∀ s, LawfulIteratorLoop (σ s) Id Id]
     [ToForwardSearcher pat σ] [LawfulToForwardSearcherModel pat] {s : Slice} :
     s.contains pat = false ↔ ∀ (pos : s.Pos), ¬ MatchesAt pat pos := by
   rw [← find?_eq_none_iff, Slice.find?_eq_none_iff]
 
-theorem Pattern.Model.contains_eq_true_iff {ρ : Type} (pat : ρ) [PatternModel pat] {σ : Slice → Type}
-    [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
+theorem Pattern.Model.contains_eq_true_iff {ρ : Type} (pat : ρ) [PatternModel pat] [StrictPatternModel pat]
+    {σ : Slice → Type} [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
     [∀ s, IteratorLoop (σ s) Id Id] [∀ s, LawfulIteratorLoop (σ s) Id Id]
     [ToForwardSearcher pat σ] [LawfulToForwardSearcherModel pat] {s : Slice} :
     s.contains pat ↔ ∃ (pos : s.Pos), MatchesAt pat pos := by
@@ -85,7 +85,7 @@ theorem Pos.find?_eq_find?_sliceFrom {ρ : Type} {pat : ρ} {σ : Slice → Type
     p.find? pat = ((s.sliceFrom p).find? pat).map Pos.ofSliceFrom :=
   (rfl)
 
-theorem Pattern.Model.posFind?_eq_some_iff {ρ : Type} {pat : ρ} [PatternModel pat] {σ : Slice → Type}
+theorem Pattern.Model.posFind?_eq_some_iff {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {σ : Slice → Type}
     [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
     [∀ s, IteratorLoop (σ s) Id Id] [∀ s, LawfulIteratorLoop (σ s) Id Id]
     [ToForwardSearcher pat σ] [LawfulToForwardSearcherModel pat] {s : Slice} {pos pos' : s.Pos} :
@@ -100,8 +100,8 @@ theorem Pattern.Model.posFind?_eq_some_iff {ρ : Type} {pat : ρ} [PatternModel
     refine ⟨Pos.sliceFrom _ _ h₁, ⟨by simpa using h₂, fun p hp₁ hp₂ => ?_⟩, by simp⟩
     exact h₃ (Pos.ofSliceFrom p) Slice.Pos.le_ofSliceFrom (Pos.lt_sliceFrom_iff.1 hp₁) hp₂
 
-theorem Pattern.Model.posFind?_eq_none_iff {ρ : Type} {pat : ρ} [PatternModel pat] {σ : Slice → Type}
-    [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
+theorem Pattern.Model.posFind?_eq_none_iff {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat]
+    {σ : Slice → Type} [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
     [∀ s, IteratorLoop (σ s) Id Id] [∀ s, LawfulIteratorLoop (σ s) Id Id]
     [ToForwardSearcher pat σ] [LawfulToForwardSearcherModel pat] {s : Slice} {pos : s.Pos} :
     pos.find? pat = none ↔ ∀ pos', pos ≤ pos' → ¬ MatchesAt pat pos' := by

src/Init/Data/String/Lemmas/Pattern/Find/String.lean

@@ -49,9 +49,10 @@ theorem contains_slice_iff {t s : Slice} :
   by_cases ht : t.isEmpty
   · simp [contains_eq_true_of_isEmpty ht s, copy_eq_empty_iff.mpr ht, String.toList_empty]
   · simp only [Bool.not_eq_true] at ht
+    have := Pattern.Model.ForwardSliceSearcher.strictPatternModel ht
     have := Pattern.Model.ForwardSliceSearcher.lawfulToForwardSearcherModel ht
     simp only [Pattern.Model.contains_eq_true_iff,
-      Pattern.Model.ForwardSliceSearcher.exists_matchesAt_iff_eq_append ht, isInfix_toList_iff]
+      Pattern.Model.ForwardSliceSearcher.exists_matchesAt_iff_eq_append, isInfix_toList_iff]
 
 @[simp]
 theorem contains_string_iff {t : String} {s : Slice} :

src/Init/Data/String/Lemmas/Pattern/Pred.lean

@@ -18,6 +18,7 @@ import Init.Data.String.Lemmas.Basic
 import Init.Data.String.Lemmas.Order
 import Init.Data.Order.Lemmas
 import Init.Data.String.OrderInstances
+import Init.Data.String.Lemmas.Iterate
 import Init.Omega
 import Init.Data.String.Lemmas.FindPos
 
@@ -27,8 +28,9 @@ namespace String.Slice.Pattern.Model.CharPred
 
 instance {p : Char → Bool} : PatternModel p where
   Matches s := ∃ c, s = singleton c ∧ p c
-  not_matches_empty := by
-    simp
+
+instance {p : Char → Bool} : StrictPatternModel p where
+  not_matches_empty := by simp [PatternModel.Matches]
 
 instance {p : Char → Bool} : NoPrefixPatternModel p :=
   .of_length_eq (by simp +contextual [PatternModel.Matches])
@@ -71,6 +73,39 @@ theorem isLongestMatchAt_iff {p : Char → Bool} {s : Slice} {pos pos' : s.Pos}
   simp +contextual [Model.isLongestMatchAt_iff, isLongestMatch_iff, ← Pos.ofSliceFrom_inj,
     Pos.get_eq_get_ofSliceFrom, Pos.ofSliceFrom_next]
 
+theorem isLongestMatchAtChain_iff {p : Char → Bool} {s : Slice} {pos pos' : s.Pos} :
+    IsLongestMatchAtChain p pos pos' ↔ pos ≤ pos' ∧ ∀ pos'', pos ≤ pos'' → (h : pos'' < pos') → p (pos''.get (Pos.ne_endPos_of_lt h)) := by
+  induction pos using WellFounded.induction Pos.wellFounded_gt with | h pos ih
+  obtain (h|rfl|h) := Std.lt_trichotomy pos pos'
+  · refine ⟨fun h => ?_, fun ⟨h₁, h₂⟩ => ?_⟩
+    · cases h with
+      | nil => exact (Std.lt_irrefl h).elim
+      | cons _ mid _ h₁ h₂ =>
+        obtain ⟨h₀, rfl, h₁'⟩ := isLongestMatchAt_iff.1 h₁
+        refine ⟨Std.le_of_lt h, fun pos'' hp₁ hp₂ => ?_⟩
+        obtain (hh|rfl) := Std.le_iff_lt_or_eq.1 hp₁
+        · exact ((ih (pos.next (Pos.ne_endPos_of_lt h)) Pos.lt_next).1 h₂).2 _ (by simpa) hp₂
+        · exact h₁'
+    · refine .cons _ (pos.next (Pos.ne_endPos_of_lt h)) _ ?_ ((ih _ Pos.lt_next).2 ?_)
+      · exact isLongestMatchAt_iff.2 ⟨Pos.ne_endPos_of_lt h, rfl, h₂ _ (by simp) h⟩
+      · exact ⟨by simpa, fun pos'' hp₁ hp₂ => h₂ _ (Std.le_trans Pos.le_next hp₁) hp₂⟩
+  · simpa using fun _ h₁ h₂ => (Std.lt_irrefl (Std.lt_of_le_of_lt h₁ h₂)).elim
+  · simpa [Std.not_le.2 h] using fun h' => (Std.not_le.2 h h'.le).elim
+
+theorem isLongestMatchAtChain_iff_toList {p : Char → Bool} {s : Slice} {pos pos' : s.Pos} :
+    IsLongestMatchAtChain p pos pos' ↔ ∃ (h : pos ≤ pos'), ∀ c, c ∈ (s.slice pos pos' h).copy.toList → p c := by
+  simp only [isLongestMatchAtChain_iff, mem_toList_copy_iff_exists_get, Pos.get_eq_get_ofSlice,
+    forall_exists_index]
+  refine ⟨fun ⟨h₁, h₂⟩ => ⟨h₁, fun c p' hp => ?_⟩, fun ⟨h₁, h₂⟩ => ⟨h₁, fun p' hp₁ hp₂ => ?_⟩⟩
+  · rintro rfl
+    exact h₂ _ Pos.le_ofSlice (by simp [Pos.ofSlice_lt_iff, h₁, hp])
+  · refine h₂ _ (Pos.slice p' _ _ hp₁ (Std.le_of_lt hp₂)) ?_ (by simp)
+    rwa [← Pos.lt_endPos_iff, ← Pos.slice_eq_endPos (h := h₁), Pos.slice_lt_slice_iff]
+
+theorem isLongestMatchAtChain_startPos_endPos_iff_toList {p : Char → Bool} {s : Slice} :
+    IsLongestMatchAtChain p s.startPos s.endPos ↔ ∀ c, c ∈ s.copy.toList → p c := by
+  simp [isLongestMatchAtChain_iff_toList]
+
 theorem isLongestRevMatchAt_iff {p : Char → Bool} {s : Slice} {pos pos' : s.Pos} :
     IsLongestRevMatchAt p pos pos' ↔ ∃ h, pos = pos'.prev h ∧ p ((pos'.prev h).get (by simp)) := by
   simp +contextual [Model.isLongestRevMatchAt_iff, isLongestRevMatch_iff, ← Pos.ofSliceTo_inj,
@@ -84,6 +119,35 @@ theorem isLongestRevMatchAt_of_get {p : Char → Bool} {s : Slice} {pos : s.Pos}
     (hc : p ((pos.prev h).get (by simp))) : IsLongestRevMatchAt p (pos.prev h) pos :=
   isLongestRevMatchAt_iff.2 ⟨h, by simp [hc]⟩
 
+theorem isLongestRevMatchAtChain_iff {p : Char → Bool} {s : Slice} {pos pos' : s.Pos} :
+    IsLongestRevMatchAtChain p pos pos' ↔ pos ≤ pos' ∧ ∀ pos'', pos ≤ pos'' → (h : pos'' < pos') → p (pos''.get (Pos.ne_endPos_of_lt h)) := by
+  induction pos' using WellFounded.induction Pos.wellFounded_lt with | h pos' ih
+  obtain (h|rfl|h) := Std.lt_trichotomy pos pos'
+  · refine ⟨fun h => ?_, fun ⟨h₁, h₂⟩ => ?_⟩
+    · cases h with
+      | nil => exact (Std.lt_irrefl h).elim
+      | cons _ _ hchain hmatch =>
+        obtain ⟨hne, hmid, hp⟩ := isLongestRevMatchAt_iff.1 hmatch
+        refine ⟨Std.le_of_lt h, fun pos'' hp₁ hp₂ => ?_⟩
+        rcases Std.le_iff_lt_or_eq.1 (Pos.le_prev_iff_lt.2 hp₂) with hh | heq
+        · exact ((ih _ Pos.prev_lt).1 (hmid ▸ hchain)).2 _ hp₁ hh
+        · exact heq ▸ hp
+    · have hne : pos' ≠ s.startPos := Slice.Pos.ne_startPos_of_lt h
+      refine .cons _ (pos'.prev hne) _ ((ih _ Pos.prev_lt).2 ?_)
+        (isLongestRevMatchAt_of_get (h₂ _ (Pos.le_prev_iff_lt.2 h) Pos.prev_lt))
+      exact ⟨Pos.le_prev_iff_lt.2 h, fun pos'' hp₁ hp₂ =>
+        h₂ _ hp₁ (Std.lt_trans hp₂ Pos.prev_lt)⟩
+  · simpa using fun _ h₁ h₂ => (Std.lt_irrefl (Std.lt_of_le_of_lt h₁ h₂)).elim
+  · simpa [Std.not_le.2 h] using fun h' => (Std.not_le.2 h h'.le).elim
+
+theorem isLongestRevMatchAtChain_iff_toList {p : Char → Bool} {s : Slice} {pos pos' : s.Pos} :
+    IsLongestRevMatchAtChain p pos pos' ↔ ∃ (h : pos ≤ pos'), ∀ c, c ∈ (s.slice pos pos' h).copy.toList → p c :=
+  isLongestRevMatchAtChain_iff.trans (isLongestMatchAtChain_iff.symm.trans isLongestMatchAtChain_iff_toList)
+
+theorem isLongestRevMatchAtChain_startPos_endPos_iff_toList {p : Char → Bool} {s : Slice} :
+    IsLongestRevMatchAtChain p s.startPos s.endPos ↔ ∀ c, c ∈ s.copy.toList → p c := by
+  simp [isLongestRevMatchAtChain_iff_toList]
+
 instance {p : Char → Bool} : LawfulForwardPatternModel p where
   skipPrefix?_eq_some_iff {s} pos := by
     simp [isLongestMatch_iff, ForwardPattern.skipPrefix?, and_comm, eq_comm (b := pos)]
@@ -128,7 +192,9 @@ namespace Decidable
 
 instance {p : Char → Prop} [DecidablePred p] : PatternModel p where
   Matches := PatternModel.Matches (decide <| p ·)
-  not_matches_empty := PatternModel.not_matches_empty (pat := (decide <| p ·))
+
+instance {p : Char → Prop} [DecidablePred p] : StrictPatternModel p where
+  not_matches_empty := StrictPatternModel.not_matches_empty (pat := (decide <| p ·))
 
 instance {p : Char → Prop} [DecidablePred p] : NoPrefixPatternModel p where
   eq_empty := NoPrefixPatternModel.eq_empty (pat := (decide <| p ·))
@@ -182,6 +248,32 @@ theorem isLongestRevMatchAt_iff_isLongestRevMatchAt_decide {p : Char → Prop} [
     IsLongestRevMatchAt p pos pos' ↔ IsLongestRevMatchAt (decide <| p ·) pos pos' := by
   simp [Model.isLongestRevMatchAt_iff, isLongestRevMatch_iff_isLongestRevMatch_decide]
 
+theorem isLongestMatchAtChain_iff_isLongestMatchAtChain_decide {p : Char → Prop} [DecidablePred p]
+    {s : Slice} {pos pos' : s.Pos} :
+    IsLongestMatchAtChain p pos pos' ↔ IsLongestMatchAtChain (decide <| p ·) pos pos' := by
+  constructor
+  · intro h; induction h with
+    | nil => exact .nil _
+    | cons _ mid _ hmatch hchain ih =>
+      exact .cons _ mid _ (isLongestMatchAt_iff_isLongestMatchAt_decide.1 hmatch) ih
+  · intro h; induction h with
+    | nil => exact .nil _
+    | cons _ mid _ hmatch hchain ih =>
+      exact .cons _ mid _ (isLongestMatchAt_iff_isLongestMatchAt_decide.2 hmatch) ih
+
+theorem isLongestRevMatchAtChain_iff_isLongestRevMatchAtChain_decide {p : Char → Prop} [DecidablePred p]
+    {s : Slice} {pos pos' : s.Pos} :
+    IsLongestRevMatchAtChain p pos pos' ↔ IsLongestRevMatchAtChain (decide <| p ·) pos pos' := by
+  constructor
+  · intro h; induction h with
+    | nil => exact .nil _
+    | cons _ _ hchain hmatch ih =>
+      exact .cons _ _ _ ih (isLongestRevMatchAt_iff_isLongestRevMatchAt_decide.1 hmatch)
+  · intro h; induction h with
+    | nil => exact .nil _
+    | cons _ _ hchain hmatch ih =>
+      exact .cons _ _ _ ih (isLongestRevMatchAt_iff_isLongestRevMatchAt_decide.2 hmatch)
+
 theorem isLongestMatchAt_iff {p : Char → Prop} [DecidablePred p] {s : Slice}
     {pos pos' : s.Pos} :
     IsLongestMatchAt p pos pos' ↔ ∃ h, pos' = pos.next h ∧ p (pos.get h) := by
@@ -319,6 +411,9 @@ theorem dropPrefix_prop_eq_dropPrefix_decide {p : Char → Prop} [DecidablePred
 theorem skipPrefix?_prop_eq_skipPrefix?_decide {p : Char → Prop} [DecidablePred p] {s : Slice} :
     s.skipPrefix? p = s.skipPrefix? (decide <| p ·) := (rfl)
 
+theorem Pos.skip?_prop_eq_skip?_decide {p : Char → Prop} [DecidablePred p] {s : Slice} {pos : s.Pos} :
+    pos.skip? p = pos.skip? (decide <| p ·) := (rfl)
+
 theorem Pattern.ForwardPattern.skipPrefix?_prop_eq_skipPrefix?_decide
     {p : Char → Prop} [DecidablePred p] {s : Slice} :
     skipPrefix? p s = skipPrefix? (decide <| p ·) s := (rfl)
@@ -329,13 +424,13 @@ theorem Pos.skipWhile_prop_eq_skipWhile_decide {p : Char → Prop} [DecidablePre
   fun_induction Pos.skipWhile curr p with
   | case1 pos nextCurr h₁ h₂ ih =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pattern.ForwardPattern.skipPrefix?_prop_eq_skipPrefix?_decide, h₁, h₂, ih]
+    simp [← Pos.skip?_prop_eq_skip?_decide, h₁, h₂, ih]
   | case2 pos nextCurr h ih =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pattern.ForwardPattern.skipPrefix?_prop_eq_skipPrefix?_decide, h, ih]
+    simp [← Pos.skip?_prop_eq_skip?_decide, h, ih]
   | case3 pos h =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pattern.ForwardPattern.skipPrefix?_prop_eq_skipPrefix?_decide]
+    simp [← Pos.skip?_prop_eq_skip?_decide, h]
 
 theorem skipPrefixWhile_prop_eq_skipPrefixWhile_decide {p : Char → Prop} [DecidablePred p]
     {s : Slice} :
@@ -352,7 +447,7 @@ theorem takeWhile_prop_eq_takeWhile_decide {p : Char → Prop} [DecidablePred p]
 
 theorem all_prop_eq_all_decide {p : Char → Prop} [DecidablePred p] {s : Slice} :
     s.all p = s.all (decide <| p ·) := by
-  simp only [all, dropWhile_prop_eq_dropWhile_decide]
+  simp only [all, skipPrefixWhile_prop_eq_skipPrefixWhile_decide]
 
 theorem find?_prop_eq_find?_decide {p : Char → Prop} [DecidablePred p] {s : Slice} :
     s.find? p = s.find? (decide <| p ·) :=
@@ -383,19 +478,22 @@ theorem Pattern.BackwardPattern.skipSuffix?_prop_eq_skipSuffix?_decide
     {p : Char → Prop} [DecidablePred p] {s : Slice} :
     skipSuffix? p s = skipSuffix? (decide <| p ·) s := (rfl)
 
+theorem Pos.revSkip?_prop_eq_revSkip?_decide {p : Char → Prop} [DecidablePred p] {s : Slice} {pos : s.Pos} :
+    pos.revSkip? p = pos.revSkip? (decide <| p ·) := (rfl)
+
 theorem Pos.revSkipWhile_prop_eq_revSkipWhile_decide {p : Char → Prop} [DecidablePred p]
     {s : Slice} (curr : s.Pos) :
     Pos.revSkipWhile curr p = Pos.revSkipWhile curr (decide <| p ·) := by
   fun_induction Pos.revSkipWhile curr p with
   | case1 pos nextCurr h₁ h₂ ih =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pattern.BackwardPattern.skipSuffix?_prop_eq_skipSuffix?_decide, h₁, h₂, ih]
+    simp [← Pos.revSkip?_prop_eq_revSkip?_decide, h₁, h₂, ih]
   | case2 pos nextCurr h ih =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pattern.BackwardPattern.skipSuffix?_prop_eq_skipSuffix?_decide, h, ih]
+    simp [← Pos.revSkip?_prop_eq_revSkip?_decide, h, ih]
   | case3 pos h =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pattern.BackwardPattern.skipSuffix?_prop_eq_skipSuffix?_decide]
+    simp [← Pos.revSkip?_prop_eq_revSkip?_decide, h]
 
 theorem skipSuffixWhile_prop_eq_skipSuffixWhile_decide {p : Char → Prop} [DecidablePred p]
     {s : Slice} :
@@ -412,4 +510,8 @@ theorem takeEndWhile_prop_eq_takeEndWhile_decide {p : Char → Prop} [DecidableP
     s.takeEndWhile p = s.takeEndWhile (decide <| p ·) := by
   simp only [takeEndWhile]; exact congrArg _ skipSuffixWhile_prop_eq_skipSuffixWhile_decide
 
+theorem revAll_prop_eq_revAll_decide {p : Char → Prop} [DecidablePred p] {s : Slice} :
+    s.revAll p = s.revAll (decide <| p ·) := by
+  simp only [revAll, skipSuffixWhile_prop_eq_skipSuffixWhile_decide]
+
 end String.Slice

src/Init/Data/String/Lemmas/Pattern/Split/Basic.lean

@@ -36,7 +36,7 @@ This gives a low-level correctness proof from which higher-level API lemmas can
 namespace String.Slice.Pattern.Model
 
 @[cbv_opaque]
-public protected noncomputable def split {ρ : Type} (pat : ρ) [PatternModel pat] {s : Slice}
+public protected noncomputable def split {ρ : Type} (pat : ρ) [PatternModel pat] [StrictPatternModel pat] {s : Slice}
     (firstRejected curr : s.Pos) (hle : firstRejected ≤ curr) : List s.Subslice :=
   if h : curr = s.endPos then
     [s.subslice _ _ hle]
@@ -49,12 +49,12 @@ public protected noncomputable def split {ρ : Type} (pat : ρ) [PatternModel pa
 termination_by curr
 
 @[simp]
-public theorem split_endPos {ρ : Type} {pat : ρ} [PatternModel pat] {s : Slice}
+public theorem split_endPos {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice}
     {firstRejected : s.Pos} :
     Model.split (s := s) pat firstRejected s.endPos (by simp) = [s.subslice firstRejected s.endPos (by simp)] := by
   simp [Model.split]
 
-public theorem split_eq_of_isLongestMatchAt {ρ : Type} {pat : ρ} [PatternModel pat]
+public theorem split_eq_of_isLongestMatchAt {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat]
     {s : Slice} {firstRejected start stop : s.Pos} {hle} (h : IsLongestMatchAt pat start stop) :
     Model.split pat firstRejected start hle =
       s.subslice _ _ hle :: Model.split pat stop stop (by exact Std.le_refl _) := by
@@ -63,7 +63,7 @@ public theorem split_eq_of_isLongestMatchAt {ρ : Type} {pat : ρ} [PatternModel
   · congr <;> exact (matchAt?_eq_some_iff.1 ‹_›).eq h
   · simp [matchAt?_eq_some_iff.2 ‹_›] at *
 
-public theorem split_eq_of_not_matchesAt {ρ : Type} {pat : ρ} [PatternModel pat]
+public theorem split_eq_of_not_matchesAt {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat]
     {s : Slice} {firstRejected start} (stop : s.Pos) (h₀ : start ≤ stop) {hle}
     (h : ∀ p, start ≤ p → p < stop → ¬ MatchesAt pat p) :
     Model.split pat firstRejected start hle =
@@ -80,7 +80,7 @@ public theorem split_eq_of_not_matchesAt {ρ : Type} {pat : ρ} [PatternModel pa
   · obtain rfl : start = stop := Std.le_antisymm h₀ (Std.not_lt.1 h')
     simp
 
-public theorem split_eq_next_of_not_matchesAt {ρ : Type} {pat : ρ} [PatternModel pat]
+public theorem split_eq_next_of_not_matchesAt {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat]
     {s : Slice} {firstRejected start} {hle} (hs : start ≠ s.endPos) (h : ¬ MatchesAt pat start) :
     Model.split pat firstRejected start hle =
       Model.split pat firstRejected (start.next hs) (by exact Std.le_trans hle (by simp)) := by
@@ -103,7 +103,7 @@ def splitFromSteps {s : Slice} (currPos : s.Pos) (l : List (SearchStep s)) : Lis
   | .matched p q :: l => s.subslice! currPos p :: splitFromSteps q l
 
 theorem IsValidSearchFrom.splitFromSteps_eq_extend_split {ρ : Type} (pat : ρ)
-    [PatternModel pat] (l : List (SearchStep s)) (pos pos' : s.Pos) (h₀ : pos ≤ pos')
+    [PatternModel pat] [StrictPatternModel pat] (l : List (SearchStep s)) (pos pos' : s.Pos) (h₀ : pos ≤ pos')
     (h' : ∀ p, pos ≤ p → p < pos' → ¬ MatchesAt pat p)
     (h : IsValidSearchFrom pat pos' l) :
     splitFromSteps pos l = Model.split pat pos pos' h₀ := by
@@ -155,7 +155,7 @@ end Model
 open Model
 
 @[cbv_eval]
-public theorem toList_splitToSubslice_eq_modelSplit {ρ : Type} (pat : ρ) [PatternModel pat]
+public theorem toList_splitToSubslice_eq_modelSplit {ρ : Type} (pat : ρ) [PatternModel pat] [StrictPatternModel pat]
     {σ : Slice → Type} [ToForwardSearcher pat σ] [∀ s, Std.Iterator (σ s) Id (SearchStep s)]
     [∀ s, Std.Iterators.Finite (σ s) Id] [LawfulToForwardSearcherModel pat] (s : Slice) :
     (s.splitToSubslice pat).toList = Model.split pat s.startPos s.startPos (by exact Std.le_refl _) := by
@@ -168,7 +168,7 @@ end Pattern
 open Pattern
 
 public theorem toList_splitToSubslice_of_isEmpty {ρ : Type} (pat : ρ)
-    [Model.PatternModel pat] {σ : Slice → Type}
+    [Model.PatternModel pat] [Model.StrictPatternModel pat] {σ : Slice → Type}
     [ToForwardSearcher pat σ] [∀ s, Std.Iterator (σ s) Id (SearchStep s)]
     [∀ s, Std.Iterators.Finite (σ s) Id] [Model.LawfulToForwardSearcherModel pat] {s : Slice}
     (h : s.isEmpty = true) :
@@ -182,7 +182,7 @@ public theorem toList_split_eq_splitToSubslice {ρ : Type} (pat : ρ) {σ : Slic
   simp [split, Std.Iter.toList_map]
 
 public theorem toList_split_of_isEmpty {ρ : Type} (pat : ρ)
-    [Model.PatternModel pat] {σ : Slice → Type}
+    [Model.PatternModel pat] [Model.StrictPatternModel pat] {σ : Slice → Type}
     [ToForwardSearcher pat σ] [∀ s, Std.Iterator (σ s) Id (SearchStep s)]
     [∀ s, Std.Iterators.Finite (σ s) Id] [Model.LawfulToForwardSearcherModel pat] {s : Slice}
     (h : s.isEmpty = true) :
@@ -200,7 +200,7 @@ public theorem split_eq_split_toSlice {ρ : Type} {pat : ρ} {σ : Slice → Typ
 
 @[simp]
 public theorem toList_split_empty {ρ : Type} (pat : ρ)
-    [Model.PatternModel pat] {σ : Slice → Type}
+    [Model.PatternModel pat] [Model.StrictPatternModel pat] {σ : Slice → Type}
     [ToForwardSearcher pat σ] [∀ s, Std.Iterator (σ s) Id (SearchStep s)]
     [∀ s, Std.Iterators.Finite (σ s) Id] [Model.LawfulToForwardSearcherModel pat] :
     ("".split pat).toList.map Slice.copy = [""] := by

src/Init/Data/String/Lemmas/Pattern/String/Basic.lean

@@ -10,6 +10,9 @@ public import Init.Data.String.Pattern.String
 public import Init.Data.String.Lemmas.Pattern.Basic
 import Init.Data.String.Lemmas.IsEmpty
 import Init.Data.String.Lemmas.Basic
+import Init.Data.String.Lemmas.Intercalate
+import Init.Data.String.OrderInstances
+import Init.Data.String.Lemmas.Splits
 import Init.Data.ByteArray.Lemmas
 import Init.Omega
 
@@ -20,17 +23,10 @@ namespace String.Slice.Pattern.Model
 namespace ForwardSliceSearcher
 
 instance {pat : Slice} : PatternModel pat where
-  /-
-  See the docstring of `PatternModel` for an explanation about why we disallow matching the
-  empty string.
+  Matches s := s = pat.copy
 
-  Requiring `s ≠ ""` is a trick that allows us to give a `PatternModel` instance
-  unconditionally, without forcing `pat.copy` to be non-empty (which would make it very awkward
-  to state theorems about the instance). It does not change anything about the fact that all lemmas
-  about this instance require `pat.isEmpty = false`.
-  -/
-  Matches s := s ≠ "" ∧ s = pat.copy
-  not_matches_empty := by simp
+theorem strictPatternModel {pat : Slice} (hpat : pat.isEmpty = false) : StrictPatternModel pat where
+  not_matches_empty := by simpa [PatternModel.Matches]
 
 instance {pat : Slice} : NoPrefixPatternModel pat :=
   .of_length_eq (by simp +contextual [PatternModel.Matches])
@@ -38,59 +34,111 @@ instance {pat : Slice} : NoPrefixPatternModel pat :=
 instance {pat : Slice} : NoSuffixPatternModel pat :=
   .of_length_eq (by simp +contextual [PatternModel.Matches])
 
-theorem isMatch_iff {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
+theorem isMatch_iff {pat s : Slice} {pos : s.Pos} :
     IsMatch pat pos ↔ (s.sliceTo pos).copy = pat.copy := by
-  simp only [Model.isMatch_iff, PatternModel.Matches, ne_eq, copy_eq_empty_iff,
-    Bool.not_eq_true, and_iff_right_iff_imp]
-  intro h'
-  rw [← isEmpty_copy (s := s.sliceTo pos), h', isEmpty_copy, h]
+  simp [Model.isMatch_iff, PatternModel.Matches]
 
-theorem isRevMatch_iff {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
+theorem isRevMatch_iff {pat s : Slice} {pos : s.Pos} :
     IsRevMatch pat pos ↔ (s.sliceFrom pos).copy = pat.copy := by
-  simp only [Model.isRevMatch_iff, PatternModel.Matches, ne_eq, copy_eq_empty_iff,
-    Bool.not_eq_true, and_iff_right_iff_imp]
-  intro h'
-  rw [← isEmpty_copy (s := s.sliceFrom pos), h', isEmpty_copy, h]
+  simp [Model.isRevMatch_iff, PatternModel.Matches]
 
-theorem isLongestMatch_iff {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
+theorem isLongestMatch_iff {pat s : Slice} {pos : s.Pos} :
     IsLongestMatch pat pos ↔ (s.sliceTo pos).copy = pat.copy := by
-  rw [isLongestMatch_iff_isMatch, isMatch_iff h]
+  rw [isLongestMatch_iff_isMatch, isMatch_iff]
 
-theorem isLongestRevMatch_iff {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
+theorem isLongestRevMatch_iff {pat s : Slice} {pos : s.Pos} :
     IsLongestRevMatch pat pos ↔ (s.sliceFrom pos).copy = pat.copy := by
-  rw [isLongestRevMatch_iff_isRevMatch, isRevMatch_iff h]
+  rw [isLongestRevMatch_iff_isRevMatch, isRevMatch_iff]
 
-theorem isLongestMatchAt_iff {pat s : Slice} {pos₁ pos₂ : s.Pos} (h : pat.isEmpty = false) :
+theorem isLongestMatchAt_iff {pat s : Slice} {pos₁ pos₂ : s.Pos} :
     IsLongestMatchAt pat pos₁ pos₂ ↔ ∃ h, (s.slice pos₁ pos₂ h).copy = pat.copy := by
-  simp [Model.isLongestMatchAt_iff, isLongestMatch_iff h]
+  simp [Model.isLongestMatchAt_iff, isLongestMatch_iff]
 
-theorem isLongestRevMatchAt_iff {pat s : Slice} {pos₁ pos₂ : s.Pos} (h : pat.isEmpty = false) :
+theorem isLongestMatchAtChain_iff {pat s : Slice} {pos₁ pos₂ : s.Pos} :
+    IsLongestMatchAtChain pat pos₁ pos₂ ↔
+      ∃ h n, (s.slice pos₁ pos₂ h).copy = String.join (List.replicate n pat.copy) := by
+  refine ⟨fun h => ⟨h.le, ?_⟩, fun ⟨h, n, h'⟩ => ?_⟩
+  · induction h with
+    | nil => simpa using ⟨0, by simp⟩
+    | cons p₁ p₂ p₃ h₁ h₂ ih =>
+      rw [isLongestMatchAt_iff] at h₁
+      obtain ⟨n, ih⟩ := ih
+      obtain ⟨h₀, h₁⟩ := h₁
+      have : (s.slice p₁ p₃ (Std.le_trans h₀ h₂.le)).copy = (s.slice p₁ p₂ h₀).copy ++ (s.slice p₂ p₃ h₂.le).copy := by
+        simp [(Slice.Pos.slice p₂ _ _ h₀ h₂.le).splits.eq_append]
+      refine ⟨n + 1, ?_⟩
+      rw [this, h₁, ih]
+      simp [← String.join_cons, ← List.replicate_succ]
+  · induction n generalizing pos₁ pos₂ with
+    | zero => simp_all
+    | succ n ih =>
+      rw [List.replicate_succ, String.join_cons] at h'
+      refine .cons _ (Pos.ofSlice (Pos.ofEqAppend h')) _ ?_ (ih ?_ Pos.ofSlice_le ?_)
+      · simpa [isLongestMatchAt_iff] using (Pos.splits_ofEqAppend h').copy_sliceTo_eq
+      · simpa [sliceFrom_slice ▸ (Pos.splits_ofEqAppend h').copy_sliceFrom_eq] using ⟨n, rfl⟩
+      · simpa using (Pos.splits_ofEqAppend h').copy_sliceFrom_eq
+
+theorem isLongestMatchAtChain_startPos_endPos_iff {pat s : Slice} :
+    IsLongestMatchAtChain pat s.startPos s.endPos ↔
+      ∃ n, s.copy = String.join (List.replicate n pat.copy) := by
+  simp [isLongestMatchAtChain_iff]
+
+theorem isLongestRevMatchAt_iff {pat s : Slice} {pos₁ pos₂ : s.Pos} :
     IsLongestRevMatchAt pat pos₁ pos₂ ↔ ∃ h, (s.slice pos₁ pos₂ h).copy = pat.copy := by
-  simp [Model.isLongestRevMatchAt_iff, isLongestRevMatch_iff h]
+  simp [Model.isLongestRevMatchAt_iff, isLongestRevMatch_iff]
 
-theorem isLongestMatchAt_iff_splits {pat s : Slice} {pos₁ pos₂ : s.Pos} (h : pat.isEmpty = false) :
+theorem isLongestRevMatchAtChain_iff {pat s : Slice} {pos₁ pos₂ : s.Pos} :
+    IsLongestRevMatchAtChain pat pos₁ pos₂ ↔
+      ∃ h n, (s.slice pos₁ pos₂ h).copy = String.join (List.replicate n pat.copy) := by
+  refine ⟨fun h => ⟨h.le, ?_⟩, fun ⟨h, n, h'⟩ => ?_⟩
+  · induction h with
+    | nil => simpa using ⟨0, by simp⟩
+    | cons p₂ p₃ h₁ h₂ ih =>
+      rw [isLongestRevMatchAt_iff] at h₂
+      obtain ⟨n, ih⟩ := ih
+      obtain ⟨h₀, h₂⟩ := h₂
+      have : (s.slice pos₁ p₃ (Std.le_trans h₁.le h₀)).copy = (s.slice pos₁ p₂ h₁.le).copy ++ (s.slice p₂ p₃ h₀).copy := by
+        simp [(Slice.Pos.slice p₂ _ _ (IsLongestRevMatchAtChain.le ‹_›) h₀).splits.eq_append]
+      refine ⟨n + 1, ?_⟩
+      rw [this, h₂, ih]
+      simp [← List.replicate_append_replicate]
+  · induction n generalizing pos₁ pos₂ with
+    | zero => simp_all
+    | succ n ih =>
+      have h'' : (s.slice pos₁ pos₂ h).copy = String.join (List.replicate n pat.copy) ++ pat.copy := by
+        rw [h', List.replicate_succ', String.join_append]; simp
+      refine .cons _ (Pos.ofSlice (Pos.ofEqAppend h'')) _ (ih ?_ Pos.le_ofSlice ?_) ?_
+      · simpa [sliceTo_slice ▸ (Pos.splits_ofEqAppend h'').copy_sliceTo_eq] using ⟨n, rfl⟩
+      · simpa using (Pos.splits_ofEqAppend h'').copy_sliceTo_eq
+      · simpa [isLongestRevMatchAt_iff] using (Pos.splits_ofEqAppend h'').copy_sliceFrom_eq
+
+theorem isLongestRevMatchAtChain_startPos_endPos_iff {pat s : Slice} :
+    IsLongestRevMatchAtChain pat s.startPos s.endPos ↔
+      ∃ n, s.copy = String.join (List.replicate n pat.copy) := by
+  simp [isLongestRevMatchAtChain_iff]
+
+theorem isLongestMatchAt_iff_splits {pat s : Slice} {pos₁ pos₂ : s.Pos} :
     IsLongestMatchAt pat pos₁ pos₂ ↔ ∃ t₁ t₂, pos₁.Splits t₁ (pat.copy ++ t₂) ∧
       pos₂.Splits (t₁ ++ pat.copy) t₂ := by
-  simp only [isLongestMatchAt_iff h, copy_slice_eq_iff_splits]
+  simp only [isLongestMatchAt_iff, copy_slice_eq_iff_splits]
 
-theorem isLongestRevMatchAt_iff_splits {pat s : Slice} {pos₁ pos₂ : s.Pos}
-    (h : pat.isEmpty = false) :
+theorem isLongestRevMatchAt_iff_splits {pat s : Slice} {pos₁ pos₂ : s.Pos} :
     IsLongestRevMatchAt pat pos₁ pos₂ ↔ ∃ t₁ t₂, pos₁.Splits t₁ (pat.copy ++ t₂) ∧
       pos₂.Splits (t₁ ++ pat.copy) t₂ := by
-  simp only [isLongestRevMatchAt_iff h, copy_slice_eq_iff_splits]
+  simp only [isLongestRevMatchAt_iff, copy_slice_eq_iff_splits]
 
-theorem isLongestMatch_iff_splits {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
+theorem isLongestMatch_iff_splits {pat s : Slice} {pos : s.Pos} :
     IsLongestMatch pat pos ↔ ∃ t, pos.Splits pat.copy t := by
-  rw [isLongestMatch_iff h, copy_sliceTo_eq_iff_exists_splits]
+  rw [isLongestMatch_iff, copy_sliceTo_eq_iff_exists_splits]
 
-theorem isLongestRevMatch_iff_splits {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
+theorem isLongestRevMatch_iff_splits {pat s : Slice} {pos : s.Pos} :
     IsLongestRevMatch pat pos ↔ ∃ t, pos.Splits t pat.copy := by
-  rw [isLongestRevMatch_iff h, copy_sliceFrom_eq_iff_exists_splits]
+  rw [isLongestRevMatch_iff, copy_sliceFrom_eq_iff_exists_splits]
 
 theorem isLongestMatchAt_iff_extract {pat s : Slice} {pos₁ pos₂ : s.Pos} (h : pat.isEmpty = false) :
     IsLongestMatchAt pat pos₁ pos₂ ↔
       s.copy.toByteArray.extract pos₁.offset.byteIdx pos₂.offset.byteIdx = pat.copy.toByteArray := by
-  rw [isLongestMatchAt_iff h]
+  rw [isLongestMatchAt_iff]
   refine ⟨fun ⟨h, h'⟩ => ?_, fun h' => ?_⟩
   · simp [← h', toByteArray_copy_slice]
   · rw [← Slice.toByteArray_copy_ne_empty_iff, ← h', ne_eq, ByteArray.extract_eq_empty_iff] at h
@@ -102,7 +150,7 @@ theorem isLongestRevMatchAt_iff_extract {pat s : Slice} {pos₁ pos₂ : s.Pos}
     IsLongestRevMatchAt pat pos₁ pos₂ ↔
       s.copy.toByteArray.extract pos₁.offset.byteIdx pos₂.offset.byteIdx =
         pat.copy.toByteArray := by
-  rw [isLongestRevMatchAt_iff h]
+  rw [isLongestRevMatchAt_iff]
   refine ⟨fun ⟨h, h'⟩ => ?_, fun h' => ?_⟩
   · simp [← h', toByteArray_copy_slice]
   · rw [← Slice.toByteArray_copy_ne_empty_iff, ← h', ne_eq, ByteArray.extract_eq_empty_iff] at h
@@ -130,21 +178,21 @@ theorem offset_of_isLongestRevMatchAt {pat s : Slice} {pos₁ pos₂ : s.Pos}
   suffices pos₂.offset.byteIdx ≤ s.utf8ByteSize by omega
   simpa [Pos.le_iff, Pos.Raw.le_iff] using pos₂.le_endPos
 
-theorem matchesAt_iff_splits {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
+theorem matchesAt_iff_splits {pat s : Slice} {pos : s.Pos} :
     MatchesAt pat pos ↔ ∃ t₁ t₂, pos.Splits t₁ (pat.copy ++ t₂) := by
-  simp only [matchesAt_iff_exists_isLongestMatchAt, isLongestMatchAt_iff_splits h]
+  simp only [matchesAt_iff_exists_isLongestMatchAt, isLongestMatchAt_iff_splits]
   exact ⟨fun ⟨e, t₁, t₂, ht₁, ht₂⟩ => ⟨t₁, t₂, ht₁⟩,
     fun ⟨t₁, t₂, ht⟩ => ⟨ht.rotateRight, t₁, t₂, ht, ht.splits_rotateRight⟩⟩
 
-theorem revMatchesAt_iff_splits {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
+theorem revMatchesAt_iff_splits {pat s : Slice} {pos : s.Pos} :
     RevMatchesAt pat pos ↔ ∃ t₁ t₂, pos.Splits (t₁ ++ pat.copy) t₂ := by
-  simp only [revMatchesAt_iff_exists_isLongestRevMatchAt, isLongestRevMatchAt_iff_splits h]
+  simp only [revMatchesAt_iff_exists_isLongestRevMatchAt, isLongestRevMatchAt_iff_splits]
   exact ⟨fun ⟨e, t₁, t₂, ht₁, ht₂⟩ => ⟨t₁, t₂, ht₂⟩,
     fun ⟨t₁, t₂, ht⟩ => ⟨ht.rotateLeft, t₁, t₂, ht.splits_rotateLeft, ht⟩⟩
 
-theorem exists_matchesAt_iff_eq_append {pat s : Slice} (h : pat.isEmpty = false) :
+theorem exists_matchesAt_iff_eq_append {pat s : Slice} :
     (∃ (pos : s.Pos), MatchesAt pat pos) ↔ ∃ t₁ t₂, s.copy = t₁ ++ pat.copy ++ t₂ := by
-  simp only [matchesAt_iff_splits h]
+  simp only [matchesAt_iff_splits]
   constructor
   · rintro ⟨pos, t₁, t₂, hsplit⟩
     exact ⟨t₁, t₂, by rw [hsplit.eq_append, append_assoc]⟩
@@ -154,9 +202,9 @@ theorem exists_matchesAt_iff_eq_append {pat s : Slice} (h : pat.isEmpty = false)
         ⟨t₁, pat.copy ++ t₂, by rw [← append_assoc]; exact heq, rfl⟩
     exact ⟨s.pos _ hvalid, t₁, t₂, ⟨by rw [← append_assoc]; exact heq, by simp⟩⟩
 
-theorem exists_revMatchesAt_iff_eq_append {pat s : Slice} (h : pat.isEmpty = false) :
+theorem exists_revMatchesAt_iff_eq_append {pat s : Slice} :
     (∃ (pos : s.Pos), RevMatchesAt pat pos) ↔ ∃ t₁ t₂, s.copy = t₁ ++ pat.copy ++ t₂ := by
-  simp only [revMatchesAt_iff_splits h]
+  simp only [revMatchesAt_iff_splits]
   constructor
   · rintro ⟨pos, t₁, t₂, hsplit⟩
     exact ⟨t₁, t₂, by rw [hsplit.eq_append, append_assoc]⟩
@@ -233,8 +281,10 @@ end ForwardSliceSearcher
 namespace ForwardStringSearcher
 
 instance {pat : String} : PatternModel pat where
-  Matches s := s ≠ "" ∧ s = pat
-  not_matches_empty := by simp
+  Matches s := s = pat
+
+theorem strictPatternModel {pat : String} (h : pat ≠ "") : StrictPatternModel pat where
+  not_matches_empty := by simpa [PatternModel.Matches]
 
 instance {pat : String} : NoPrefixPatternModel pat :=
   .of_length_eq (by simp +contextual [PatternModel.Matches])
@@ -267,12 +317,60 @@ theorem isLongestMatchAt_iff_isLongestMatchAt_toSlice {pat : String} {s : Slice}
       IsLongestMatchAt (ρ := Slice) pat.toSlice pos₁ pos₂ := by
   simp [Model.isLongestMatchAt_iff, isLongestMatch_iff_isLongestMatch_toSlice]
 
+theorem isLongestMatchAtChain_iff_isLongestMatchAtChain_toSlice {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
+    IsLongestMatchAtChain pat pos₁ pos₂ ↔
+      IsLongestMatchAtChain pat.toSlice pos₁ pos₂ := by
+  refine ⟨fun h => ?_, fun h => ?_⟩
+  · induction h with
+    | nil => simp
+    | cons p₁ p₂ p₃ h₁ h₂ ih =>
+      exact .cons _ _ _ (isLongestMatchAt_iff_isLongestMatchAt_toSlice.1 h₁) ih
+  · induction h with
+    | nil => simp
+    | cons p₁ p₂ p₃ h₁ h₂ ih =>
+      exact .cons _ _ _ (isLongestMatchAt_iff_isLongestMatchAt_toSlice.2 h₁) ih
+
+theorem isLongestMatchAtChain_iff {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
+    IsLongestMatchAtChain pat pos₁ pos₂ ↔
+      ∃ h n, (s.slice pos₁ pos₂ h).copy = String.join (List.replicate n pat) := by
+  simp [isLongestMatchAtChain_iff_isLongestMatchAtChain_toSlice,
+    ForwardSliceSearcher.isLongestMatchAtChain_iff]
+
+theorem isLongestMatchAtChain_startPos_endPos_iff {pat : String} {s : Slice} :
+    IsLongestMatchAtChain pat s.startPos s.endPos ↔
+      ∃ n, s.copy = String.join (List.replicate n pat) := by
+  simp [isLongestMatchAtChain_iff]
+
 theorem isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice {pat : String} {s : Slice}
     {pos₁ pos₂ : s.Pos} :
     IsLongestRevMatchAt (ρ := String) pat pos₁ pos₂ ↔
       IsLongestRevMatchAt (ρ := Slice) pat.toSlice pos₁ pos₂ := by
   simp [Model.isLongestRevMatchAt_iff, isLongestRevMatch_iff_isLongestRevMatch_toSlice]
 
+theorem isLongestRevMatchAtChain_iff_isLongestRevMatchAtChain_toSlice {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
+    IsLongestRevMatchAtChain pat pos₁ pos₂ ↔
+      IsLongestRevMatchAtChain pat.toSlice pos₁ pos₂ := by
+  refine ⟨fun h => ?_, fun h => ?_⟩
+  · induction h with
+    | nil => simp
+    | cons p₂ p₃ _ hmatch ih =>
+      exact .cons _ _ _ ih (isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice.1 hmatch)
+  · induction h with
+    | nil => simp
+    | cons p₂ p₃ _ hmatch ih =>
+      exact .cons _ _ _ ih (isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice.2 hmatch)
+
+theorem isLongestRevMatchAtChain_iff {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
+    IsLongestRevMatchAtChain pat pos₁ pos₂ ↔
+      ∃ h n, (s.slice pos₁ pos₂ h).copy = String.join (List.replicate n pat) := by
+  simp [isLongestRevMatchAtChain_iff_isLongestRevMatchAtChain_toSlice,
+    ForwardSliceSearcher.isLongestRevMatchAtChain_iff]
+
+theorem isLongestRevMatchAtChain_startPos_endPos_iff {pat : String} {s : Slice} :
+    IsLongestRevMatchAtChain pat s.startPos s.endPos ↔
+      ∃ n, s.copy = String.join (List.replicate n pat) := by
+  simp [isLongestRevMatchAtChain_iff]
+
 theorem matchesAt_iff_toSlice {pat : String} {s : Slice} {pos : s.Pos} :
     MatchesAt (ρ := String) pat pos ↔ MatchesAt (ρ := Slice) pat.toSlice pos := by
   simp [matchesAt_iff_exists_isLongestMatchAt, isLongestMatchAt_iff_isLongestMatchAt_toSlice]
@@ -282,61 +380,55 @@ theorem revMatchesAt_iff_toSlice {pat : String} {s : Slice} {pos : s.Pos} :
   simp [revMatchesAt_iff_exists_isLongestRevMatchAt,
     isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice]
 
-private theorem toSlice_isEmpty (h : pat ≠ "") : pat.toSlice.isEmpty = false := by
-  rwa [isEmpty_toSlice, isEmpty_eq_false_iff]
-
-theorem isMatch_iff {pat : String} {s : Slice} {pos : s.Pos} (h : pat ≠ "") :
+theorem isMatch_iff {pat : String} {s : Slice} {pos : s.Pos} :
     IsMatch pat pos ↔ (s.sliceTo pos).copy = pat := by
-  rw [isMatch_iff_slice, ForwardSliceSearcher.isMatch_iff (toSlice_isEmpty h)]
+  rw [isMatch_iff_slice, ForwardSliceSearcher.isMatch_iff]
   simp
 
-theorem isRevMatch_iff {pat : String} {s : Slice} {pos : s.Pos} (h : pat ≠ "") :
+theorem isRevMatch_iff {pat : String} {s : Slice} {pos : s.Pos} :
     IsRevMatch pat pos ↔ (s.sliceFrom pos).copy = pat := by
-  rw [isRevMatch_iff_slice, ForwardSliceSearcher.isRevMatch_iff (toSlice_isEmpty h)]
+  rw [isRevMatch_iff_slice, ForwardSliceSearcher.isRevMatch_iff]
   simp
 
-theorem isLongestMatch_iff {pat : String} {s : Slice} {pos : s.Pos} (h : pat ≠ "") :
+theorem isLongestMatch_iff {pat : String} {s : Slice} {pos : s.Pos} :
     IsLongestMatch pat pos ↔ (s.sliceTo pos).copy = pat := by
-  rw [isLongestMatch_iff_isMatch, isMatch_iff h]
+  rw [isLongestMatch_iff_isMatch, isMatch_iff]
 
-theorem isLongestRevMatch_iff {pat : String} {s : Slice} {pos : s.Pos} (h : pat ≠ "") :
+theorem isLongestRevMatch_iff {pat : String} {s : Slice} {pos : s.Pos} :
     IsLongestRevMatch pat pos ↔ (s.sliceFrom pos).copy = pat := by
-  rw [isLongestRevMatch_iff_isRevMatch, isRevMatch_iff h]
+  rw [isLongestRevMatch_iff_isRevMatch, isRevMatch_iff]
 
-theorem isLongestMatchAt_iff {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} (h : pat ≠ "") :
+theorem isLongestMatchAt_iff {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
     IsLongestMatchAt pat pos₁ pos₂ ↔ ∃ h, (s.slice pos₁ pos₂ h).copy = pat := by
   rw [isLongestMatchAt_iff_isLongestMatchAt_toSlice,
-    ForwardSliceSearcher.isLongestMatchAt_iff (toSlice_isEmpty h)]
+    ForwardSliceSearcher.isLongestMatchAt_iff]
   simp
 
-theorem isLongestRevMatchAt_iff {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} (h : pat ≠ "") :
+theorem isLongestRevMatchAt_iff {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
     IsLongestRevMatchAt pat pos₁ pos₂ ↔ ∃ h, (s.slice pos₁ pos₂ h).copy = pat := by
   rw [isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice,
-    ForwardSliceSearcher.isLongestRevMatchAt_iff (toSlice_isEmpty h)]
+    ForwardSliceSearcher.isLongestRevMatchAt_iff]
   simp
 
-theorem isLongestMatchAt_iff_splits {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos}
-    (h : pat ≠ "") :
+theorem isLongestMatchAt_iff_splits {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
     IsLongestMatchAt pat pos₁ pos₂ ↔
       ∃ t₁ t₂, pos₁.Splits t₁ (pat ++ t₂) ∧ pos₂.Splits (t₁ ++ pat) t₂ := by
   rw [isLongestMatchAt_iff_isLongestMatchAt_toSlice,
-    ForwardSliceSearcher.isLongestMatchAt_iff_splits (toSlice_isEmpty h)]
+    ForwardSliceSearcher.isLongestMatchAt_iff_splits]
   simp
 
-theorem isLongestRevMatchAt_iff_splits {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos}
-    (h : pat ≠ "") :
+theorem isLongestRevMatchAt_iff_splits {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
     IsLongestRevMatchAt pat pos₁ pos₂ ↔
       ∃ t₁ t₂, pos₁.Splits t₁ (pat ++ t₂) ∧ pos₂.Splits (t₁ ++ pat) t₂ := by
   rw [isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice,
-    ForwardSliceSearcher.isLongestRevMatchAt_iff_splits (toSlice_isEmpty h)]
+    ForwardSliceSearcher.isLongestRevMatchAt_iff_splits]
   simp
 
-theorem isLongestMatchAt_iff_extract {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos}
-    (h : pat ≠ "") :
+theorem isLongestMatchAt_iff_extract {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} (h : pat ≠ "") :
     IsLongestMatchAt pat pos₁ pos₂ ↔
       s.copy.toByteArray.extract pos₁.offset.byteIdx pos₂.offset.byteIdx = pat.toByteArray := by
   rw [isLongestMatchAt_iff_isLongestMatchAt_toSlice,
-    ForwardSliceSearcher.isLongestMatchAt_iff_extract (toSlice_isEmpty h)]
+    ForwardSliceSearcher.isLongestMatchAt_iff_extract (by simpa)]
   simp
 
 theorem isLongestRevMatchAt_iff_extract {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos}
@@ -344,38 +436,38 @@ theorem isLongestRevMatchAt_iff_extract {pat : String} {s : Slice} {pos₁ pos
     IsLongestRevMatchAt pat pos₁ pos₂ ↔
       s.copy.toByteArray.extract pos₁.offset.byteIdx pos₂.offset.byteIdx = pat.toByteArray := by
   rw [isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice,
-    ForwardSliceSearcher.isLongestRevMatchAt_iff_extract (toSlice_isEmpty h)]
+    ForwardSliceSearcher.isLongestRevMatchAt_iff_extract (by simpa)]
   simp
 
 theorem offset_of_isLongestMatchAt {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos}
     (h : pat ≠ "") (h' : IsLongestMatchAt pat pos₁ pos₂) :
     pos₂.offset = pos₁.offset.increaseBy pat.utf8ByteSize := by
   rw [show pat.utf8ByteSize = pat.toSlice.utf8ByteSize from utf8ByteSize_toSlice.symm]
-  exact ForwardSliceSearcher.offset_of_isLongestMatchAt (toSlice_isEmpty h)
+  exact ForwardSliceSearcher.offset_of_isLongestMatchAt (by simpa)
     (isLongestMatchAt_iff_isLongestMatchAt_toSlice.1 h')
 
 theorem offset_of_isLongestRevMatchAt {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos}
     (h : pat ≠ "") (h' : IsLongestRevMatchAt pat pos₁ pos₂) :
     pos₂.offset = pos₁.offset.increaseBy pat.utf8ByteSize := by
   rw [show pat.utf8ByteSize = pat.toSlice.utf8ByteSize from utf8ByteSize_toSlice.symm]
-  exact ForwardSliceSearcher.offset_of_isLongestRevMatchAt (toSlice_isEmpty h)
+  exact ForwardSliceSearcher.offset_of_isLongestRevMatchAt (by simpa)
     (isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice.1 h')
 
-theorem matchesAt_iff_splits {pat : String} {s : Slice} {pos : s.Pos} (h : pat ≠ "") :
+theorem matchesAt_iff_splits {pat : String} {s : Slice} {pos : s.Pos} :
     MatchesAt pat pos ↔ ∃ t₁ t₂, pos.Splits t₁ (pat ++ t₂) := by
   rw [matchesAt_iff_toSlice,
-    ForwardSliceSearcher.matchesAt_iff_splits (toSlice_isEmpty h)]
+    ForwardSliceSearcher.matchesAt_iff_splits]
   simp
 
-theorem revMatchesAt_iff_splits {pat : String} {s : Slice} {pos : s.Pos} (h : pat ≠ "") :
+theorem revMatchesAt_iff_splits {pat : String} {s : Slice} {pos : s.Pos} :
     RevMatchesAt pat pos ↔ ∃ t₁ t₂, pos.Splits (t₁ ++ pat) t₂ := by
   rw [revMatchesAt_iff_toSlice,
-    ForwardSliceSearcher.revMatchesAt_iff_splits (toSlice_isEmpty h)]
+    ForwardSliceSearcher.revMatchesAt_iff_splits]
   simp
 
-theorem exists_matchesAt_iff_eq_append {pat : String} {s : Slice} (h : pat ≠ "") :
+theorem exists_matchesAt_iff_eq_append {pat : String} {s : Slice} :
     (∃ (pos : s.Pos), MatchesAt pat pos) ↔ ∃ t₁ t₂, s.copy = t₁ ++ pat ++ t₂ := by
-  simp only [matchesAt_iff_splits h]
+  simp only [matchesAt_iff_splits]
   constructor
   · rintro ⟨pos, t₁, t₂, hsplit⟩
     exact ⟨t₁, t₂, by rw [hsplit.eq_append, append_assoc]⟩
@@ -385,12 +477,12 @@ theorem exists_matchesAt_iff_eq_append {pat : String} {s : Slice} (h : pat ≠ "
         ⟨t₁, pat ++ t₂, by rw [← append_assoc]; exact heq, rfl⟩
     exact ⟨s.pos _ hvalid, t₁, t₂, ⟨by rw [← append_assoc]; exact heq, by simp⟩⟩
 
-theorem exists_revMatchesAt_iff_eq_append {pat : String} {s : Slice} (h : pat ≠ "") :
+theorem exists_revMatchesAt_iff_eq_append {pat : String} {s : Slice} :
     (∃ (pos : s.Pos), RevMatchesAt pat pos) ↔ ∃ t₁ t₂, s.copy = t₁ ++ pat ++ t₂ := by
   rw [show (∃ (pos : s.Pos), RevMatchesAt (ρ := String) pat pos) ↔
       (∃ (pos : s.Pos), RevMatchesAt (ρ := Slice) pat.toSlice pos) from by
     simp [revMatchesAt_iff_toSlice],
-    ForwardSliceSearcher.exists_revMatchesAt_iff_eq_append (toSlice_isEmpty h)]
+    ForwardSliceSearcher.exists_revMatchesAt_iff_eq_append]
   simp
 
 theorem matchesAt_iff_isLongestMatchAt {pat : String} {s : Slice} {pos : s.Pos}
@@ -398,7 +490,7 @@ theorem matchesAt_iff_isLongestMatchAt {pat : String} {s : Slice} {pos : s.Pos}
     MatchesAt pat pos ↔ ∃ (h : (pos.offset.increaseBy pat.utf8ByteSize).IsValidForSlice s),
       IsLongestMatchAt pat pos (s.pos _ h) := by
   have key := ForwardSliceSearcher.matchesAt_iff_isLongestMatchAt (pat := pat.toSlice)
-    (toSlice_isEmpty h) (pos := pos)
+    (by simpa) (pos := pos)
   simp only [utf8ByteSize_toSlice, ← isLongestMatchAt_iff_isLongestMatchAt_toSlice] at key
   rwa [matchesAt_iff_toSlice]
 
@@ -408,7 +500,7 @@ theorem revMatchesAt_iff_isLongestRevMatchAt {pat : String} {s : Slice} {pos : s
       ∃ (h : (pos.offset.decreaseBy pat.utf8ByteSize).IsValidForSlice s),
         IsLongestRevMatchAt pat (s.pos _ h) pos := by
   have key := ForwardSliceSearcher.revMatchesAt_iff_isLongestRevMatchAt (pat := pat.toSlice)
-    (toSlice_isEmpty h) (pos := pos)
+    (by simpa) (pos := pos)
   simp only [utf8ByteSize_toSlice, ← isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice] at key
   rwa [revMatchesAt_iff_toSlice]
 
@@ -418,14 +510,14 @@ theorem matchesAt_iff_getElem {pat : String} {s : Slice} {pos : s.Pos} (h : pat
         ∀ (j), (hj : j < pat.toByteArray.size) →
           pat.toByteArray[j] = s.copy.toByteArray[pos.offset.byteIdx + j] := by
   have key := ForwardSliceSearcher.matchesAt_iff_getElem (pat := pat.toSlice)
-    (toSlice_isEmpty h) (pos := pos)
+    (by simpa) (pos := pos)
   simp only [copy_toSlice] at key
   rwa [matchesAt_iff_toSlice]
 
 theorem le_of_matchesAt {pat : String} {s : Slice} {pos : s.Pos} (h : pat ≠ "")
     (h' : MatchesAt pat pos) : pos.offset.increaseBy pat.utf8ByteSize ≤ s.rawEndPos := by
   rw [show pat.utf8ByteSize = pat.toSlice.utf8ByteSize from utf8ByteSize_toSlice.symm]
-  exact ForwardSliceSearcher.le_of_matchesAt (toSlice_isEmpty h)
+  exact ForwardSliceSearcher.le_of_matchesAt (by simpa)
     (matchesAt_iff_toSlice.1 h')
 
 theorem matchesAt_iff_matchesAt_toSlice {pat : String} {s : Slice}

src/Init/Data/String/Lemmas/Pattern/String/ForwardPattern.lean

@@ -56,7 +56,7 @@ theorem skipPrefix?_eq_some_iff {pat s : Slice} {pos : s.Pos} :
     simp only [reduceCtorEq, false_iff]
     intro heq
     have := h (s.sliceFrom pos).copy
-    simp [← heq, pos.splits.eq_append] at this
+    simp [← heq, -sliceTo_append_sliceFrom, pos.splits.eq_append] at this
 
 theorem isSome_skipPrefix? {pat s : Slice} : (skipPrefix? pat s).isSome = startsWith pat s := by
   fun_cases skipPrefix? <;> simp_all
@@ -76,14 +76,11 @@ namespace Model.ForwardSliceSearcher
 
 open Pattern.ForwardSliceSearcher
 
-public instance {pat : Slice} : LawfulForwardPattern pat where
+public instance {pat : Slice} : LawfulForwardPatternModel pat where
   skipPrefixOfNonempty?_eq _ := rfl
   startsWith_eq _ := isSome_skipPrefix?.symm
-
-public theorem lawfulForwardPatternModel {pat : Slice} (hpat : pat.isEmpty = false) :
-    LawfulForwardPatternModel pat where
   skipPrefix?_eq_some_iff pos := by
-    simp [ForwardPattern.skipPrefix?, skipPrefix?_eq_some_iff, isLongestMatch_iff hpat]
+    simp [ForwardPattern.skipPrefix?, skipPrefix?_eq_some_iff, isLongestMatch_iff]
 
 end Model.ForwardSliceSearcher
 
@@ -91,14 +88,11 @@ namespace Model.ForwardStringSearcher
 
 open Pattern.ForwardSliceSearcher
 
-public instance {pat : String} : LawfulForwardPattern pat where
+public instance {pat : String} : LawfulForwardPatternModel pat where
   skipPrefixOfNonempty?_eq _ := rfl
   startsWith_eq _ := isSome_skipPrefix?.symm
-
-public theorem lawfulForwardPatternModel {pat : String} (hpat : pat ≠ "") :
-    LawfulForwardPatternModel pat where
   skipPrefix?_eq_some_iff pos := by
-    simp [ForwardPattern.skipPrefix?, skipPrefix?_eq_some_iff, isLongestMatch_iff hpat]
+    simp [ForwardPattern.skipPrefix?, skipPrefix?_eq_some_iff, isLongestMatch_iff]
 
 end Model.ForwardStringSearcher
 
@@ -153,7 +147,7 @@ theorem skipSuffix?_eq_some_iff {pat s : Slice} {pos : s.Pos} :
     simp only [reduceCtorEq, false_iff]
     intro heq
     have := h (s.sliceTo pos).copy
-    simp [← heq, pos.splits.eq_append] at this
+    simp [← heq, -sliceTo_append_sliceFrom, pos.splits.eq_append] at this
 
 theorem isSome_skipSuffix? {pat s : Slice} : (skipSuffix? pat s).isSome = endsWith pat s := by
   fun_cases skipSuffix? <;> simp_all
@@ -173,15 +167,12 @@ namespace Model.BackwardSliceSearcher
 
 open Pattern.BackwardSliceSearcher
 
-public instance {pat : Slice} : LawfulBackwardPattern pat where
+public instance {pat : Slice} : LawfulBackwardPatternModel pat where
   skipSuffixOfNonempty?_eq _ := rfl
   endsWith_eq _ := isSome_skipSuffix?.symm
-
-public theorem lawfulBackwardPatternModel {pat : Slice} (hpat : pat.isEmpty = false) :
-    LawfulBackwardPatternModel pat where
   skipSuffix?_eq_some_iff pos := by
     simp [BackwardPattern.skipSuffix?, skipSuffix?_eq_some_iff,
-      ForwardSliceSearcher.isLongestRevMatch_iff hpat]
+      ForwardSliceSearcher.isLongestRevMatch_iff]
 
 end Model.BackwardSliceSearcher
 
@@ -189,15 +180,12 @@ namespace Model.BackwardStringSearcher
 
 open Pattern.BackwardSliceSearcher
 
-public instance {pat : String} : LawfulBackwardPattern pat where
+public instance {pat : String} : LawfulBackwardPatternModel pat where
   skipSuffixOfNonempty?_eq _ := rfl
   endsWith_eq _ := isSome_skipSuffix?.symm
-
-public theorem lawfulBackwardPatternModel {pat : String} (hpat : pat ≠ "") :
-    LawfulBackwardPatternModel pat where
   skipSuffix?_eq_some_iff pos := by
     simp [BackwardPattern.skipSuffix?, skipSuffix?_eq_some_iff,
-      ForwardStringSearcher.isLongestRevMatch_iff hpat]
+      ForwardStringSearcher.isLongestRevMatch_iff]
 
 end Model.BackwardStringSearcher
 
@@ -219,19 +207,22 @@ public theorem Pattern.ForwardPattern.skipPrefix?_string_eq_skipPrefix?_toSlice
     {pat : String} {s : Slice} :
     skipPrefix? pat s = skipPrefix? pat.toSlice s := (rfl)
 
+public theorem Pos.skip?_string_eq_skip?_toSlice {pat : String} {s : Slice} {pos : s.Pos} :
+    pos.skip? pat = pos.skip? pat.toSlice := (rfl)
+
 public theorem Pos.skipWhile_string_eq_skipWhile_toSlice {pat : String} {s : Slice}
     (curr : s.Pos) :
     Pos.skipWhile curr pat = Pos.skipWhile curr pat.toSlice := by
   fun_induction Pos.skipWhile curr pat with
   | case1 pos nextCurr h₁ h₂ ih =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pattern.ForwardPattern.skipPrefix?_string_eq_skipPrefix?_toSlice, h₁, h₂, ih]
+    simp [← Pos.skip?_string_eq_skip?_toSlice, h₁, h₂, ih]
   | case2 pos nextCurr h ih =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pattern.ForwardPattern.skipPrefix?_string_eq_skipPrefix?_toSlice, h, ih]
+    simp [← Pos.skip?_string_eq_skip?_toSlice, h, ih]
   | case3 pos h =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pattern.ForwardPattern.skipPrefix?_string_eq_skipPrefix?_toSlice]
+    simp [← Pos.skip?_string_eq_skip?_toSlice, h]
 
 public theorem skipPrefixWhile_string_eq_skipPrefixWhile_toSlice {pat : String} {s : Slice} :
     s.skipPrefixWhile pat = s.skipPrefixWhile pat.toSlice :=
@@ -247,7 +238,7 @@ public theorem takeWhile_string_eq_takeWhile_toSlice {pat : String} {s : Slice}
 
 public theorem all_string_eq_all_toSlice {pat : String} {s : Slice} :
     s.all pat = s.all pat.toSlice := by
-  simp only [all, dropWhile_string_eq_dropWhile_toSlice]
+  simp only [all, skipPrefixWhile_string_eq_skipPrefixWhile_toSlice]
 
 public theorem endsWith_string_eq_endsWith_toSlice {pat : String} {s : Slice} :
     s.endsWith pat = s.endsWith pat.toSlice := (rfl)
@@ -265,19 +256,22 @@ public theorem Pattern.BackwardPattern.skipSuffix?_string_eq_skipSuffix?_toSlice
     {pat : String} {s : Slice} :
     skipSuffix? pat s = skipSuffix? pat.toSlice s := (rfl)
 
+public theorem Pos.revSkip?_string_eq_revSkip?_toSlice {pat : String} {s : Slice} {pos : s.Pos} :
+    pos.revSkip? pat = pos.revSkip? pat.toSlice := (rfl)
+
 public theorem Pos.revSkipWhile_string_eq_revSkipWhile_toSlice {pat : String} {s : Slice}
     (curr : s.Pos) :
     Pos.revSkipWhile curr pat = Pos.revSkipWhile curr pat.toSlice := by
   fun_induction Pos.revSkipWhile curr pat with
   | case1 pos nextCurr h₁ h₂ ih =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pattern.BackwardPattern.skipSuffix?_string_eq_skipSuffix?_toSlice, h₁, h₂, ih]
+    simp [← Pos.revSkip?_string_eq_revSkip?_toSlice, h₁, h₂, ih]
   | case2 pos nextCurr h ih =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pattern.BackwardPattern.skipSuffix?_string_eq_skipSuffix?_toSlice, h, ih]
+    simp [← Pos.revSkip?_string_eq_revSkip?_toSlice, h, ih]
   | case3 pos h =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pattern.BackwardPattern.skipSuffix?_string_eq_skipSuffix?_toSlice]
+    simp [← Pos.revSkip?_string_eq_revSkip?_toSlice, h]
 
 public theorem skipSuffixWhile_string_eq_skipSuffixWhile_toSlice {pat : String} {s : Slice} :
     s.skipSuffixWhile pat = s.skipSuffixWhile pat.toSlice :=
@@ -291,4 +285,8 @@ public theorem takeEndWhile_string_eq_takeEndWhile_toSlice {pat : String} {s : S
     s.takeEndWhile pat = s.takeEndWhile pat.toSlice := by
   simp only [takeEndWhile]; exact congrArg _ skipSuffixWhile_string_eq_skipSuffixWhile_toSlice
 
+public theorem revAll_string_eq_revAll_toSlice {pat : String} {s : Slice} :
+    s.revAll pat = s.revAll pat.toSlice := by
+  simp [revAll, skipSuffixWhile_string_eq_skipSuffixWhile_toSlice]
+
 end String.Slice

src/Init/Data/String/Lemmas/Pattern/TakeDrop/Char.lean

@@ -56,6 +56,77 @@ theorem eq_append_of_dropPrefix?_char_eq_some {c : Char} {s res : Slice} (h : s.
     s.copy = singleton c ++ res.copy := by
   simpa [PatternModel.Matches] using Pattern.Model.eq_append_of_dropPrefix?_eq_some h
 
+theorem Pos.skip?_char_eq_some_iff {c : Char} {s : Slice} {pos res : s.Pos} :
+    pos.skip? c = some res ↔ ∃ h, res = pos.next h ∧ pos.get h = c := by
+  simp [Pattern.Model.Pos.skip?_eq_some_iff, Char.isLongestMatchAt_iff]
+
+@[simp]
+theorem Pos.skip?_char_eq_none_iff {c : Char} {s : Slice} {pos : s.Pos} :
+    pos.skip? c = none ↔ ∀ h, pos.get h ≠ c := by
+  simp [Pattern.Model.Pos.skip?_eq_none_iff, Char.matchesAt_iff]
+
+theorem Pos.get_skipWhile_char_ne {c : Char} {s : Slice} {pos : s.Pos} {h} :
+    (pos.skipWhile c).get h ≠ c := by
+  have := Pattern.Model.Pos.not_matchesAt_skipWhile c pos
+  simp_all [Char.matchesAt_iff]
+
+theorem Pos.skipWhile_char_eq_self_iff_get {c : Char} {s : Slice} {pos : s.Pos} :
+    pos.skipWhile c = pos ↔ ∀ h, pos.get h ≠ c := by
+  simp [Pattern.Model.Pos.skipWhile_eq_self_iff, Char.matchesAt_iff]
+
+theorem Pos.get_eq_of_lt_skipWhile_char {c : Char} {s : Slice} {pos pos' : s.Pos}
+    (h₁ : pos ≤ pos') (h₂ : pos' < pos.skipWhile c) : pos'.get (ne_endPos_of_lt h₂) = c :=
+  (Char.isLongestMatchAtChain_iff.1 (Pattern.Model.Pos.isLongestMatchAtChain_skipWhile c pos)).2 _ h₁ h₂
+
+theorem get_skipPrefixWhile_char_ne {c : Char} {s : Slice} {h} :
+    (s.skipPrefixWhile c).get h ≠ c := by
+  simp [skipPrefixWhile_eq_skipWhile_startPos, Pos.get_skipWhile_char_ne]
+
+theorem get_eq_of_lt_skipPrefixWhile_char {c : Char} {s : Slice} {pos : s.Pos} (h : pos < s.skipPrefixWhile c) :
+    pos.get (Pos.ne_endPos_of_lt h) = c :=
+  Pos.get_eq_of_lt_skipWhile_char (Pos.startPos_le _) (by rwa [skipPrefixWhile_eq_skipWhile_startPos] at h)
+
+@[simp]
+theorem all_char_iff {c : Char} {s : Slice} : s.all c ↔ s.copy.toList = List.replicate s.copy.length c := by
+  rw [Bool.eq_iff_iff]
+  simp [Pattern.Model.all_eq_true_iff, Char.isLongestMatchAtChain_startPos_endPos_iff_toList]
+
+theorem Pos.revSkip?_char_eq_some_iff {c : Char} {s : Slice} {pos res : s.Pos} :
+    pos.revSkip? c = some res ↔ ∃ h, res = pos.prev h ∧ (pos.prev h).get (by simp) = c := by
+  simp [Pattern.Model.Pos.revSkip?_eq_some_iff, Char.isLongestRevMatchAt_iff]
+
+@[simp]
+theorem Pos.revSkip?_char_eq_none_iff {c : Char} {s : Slice} {pos : s.Pos} :
+    pos.revSkip? c = none ↔ ∀ h, (pos.prev h).get (by simp) ≠ c := by
+  simp [Pattern.Model.Pos.revSkip?_eq_none_iff, Char.revMatchesAt_iff]
+
+theorem Pos.get_revSkipWhile_char_ne {c : Char} {s : Slice} {pos : s.Pos} {h} :
+    ((pos.revSkipWhile c).prev h).get (by simp) ≠ c := by
+  have := Pattern.Model.Pos.not_revMatchesAt_revSkipWhile c pos
+  simp_all [Char.revMatchesAt_iff]
+
+theorem Pos.revSkipWhile_char_eq_self_iff_get {c : Char} {s : Slice} {pos : s.Pos} :
+    pos.revSkipWhile c = pos ↔ ∀ h, (pos.prev h).get (by simp) ≠ c := by
+  simp [Pattern.Model.Pos.revSkipWhile_eq_self_iff, Char.revMatchesAt_iff]
+
+theorem Pos.get_eq_of_revSkipWhile_le_char {c : Char} {s : Slice} {pos pos' : s.Pos}
+    (h₁ : pos' < pos) (h₂ : pos.revSkipWhile c ≤ pos') : pos'.get (Pos.ne_endPos_of_lt h₁) = c :=
+  (Char.isLongestRevMatchAtChain_iff.1 (Pattern.Model.Pos.isLongestRevMatchAtChain_revSkipWhile c pos)).2 _ h₂ h₁
+
+theorem get_skipSuffixWhile_char_ne {c : Char} {s : Slice} {h} :
+    ((s.skipSuffixWhile c).prev h).get (by simp) ≠ c := by
+  simp [skipSuffixWhile_eq_revSkipWhile_endPos, Pos.get_revSkipWhile_char_ne]
+
+theorem get_eq_of_skipSuffixWhile_le_char {c : Char} {s : Slice} {pos : s.Pos}
+    (h : s.skipSuffixWhile c ≤ pos) (h' : pos < s.endPos) :
+    pos.get (Pos.ne_endPos_of_lt h') = c :=
+  Pos.get_eq_of_revSkipWhile_le_char h' (by rwa [skipSuffixWhile_eq_revSkipWhile_endPos] at h)
+
+@[simp]
+theorem revAll_char_iff {c : Char} {s : Slice} : s.revAll c ↔ s.copy.toList = List.replicate s.copy.length c := by
+  rw [Bool.eq_iff_iff]
+  simp [Pattern.Model.revAll_eq_true_iff, Char.isLongestRevMatchAtChain_startPos_endPos_iff_toList]
+
 theorem skipSuffix?_char_eq_some_iff {c : Char} {s : Slice} {pos : s.Pos} :
     s.skipSuffix? c = some pos ↔ ∃ h, pos = s.endPos.prev h ∧ (s.endPos.prev h).get (by simp) = c := by
   rw [Pattern.Model.skipSuffix?_eq_some_iff, Char.isLongestRevMatch_iff]
@@ -100,19 +171,19 @@ theorem skipPrefix?_char_eq_some_iff {c : Char} {s : String} {pos : s.Pos} :
 
 theorem startsWith_char_iff_get {c : Char} {s : String} :
     s.startsWith c ↔ ∃ h, s.startPos.get h = c := by
-  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_char_iff_get]
+  simp [← startsWith_toSlice, Slice.startsWith_char_iff_get]
 
 theorem startsWith_char_eq_false_iff_get {c : Char} {s : String} :
     s.startsWith c = false ↔ ∀ h, s.startPos.get h ≠ c := by
-  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_char_eq_false_iff_get]
+  simp [← startsWith_toSlice, Slice.startsWith_char_eq_false_iff_get]
 
 theorem startsWith_char_eq_head? {c : Char} {s : String} :
     s.startsWith c = (s.toList.head? == some c) := by
-  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_char_eq_head?]
+  simp [← startsWith_toSlice, Slice.startsWith_char_eq_head?]
 
 theorem startsWith_char_iff_exists_append {c : Char} {s : String} :
     s.startsWith c ↔ ∃ t, s = singleton c ++ t := by
-  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_char_iff_exists_append]
+  simp [← startsWith_toSlice, Slice.startsWith_char_iff_exists_append]
 
 theorem startsWith_char_eq_false_iff_forall_append {c : Char} {s : String} :
     s.startsWith c = false ↔ ∀ t, s ≠ singleton c ++ t := by
@@ -130,19 +201,19 @@ theorem skipSuffix?_char_eq_some_iff {c : Char} {s : String} {pos : s.Pos} :
 
 theorem endsWith_char_iff_get {c : Char} {s : String} :
     s.endsWith c ↔ ∃ h, (s.endPos.prev h).get (by simp) = c := by
-  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_char_iff_get, Pos.prev_toSlice]
+  simp [← endsWith_toSlice, Slice.endsWith_char_iff_get, Pos.prev_toSlice]
 
 theorem endsWith_char_eq_false_iff_get {c : Char} {s : String} :
     s.endsWith c = false ↔ ∀ h, (s.endPos.prev h).get (by simp) ≠ c := by
-  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_char_eq_false_iff_get, Pos.prev_toSlice]
+  simp [← endsWith_toSlice, Slice.endsWith_char_eq_false_iff_get, Pos.prev_toSlice]
 
 theorem endsWith_char_eq_getLast? {c : Char} {s : String} :
     s.endsWith c = (s.toList.getLast? == some c) := by
-  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_char_eq_getLast?]
+  simp [← endsWith_toSlice, Slice.endsWith_char_eq_getLast?]
 
 theorem endsWith_char_iff_exists_append {c : Char} {s : String} :
     s.endsWith c ↔ ∃ t, s = t ++ singleton c := by
-  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_char_iff_exists_append]
+  simp [← endsWith_toSlice, Slice.endsWith_char_iff_exists_append]
 
 theorem endsWith_char_eq_false_iff_forall_append {c : Char} {s : String} :
     s.endsWith c = false ↔ ∀ t, s ≠ t ++ singleton c := by

src/Init/Data/String/Lemmas/Pattern/TakeDrop/Pred.lean

@@ -8,11 +8,16 @@ module
 prelude
 public import Init.Data.String.Slice
 public import Init.Data.String.TakeDrop
+public import Init.Data.String.Lemmas.Order
 import Init.Data.String.Lemmas.Pattern.TakeDrop.Basic
 import Init.Data.String.Lemmas.Pattern.Pred
 import Init.Data.Option.Lemmas
 import Init.Data.String.Lemmas.FindPos
+import Init.Data.String.Lemmas.Intercalate
 import Init.ByCases
+import Init.Data.Order.Lemmas
+import Init.Data.String.OrderInstances
+import Init.Data.String.Lemmas.Basic
 
 public section
 
@@ -49,6 +54,80 @@ theorem eq_append_of_dropPrefix?_bool_eq_some {p : Char → Bool} {s res : Slice
   obtain ⟨_, ⟨c, ⟨rfl, h₁⟩⟩, h₂⟩ := by simpa [PatternModel.Matches] using Pattern.Model.eq_append_of_dropPrefix?_eq_some h
   exact ⟨_, h₂, h₁⟩
 
+@[simp]
+theorem Pos.skip?_bool_eq_some_iff {p : Char → Bool} {s : Slice} {pos res : s.Pos} :
+    pos.skip? p = some res ↔ ∃ h, res = pos.next h ∧ p (pos.get h) := by
+  simp [Pattern.Model.Pos.skip?_eq_some_iff, CharPred.isLongestMatchAt_iff]
+
+@[simp]
+theorem Pos.skip?_bool_eq_none_iff {p : Char → Bool} {s : Slice} {pos : s.Pos} :
+    pos.skip? p = none ↔ ∀ h, p (pos.get h) = false := by
+  simp [Pattern.Model.Pos.skip?_eq_none_iff, CharPred.matchesAt_iff]
+
+theorem Pos.apply_skipWhile_bool_eq_false {p : Char → Bool} {s : Slice} {pos : s.Pos} {h} :
+    p ((pos.skipWhile p).get h) = false := by
+  have := Pattern.Model.Pos.not_matchesAt_skipWhile p pos
+  simp_all [CharPred.matchesAt_iff]
+
+theorem Pos.skipWhile_bool_eq_self_iff_get {p : Char → Bool} {s : Slice} {pos : s.Pos} :
+    pos.skipWhile p = pos ↔ ∀ h, p (pos.get h) = false := by
+  simp [Pattern.Model.Pos.skipWhile_eq_self_iff, CharPred.matchesAt_iff]
+
+theorem Pos.apply_eq_true_of_lt_skipWhile_bool {p : Char → Bool} {s : Slice} {pos pos' : s.Pos}
+    (h₁ : pos ≤ pos') (h₂ : pos' < pos.skipWhile p) : p (pos'.get (ne_endPos_of_lt h₂)) = true :=
+  (CharPred.isLongestMatchAtChain_iff.1 (Pattern.Model.Pos.isLongestMatchAtChain_skipWhile p pos)).2 _ h₁ h₂
+
+theorem apply_skipPrefixWhile_bool_eq_false {p : Char → Bool} {s : Slice} {h} :
+    p ((s.skipPrefixWhile p).get h) = false := by
+  simp [skipPrefixWhile_eq_skipWhile_startPos, Pos.apply_skipWhile_bool_eq_false]
+
+theorem apply_eq_true_of_lt_skipPrefixWhile_bool {p : Char → Bool} {s : Slice} {pos : s.Pos} (h : pos < s.skipPrefixWhile p) :
+    p (pos.get (Pos.ne_endPos_of_lt h)) = true :=
+  Pos.apply_eq_true_of_lt_skipWhile_bool (Pos.startPos_le _) (skipPrefixWhile_eq_skipWhile_startPos ▸ h)
+
+@[simp]
+theorem all_bool_eq {p : Char → Bool} {s : Slice} : s.all p = s.copy.toList.all p := by
+  rw [Bool.eq_iff_iff, Pattern.Model.all_eq_true_iff,
+    CharPred.isLongestMatchAtChain_startPos_endPos_iff_toList, List.all_eq_true]
+
+@[simp]
+theorem Pos.skip?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s : Slice} {pos res : s.Pos} :
+    pos.skip? P = some res ↔ ∃ h, res = pos.next h ∧ P (pos.get h) := by
+  simp [Pos.skip?_prop_eq_skip?_decide, skip?_bool_eq_some_iff]
+
+@[simp]
+theorem Pos.skip?_prop_eq_none_iff {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos} :
+    pos.skip? P = none ↔ ∀ h, ¬ P (pos.get h) := by
+  simp [Pos.skip?_prop_eq_skip?_decide, skip?_bool_eq_none_iff]
+
+theorem Pos.apply_skipWhile_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos} {h} :
+    ¬ P ((pos.skipWhile P).get h) := by
+  have := Pattern.Model.Pos.not_matchesAt_skipWhile P pos
+  simp_all [CharPred.Decidable.matchesAt_iff]
+
+theorem Pos.skipWhile_prop_eq_self_iff_get {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos} :
+    pos.skipWhile P = pos ↔ ∀ h, ¬ P (pos.get h) := by
+  simp [Pos.skipWhile_prop_eq_skipWhile_decide, skipWhile_bool_eq_self_iff_get]
+
+theorem Pos.apply_of_lt_skipWhile_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {pos pos' : s.Pos}
+    (h₁ : pos ≤ pos') (h₂ : pos' < pos.skipWhile P) : P (pos'.get (ne_endPos_of_lt h₂)) := by
+  simp [Pos.skipWhile_prop_eq_skipWhile_decide] at h₂
+  simpa using apply_eq_true_of_lt_skipWhile_bool h₁ h₂
+
+theorem apply_skipPrefixWhile_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {h} :
+    ¬ P ((s.skipPrefixWhile P).get h) := by
+  simp [skipPrefixWhile_eq_skipWhile_startPos, Pos.apply_skipWhile_prop]
+
+theorem apply_of_lt_skipPrefixWhile_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos}
+    (h : pos < s.skipPrefixWhile P) : P (pos.get (Pos.ne_endPos_of_lt h)) := by
+  simp [skipPrefixWhile_prop_eq_skipPrefixWhile_decide] at h
+  simpa using apply_eq_true_of_lt_skipPrefixWhile_bool h
+
+@[simp]
+theorem all_prop_eq {P : Char → Prop} [DecidablePred P] {s : Slice} :
+    s.all P = s.copy.toList.all (decide <| P ·) := by
+  simp [all_prop_eq_all_decide]
+
 theorem skipPrefix?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos} :
     s.skipPrefix? P = some pos ↔ ∃ h, pos = s.startPos.next h ∧ P (s.startPos.get h) := by
   simp [skipPrefix?_prop_eq_skipPrefix?_decide, skipPrefix?_bool_eq_some_iff]
@@ -118,6 +197,83 @@ theorem eq_append_of_dropSuffix?_prop_eq_some {P : Char → Prop} [DecidablePred
   rw [dropSuffix?_prop_eq_dropSuffix?_decide] at h
   simpa using eq_append_of_dropSuffix?_bool_eq_some h
 
+@[simp]
+theorem Pos.revSkip?_bool_eq_some_iff {p : Char → Bool} {s : Slice} {pos res : s.Pos} :
+    pos.revSkip? p = some res ↔ ∃ h, res = pos.prev h ∧ p ((pos.prev h).get (by simp)) := by
+  simp [Pattern.Model.Pos.revSkip?_eq_some_iff, CharPred.isLongestRevMatchAt_iff]
+
+@[simp]
+theorem Pos.revSkip?_bool_eq_none_iff {p : Char → Bool} {s : Slice} {pos : s.Pos} :
+    pos.revSkip? p = none ↔ ∀ h, p ((pos.prev h).get (by simp)) = false := by
+  simp [Pattern.Model.Pos.revSkip?_eq_none_iff, CharPred.revMatchesAt_iff]
+
+theorem Pos.apply_revSkipWhile_bool_eq_false {p : Char → Bool} {s : Slice} {pos : s.Pos} {h} :
+    p (((pos.revSkipWhile p).prev h).get (by simp)) = false := by
+  have := Pattern.Model.Pos.not_revMatchesAt_revSkipWhile p pos
+  simp_all [CharPred.revMatchesAt_iff]
+
+theorem Pos.revSkipWhile_bool_eq_self_iff_get {p : Char → Bool} {s : Slice} {pos : s.Pos} :
+    pos.revSkipWhile p = pos ↔ ∀ h, p ((pos.prev h).get (by simp)) = false := by
+  simp [Pattern.Model.Pos.revSkipWhile_eq_self_iff, CharPred.revMatchesAt_iff]
+
+theorem Pos.apply_eq_true_of_revSkipWhile_le_bool {p : Char → Bool} {s : Slice} {pos pos' : s.Pos}
+    (h₁ : pos' < pos) (h₂ : pos.revSkipWhile p ≤ pos') : p (pos'.get (Pos.ne_endPos_of_lt h₁)) = true :=
+  (CharPred.isLongestRevMatchAtChain_iff.1 (Pattern.Model.Pos.isLongestRevMatchAtChain_revSkipWhile p pos)).2 _ h₂ h₁
+
+theorem apply_skipSuffixWhile_bool_eq_false {p : Char → Bool} {s : Slice} {h} :
+    p (((s.skipSuffixWhile p).prev h).get (by simp)) = false := by
+  simp [skipSuffixWhile_eq_revSkipWhile_endPos, Pos.apply_revSkipWhile_bool_eq_false]
+
+theorem apply_eq_true_of_skipSuffixWhile_le_bool {p : Char → Bool} {s : Slice} {pos : s.Pos}
+    (h : s.skipSuffixWhile p ≤ pos) (h' : pos < s.endPos) :
+    p (pos.get (Pos.ne_endPos_of_lt h')) = true :=
+  Pos.apply_eq_true_of_revSkipWhile_le_bool h' (skipSuffixWhile_eq_revSkipWhile_endPos ▸ h)
+
+@[simp]
+theorem revAll_bool_eq {p : Char → Bool} {s : Slice} : s.revAll p = s.copy.toList.all p := by
+  rw [Bool.eq_iff_iff, Pattern.Model.revAll_eq_true_iff,
+    CharPred.isLongestRevMatchAtChain_startPos_endPos_iff_toList, List.all_eq_true]
+
+@[simp]
+theorem Pos.revSkip?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s : Slice} {pos res : s.Pos} :
+    pos.revSkip? P = some res ↔ ∃ h, res = pos.prev h ∧ P ((pos.prev h).get (by simp)) := by
+  simp [Pos.revSkip?_prop_eq_revSkip?_decide, revSkip?_bool_eq_some_iff]
+
+@[simp]
+theorem Pos.revSkip?_prop_eq_none_iff {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos} :
+    pos.revSkip? P = none ↔ ∀ h, ¬ P ((pos.prev h).get (by simp)) := by
+  simp [Pos.revSkip?_prop_eq_revSkip?_decide, revSkip?_bool_eq_none_iff]
+
+theorem Pos.apply_revSkipWhile_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos} {h} :
+    ¬ P (((pos.revSkipWhile P).prev h).get (by simp)) := by
+  have := Pattern.Model.Pos.not_revMatchesAt_revSkipWhile P pos
+  simp_all [CharPred.Decidable.revMatchesAt_iff]
+
+theorem Pos.revSkipWhile_prop_eq_self_iff_get {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos} :
+    pos.revSkipWhile P = pos ↔ ∀ h, ¬ P ((pos.prev h).get (by simp)) := by
+  simp [Pos.revSkipWhile_prop_eq_revSkipWhile_decide, revSkipWhile_bool_eq_self_iff_get]
+
+theorem Pos.apply_of_revSkipWhile_le_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {pos pos' : s.Pos}
+    (h₁ : pos' < pos) (h₂ : pos.revSkipWhile P ≤ pos') : P (pos'.get (Pos.ne_endPos_of_lt h₁)) := by
+  have h₂' : pos.revSkipWhile (decide <| P ·) ≤ pos' :=
+    Pos.revSkipWhile_prop_eq_revSkipWhile_decide (p := P) pos ▸ h₂
+  simpa using Pos.apply_eq_true_of_revSkipWhile_le_bool h₁ h₂'
+
+theorem apply_skipSuffixWhile_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {h} :
+    ¬ P (((s.skipSuffixWhile P).prev h).get (by simp)) := by
+  have := Pattern.Model.Pos.not_revMatchesAt_revSkipWhile P s.endPos
+  simp_all [CharPred.Decidable.revMatchesAt_iff, skipSuffixWhile_eq_revSkipWhile_endPos]
+
+theorem apply_of_skipSuffixWhile_le_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos}
+    (h : s.skipSuffixWhile P ≤ pos) (h' : pos < s.endPos) :
+    P (pos.get (Pos.ne_endPos_of_lt h')) :=
+  Pos.apply_of_revSkipWhile_le_prop h' (skipSuffixWhile_eq_revSkipWhile_endPos (pat := P) ▸ h)
+
+@[simp]
+theorem revAll_prop_eq {P : Char → Prop} [DecidablePred P] {s : Slice} :
+    s.revAll P = s.copy.toList.all (decide <| P ·) := by
+  simp [revAll_prop_eq_revAll_decide, revAll_bool_eq]
+
 end Slice
 
 theorem skipPrefix?_bool_eq_some_iff {p : Char → Bool} {s : String} {pos : s.Pos} :
@@ -127,21 +283,58 @@ theorem skipPrefix?_bool_eq_some_iff {p : Char → Bool} {s : String} {pos : s.P
 
 theorem startsWith_bool_iff_get {p : Char → Bool} {s : String} :
     s.startsWith p ↔ ∃ h, p (s.startPos.get h) = true := by
-  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_bool_iff_get]
+  simp [← startsWith_toSlice, Slice.startsWith_bool_iff_get]
 
 theorem startsWith_bool_eq_false_iff_get {p : Char → Bool} {s : String} :
     s.startsWith p = false ↔ ∀ h, p (s.startPos.get h) = false := by
-  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_bool_eq_false_iff_get]
+  simp [← startsWith_toSlice, Slice.startsWith_bool_eq_false_iff_get]
 
 theorem startsWith_bool_eq_head? {p : Char → Bool} {s : String} :
     s.startsWith p = s.toList.head?.any p := by
-  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_bool_eq_head?]
+  simp [← startsWith_toSlice, Slice.startsWith_bool_eq_head?]
 
 theorem eq_append_of_dropPrefix?_bool_eq_some {p : Char → Bool} {s : String} {res : Slice} (h : s.dropPrefix? p = some res) :
     ∃ c, s = singleton c ++ res.copy ∧ p c = true := by
   rw [dropPrefix?_eq_dropPrefix?_toSlice] at h
   simpa using Slice.eq_append_of_dropPrefix?_bool_eq_some h
 
+@[simp]
+theorem Pos.skip?_bool_eq_some_iff {p : Char → Bool} {s : String} {pos res : s.Pos} :
+    pos.skip? p = some res ↔ ∃ h, res = pos.next h ∧ p (pos.get h) := by
+  simp [skip?_eq_skip?_toSlice, ← toSlice_inj, toSlice_next]
+
+@[simp]
+theorem Pos.skip?_bool_eq_none_iff {p : Char → Bool} {s : String} {pos : s.Pos} :
+    pos.skip? p = none ↔ ∀ h, p (pos.get h) = false := by
+  simp [skip?_eq_skip?_toSlice]
+
+theorem Pos.apply_skipWhile_bool_eq_false {p : Char → Bool} {s : String} {pos : s.Pos} {h} :
+    p ((pos.skipWhile p).get h) = false := by
+  simp [skipWhile_eq_skipWhile_toSlice, Slice.Pos.apply_skipWhile_bool_eq_false]
+
+theorem Pos.skipWhile_bool_eq_self_iff_get {p : Char → Bool} {s : String} {pos : s.Pos} :
+    pos.skipWhile p = pos ↔ ∀ h, p (pos.get h) = false := by
+  simp [skipWhile_eq_skipWhile_toSlice, ← toSlice_inj, Slice.Pos.skipWhile_bool_eq_self_iff_get]
+
+theorem Pos.apply_eq_true_of_lt_skipWhile_bool {p : Char → Bool} {s : String} {pos pos' : s.Pos}
+    (h₁ : pos ≤ pos') (h₂ : pos' < pos.skipWhile p) : p (pos'.get (ne_endPos_of_lt h₂)) = true := by
+  rw [Pos.get_eq_get_toSlice]
+  exact Slice.Pos.apply_eq_true_of_lt_skipWhile_bool (toSlice_le_toSlice_iff.2 h₁)
+    (by simpa [skipWhile_eq_skipWhile_toSlice] using h₂)
+
+theorem apply_skipPrefixWhile_bool_eq_false {p : Char → Bool} {s : String} {h} :
+    p ((s.skipPrefixWhile p).get h) = false := by
+  simp [skipPrefixWhile_eq_skipPrefixWhile_toSlice, Slice.apply_skipPrefixWhile_bool_eq_false]
+
+theorem apply_eq_true_of_lt_skipPrefixWhile_bool {p : Char → Bool} {s : String} {pos : s.Pos} (h : pos < s.skipPrefixWhile p) :
+    p (pos.get (Pos.ne_endPos_of_lt h)) = true := by
+  rw [Pos.get_eq_get_toSlice]
+  exact Slice.apply_eq_true_of_lt_skipPrefixWhile_bool (by simpa [skipPrefixWhile_eq_skipPrefixWhile_toSlice] using h)
+
+@[simp]
+theorem all_bool_eq {p : Char → Bool} {s : String} : s.all p = s.toList.all p := by
+  simp [← all_toSlice]
+
 theorem skipPrefix?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos} :
     s.skipPrefix? P = some pos ↔ ∃ h, pos = s.startPos.next h ∧ P (s.startPos.get h) := by
   simp [skipPrefix?_eq_skipPrefix?_toSlice, Slice.skipPrefix?_prop_eq_some_iff, ← Pos.toSlice_inj,
@@ -149,15 +342,15 @@ theorem skipPrefix?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s :
 
 theorem startsWith_prop_iff_get {P : Char → Prop} [DecidablePred P] {s : String} :
     s.startsWith P ↔ ∃ h, P (s.startPos.get h) := by
-  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_prop_iff_get]
+  simp [← startsWith_toSlice, Slice.startsWith_prop_iff_get]
 
 theorem startsWith_prop_eq_false_iff_get {P : Char → Prop} [DecidablePred P] {s : String} :
     s.startsWith P = false ↔ ∀ h, ¬ P (s.startPos.get h) := by
-  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_prop_eq_false_iff_get]
+  simp [← startsWith_toSlice, Slice.startsWith_prop_eq_false_iff_get]
 
 theorem startsWith_prop_eq_head? {P : Char → Prop} [DecidablePred P] {s : String} :
     s.startsWith P = s.toList.head?.any (decide <| P ·) := by
-  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_prop_eq_head?]
+  simp [← startsWith_toSlice, Slice.startsWith_prop_eq_head?]
 
 theorem eq_append_of_dropPrefix?_prop_eq_some {P : Char → Prop} [DecidablePred P] {s : String} {res : Slice}
     (h : s.dropPrefix? P = some res) : ∃ c, s = singleton c ++ res.copy ∧ P c := by
@@ -171,15 +364,15 @@ theorem skipSuffix?_bool_eq_some_iff {p : Char → Bool} {s : String} {pos : s.P
 
 theorem endsWith_bool_iff_get {p : Char → Bool} {s : String} :
     s.endsWith p ↔ ∃ h, p ((s.endPos.prev h).get (by simp)) = true := by
-  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_bool_iff_get, Pos.prev_toSlice]
+  simp [← endsWith_toSlice, Slice.endsWith_bool_iff_get, Pos.prev_toSlice]
 
 theorem endsWith_bool_eq_false_iff_get {p : Char → Bool} {s : String} :
     s.endsWith p = false ↔ ∀ h, p ((s.endPos.prev h).get (by simp)) = false := by
-  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_bool_eq_false_iff_get, Pos.prev_toSlice]
+  simp [← endsWith_toSlice, Slice.endsWith_bool_eq_false_iff_get, Pos.prev_toSlice]
 
 theorem endsWith_bool_eq_getLast? {p : Char → Bool} {s : String} :
     s.endsWith p = s.toList.getLast?.any p := by
-  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_bool_eq_getLast?]
+  simp [← endsWith_toSlice, Slice.endsWith_bool_eq_getLast?]
 
 theorem eq_append_of_dropSuffix?_bool_eq_some {p : Char → Bool} {s : String} {res : Slice} (h : s.dropSuffix? p = some res) :
     ∃ c, s = res.copy ++ singleton c ∧ p c = true := by
@@ -193,19 +386,154 @@ theorem skipSuffix?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s :
 
 theorem endsWith_prop_iff_get {P : Char → Prop} [DecidablePred P] {s : String} :
     s.endsWith P ↔ ∃ h, P ((s.endPos.prev h).get (by simp)) := by
-  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_prop_iff_get, Pos.prev_toSlice]
+  simp [← endsWith_toSlice, Slice.endsWith_prop_iff_get, Pos.prev_toSlice]
 
 theorem endsWith_prop_eq_false_iff_get {P : Char → Prop} [DecidablePred P] {s : String} :
     s.endsWith P = false ↔ ∀ h, ¬ P ((s.endPos.prev h).get (by simp)) := by
-  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_prop_eq_false_iff_get, Pos.prev_toSlice]
+  simp [← endsWith_toSlice, Slice.endsWith_prop_eq_false_iff_get, Pos.prev_toSlice]
 
 theorem endsWith_prop_eq_getLast? {P : Char → Prop} [DecidablePred P] {s : String} :
     s.endsWith P = s.toList.getLast?.any (decide <| P ·) := by
-  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_prop_eq_getLast?]
+  simp [← endsWith_toSlice, Slice.endsWith_prop_eq_getLast?]
 
 theorem eq_append_of_dropSuffix?_prop_eq_some {P : Char → Prop} [DecidablePred P] {s : String} {res : Slice}
     (h : s.dropSuffix? P = some res) : ∃ c, s = res.copy ++ singleton c ∧ P c := by
   rw [dropSuffix?_eq_dropSuffix?_toSlice] at h
   simpa using Slice.eq_append_of_dropSuffix?_prop_eq_some h
 
+@[simp]
+theorem Pos.skip?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s : String} {pos res : s.Pos} :
+    pos.skip? P = some res ↔ ∃ h, res = pos.next h ∧ P (pos.get h) := by
+  simp [skip?_eq_skip?_toSlice, ← toSlice_inj, toSlice_next]
+
+@[simp]
+theorem Pos.skip?_prop_eq_none_iff {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos} :
+    pos.skip? P = none ↔ ∀ h, ¬ P (pos.get h) := by
+  simp [skip?_eq_skip?_toSlice]
+
+theorem Pos.apply_skipWhile_prop {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos} {h} :
+    ¬ P ((pos.skipWhile P).get h) := by
+  simp [skipWhile_eq_skipWhile_toSlice, Slice.Pos.apply_skipWhile_prop]
+
+theorem Pos.skipWhile_prop_eq_self_iff_get {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos} :
+    pos.skipWhile P = pos ↔ ∀ h, ¬ P (pos.get h) := by
+  simp [skipWhile_eq_skipWhile_toSlice, ← toSlice_inj, Slice.Pos.skipWhile_prop_eq_self_iff_get]
+
+theorem Pos.apply_of_lt_skipWhile_prop {P : Char → Prop} [DecidablePred P] {s : String} {pos pos' : s.Pos}
+    (h₁ : pos ≤ pos') (h₂ : pos' < pos.skipWhile P) : P (pos'.get (ne_endPos_of_lt h₂)) := by
+  rw [Pos.get_eq_get_toSlice]
+  exact Slice.Pos.apply_of_lt_skipWhile_prop (toSlice_le_toSlice_iff.2 h₁)
+    (by simpa [skipWhile_eq_skipWhile_toSlice] using h₂)
+
+theorem apply_skipPrefixWhile_prop {P : Char → Prop} [DecidablePred P] {s : String} {h} :
+    ¬ P ((s.skipPrefixWhile P).get h) := by
+  simp [skipPrefixWhile_eq_skipPrefixWhile_toSlice, Slice.apply_skipPrefixWhile_prop]
+
+theorem apply_of_lt_skipPrefixWhile_prop {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos}
+    (h : pos < s.skipPrefixWhile P) : P (pos.get (Pos.ne_endPos_of_lt h)) := by
+  rw [Pos.get_eq_get_toSlice]
+  exact Slice.apply_of_lt_skipPrefixWhile_prop (by simpa [skipPrefixWhile_eq_skipPrefixWhile_toSlice] using h)
+
+@[simp]
+theorem all_prop_eq {P : Char → Prop} [DecidablePred P] {s : String} :
+    s.all P = s.toList.all (decide <| P ·) := by
+  simp [← all_toSlice]
+
+@[simp]
+theorem Pos.revSkip?_bool_eq_some_iff {p : Char → Bool} {s : String} {pos res : s.Pos} :
+    pos.revSkip? p = some res ↔ ∃ h, res = pos.prev h ∧ p ((pos.prev h).get (by simp)) := by
+  simp [revSkip?_eq_revSkip?_toSlice, ← toSlice_inj, toSlice_prev, get_eq_get_toSlice]
+
+@[simp]
+theorem Pos.revSkip?_bool_eq_none_iff {p : Char → Bool} {s : String} {pos : s.Pos} :
+    pos.revSkip? p = none ↔ ∀ h, p ((pos.prev h).get (by simp)) = false := by
+  simp [revSkip?_eq_revSkip?_toSlice, Pos.prev_toSlice]
+
+theorem Pos.apply_revSkipWhile_bool_eq_false {p : Char → Bool} {s : String} {pos : s.Pos} {h} :
+    p (((pos.revSkipWhile p).prev h).get (by simp)) = false := by
+  have h' : pos.toSlice.revSkipWhile p ≠ s.toSlice.startPos := by
+    simpa [Pos.revSkipWhile_eq_revSkipWhile_toSlice, ← toSlice_inj] using h
+  have := Slice.Pos.apply_revSkipWhile_bool_eq_false (pos := pos.toSlice) (h := h')
+  simpa [Pos.revSkipWhile_eq_revSkipWhile_toSlice, Pos.prev_ofToSlice]
+
+theorem Pos.revSkipWhile_bool_eq_self_iff_get {p : Char → Bool} {s : String} {pos : s.Pos} :
+    pos.revSkipWhile p = pos ↔ ∀ h, p ((pos.prev h).get (by simp)) = false := by
+  simp [Pos.revSkipWhile_eq_revSkipWhile_toSlice, ← toSlice_inj, Slice.Pos.revSkipWhile_bool_eq_self_iff_get,
+    Pos.prev_toSlice]
+
+theorem Pos.apply_eq_true_of_revSkipWhile_le_bool {p : Char → Bool} {s : String} {pos pos' : s.Pos}
+    (h₁ : pos' < pos) (h₂ : pos.revSkipWhile p ≤ pos') : p (pos'.get (ne_endPos_of_lt h₁)) = true := by
+  rw [Pos.get_eq_get_toSlice]
+  exact Slice.Pos.apply_eq_true_of_revSkipWhile_le_bool
+    (Pos.toSlice_lt_toSlice_iff.2 h₁)
+    (by simpa [Pos.revSkipWhile_eq_revSkipWhile_toSlice, Pos.ofToSlice_le_iff] using h₂)
+
+theorem apply_skipSuffixWhile_bool_eq_false {p : Char → Bool} {s : String} {h} :
+    p (((s.skipSuffixWhile p).prev h).get (by simp)) = false := by
+  have h' : s.toSlice.skipSuffixWhile p ≠ s.toSlice.startPos := by
+    simpa [skipSuffixWhile_eq_skipSuffixWhile_toSlice, ← Pos.toSlice_inj] using h
+  have := Slice.apply_skipSuffixWhile_bool_eq_false (s := s.toSlice) (h := h')
+  simpa [skipSuffixWhile_eq_skipSuffixWhile_toSlice, Pos.prev_ofToSlice]
+
+theorem apply_eq_true_of_skipSuffixWhile_le_bool {p : Char → Bool} {s : String} {pos : s.Pos}
+    (h : s.skipSuffixWhile p ≤ pos) (h' : pos < s.endPos) :
+    p (pos.get (Pos.ne_endPos_of_lt h')) = true := by
+  rw [Pos.get_eq_get_toSlice]
+  exact Slice.apply_eq_true_of_skipSuffixWhile_le_bool
+    (by simpa [skipSuffixWhile_eq_skipSuffixWhile_toSlice, Pos.ofToSlice_le_iff] using h)
+    (by simpa [Pos.toSlice_lt_toSlice_iff] using h')
+
+@[simp]
+theorem revAll_bool_eq {p : Char → Bool} {s : String} : s.revAll p = s.toList.all p := by
+  simp [← revAll_toSlice]
+
+@[simp]
+theorem Pos.revSkip?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s : String} {pos res : s.Pos} :
+    pos.revSkip? P = some res ↔ ∃ h, res = pos.prev h ∧ P ((pos.prev h).get (by simp)) := by
+  simp [revSkip?_eq_revSkip?_toSlice, ← toSlice_inj, toSlice_prev, get_eq_get_toSlice]
+
+@[simp]
+theorem Pos.revSkip?_prop_eq_none_iff {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos} :
+    pos.revSkip? P = none ↔ ∀ h, ¬ P ((pos.prev h).get (by simp)) := by
+  simp [revSkip?_eq_revSkip?_toSlice, Pos.prev_toSlice]
+
+theorem Pos.apply_revSkipWhile_prop {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos} {h} :
+    ¬ P (((pos.revSkipWhile P).prev h).get (by simp)) := by
+  have h' : pos.toSlice.revSkipWhile P ≠ s.toSlice.startPos := by
+    simpa [Pos.revSkipWhile_eq_revSkipWhile_toSlice, ← toSlice_inj] using h
+  have := Slice.Pos.apply_revSkipWhile_prop (pos := pos.toSlice) (h := h')
+  simpa [Pos.revSkipWhile_eq_revSkipWhile_toSlice, Pos.prev_ofToSlice]
+
+theorem Pos.revSkipWhile_prop_eq_self_iff_get {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos} :
+    pos.revSkipWhile P = pos ↔ ∀ h, ¬ P ((pos.prev h).get (by simp)) := by
+  simp [Pos.revSkipWhile_eq_revSkipWhile_toSlice, ← toSlice_inj,
+    Slice.Pos.revSkipWhile_prop_eq_self_iff_get, Pos.prev_toSlice]
+
+theorem Pos.apply_of_revSkipWhile_le_prop {P : Char → Prop} [DecidablePred P] {s : String} {pos pos' : s.Pos}
+    (h₁ : pos' < pos) (h₂ : pos.revSkipWhile P ≤ pos') : P (pos'.get (ne_endPos_of_lt h₁)) := by
+  rw [Pos.get_eq_get_toSlice]
+  exact Slice.Pos.apply_of_revSkipWhile_le_prop
+    (Pos.toSlice_lt_toSlice_iff.2 h₁)
+    (by simpa [Pos.revSkipWhile_eq_revSkipWhile_toSlice, Pos.ofToSlice_le_iff] using h₂)
+
+theorem apply_skipSuffixWhile_prop {P : Char → Prop} [DecidablePred P] {s : String} {h} :
+    ¬ P (((s.skipSuffixWhile P).prev h).get (by simp)) := by
+  have h' : s.toSlice.skipSuffixWhile P ≠ s.toSlice.startPos := by
+    simpa [skipSuffixWhile_eq_skipSuffixWhile_toSlice, ← Pos.toSlice_inj] using h
+  have := Slice.apply_skipSuffixWhile_prop (s := s.toSlice) (h := h')
+  simpa [skipSuffixWhile_eq_skipSuffixWhile_toSlice, Pos.prev_ofToSlice]
+
+theorem apply_of_skipSuffixWhile_le_prop {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos}
+    (h : s.skipSuffixWhile P ≤ pos) (h' : pos < s.endPos) :
+    P (pos.get (Pos.ne_endPos_of_lt h')) := by
+  rw [Pos.get_eq_get_toSlice]
+  exact Slice.apply_of_skipSuffixWhile_le_prop
+    (by simpa [skipSuffixWhile_eq_skipSuffixWhile_toSlice, Pos.ofToSlice_le_iff] using h)
+    (by simpa [Pos.toSlice_lt_toSlice_iff] using h')
+
+@[simp]
+theorem revAll_prop_eq {P : Char → Prop} [DecidablePred P] {s : String} :
+    s.revAll P = s.toList.all (decide <| P ·) := by
+  simp [← revAll_toSlice]
+
 end String

src/Init/Data/String/Lemmas/Pattern/TakeDrop/String.lean

@@ -30,11 +30,7 @@ theorem skipPrefix?_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true)
 @[simp]
 theorem skipPrefix?_slice_eq_some_iff {pat s : Slice} {pos : s.Pos} :
     s.skipPrefix? pat = some pos ↔ ∃ t, pos.Splits pat.copy t := by
-  match h : pat.isEmpty with
-  | false =>
-    have := ForwardSliceSearcher.lawfulForwardPatternModel h
-    rw [Pattern.Model.skipPrefix?_eq_some_iff, ForwardSliceSearcher.isLongestMatch_iff_splits h]
-  | true => simp [skipPrefix?_slice_of_isEmpty h, (show pat.copy = "" by simpa), eq_comm]
+  rw [Pattern.Model.skipPrefix?_eq_some_iff, ForwardSliceSearcher.isLongestMatch_iff_splits]
 
 theorem startsWith_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true) :
     s.startsWith pat = true := by
@@ -43,14 +39,10 @@ theorem startsWith_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true)
 @[simp]
 theorem startsWith_slice_iff {pat s : Slice} :
     s.startsWith pat ↔ pat.copy.toList <+: s.copy.toList := by
-  match h : pat.isEmpty with
-  | false =>
-    have := ForwardSliceSearcher.lawfulForwardPatternModel h
-    simp only [Model.startsWith_iff, ForwardSliceSearcher.matchesAt_iff_splits h,
-      splits_startPos_iff, exists_and_left, exists_eq_left]
-    simp only [← toList_inj, toList_append, List.prefix_iff_exists_append_eq]
-    exact ⟨fun ⟨t, ht⟩ => ⟨t.toList, by simp [ht]⟩, fun ⟨t, ht⟩ => ⟨String.ofList t, by simp [← ht]⟩⟩
-  | true => simp [startsWith_slice_of_isEmpty h, (show pat.copy = "" by simpa)]
+  simp only [Model.startsWith_iff, ForwardSliceSearcher.matchesAt_iff_splits,
+    splits_startPos_iff, exists_and_left, exists_eq_left]
+  simp only [← toList_inj, toList_append, List.prefix_iff_exists_append_eq]
+  exact ⟨fun ⟨t, ht⟩ => ⟨t.toList, by simp [ht]⟩, fun ⟨t, ht⟩ => ⟨String.ofList t, by simp [← ht]⟩⟩
 
 @[simp]
 theorem startsWith_slice_eq_false_iff {pat s : Slice} :
@@ -63,14 +55,18 @@ theorem dropPrefix?_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true)
 
 theorem eq_append_of_dropPrefix?_slice_eq_some {pat s res : Slice} (h : s.dropPrefix? pat = some res) :
     s.copy = pat.copy ++ res.copy := by
-  match hpat : pat.isEmpty with
-  | false =>
-    have := ForwardSliceSearcher.lawfulForwardPatternModel hpat
-    have := Pattern.Model.eq_append_of_dropPrefix?_eq_some h
-    simp only [PatternModel.Matches] at this
-    obtain ⟨_, ⟨-, rfl⟩, h⟩ := this
-    exact h
-  | true => simp [Option.some.inj (h ▸ dropPrefix?_slice_of_isEmpty hpat), (show pat.copy = "" by simpa)]
+  have := Pattern.Model.eq_append_of_dropPrefix?_eq_some h
+  simp only [PatternModel.Matches] at this
+  obtain ⟨_, ⟨-, rfl⟩, h⟩ := this
+  exact h
+
+@[simp]
+theorem all_slice_iff {pat s : Slice} : s.all pat ↔ ∃ n, s.copy = String.join (List.replicate n pat.copy) := by
+  simp [Pattern.Model.all_eq_true_iff, ForwardSliceSearcher.isLongestMatchAtChain_startPos_endPos_iff]
+
+@[simp]
+theorem revAll_slice_iff {pat s : Slice} : s.revAll pat ↔ ∃ n, s.copy = String.join (List.replicate n pat.copy) := by
+  simp [Pattern.Model.revAll_eq_true_iff, ForwardSliceSearcher.isLongestRevMatchAtChain_startPos_endPos_iff]
 
 @[simp]
 theorem skipPrefix?_string_eq_some_iff {pat : String} {s : Slice} {pos : s.Pos} :
@@ -104,6 +100,7 @@ theorem eq_append_of_dropPrefix?_string_eq_some {pat : String} {s res : Slice} (
   rw [dropPrefix?_string_eq_dropPrefix?_toSlice] at h
   simpa using eq_append_of_dropPrefix?_slice_eq_some h
 
+
 theorem skipSuffix?_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true) :
     s.skipSuffix? pat = some s.endPos := by
   rw [skipSuffix?_eq_backwardPatternSkipSuffix?, BackwardSliceSearcher.skipSuffix?_of_isEmpty hpat]
@@ -111,11 +108,7 @@ theorem skipSuffix?_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true)
 @[simp]
 theorem skipSuffix?_slice_eq_some_iff {pat s : Slice} {pos : s.Pos} :
     s.skipSuffix? pat = some pos ↔ ∃ t, pos.Splits t pat.copy := by
-  match h : pat.isEmpty with
-  | false =>
-    have := BackwardSliceSearcher.lawfulBackwardPatternModel h
-    rw [Pattern.Model.skipSuffix?_eq_some_iff, ForwardSliceSearcher.isLongestRevMatch_iff_splits h]
-  | true => simp [skipSuffix?_slice_of_isEmpty h, (show pat.copy = "" by simpa), eq_comm]
+  rw [Pattern.Model.skipSuffix?_eq_some_iff, ForwardSliceSearcher.isLongestRevMatch_iff_splits]
 
 theorem endsWith_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true) :
     s.endsWith pat = true := by
@@ -124,14 +117,10 @@ theorem endsWith_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true) :
 @[simp]
 theorem endsWith_slice_iff {pat s : Slice} :
     s.endsWith pat ↔ pat.copy.toList <:+ s.copy.toList := by
-  match h : pat.isEmpty with
-  | false =>
-    have := BackwardSliceSearcher.lawfulBackwardPatternModel h
-    simp only [Model.endsWith_iff, ForwardSliceSearcher.revMatchesAt_iff_splits h,
-      splits_endPos_iff, exists_eq_right]
-    simp only [← toList_inj, toList_append, List.suffix_iff_exists_append_eq]
-    exact ⟨fun ⟨t, ht⟩ => ⟨t.toList, by simp [ht]⟩, fun ⟨t, ht⟩ => ⟨String.ofList t, by simp [← ht]⟩⟩
-  | true => simp [endsWith_slice_of_isEmpty h, (show pat.copy = "" by simpa)]
+  simp only [Model.endsWith_iff, ForwardSliceSearcher.revMatchesAt_iff_splits,
+    splits_endPos_iff, exists_eq_right]
+  simp only [← toList_inj, toList_append, List.suffix_iff_exists_append_eq]
+  exact ⟨fun ⟨t, ht⟩ => ⟨t.toList, by simp [ht]⟩, fun ⟨t, ht⟩ => ⟨String.ofList t, by simp [← ht]⟩⟩
 
 @[simp]
 theorem endsWith_slice_eq_false_iff {pat s : Slice} :
@@ -144,14 +133,10 @@ theorem dropSuffix?_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true)
 
 theorem eq_append_of_dropSuffix?_slice_eq_some {pat s res : Slice} (h : s.dropSuffix? pat = some res) :
     s.copy = res.copy ++ pat.copy := by
-  match hpat : pat.isEmpty with
-  | false =>
-    have := BackwardSliceSearcher.lawfulBackwardPatternModel hpat
-    have := Pattern.Model.eq_append_of_dropSuffix?_eq_some h
-    simp only [PatternModel.Matches] at this
-    obtain ⟨_, ⟨-, rfl⟩, h⟩ := this
-    exact h
-  | true => simp [Option.some.inj (h ▸ dropSuffix?_slice_of_isEmpty hpat), (show pat.copy = "" by simpa)]
+  have := Pattern.Model.eq_append_of_dropSuffix?_eq_some h
+  simp only [PatternModel.Matches] at this
+  obtain ⟨_, ⟨-, rfl⟩, h⟩ := this
+  exact h
 
 @[simp]
 theorem skipSuffix?_string_eq_some_iff' {pat : String} {s : Slice} {pos : s.Pos} :
@@ -208,12 +193,12 @@ theorem startsWith_slice_of_isEmpty {pat : Slice} {s : String} (hpat : pat.isEmp
 @[simp]
 theorem startsWith_slice_iff {pat : Slice} {s : String} :
     s.startsWith pat ↔ pat.copy.toList <+: s.toList := by
-  simp [startsWith_eq_startsWith_toSlice]
+  simp [← startsWith_toSlice]
 
 @[simp]
 theorem startsWith_slice_eq_false_iff {pat : Slice} {s : String} :
     s.startsWith pat = false ↔ ¬ (pat.copy.toList <+: s.toList) := by
-  simp [startsWith_eq_startsWith_toSlice]
+  simp [← startsWith_toSlice]
 
 theorem dropPrefix?_slice_of_isEmpty {pat : Slice} {s : String} (hpat : pat.isEmpty = true) :
     s.dropPrefix? pat = some s.toSlice := by
@@ -239,21 +224,21 @@ theorem skipPrefix?_string_eq_some_iff {pat s : String} {pos : s.Pos} :
 
 @[simp]
 theorem startsWith_string_empty {s : String} : s.startsWith "" = true := by
-  simp [startsWith_eq_startsWith_toSlice]
+  simp [← startsWith_toSlice]
 
 @[simp]
 theorem startsWith_string_iff {pat s : String} :
     s.startsWith pat ↔ pat.toList <+: s.toList := by
-  simp [startsWith_eq_startsWith_toSlice]
+  simp [← startsWith_toSlice]
 
 @[simp]
 theorem startsWith_string_eq_false_iff {pat s : String} :
     s.startsWith pat = false ↔ ¬ (pat.toList <+: s.toList) := by
-  simp [startsWith_eq_startsWith_toSlice]
+  simp [← startsWith_toSlice]
 
 @[simp]
 theorem dropPrefix?_string_empty {s : String} : s.dropPrefix? "" = some s.toSlice := by
-  simp [dropPrefix?_eq_dropPrefix?_toSlice]
+  simp [← dropPrefix?_toSlice]
 
 theorem eq_append_of_dropPrefix?_string_eq_some {s pat : String} {res : Slice} (h : s.dropPrefix? pat = some res) :
     s = pat ++ res.copy := by

src/Init/Data/String/Lemmas/Splits.lean

@@ -99,6 +99,11 @@ theorem Pos.splits {s : String} (p : s.Pos) :
   eq_append := by simp [← toByteArray_inj, Slice.toByteArray_copy, ← size_toByteArray]
   offset_eq_rawEndPos := by simp
 
+@[simp]
+theorem sliceTo_append_sliceFrom {s : String} {pos : s.Pos} :
+    (s.sliceTo pos).copy ++ (s.sliceFrom pos).copy = s :=
+  pos.splits.eq_append.symm
+
 theorem Slice.Pos.splits {s : Slice} (p : s.Pos) :
     p.Splits (s.sliceTo p).copy (s.sliceFrom p).copy where
   eq_append := copy_eq_copy_sliceTo
@@ -375,6 +380,10 @@ theorem Slice.copy_sliceTo_eq_iff_exists_splits {s : Slice} {p : s.Pos} {t₁ :
   · rintro ⟨t₂, h⟩
     exact p.splits.eq_left h
 
+theorem Slice.copy_sliceTo_eq_iff_splits {s : Slice} {p : s.Pos} {t₁ : String} :
+    (s.sliceTo p).copy = t₁ ↔ p.Splits t₁ (s.sliceFrom p).copy :=
+  ⟨fun h => h ▸ p.splits, p.splits.eq_left⟩
+
 theorem Slice.copy_sliceFrom_eq_iff_exists_splits {s : Slice} {p : s.Pos} {t₂ : String} :
     (s.sliceFrom p).copy = t₂ ↔ ∃ t₁, p.Splits t₁ t₂ := by
   refine ⟨?_, ?_⟩
@@ -383,14 +392,26 @@ theorem Slice.copy_sliceFrom_eq_iff_exists_splits {s : Slice} {p : s.Pos} {t₂
   · rintro ⟨t₂, h⟩
     exact p.splits.eq_right h
 
+theorem Slice.copy_sliceFrom_eq_iff_splits {s : Slice} {p : s.Pos} {t₂ : String} :
+    (s.sliceFrom p).copy = t₂ ↔ p.Splits (s.sliceTo p).copy t₂ :=
+  ⟨fun h => h ▸ p.splits, p.splits.eq_right⟩
+
 theorem copy_sliceTo_eq_iff_exists_splits {s : String} {p : s.Pos} {t₁ : String} :
     (s.sliceTo p).copy = t₁ ↔ ∃ t₂, p.Splits t₁ t₂ := by
   simp [← Pos.splits_toSlice_iff, ← Slice.copy_sliceTo_eq_iff_exists_splits]
 
+theorem copy_sliceTo_eq_iff_splits {s : String} {p : s.Pos} {t₁ : String} :
+    (s.sliceTo p).copy = t₁ ↔ p.Splits t₁ (s.sliceFrom p).copy :=
+  ⟨fun h => h ▸ p.splits, p.splits.eq_left⟩
+
 theorem copy_sliceFrom_eq_iff_exists_splits {s : String} {p : s.Pos} {t₂ : String} :
     (s.sliceFrom p).copy = t₂ ↔ ∃ t₁, p.Splits t₁ t₂ := by
   simp [← Pos.splits_toSlice_iff, ← Slice.copy_sliceFrom_eq_iff_exists_splits]
 
+theorem copy_sliceFrom_eq_iff_splits {s : String} {p : s.Pos} {t₂ : String} :
+    (s.sliceFrom p).copy = t₂ ↔ p.Splits (s.sliceTo p).copy t₂ :=
+  ⟨fun h => h ▸ p.splits, p.splits.eq_right⟩
+
 theorem Pos.Splits.offset_eq_decreaseBy {s : String} {p : s.Pos} (h : p.Splits t₁ t₂) :
     p.offset = s.rawEndPos.decreaseBy t₂.utf8ByteSize := by
   simp [h.offset_eq_rawEndPos, h.eq_append, Pos.Raw.ext_iff]
@@ -641,6 +662,28 @@ theorem Pos.splits_append_rawEndPos {s t : String} :
   eq_append := rfl
   offset_eq_rawEndPos := rfl
 
+/--
+Given a slice `s` such that `s.copy = t₁ ++ t₂`, obtain the position sitting between `t₁` and `t₂`.
+-/
+def Slice.Pos.ofEqAppend {s : Slice} {t₁ t₂ : String} (h : s.copy = t₁ ++ t₂) : s.Pos :=
+  s.pos t₁.rawEndPos
+    (by simpa [← Pos.Raw.isValid_copy_iff, h] using ((Pos.Raw.isValid_rawEndPos).append_right t₂))
+
+theorem Slice.Pos.splits_ofEqAppend {s : Slice} {t₁ t₂ : String} (h : s.copy = t₁ ++ t₂) :
+    (ofEqAppend h).Splits t₁ t₂ where
+  eq_append := h
+  offset_eq_rawEndPos := by simp [ofEqAppend]
+
+/--
+Given a string `s` such that `s = t₁ ++ t₂`, obtain the position sitting between `t₁` and `t₂`.
+-/
+def Pos.ofEqAppend {s t₁ t₂ : String} (h : s = t₁ ++ t₂) : s.Pos :=
+  ((t₁ ++ t₂).pos t₁.rawEndPos ((Pos.Raw.isValid_rawEndPos).append_right t₂)).cast h.symm
+
+theorem Pos.splits_ofEqAppend {s t₁ t₂ : String} (h : s = t₁ ++ t₂) : (ofEqAppend h).Splits t₁ t₂ where
+  eq_append := h
+  offset_eq_rawEndPos := by simp [ofEqAppend]
+
 theorem Pos.Splits.copy_sliceTo_eq {s : String} {p : s.Pos} (h : p.Splits t₁ t₂) :
     (s.sliceTo p).copy = t₁ :=
   p.splits.eq_left h
@@ -740,4 +783,44 @@ theorem splits_prevn_endPos (s : String) (n : Nat) :
     (s.endPos.prevn n).Splits (String.ofList (s.toList.take (s.length - n))) (String.ofList (s.toList.drop (s.length - n))) := by
   simpa using s.splits_endPos.prevn n
 
+@[simp]
+theorem Slice.copy_sliceFrom_cast {s t : Slice} (hst : s.copy = t.copy) {pos : s.Pos} :
+    (t.sliceFrom (pos.cast hst)).copy = (s.sliceFrom pos).copy := by
+  simpa [copy_sliceFrom_eq_iff_exists_splits] using ⟨_, pos.splits⟩
+
+@[simp]
+theorem Slice.copy_sliceTo_cast {s t : Slice} (hst : s.copy = t.copy) {pos : s.Pos} :
+    (t.sliceTo (pos.cast hst)).copy = (s.sliceTo pos).copy := by
+  simpa [copy_sliceTo_eq_iff_exists_splits] using ⟨_, pos.splits⟩
+
+@[simp]
+theorem copy_sliceFrom_cast {s t : String} (hst : s = t) {pos : s.Pos} :
+    (t.sliceFrom (pos.cast hst)).copy = (s.sliceFrom pos).copy := by
+  simpa [copy_sliceFrom_eq_iff_exists_splits] using ⟨_, pos.splits⟩
+
+@[simp]
+theorem copy_sliceTo_cast {s t : String} (hst : s = t) {pos : s.Pos} :
+    (t.sliceTo (pos.cast hst)).copy = (s.sliceTo pos).copy := by
+  simpa [copy_sliceTo_eq_iff_exists_splits] using ⟨_, pos.splits⟩
+
+theorem Slice.Pos.sliceFrom_cast {s t : Slice} {hst : s.copy = t.copy} (p q : s.Pos) {h} :
+    Slice.Pos.sliceFrom (p.cast hst) (q.cast hst) h =
+      (Slice.Pos.sliceFrom p q (by simpa using h)).cast (by simp) := by
+  ext1; simp
+
+theorem Slice.Pos.sliceTo_cast {s t : Slice} {hst : s.copy = t.copy} (p q : s.Pos) {h} :
+    Slice.Pos.sliceTo (p.cast hst) (q.cast hst) h =
+      (Slice.Pos.sliceTo p q (by simpa using h)).cast (by simp) := by
+  ext1; simp
+
+theorem Pos.sliceFrom_cast {s t : String} {hst : s = t} (p q : s.Pos) {h} :
+    Pos.sliceFrom (p.cast hst) (q.cast hst) h =
+      (Pos.sliceFrom p q (by simpa using h)).cast (by simp) := by
+  ext1; simp
+
+theorem Pos.sliceTo_cast {s t : String} {hst : s = t} (p q : s.Pos) {h} :
+    Pos.sliceTo (p.cast hst) (q.cast hst) h =
+      (Pos.sliceTo p q (by simpa using h)).cast (by simp) := by
+  ext1; simp
+
 end String

src/Init/Data/String/Pattern/Basic.lean

@@ -96,6 +96,44 @@ theorem endPos_ofSliceFrom {s : Slice} {p : s.Pos} {st : SearchStep (s.sliceFrom
     st.ofSliceFrom.endPos = Slice.Pos.ofSliceFrom st.endPos := by
   cases st <;> simp [ofSliceFrom]
 
+/--
+Converts a {lean}`SearchStep s` into a {lean}`SearchStep t` by applying {name}`Slice.Pos.cast` to the
+start and end position.
+-/
+@[inline]
+def cast {s t : Slice} (hst : s.copy = t.copy) : SearchStep s → SearchStep t
+  | .rejected startPos endPos => .rejected (startPos.cast hst) (endPos.cast hst)
+  | .matched startPos endPos => .matched (startPos.cast hst) (endPos.cast hst)
+
+@[simp]
+theorem cast_rejected {s t : Slice} {hst : s.copy = t.copy} {startPos endPos : s.Pos} :
+    (SearchStep.rejected startPos endPos).cast hst = .rejected (startPos.cast hst) (endPos.cast hst) :=
+  (rfl)
+
+@[simp]
+theorem cast_matched {s t : Slice} {hst : s.copy = t.copy} {startPos endPos : s.Pos} :
+    (SearchStep.matched startPos endPos).cast hst = .matched (startPos.cast hst) (endPos.cast hst) :=
+  (rfl)
+
+@[simp]
+theorem startPos_cast {s t : Slice} (hst : s.copy = t.copy) {st : SearchStep s} :
+    (st.cast hst).startPos = st.startPos.cast hst := by
+  cases st <;> simp
+
+@[simp]
+theorem endPos_cast {s t : Slice} (hst : s.copy = t.copy) {st : SearchStep s} :
+    (st.cast hst).endPos = st.endPos.cast hst := by
+  cases st <;> simp
+
+@[simp]
+theorem cast_rfl {s : Slice} {st : SearchStep s} : st.cast rfl = st := by
+  cases st <;> simp
+
+@[simp]
+theorem cast_cast {s t u : Slice} {hst : s.copy = t.copy} {htu : t.copy = u.copy} {st : SearchStep s} :
+    (st.cast hst).cast htu = st.cast (hst.trans htu) := by
+  cases st <;> simp
+
 end SearchStep
 
 /--

src/Init/Data/String/Search.lean

@@ -311,23 +311,6 @@ def Internal.containsImpl (s : String) (c : Char) : Bool :=
 def Internal.anyImpl (s : String) (p : Char → Bool) :=
   String.any s p
 
-/--
-Checks whether a slice only consists of matches of the pattern {name}`pat`.
-
-Short-circuits at the first pattern mis-match.
-
-This function is generic over all currently supported patterns.
-
-Examples:
- * {lean}`"brown".all Char.isLower = true`
- * {lean}`"brown and orange".all Char.isLower = false`
- * {lean}`"aaaaaa".all 'a' = true`
- * {lean}`"aaaaaa".all "aa" = true`
- * {lean}`"aaaaaaa".all "aa" = false`
--/
-@[inline, suggest_for String.every] def all (s : String) (pat : ρ) [ForwardPattern pat] : Bool :=
-  s.toSlice.all pat
-
 /--
 Checks whether the string can be interpreted as the decimal representation of a natural number.
 

src/Init/Data/String/Slice.lean

@@ -426,13 +426,13 @@ Advances {name}`pos` as long as {name}`pat` matches.
 -/
 @[specialize pat]
 def Pos.skipWhile {s : Slice} (pos : s.Pos) (pat : ρ) [ForwardPattern pat] : s.Pos :=
-  if let some nextCurr := ForwardPattern.skipPrefix? pat (s.sliceFrom pos) then
-    if pos < Pos.ofSliceFrom nextCurr then
-      skipWhile (Pos.ofSliceFrom nextCurr) pat
+  match pos.skip? pat with
+  | some nextCurr =>
+    if pos < nextCurr then
+      skipWhile nextCurr pat
     else
       pos
-  else
-    pos
+  | none => pos
 termination_by pos
 
 /--
@@ -572,7 +572,7 @@ Examples:
 -/
 @[inline]
 def all (s : Slice) (pat : ρ) [ForwardPattern pat] : Bool :=
-  s.dropWhile pat |>.isEmpty
+  s.skipPrefixWhile pat == s.endPos
 
 end ForwardPatternUsers
 
@@ -707,7 +707,7 @@ This function is generic over all currently supported patterns.
 -/
 @[inline]
 def Pos.revSkip? {s : Slice} (pos : s.Pos) (pat : ρ) [BackwardPattern pat] : Option s.Pos :=
-  ((s.sliceFrom pos).skipSuffix? pat).map Pos.ofSliceFrom
+  ((s.sliceTo pos).skipSuffix? pat).map Pos.ofSliceTo
 
 /--
 If {name}`pat` matches a suffix of {name}`s`, returns the remainder. Returns {name}`none` otherwise.
@@ -765,13 +765,13 @@ Rewinds {name}`pos` as long as {name}`pat` matches.
 -/
 @[specialize pat]
 def Pos.revSkipWhile {s : Slice} (pos : s.Pos) (pat : ρ) [BackwardPattern pat] : s.Pos :=
-  if let some nextCurr := BackwardPattern.skipSuffix? pat (s.sliceTo pos) then
-    if Pos.ofSliceTo nextCurr < pos then
-      revSkipWhile (Pos.ofSliceTo nextCurr) pat
+  match pos.revSkip? pat with
+  | some nextCurr =>
+    if nextCurr < pos then
+      revSkipWhile nextCurr pat
     else
       pos
-  else
-    pos
+  | none => pos
 termination_by pos.down
 
 /--
@@ -782,6 +782,36 @@ Returns the position at the start of the longest suffix of {name}`s` for which {
 def skipSuffixWhile (s : Slice) (pat : ρ) [BackwardPattern pat] : s.Pos :=
   s.endPos.revSkipWhile pat
 
+/--
+Checks whether a slice only consists of matches of the pattern {name}`pat`, starting from the back
+of the string.
+
+Short-circuits at the first pattern mis-match.
+
+This function is generic over all currently supported patterns.
+
+For many types of patterns, this function can be expected to return the same result as
+{name}`Slice.all`. If mismatches are expected to occur close to the end of the string, this function
+might be more efficient.
+
+For some types of patterns, this function will return a different result than {name}`Slice.all`.
+Consider, for example, a pattern that matches the longest string at the given position that matches
+the regular expression {lean}`"a|aa|ab"`. Then, given the input string {lean}`"aab"`, performing
+{name}`Slice.all` will greedily match the prefix {lean}`"aa"` and then get stuck on the remainder
+{lean}`"b"`, causing it to return {lean}`false`. On the other hand, {name}`Slice.revAll` will match
+the suffix {lean}`"ab"` and then match the remainder {lean}`"a"`, so it will return {lean}`true`.
+
+Examples:
+ * {lean}`"brown".toSlice.revAll Char.isLower = true`
+ * {lean}`"brown and orange".toSlice.revAll Char.isLower = false`
+ * {lean}`"aaaaaa".toSlice.revAll 'a' = true`
+ * {lean}`"aaaaaa".toSlice.revAll "aa" = true`
+ * {lean}`"aaaaaaa".toSlice.revAll "aa" = false`
+-/
+@[inline]
+def revAll (s : Slice) (pat : ρ) [BackwardPattern pat] : Bool :=
+  s.skipSuffixWhile pat == s.startPos
+
 /--
 Creates a new slice that contains the longest suffix of {name}`s` for which {name}`pat` matched
 (potentially repeatedly).

src/Init/Data/String/TakeDrop.lean

@@ -224,6 +224,53 @@ Returns the position after the longest prefix of {name}`s` for which {name}`pat`
 @[inline] def skipPrefixWhile (s : String) (pat : ρ) [ForwardPattern pat] : s.Pos :=
   Pos.ofToSlice (s.toSlice.skipPrefixWhile pat)
 
+/--
+Checks whether a string only consists of matches of the pattern {name}`pat`.
+
+Short-circuits at the first pattern mis-match.
+
+This function is generic over all currently supported patterns.
+
+Examples:
+ * {lean}`"brown".all Char.isLower = true`
+ * {lean}`"brown and orange".all Char.isLower = false`
+ * {lean}`"aaaaaa".all 'a' = true`
+ * {lean}`"aaaaaa".all "aa" = true`
+ * {lean}`"aaaaaaa".all "aa" = false`
+-/
+@[inline, suggest_for String.every] def all (s : String) (pat : ρ) [ForwardPattern pat] : Bool :=
+  s.toSlice.all pat
+
+/--
+Checks whether a string only consists of matches of the pattern {name}`pat`, starting from the back
+of the string.
+
+Short-circuits at the first pattern mis-match.
+
+This function is generic over all currently supported patterns.
+
+For many types of patterns, this function can be expected to return the same result as
+{name}`String.all`. If mismatches are expected to occur close to the end of the string, this function
+might be more efficient.
+
+For some types of patterns, this function will return a different result than {name}`String.all`.
+Consider, for example, a pattern that matches the longest string at the given position that matches
+the regular expression {lean}`"a|aa|ab"`. Then, given the input string {lean}`"aab"`, performing
+{name}`String.all` will greedily match the prefix {lean}`"aa"` and then get stuck on the remainder
+{lean}`"b"`, causing it to return {lean}`false`. On the other hand, {name}`String.revAll` will match
+the suffix {lean}`"ab"` and then match the remainder {lean}`"a"`, so it will return {lean}`true`.
+
+Examples:
+ * {lean}`"brown".revAll Char.isLower = true`
+ * {lean}`"brown and orange".revAll Char.isLower = false`
+ * {lean}`"aaaaaa".revAll 'a' = true`
+ * {lean}`"aaaaaa".revAll "aa" = true`
+ * {lean}`"aaaaaaa".revAll "aa" = false`
+-/
+@[inline]
+def revAll (s : String) (pat : ρ) [BackwardPattern pat] : Bool :=
+  s.toSlice.revAll pat
+
 /--
 If {name}`pat` matches at {name}`pos`, returns the position after the end of the match.
 Returns {name}`none` otherwise.

src/Lean/Compiler/LCNF/Basic.lean

@@ -1230,7 +1230,14 @@ def instantiateRevRangeArgs (e : Expr) (beginIdx endIdx : Nat) (args : Array (Ar
   else
     e.instantiateRevRange beginIdx endIdx (args.map (·.toExpr))
 
-/-- Lookup function for compiler extensions with sorted persisted state that works in both `lean` and `leanir`. -/
+/--
+Lookup function for compiler extensions with sorted persisted state that works in both `lean` and
+`leanir`.
+
+`preferImported` defaults to false because in `leanir`, we do not want to mix information from
+`meta` compilation in `lean` with our own state. But in `lean`, setting `preferImported` can help
+with avoiding unnecessary task blocks.
+-/
 @[inline] def findExtEntry? [Inhabited σ] (env : Environment) (ext : PersistentEnvExtension α β σ) (declName : Name)
     (findAtSorted? : Array α → Name → Option α')
     (findInState? : σ → Name → Option α') : Option α' :=

src/Lean/Compiler/LCNF/Main.lean

@@ -78,9 +78,13 @@ def isValidMainType (type : Expr) : Bool :=
     isValidResultName resultName
   | _ => false
 
+/-- A postponed call of `compileDecls`. -/
 structure PostponedCompileDecls where
+  /-- Declaration names of this mutual group. -/
   declNames : Array Name
-deriving BEq, Hashable
+  /-- Options at time of original call, to be restored for tracing etc. -/
+  options : Options
+deriving BEq
 
 /--
 Saves postponed `compileDecls` calls.
@@ -101,16 +105,20 @@ builtin_initialize postponedCompileDeclsExt : SimplePersistentEnvExtension Postp
       { exported := #[], server := #[], «private» := es.toArray }
   }
 
-def resumeCompilation (declName : Name) : CoreM Unit := do
+def resumeCompilation (declName : Name) (baseOpts : Options) : CoreM Unit := do
   let some decls := postponedCompileDeclsExt.getState (← getEnv) |>.find? declName | return
+  let opts := baseOpts.mergeBy (fun _ base _ => base) decls.options
+  let opts := compiler.postponeCompile.set opts false
   modifyEnv (postponedCompileDeclsExt.modifyState · fun s => decls.declNames.foldl (·.erase) s)
-  withOptions (compiler.postponeCompile.set · false) do
+  -- NOTE: we *must* throw away the current options as they could depend on the specific recursion
+  -- we did to get here.
+  withOptions (fun _ => opts) do
   Core.prependError m!"Failed to compile `{declName}`" do
-    (← compileDeclsRef.get) decls.declNames
+    (← compileDeclsRef.get) decls.declNames baseOpts
 
 namespace PassManager
 
-partial def run (declNames : Array Name) : CompilerM Unit := withAtLeastMaxRecDepth 8192 do
+partial def run (declNames : Array Name) (baseOpts : Options) : CompilerM Unit := withAtLeastMaxRecDepth 8192 do
   /-
   Note: we need to increase the recursion depth because we currently do to save phase1
   declarations in .olean files. Then, we have to recursively compile all dependencies,
@@ -141,11 +149,14 @@ partial def run (declNames : Array Name) : CompilerM Unit := withAtLeastMaxRecDe
 
   -- Now that we have done all input checks, check for postponement
   if (← getEnv).header.isModule && (← compiler.postponeCompile.getM) then
-    modifyEnv (postponedCompileDeclsExt.addEntry · { declNames := decls.map (·.name) })
+    modifyEnv (postponedCompileDeclsExt.addEntry · { declNames := decls.map (·.name), options := ← getOptions })
     -- meta defs are compiled locally so they are available for execution/compilation without
     -- importing `.ir` but still marked for `leanir` compilation so that we do not have to persist
     -- module-local compilation information between the two processes
-    if !decls.any (isMarkedMeta (← getEnv) ·.name) then
+    if decls.any (isMarkedMeta (← getEnv) ·.name) then
+      -- avoid re-compiling the meta defs in this process; the entry for `leanir` is not affected
+      modifyEnv (postponedCompileDeclsExt.modifyState · fun s => decls.foldl (·.erase ·.name) s)
+    else
       trace[Compiler] "postponing compilation of {decls.map (·.name)}"
       return
 
@@ -157,7 +168,7 @@ partial def run (declNames : Array Name) : CompilerM Unit := withAtLeastMaxRecDe
       let .let { value := .const c .., .. } .. := c | return
       -- Need to do some lookups to get the actual name passed to `compileDecls`
       let c := Compiler.getImplementedBy? (← getEnv) c |>.getD c
-      resumeCompilation c
+      resumeCompilation c baseOpts
 
   let decls := markRecDecls decls
   let manager ← getPassManager
@@ -200,9 +211,9 @@ where
 
 end PassManager
 
-def main (declNames : Array Name) : CoreM Unit := do
+def main (declNames : Array Name) (baseOpts : Options) : CoreM Unit := do
   withTraceNode `Compiler (fun _ => return m!"compiling: {declNames}") do
-    CompilerM.run <| PassManager.run declNames
+    CompilerM.run <| PassManager.run declNames baseOpts
 
 builtin_initialize
   compileDeclsRef.set main

src/Lean/Compiler/LCNF/ToMono.lean

@@ -279,13 +279,13 @@ partial def casesFloatArrayToMono (c : Cases .pure) (_ : c.typeName == ``FloatAr
   let k ← k.toMono
   return .let decl k
 
-/-- Eliminate `cases` for `String. -/
+/-- Eliminate `cases` for `String`. -/
 partial def casesStringToMono (c : Cases .pure) (_ : c.typeName == ``String) : ToMonoM (Code .pure) := do
   assert! c.alts.size == 1
   let .alt _ ps k := c.alts[0]! | unreachable!
   eraseParams ps
   let p := ps[0]!
-  let decl := { fvarId := p.fvarId, binderName := p.binderName, type := anyExpr, value := .const ``String.toList [] #[.fvar c.discr] }
+  let decl := { fvarId := p.fvarId, binderName := p.binderName, type := anyExpr, value := .const ``String.toByteArray [] #[.fvar c.discr] }
   modifyLCtx fun lctx => lctx.addLetDecl decl
   let k ← k.toMono
   return .let decl k

src/Lean/Compiler/Main.lean

@@ -19,7 +19,7 @@ that fulfill the requirements of `shouldGenerateCode`.
 def compile (declNames : Array Name) : CoreM Unit := do profileitM Exception "compiler new" (← getOptions) do
   withOptions (compiler.postponeCompile.set · false) do
   withTraceNode `Compiler (fun _ => return m!"compiling: {declNames}") do
-    LCNF.main declNames
+    LCNF.main declNames {}
 
 builtin_initialize
   registerTraceClass `Compiler

src/Lean/CoreM.lean

@@ -711,11 +711,11 @@ breaks the cycle by making `compileDeclsImpl` a "dynamic" call through the ref t
 to the linker. In the compiler there is a matching `builtin_initialize` to set this ref to the
 actual implementation of compileDeclsRef.
 -/
-builtin_initialize compileDeclsRef : IO.Ref (Array Name → CoreM Unit) ←
-  IO.mkRef (fun _ => throwError m!"call to compileDecls with uninitialized compileDeclsRef")
+builtin_initialize compileDeclsRef : IO.Ref (Array Name → Options → CoreM Unit) ←
+  IO.mkRef (fun _ _ => throwError m!"call to compileDecls with uninitialized compileDeclsRef")
 
 private def compileDeclsImpl (declNames : Array Name) : CoreM Unit := do
-  (← compileDeclsRef.get) declNames
+  (← compileDeclsRef.get) declNames {}
 
 -- `ref?` is used for error reporting if available
 def compileDecls (decls : Array Name) (logErrors := true) : CoreM Unit := do

src/Lean/Data/Options.lean

@@ -82,11 +82,17 @@ def mergeBy (f : Name → DataValue → DataValue → DataValue) (o1 o2 : Option
 
 end Options
 
+structure OptionDeprecation where
+  since    : String
+  text?    : Option String := none
+  deriving Inhabited
+
 structure OptionDecl where
   name     : Name
   declName : Name := by exact decl_name%
   defValue : DataValue
   descr    : String := ""
+  deprecation? : Option OptionDeprecation := none
   deriving Inhabited
 
 def OptionDecl.fullDescr (self : OptionDecl) : String := Id.run do
@@ -183,6 +189,7 @@ namespace Option
 protected structure Decl (α : Type) where
   defValue : α
   descr    : String := ""
+  deprecation? : Option OptionDeprecation := none
 
 protected def get? [KVMap.Value α] (opts : Options) (opt : Lean.Option α) : Option α :=
   opts.get? opt.name
@@ -214,6 +221,7 @@ protected def register [KVMap.Value α] (name : Name) (decl : Lean.Option.Decl
     declName := ref
     defValue := KVMap.Value.toDataValue decl.defValue
     descr := decl.descr
+    deprecation? := decl.deprecation?
   }
   return { name := name, defValue := decl.defValue }
 

src/Lean/Elab/App.lean

@@ -1832,13 +1832,15 @@ To infer a namespace from the expected type, we do the following operations:
 - if the type is of the form `c x₁ ... xₙ` with `c` a constant, then try using `c` as the namespace,
   and if that doesn't work, try unfolding the expression and continuing.
 -/
-private partial def resolveDottedIdentFn (idRef : Syntax) (id : Name) (expectedType? : Option Expr) : TermElabM (List (Expr × Syntax × List Syntax)) := do
+private partial def resolveDottedIdentFn (idRef : Syntax) (id : Name) (explicitUnivs : List Level) (expectedType? : Option Expr) : TermElabM (List (Expr × Syntax × List Syntax)) := do
   unless id.isAtomic do
     throwError "Invalid dotted identifier notation: The name `{id}` must be atomic"
   tryPostponeIfNoneOrMVar expectedType?
   let some expectedType := expectedType?
     | throwNoExpectedType
   addCompletionInfo <| CompletionInfo.dotId idRef id (← getLCtx) expectedType?
+  -- We will check deprecations in `elabAppFnResolutions`.
+  withoutCheckDeprecated do
   withForallBody expectedType fun resultType => do
     go resultType expectedType #[]
 where
@@ -1878,8 +1880,10 @@ where
           |>.filter (fun (_, fieldList) => fieldList.isEmpty)
           |>.map Prod.fst
         if !candidates.isEmpty then
-          candidates.mapM fun resolvedName => return (← mkConst resolvedName, ← getRef, [])
+          candidates.mapM fun resolvedName => return (← mkConst resolvedName explicitUnivs, ← getRef, [])
         else if let some (fvar, []) ← resolveLocalName fullName then
+          unless explicitUnivs.isEmpty do
+            throwInvalidExplicitUniversesForLocal fvar
           return [(fvar, ← getRef, [])]
         else
           throwUnknownIdentifierAt (← getRef) (declHint := fullName) <| m!"Unknown constant `{.ofConstName fullName}`"
@@ -1919,6 +1923,10 @@ private partial def elabAppFn (f : Syntax) (lvals : List LVal) (namedArgs : Arra
       let some idx := idxStx.isFieldIdx?
         | throwError "Internal error: Unexpected field index syntax `{idxStx}`"
       elabAppFn e (LVal.fieldIdx idxStx idx :: lvals) namedArgs args expectedType? explicit ellipsis overloaded acc
+    let elabDottedIdent (id : Syntax) (explicitUnivs : List Level) (explicit : Bool) : TermElabM (Array (TermElabResult Expr)) := do
+      let res ← withRef f <| resolveDottedIdentFn id id.getId.eraseMacroScopes explicitUnivs expectedType?
+      -- Use (forceTermInfo := true) because we want to record the result of .ident resolution even in patterns
+      elabAppFnResolutions f res lvals namedArgs args expectedType? explicit ellipsis overloaded acc (forceTermInfo := true)
     match f with
     | `($(e).$idx:fieldIdx) => elabFieldIdx e idx explicit
     | `($e |>.$idx:fieldIdx) => elabFieldIdx e idx explicit
@@ -1934,16 +1942,17 @@ private partial def elabAppFn (f : Syntax) (lvals : List LVal) (namedArgs : Arra
     | `($id:ident.{$us,*}) => do
       let us ← elabExplicitUnivs us
       elabAppFnId id us lvals namedArgs args expectedType? explicit ellipsis overloaded acc
-    | `(@$id:ident) =>
-      elabAppFn id lvals namedArgs args expectedType? (explicit := true) ellipsis overloaded acc
-    | `(@$_:ident.{$_us,*}) =>
+    | `(.$id:ident) => elabDottedIdent id [] explicit
+    | `(.$id:ident.{$us,*}) =>
+      let us ← elabExplicitUnivs us
+      elabDottedIdent id us explicit
+    | `(@$_:ident)
+    | `(@$_:ident.{$_us,*})
+    | `(@.$_:ident)
+    | `(@.$_:ident.{$_us,*}) =>
       elabAppFn (f.getArg 1) lvals namedArgs args expectedType? (explicit := true) ellipsis overloaded acc
     | `(@$_)     => throwUnsupportedSyntax -- invalid occurrence of `@`
     | `(_)       => throwError "A placeholder `_` cannot be used where a function is expected"
-    | `(.$id:ident) =>
-        let res ← withRef f <| resolveDottedIdentFn id id.getId.eraseMacroScopes expectedType?
-        -- Use (forceTermInfo := true) because we want to record the result of .ident resolution even in patterns
-        elabAppFnResolutions f res lvals namedArgs args expectedType? explicit ellipsis overloaded acc (forceTermInfo := true)
     | _ => do
       let catchPostpone := !overloaded
       /- If we are processing a choice node, then we should use `catchPostpone == false` when elaborating terms.
@@ -2086,13 +2095,15 @@ private def elabAtom : TermElab := fun stx expectedType? => do
 
 @[builtin_term_elab explicit] def elabExplicit : TermElab := fun stx expectedType? =>
   match stx with
-  | `(@$_:ident)          => elabAtom stx expectedType?  -- Recall that `elabApp` also has support for `@`
-  | `(@$_:ident.{$_us,*}) => elabAtom stx expectedType?
-  | `(@$(_).$_:fieldIdx)  => elabAtom stx expectedType?
-  | `(@$(_).$_:ident)     => elabAtom stx expectedType?
-  | `(@($t))             => elabTerm t expectedType? (implicitLambda := false)    -- `@` is being used just to disable implicit lambdas
-  | `(@$t)               => elabTerm t expectedType? (implicitLambda := false)   -- `@` is being used just to disable implicit lambdas
-  | _                    => throwUnsupportedSyntax
+  | `(@$_:ident)           => elabAtom stx expectedType?  -- Recall that `elabApp` also has support for `@`
+  | `(@$_:ident.{$_us,*})  => elabAtom stx expectedType?
+  | `(@$(_).$_:fieldIdx)   => elabAtom stx expectedType?
+  | `(@$(_).$_:ident)      => elabAtom stx expectedType?
+  | `(@.$_:ident)          => elabAtom stx expectedType?
+  | `(@.$_:ident.{$_us,*}) => elabAtom stx expectedType?
+  | `(@($t))               => elabTerm t expectedType? (implicitLambda := false)   -- `@` is being used just to disable implicit lambdas
+  | `(@$t)                 => elabTerm t expectedType? (implicitLambda := false)   -- `@` is being used just to disable implicit lambdas
+  | _                      => throwUnsupportedSyntax
 
 @[builtin_term_elab choice] def elabChoice : TermElab := elabAtom
 @[builtin_term_elab proj] def elabProj : TermElab := elabAtom

src/Lean/Elab/BuiltinCommand.lean

@@ -510,7 +510,8 @@ def failIfSucceeds (x : CommandElabM Unit) : CommandElabM Unit := do
     pure ()
 
 @[builtin_command_elab «set_option»] def elabSetOption : CommandElab := fun stx => do
-  let options ← Elab.elabSetOption stx[1] stx[3]
+  let (options, decl) ← Elab.elabSetOption stx[1] stx[3]
+  withRef stx[1] <| Elab.checkDeprecatedOption (stx[1].getId.eraseMacroScopes) decl
   modify fun s => { s with maxRecDepth := maxRecDepth.get options }
   modifyScope fun scope => { scope with opts := options }
 

src/Lean/Elab/BuiltinDo/Let.lean

@@ -81,8 +81,15 @@ private def pushTypeIntoReassignment (letOrReassign : LetOrReassign) (decl : TSy
   else
     pure decl
 
-partial def elabDoLetOrReassign (letOrReassign : LetOrReassign) (decl : TSyntax ``letDecl)
+private def checkLetConfigInDo (config : Term.LetConfig) : DoElabM Unit := do
+  if config.postponeValue then
+    throwError "`+postponeValue` is not supported in `do` blocks"
+  if config.generalize then
+    throwError "`+generalize` is not supported in `do` blocks"
+
+partial def elabDoLetOrReassign (config : Term.LetConfig) (letOrReassign : LetOrReassign) (decl : TSyntax ``letDecl)
     (dec : DoElemCont) : DoElabM Expr := do
+  checkLetConfigInDo config
   let vars ← getLetDeclVars decl
   letOrReassign.checkMutVars vars
   -- Some decl preprocessing on the patterns and expected types:
@@ -91,7 +98,7 @@ partial def elabDoLetOrReassign (letOrReassign : LetOrReassign) (decl : TSyntax
   match decl with
   | `(letDecl| $decl:letEqnsDecl) =>
     let declNew ← `(letDecl| $(⟨← liftMacroM <| Term.expandLetEqnsDecl decl⟩):letIdDecl)
-    return ← Term.withMacroExpansion decl declNew <| elabDoLetOrReassign letOrReassign declNew dec
+    return ← Term.withMacroExpansion decl declNew <| elabDoLetOrReassign config letOrReassign declNew dec
   | `(letDecl| $pattern:term $[: $xType?]? := $rhs) =>
     let rhs ← match xType? with | some xType => `(($rhs : $xType)) | none => pure rhs
     let contElab : DoElabM Expr := elabWithReassignments letOrReassign vars dec.continueWithUnit
@@ -99,15 +106,21 @@ partial def elabDoLetOrReassign (letOrReassign : LetOrReassign) (decl : TSyntax
     -- The infamous MVar postponement trick below popularized by `if` is necessary in Lake.CLI.Main.
     -- We need it because we specify a constant motive, otherwise the `match` elaborator would have postponed.
     let mvar ← Lean.withRef rhs `(?m)
-    let term ← `(let_mvar% ?m := $rhs;
-                 wait_if_type_mvar% ?m;
-                 match (motive := ∀_, $(← Term.exprToSyntax mγ)) $mvar:term with
-                 | $pattern:term => $body)
+    let term ← if let some h := config.eq? then
+      `(let_mvar% ?m := $rhs;
+        wait_if_type_mvar% ?m;
+        match $h:ident : $mvar:term with
+        | $pattern:term => $body)
+    else
+      `(let_mvar% ?m := $rhs;
+        wait_if_type_mvar% ?m;
+        match (motive := ∀_, $(← Term.exprToSyntax mγ)) $mvar:term with
+        | $pattern:term => $body)
     Term.withMacroExpansion (← getRef) term do Term.elabTermEnsuringType term (some mγ)
   | `(letDecl| $decl:letIdDecl) =>
     let { id, binders, type, value } := Term.mkLetIdDeclView decl
     let id ← if id.isIdent then pure id else Term.mkFreshIdent id (canonical := true)
-    let nondep := letOrReassign matches .have
+    let nondep := config.nondep || letOrReassign matches .have
     -- Only non-`mut` lets will be elaborated as `let`s; `let mut` and reassigns behave as `have`s.
     -- See `elabLetDeclAux` for rationale.
     let (type, val) ← Term.elabBindersEx binders fun xs => do
@@ -128,8 +141,25 @@ partial def elabDoLetOrReassign (letOrReassign : LetOrReassign) (decl : TSyntax
     withLetDecl id.getId (kind := kind) type val (nondep := nondep) fun x => do
       Term.addLocalVarInfo id x
       elabWithReassignments letOrReassign vars do
-      let body ← dec.continueWithUnit
-      mkLetFVars #[x] body (usedLetOnly := false) (generalizeNondepLet := false)
+      match config.eq? with
+      | none =>
+        let body ← dec.continueWithUnit
+        if config.zeta then
+          pure <| (← body.abstractM #[x]).instantiate1 val
+        else
+          mkLetFVars #[x] body (usedLetOnly := config.usedOnly) (generalizeNondepLet := false)
+      | some h =>
+        let hTy ← mkEq x val
+        withLetDecl h.getId hTy (← mkEqRefl x) (nondep := true) fun h' => do
+          Term.addLocalVarInfo h h'
+          let body ← dec.continueWithUnit
+          if config.zeta then
+            pure <| (← body.abstractM #[x, h']).instantiateRev #[val, ← mkEqRefl val]
+          else if nondep then
+            let f ← mkLambdaFVars #[x, h'] body
+            return mkApp2 f val (← mkEqRefl val)
+          else
+            mkLetFVars #[x, h'] body (usedLetOnly := config.usedOnly) (generalizeNondepLet := false)
   | _ => throwUnsupportedSyntax
 
 def elabDoArrow (letOrReassign : LetOrReassign) (stx : TSyntax [``doIdDecl, ``doPatDecl]) (dec : DoElemCont) : DoElabM Expr := do
@@ -168,13 +198,21 @@ def elabDoArrow (letOrReassign : LetOrReassign) (stx : TSyntax [``doIdDecl, ``do
         elabDoElem (← `(doElem| $pattern:term := $x)) dec
   | _ => throwUnsupportedSyntax
 
+private def getLetConfigAndCheckMut (letConfigStx : TSyntax ``Parser.Term.letConfig)
+    (mutTk? : Option Syntax) (initConfig : Term.LetConfig := {}) : DoElabM Term.LetConfig := do
+  if mutTk?.isSome && !letConfigStx.raw[0].getArgs.isEmpty then
+    throwErrorAt letConfigStx "configuration options are not allowed with `let mut`"
+  Term.mkLetConfig letConfigStx initConfig
+
 @[builtin_doElem_elab Lean.Parser.Term.doLet] def elabDoLet : DoElab := fun stx dec => do
-  let `(doLet| let $[mut%$mutTk?]? $decl:letDecl) := stx | throwUnsupportedSyntax
-  elabDoLetOrReassign (.let mutTk?) decl dec
+  let `(doLet| let $[mut%$mutTk?]? $config:letConfig $decl:letDecl) := stx | throwUnsupportedSyntax
+  let config ← getLetConfigAndCheckMut config mutTk?
+  elabDoLetOrReassign config (.let mutTk?) decl dec
 
 @[builtin_doElem_elab Lean.Parser.Term.doHave] def elabDoHave : DoElab := fun stx dec => do
-  let `(doHave| have $decl:letDecl) := stx | throwUnsupportedSyntax
-  elabDoLetOrReassign .have decl dec
+  let `(doHave| have $config:letConfig $decl:letDecl) := stx | throwUnsupportedSyntax
+  let config ← Term.mkLetConfig config { nondep := true }
+  elabDoLetOrReassign config .have decl dec
 
 @[builtin_doElem_elab Lean.Parser.Term.doLetRec] def elabDoLetRec : DoElab := fun stx dec => do
   let `(doLetRec| let rec $decls:letRecDecls) := stx | throwUnsupportedSyntax
@@ -192,14 +230,17 @@ def elabDoArrow (letOrReassign : LetOrReassign) (stx : TSyntax [``doIdDecl, ``do
   | `(doReassign| $x:ident $[: $xType?]? := $rhs) =>
     let decl : TSyntax ``letIdDecl ← `(letIdDecl| $x:ident $[: $xType?]? := $rhs)
     let decl : TSyntax ``letDecl := ⟨mkNode ``letDecl #[decl]⟩
-    elabDoLetOrReassign .reassign decl dec
+    elabDoLetOrReassign {} .reassign decl dec
   | `(doReassign| $decl:letPatDecl) =>
     let decl : TSyntax ``letDecl := ⟨mkNode ``letDecl #[decl]⟩
-    elabDoLetOrReassign .reassign decl dec
+    elabDoLetOrReassign {} .reassign decl dec
   | _ => throwUnsupportedSyntax
 
 @[builtin_doElem_elab Lean.Parser.Term.doLetElse] def elabDoLetElse : DoElab := fun stx dec => do
-  let `(doLetElse| let $[mut%$mutTk?]? $pattern := $rhs | $otherwise $(body?)?) := stx | throwUnsupportedSyntax
+  let `(doLetElse| let $[mut%$mutTk?]? $cfg:letConfig $pattern := $rhs | $otherwise $(body?)?) := stx
+    | throwUnsupportedSyntax
+  let config ← getLetConfigAndCheckMut cfg mutTk?
+  checkLetConfigInDo config
   let letOrReassign := LetOrReassign.let mutTk?
   let vars ← getPatternVarsEx pattern
   letOrReassign.checkMutVars vars
@@ -208,10 +249,17 @@ def elabDoArrow (letOrReassign : LetOrReassign) (stx : TSyntax [``doIdDecl, ``do
   if mutTk?.isSome then
     for var in vars do
       body ← `(doSeqIndent| let mut $var := $var; do $body:doSeqIndent)
-  elabDoElem (← `(doElem| match $rhs:term with | $pattern => $body:doSeqIndent | _ => $otherwise:doSeqIndent)) dec
+  if let some h := config.eq? then
+    elabDoElem (← `(doElem| match $h:ident : $rhs:term with | $pattern => $body:doSeqIndent | _ => $otherwise:doSeqIndent)) dec
+  else
+    elabDoElem (← `(doElem| match $rhs:term with | $pattern => $body:doSeqIndent | _ => $otherwise:doSeqIndent)) dec
 
 @[builtin_doElem_elab Lean.Parser.Term.doLetArrow] def elabDoLetArrow : DoElab := fun stx dec => do
-  let `(doLetArrow| let $[mut%$mutTk?]? $decl) := stx | throwUnsupportedSyntax
+  let `(doLetArrow| let $[mut%$mutTk?]? $cfg:letConfig $decl) := stx | throwUnsupportedSyntax
+  let config ← getLetConfigAndCheckMut cfg mutTk?
+  checkLetConfigInDo config
+  if config.nondep || config.usedOnly || config.zeta || config.eq?.isSome then
+    throwErrorAt cfg "configuration options are not supported with `←`"
   elabDoArrow (.let mutTk?) decl dec
 
 @[builtin_doElem_elab Lean.Parser.Term.doReassignArrow] def elabDoReassignArrow : DoElab := fun stx dec => do

src/Lean/Elab/BuiltinTerm.lean

@@ -371,7 +371,8 @@ private def mkSilentAnnotationIfHole (e : Expr) : TermElabM Expr := do
     popScope
 
 @[builtin_term_elab «set_option»] def elabSetOption : TermElab := fun stx expectedType? => do
-  let options ← Elab.elabSetOption stx[1] stx[3]
+  let (options, decl) ← Elab.elabSetOption stx[1] stx[3]
+  withRef stx[1] <| Elab.checkDeprecatedOption (stx[1].getId.eraseMacroScopes) decl
   withOptions (fun _ => options) do
     try
       elabTerm stx[5] expectedType?

src/Lean/Elab/Command.lean

@@ -875,7 +875,7 @@ first evaluates any local `set_option ... in ...` clauses and then invokes `cmd`
 partial def withSetOptionIn (cmd : CommandElab) : CommandElab := fun stx => do
   if stx.getKind == ``Lean.Parser.Command.in &&
      stx[0].getKind == ``Lean.Parser.Command.set_option then
-      let opts ← Elab.elabSetOption stx[0][1] stx[0][3]
+      let (opts, _) ← Elab.elabSetOption stx[0][1] stx[0][3]
       Command.withScope (fun scope => { scope with opts }) do
         withSetOptionIn cmd stx[2]
   else

src/Lean/Elab/Do/InferControlInfo.lean

@@ -94,12 +94,12 @@ partial def ofElem (stx : TSyntax `doElem) : TermElabM ControlInfo := do
   | `(doExpr| $_:term) => return { numRegularExits := 1 }
   | `(doElem| do $doSeq) => ofSeq doSeq
   -- Let
-  | `(doElem| let $[mut]? $_:letDecl) => return .pure
-  | `(doElem| have $_:letDecl) => return .pure
+  | `(doElem| let $[mut]? $_:letConfig $_:letDecl) => return .pure
+  | `(doElem| have $_:letConfig $_:letDecl) => return .pure
   | `(doElem| let rec $_:letRecDecl) => return .pure
-  | `(doElem| let $[mut]? $_ := $_ | $otherwise $(body?)?) =>
+  | `(doElem| let $[mut]? $_:letConfig $_ := $_ | $otherwise $(body?)?) =>
     ofLetOrReassign #[] none otherwise body?
-  | `(doElem| let $[mut]? $decl) =>
+  | `(doElem| let $[mut]? $_:letConfig $decl) =>
     ofLetOrReassignArrow false decl
   | `(doElem| $decl:letIdDeclNoBinders) =>
     ofLetOrReassign (← getLetIdDeclVars ⟨decl⟩) none none none
@@ -169,15 +169,16 @@ partial def ofElem (stx : TSyntax `doElem) : TermElabM ControlInfo := do
     let bodyInfo ← match body? with | none => pure {} | some body => ofSeq ⟨body⟩
     return otherwiseInfo.alternative bodyInfo
   | _ =>
-    let handlers := controlInfoElemAttribute.getEntries (← getEnv) stx.raw.getKind
+    let kind := stx.raw.getKind
+    let handlers := controlInfoElemAttribute.getEntries (← getEnv) kind
     for handler in handlers do
       let res ← catchInternalId unsupportedSyntaxExceptionId
         (some <$> handler.value stx)
         (fun _ => pure none)
       if let some info := res then return info
     throwError
-      "No `ControlInfo` inference handler found for `{stx.raw.getKind}` in syntax {indentD stx}\n\
-       Register a handler with `@[doElem_control_info {stx.raw.getKind}]`."
+      "No `ControlInfo` inference handler found for `{kind}` in syntax {indentD stx}\n\
+       Register a handler with `@[doElem_control_info {kind}]`."
 
 partial def ofLetOrReassignArrow (reassignment : Bool) (decl : TSyntax [``doIdDecl, ``doPatDecl]) : TermElabM ControlInfo := do
   match decl with

src/Lean/Elab/Do/Legacy.lean

@@ -36,6 +36,7 @@ private def getDoSeq (doStx : Syntax) : Syntax :=
 def elabLiftMethod : TermElab := fun stx _ =>
   throwErrorAt stx "invalid use of `(<- ...)`, must be nested inside a 'do' expression"
 
+
 /-- Return true if we should not lift `(<- ...)` actions nested in the syntax nodes with the given kind. -/
 private def liftMethodDelimiter (k : SyntaxNodeKind) : Bool :=
   k == ``Parser.Term.do ||
@@ -76,9 +77,9 @@ private def liftMethodForbiddenBinder (stx : Syntax) : Bool :=
   else if k == ``Parser.Term.let then
     letDeclHasBinders stx[1]
   else if k == ``Parser.Term.doLet then
-    letDeclHasBinders stx[2]
+    letDeclHasBinders stx[3]
   else if k == ``Parser.Term.doLetArrow then
-    letDeclArgHasBinders stx[2]
+    letDeclArgHasBinders stx[3]
   else
     false
 
@@ -701,12 +702,12 @@ def getLetDeclVars (letDecl : Syntax) : TermElabM (Array Var) := do
     throwError "unexpected kind of let declaration"
 
 def getDoLetVars (doLet : Syntax) : TermElabM (Array Var) :=
-  -- leading_parser "let " >> optional "mut " >> letDecl
-  getLetDeclVars doLet[2]
+  -- leading_parser "let " >> optional "mut " >> letConfig >> letDecl
+  getLetDeclVars doLet[3]
 
 def getDoHaveVars (doHave : Syntax) : TermElabM (Array Var) :=
-  -- leading_parser "have" >> letDecl
-  getLetDeclVars doHave[1]
+  -- leading_parser "have" >> letConfig >> letDecl
+  getLetDeclVars doHave[2]
 
 def getDoLetRecVars (doLetRec : Syntax) : TermElabM (Array Var) := do
   -- letRecDecls is an array of `(group (optional attributes >> letDecl))`
@@ -727,9 +728,9 @@ def getDoPatDeclVars (doPatDecl : Syntax) : TermElabM (Array Var) := do
   let pattern := doPatDecl[0]
   getPatternVarsEx pattern
 
--- leading_parser "let " >> optional "mut " >> (doIdDecl <|> doPatDecl)
+-- leading_parser "let " >> optional "mut " >> letConfig >> (doIdDecl <|> doPatDecl)
 def getDoLetArrowVars (doLetArrow : Syntax) : TermElabM (Array Var) := do
-  let decl := doLetArrow[2]
+  let decl := doLetArrow[3]
   if decl.getKind == ``Parser.Term.doIdDecl then
     return #[getDoIdDeclVar decl]
   else if decl.getKind == ``Parser.Term.doPatDecl then
@@ -1060,14 +1061,15 @@ def seqToTerm (action : Syntax) (k : Syntax) : M Syntax := withRef action <| wit
 def declToTerm (decl : Syntax) (k : Syntax) : M Syntax := withRef decl <| withFreshMacroScope do
   let kind := decl.getKind
   if kind == ``Parser.Term.doLet then
-    let letDecl := decl[2]
-    `(let $letDecl:letDecl; $k)
+    let letConfig : TSyntax ``Parser.Term.letConfig := ⟨decl[2]⟩
+    let letDecl := decl[3]
+    `(let $letConfig:letConfig $letDecl:letDecl; $k)
   else if kind == ``Parser.Term.doLetRec then
     let letRecToken := decl[0]
     let letRecDecls := decl[1]
     return mkNode ``Parser.Term.letrec #[letRecToken, letRecDecls, mkNullNode, k]
   else if kind == ``Parser.Term.doLetArrow then
-    let arg := decl[2]
+    let arg := decl[3]
     if arg.getKind == ``Parser.Term.doIdDecl then
       let id     := arg[0]
       let type   := expandOptType id arg[1]
@@ -1415,7 +1417,7 @@ mutual
   /-- Generate `CodeBlock` for `doLetArrow; doElems`
      `doLetArrow` is of the form
      ```
-     "let " >> optional "mut " >> (doIdDecl <|> doPatDecl)
+     "let " >> optional "mut " >> letConfig >> (doIdDecl <|> doPatDecl)
      ```
      where
      ```
@@ -1424,7 +1426,7 @@ mutual
      ```
   -/
   partial def doLetArrowToCode (doLetArrow : Syntax) (doElems : List Syntax) : M CodeBlock := do
-    let decl    := doLetArrow[2]
+    let decl    := doLetArrow[3]
     if decl.getKind == ``Parser.Term.doIdDecl then
       let y := decl[0]
       checkNotShadowingMutable #[y]
@@ -1475,11 +1477,11 @@ mutual
       throwError "unexpected kind of `do` declaration"
 
   partial def doLetElseToCode (doLetElse : Syntax) (doElems : List Syntax) : M CodeBlock := do
-    -- "let " >> optional "mut " >> termParser >> " := " >> termParser >> (checkColGt >> " | " >> doSeq) >> optional doSeq
-    let pattern := doLetElse[2]
-    let val     := doLetElse[4]
-    let elseSeq := doLetElse[6]
-    let bodySeq := doLetElse[7][0]
+    -- "let " >> optional "mut " >> letConfig >> termParser >> " := " >> termParser >> (checkColGt >> " | " >> doSeq) >> optional doSeq
+    let pattern := doLetElse[3]
+    let val     := doLetElse[5]
+    let elseSeq := doLetElse[7]
+    let bodySeq := doLetElse[8][0]
     let contSeq ← if isMutableLet doLetElse then
       let vars ← (← getPatternVarsEx pattern).mapM fun var => `(doElem| let mut $var := $var)
       pure (vars ++ (getDoSeqElems bodySeq).toArray)

src/Lean/Elab/Match.lean

@@ -1042,7 +1042,16 @@ def mkRedundantAlternativeMsg (altName? : Option Name) (altMsg? : Option Message
 
 def reportMatcherResultErrors (altLHSS : List AltLHS) (result : MatcherResult) : TermElabM Unit := do
   unless result.counterExamples.isEmpty do
-    withHeadRefOnly <| logError m!"Missing cases:\n{Meta.Match.counterExamplesToMessageData result.counterExamples}"
+    let maxCEx := Meta.Match.match.maxCounterExamples.get (← getOptions)
+    let (shown, truncated) :=
+      if result.counterExamples.size > maxCEx then
+        (result.counterExamples.take maxCEx, true)
+      else
+        (result.counterExamples, false)
+    let mut msg := m!"Missing cases:\n{Meta.Match.counterExamplesToMessageData shown}"
+    if truncated then
+      msg := msg ++ m!"\n(further cases omitted, increase `set_option match.maxCounterExamples {maxCEx}` to see more)"
+    withHeadRefOnly <| logError msg
     return ()
   unless match.ignoreUnusedAlts.get (← getOptions) || result.unusedAltIdxs.isEmpty do
     let mut i := 0

src/Lean/Elab/PatternVar.lean

@@ -69,6 +69,8 @@ private def throwCtorExpected {α} (ident : Option Syntax) : M α := do
 
   if candidates.size = 0 then
     throwError message
+  -- Sort for deterministic output (iteration order of `env.constants` is not stable)
+  candidates := candidates.qsort Name.lt
   let oneOfThese := if h : candidates.size = 1 then m!"`{candidates[0]}`" else m!"one of these"
   let hint ← m!"Using {oneOfThese} would be valid:".hint (ref? := idStx) (candidates.map fun candidate => {
     suggestion := mkIdent candidate
@@ -320,7 +322,7 @@ where
     if f.getKind == ``Parser.Term.dotIdent then
       let namedArgsNew ← namedArgs.mapM fun
         -- We must ensure that `ref[1]` remains original to allow named-argument hints
-        | { ref, name, val := Arg.stx arg } => withRef ref do `(Lean.Parser.Term.namedArgument| ($(ref[1]) := $(← collect arg)))
+        | { ref, name, val := Arg.stx arg, .. } => withRef ref do `(Lean.Parser.Term.namedArgument| ($(ref[1]) := $(← collect arg)))
         | _ => unreachable!
       let mut argsNew ← args.mapM fun | Arg.stx arg => collect arg | _ => unreachable!
       if ellipsis then

src/Lean/Elab/SetOption.lean

@@ -12,6 +12,11 @@ public import Init.Syntax
 public section
 namespace Lean.Elab
 
+register_builtin_option linter.deprecated.options : Bool := {
+  defValue := true
+  descr := "if true, generate deprecation warnings for deprecated options"
+}
+
 variable [Monad m] [MonadOptions m] [MonadError m] [MonadLiftT (EIO Exception) m] [MonadInfoTree m]
 
 private def throwUnconfigurable {α} (optionName : Name) : m α :=
@@ -43,7 +48,7 @@ where
         {indentExpr defValType}"
     | _ => throwUnconfigurable optionName
 
-def elabSetOption (id : Syntax) (val : Syntax) : m Options := do
+def elabSetOption (id : Syntax) (val : Syntax) : m (Options × OptionDecl) := do
   let ref ← getRef
   -- For completion purposes, we discard `val` and any later arguments.
   -- We include the first argument (the keyword) for position information in case `id` is `missing`.
@@ -51,9 +56,9 @@ def elabSetOption (id : Syntax) (val : Syntax) : m Options := do
   let optionName := id.getId.eraseMacroScopes
   let decl ← IO.toEIO (fun (ex : IO.Error) => Exception.error ref ex.toString) (getOptionDecl optionName)
   pushInfoLeaf <| .ofOptionInfo { stx := id, optionName, declName := decl.declName }
-  let rec setOption (val : DataValue) : m Options := do
+  let rec setOption (val : DataValue) : m (Options × OptionDecl) := do
     validateOptionValue optionName decl val
-    return (← getOptions).set optionName val
+    return ((← getOptions).set optionName val, decl)
   match val.isStrLit? with
   | some str => setOption (DataValue.ofString str)
   | none     =>
@@ -70,3 +75,17 @@ def elabSetOption (id : Syntax) (val : Syntax) : m Options := do
       throwUnconfigurable optionName
 
 end Lean.Elab
+
+namespace Lean.Elab
+
+variable {m : Type → Type} [Monad m] [MonadOptions m] [MonadLog m] [AddMessageContext m]
+
+def checkDeprecatedOption (optionName : Name) (decl : OptionDecl) : m Unit := do
+  unless linter.deprecated.options.get (← getOptions) do return
+  let some dep := decl.deprecation? | return
+  let extraMsg := match dep.text? with
+    | some text => m!": {text}"
+    | none => m!""
+  logWarning m!"`{optionName}` has been deprecated{extraMsg}"
+
+end Lean.Elab

src/Lean/Elab/StructInst.lean

@@ -574,8 +574,14 @@ private def addSourceFields (structName : Name) (sources : Array ExplicitSourceV
 
 private structure StructInstContext where
   view : StructInstView
-  /-- True if the structure instance has a trailing `..`. -/
-  ellipsis : Bool
+  /-- If true, then try using parent instances for missing fields. -/
+  useParentInstanceFields : Bool
+  /-- If true, then try using default values or autoParams for missing fields.
+  (Considered after `useParentInstanceFields`.) -/
+  useDefaults : Bool
+  /-- If true, then missing fields after default value synthesis remain as metavariables rather than yielding an error.
+  Only applies if `useDefaults` is true. -/
+  unsynthesizedAsMVars : Bool
   structName : Name
   structType : Expr
   /-- Structure universe levels. -/
@@ -748,6 +754,8 @@ private structure PendingField where
   deps : NameSet
   val? : Option Expr
 
+private def registerFieldMVarError (e : Expr) (ref : Syntax) (fieldName : Name) : StructInstM Unit :=
+  registerCustomErrorIfMVar e ref m!"Cannot synthesize placeholder for field `{fieldName}`"
 
 /--
 Synthesize pending optParams.
@@ -778,7 +786,7 @@ private def synthOptParamFields : StructInstM Unit := do
   -- Process default values for pending optParam fields.
   let mut pendingFields : Array PendingField ← optParamFields.filterMapM fun (fieldName, fieldType, required) => do
     if required || (← isFieldNotSolved? fieldName).isSome then
-      let (deps, val?) ← getFieldDefaultValue? fieldName
+      let (deps, val?) ← if (← read).useDefaults then getFieldDefaultValue? fieldName else pure ({}, none)
       if let some val := val? then
         trace[Elab.struct] "default value for {fieldName}:{indentExpr val}"
       else
@@ -831,44 +839,46 @@ private def synthOptParamFields : StructInstM Unit := do
               pending
         toRemove := toRemove.push selected.fieldName
     if toRemove.isEmpty then
-      if (← read).ellipsis then
-        for pendingField in pendingFields do
-          if let some mvarId ← isFieldNotSolved? pendingField.fieldName then
-            registerCustomErrorIfMVar (.mvar mvarId) (← read).view.ref m!"\
-              Cannot synthesize placeholder for field `{pendingField.fieldName}`"
-        return
-      let assignErrorsMsg := MessageData.joinSep (assignErrors.map (m!"\n\n" ++ ·)).toList ""
-      let mut requiredErrors : Array MessageData := #[]
-      let mut unsolvedFields : Std.HashSet Name := {}
-      for pendingField in pendingFields do
-        if (← isFieldNotSolved? pendingField.fieldName).isNone then
-          unsolvedFields := unsolvedFields.insert pendingField.fieldName
-          let e := (← get).fieldMap.get! pendingField.fieldName
-          requiredErrors := requiredErrors.push m!"\
-            Field `{pendingField.fieldName}` must be explicitly provided; its synthesized value is{indentExpr e}"
-      let requiredErrorsMsg := MessageData.joinSep (requiredErrors.map (m!"\n\n" ++ ·)).toList ""
-      let missingFields := pendingFields |>.filter (fun pending => pending.val?.isNone)
-      -- TODO(kmill): when fields are all stuck, report better.
-      -- For now, just report all pending fields in case there are no obviously missing ones.
-      let missingFields := if missingFields.isEmpty then pendingFields else missingFields
-      let missing := missingFields |>.map (s!"`{·.fieldName}`") |>.toList
-      let missingFieldsValues ← missingFields.mapM fun field => do
-        if unsolvedFields.contains field.fieldName then
-          pure <| (field.fieldName, some <| (← get).fieldMap.get! field.fieldName)
-        else pure (field.fieldName, none)
-      let missingFieldsHint ← mkMissingFieldsHint missingFieldsValues (← read).view.ref
-      let msg := m!"Fields missing: {", ".intercalate missing}{assignErrorsMsg}{requiredErrorsMsg}{missingFieldsHint}"
-      if (← readThe Term.Context).errToSorry then
-        -- Assign all pending problems using synthetic sorries and log an error.
-        for pendingField in pendingFields do
-          if let some mvarId ← isFieldNotSolved? pendingField.fieldName then
-            mvarId.assign <| ← mkLabeledSorry (← mvarId.getType) (synthetic := true) (unique := true)
-        logError msg
-        return
-      else
-        throwError msg
+      return ← handleStuck pendingFields assignErrors
     pendingSet := pendingSet.filter (!toRemove.contains ·)
     pendingFields := pendingFields.filter fun pendingField => pendingField.val?.isNone || !toRemove.contains pendingField.fieldName
+where
+  handleStuck (pendingFields : Array PendingField) (assignErrors : Array MessageData) : StructInstM Unit := do
+    if (← read).unsynthesizedAsMVars then
+      for pendingField in pendingFields do
+        if let some mvarId ← isFieldNotSolved? pendingField.fieldName then
+          registerFieldMVarError (.mvar mvarId) (← read).view.ref pendingField.fieldName
+      return
+    let assignErrorsMsg := MessageData.joinSep (assignErrors.map (m!"\n\n" ++ ·)).toList ""
+    let mut requiredErrors : Array MessageData := #[]
+    let mut unsolvedFields : Std.HashSet Name := {}
+    for pendingField in pendingFields do
+      if (← isFieldNotSolved? pendingField.fieldName).isNone then
+        unsolvedFields := unsolvedFields.insert pendingField.fieldName
+        let e := (← get).fieldMap.get! pendingField.fieldName
+        requiredErrors := requiredErrors.push m!"\
+          Field `{pendingField.fieldName}` must be explicitly provided; its synthesized value is{indentExpr e}"
+    let requiredErrorsMsg := MessageData.joinSep (requiredErrors.map (m!"\n\n" ++ ·)).toList ""
+    let missingFields := pendingFields |>.filter (fun pending => pending.val?.isNone)
+    -- TODO(kmill): when fields are all stuck, report better.
+    -- For now, just report all pending fields in case there are no obviously missing ones.
+    let missingFields := if missingFields.isEmpty then pendingFields else missingFields
+    let missing := missingFields |>.map (s!"`{·.fieldName}`") |>.toList
+    let missingFieldsValues ← missingFields.mapM fun field => do
+      if unsolvedFields.contains field.fieldName then
+        pure <| (field.fieldName, some <| (← get).fieldMap.get! field.fieldName)
+      else pure (field.fieldName, none)
+    let missingFieldsHint ← mkMissingFieldsHint missingFieldsValues (← read).view.ref
+    let msg := m!"Fields missing: {", ".intercalate missing}{assignErrorsMsg}{requiredErrorsMsg}{missingFieldsHint}"
+    if (← readThe Term.Context).errToSorry then
+      -- Assign all pending problems using synthetic sorries and log an error.
+      for pendingField in pendingFields do
+        if let some mvarId ← isFieldNotSolved? pendingField.fieldName then
+          mvarId.assign <| ← mkLabeledSorry (← mvarId.getType) (synthetic := true) (unique := true)
+      logError msg
+      return
+    else
+      throwError msg
 
 private def finalize : StructInstM Expr := withViewRef do
   let val := (← read).val.beta (← get).fields
@@ -1049,19 +1059,13 @@ These fields can still be solved for by parent instance synthesis later.
 -/
 private def processNoField (loop : StructInstM α) (fieldName : Name) (binfo : BinderInfo) (fieldType : Expr) : StructInstM α := do
   trace[Elab.struct] "processNoField `{fieldName}` of type {fieldType}"
-  if (← read).ellipsis && (← readThe Term.Context).inPattern then
-    -- See the note in `ElabAppArgs.processExplicitArg`
-    -- In ellipsis & pattern mode, do not use optParams or autoParams.
-    let e ← addStructFieldMVar fieldName fieldType
-    registerCustomErrorIfMVar e (← read).view.ref m!"don't know how to synthesize placeholder for field `{fieldName}`"
-    loop
-  else
+  if (← read).useDefaults then
     let autoParam? := fieldType.getAutoParamTactic?
     let fieldType := fieldType.consumeTypeAnnotations
     if binfo.isInstImplicit then
       let e ← addStructFieldMVar fieldName fieldType .synthetic
       modify fun s => { s with instMVars := s.instMVars.push e.mvarId! }
-      loop
+      return ← loop
     else if let some (.const tacticDecl ..) := autoParam? then
       match evalSyntaxConstant (← getEnv) (← getOptions) tacticDecl with
       | .error err       => throwError err
@@ -1078,12 +1082,11 @@ private def processNoField (loop : StructInstM α) (fieldName : Name) (binfo : B
         -- (See `processExplicitArg` for a comment about this.)
         addTermInfo' stx mvar
         addStructFieldAux fieldName mvar
-        loop
-    else
-      -- Default case: natural metavariable, register it for optParams
-      discard <| addStructFieldMVar fieldName fieldType
-      modify fun s => { s with optParamFields := s.optParamFields.push (fieldName, fieldType, binfo.isExplicit) }
-      loop
+        return ← loop
+  -- Default case: natural metavariable, register it for optParams
+  discard <| addStructFieldMVar fieldName fieldType
+  modify fun s => { s with optParamFields := s.optParamFields.push (fieldName, fieldType, binfo.isExplicit) }
+  loop
 
 private partial def loop : StructInstM Expr := withViewRef do
   let type := (← get).type
@@ -1178,8 +1181,7 @@ private partial def addParentInstanceFields : StructInstM Unit := do
 
 private def main : StructInstM Expr := do
   initializeState
-  unless (← read).ellipsis && (← readThe Term.Context).inPattern do
-    -- Inside a pattern with ellipsis mode, users expect to match just the fields provided.
+  if (← read).useParentInstanceFields then
     addParentInstanceFields
   loop
 
@@ -1198,7 +1200,17 @@ private def elabStructInstView (s : StructInstView) (structName : Name) (structT
   trace[Elab.struct] "expanded fields:\n{MessageData.joinSep (fields.toList.map (fun (_, field) => m!"- {MessageData.nestD (toMessageData field)}")) "\n"}"
   let ellipsis := s.sources.implicit.isSome
   let (val, _) ← main
-    |>.run { view := s, structName, structType, levels, params, fieldViews := fields, val := ctorFn, ellipsis }
+    |>.run { view := s, structName, structType, levels, params, fieldViews := fields, val := ctorFn
+             -- See the note in `ElabAppArgs.processExplicitArg`
+             -- For structure instances though, there's a sense in which app-style ellipsis mode is always enabled,
+             -- so we do not specifically check for it to disable defaults.
+             -- An effect of this is that if a user forgets `..` they'll be reminded with a "Fields missing" error.
+             useDefaults := !(← readThe Term.Context).inPattern
+             -- Similarly, for patterns we disable using parent instances to fill in fields
+             useParentInstanceFields := !(← readThe Term.Context).inPattern
+             -- In ellipsis mode, unsynthesized missing fields become metavariables, rather than being an error
+             unsynthesizedAsMVars := ellipsis
+     }
     |>.run { type := ctorFnType }
   return val
 

src/Lean/Elab/Tactic/BuiltinTactic.lean

@@ -190,7 +190,8 @@ private def getOptRotation (stx : Syntax) : Nat :=
     popScope
 
 @[builtin_tactic Parser.Tactic.set_option] def elabSetOption : Tactic := fun stx => do
-  let options ← Elab.elabSetOption stx[1] stx[3]
+  let (options, decl) ← Elab.elabSetOption stx[1] stx[3]
+  withRef stx[1] <| Elab.checkDeprecatedOption (stx[1].getId.eraseMacroScopes) decl
   withOptions (fun _ => options) do
     try
       evalTactic stx[5]

src/Lean/Elab/Tactic/Grind/BuiltinTactic.lean

@@ -437,7 +437,8 @@ where
   replaceMainGoal [{ goal with mvarId }]
 
 @[builtin_grind_tactic setOption] def elabSetOption : GrindTactic := fun stx => do
-  let options ← Elab.elabSetOption stx[1] stx[3]
+  let (options, decl) ← Elab.elabSetOption stx[1] stx[3]
+  withRef stx[1] <| Elab.checkDeprecatedOption (stx[1].getId.eraseMacroScopes) decl
   withOptions (fun _ => options) do evalGrindTactic stx[5]
 
 @[builtin_grind_tactic setConfig] def elabSetConfig : GrindTactic := fun stx => do

src/Lean/Elab/Term/TermElabM.lean

@@ -2124,11 +2124,14 @@ private def mkConsts (candidates : List (Name × List String)) (explicitLevels :
     let const ← withoutCheckDeprecated <| mkConst declName explicitLevels
     return (const, projs) :: result
 
+def throwInvalidExplicitUniversesForLocal {α} (e : Expr) : TermElabM α :=
+  throwError "invalid use of explicit universe parameters, `{e}` is a local variable"
+
 def resolveName (stx : Syntax) (n : Name) (preresolved : List Syntax.Preresolved) (explicitLevels : List Level) (expectedType? : Option Expr := none) : TermElabM (List (Expr × List String)) := do
   addCompletionInfo <| CompletionInfo.id stx stx.getId (danglingDot := false) (← getLCtx) expectedType?
   if let some (e, projs) ← resolveLocalName n then
     unless explicitLevels.isEmpty do
-      throwError "invalid use of explicit universe parameters, `{e}` is a local variable"
+      throwInvalidExplicitUniversesForLocal e
     return [(e, projs)]
   let preresolved := preresolved.filterMap fun
     | .decl n projs => some (n, projs)

src/Lean/Environment.lean

@@ -2255,13 +2255,13 @@ def finalizeImport (s : ImportState) (imports : Array Import) (opts : Options) (
     return data
   let numPrivateConsts := moduleData.foldl (init := 0) fun numPrivateConsts data =>
     numPrivateConsts + data.constants.size
-  let numPrivateConsts := irData.foldl (init := numPrivateConsts) fun numPrivateConsts data =>
-    numPrivateConsts + data.extraConstNames.size
+  let numExtraConsts := irData.foldl (init := 0) fun numExtraConsts data =>
+    numExtraConsts + data.extraConstNames.size
   let numPublicConsts := modules.foldl (init := 0) fun numPublicConsts mod => Id.run do
     if !mod.isExported then numPublicConsts else
       let some data := mod.publicModule? | numPublicConsts
       numPublicConsts + data.constants.size
-  let mut const2ModIdx : Std.HashMap Name ModuleIdx := Std.HashMap.emptyWithCapacity (capacity := numPrivateConsts + numPublicConsts)
+  let mut const2ModIdx : Std.HashMap Name ModuleIdx := Std.HashMap.emptyWithCapacity (capacity := numPrivateConsts + numExtraConsts)
   let mut privateConstantMap : Std.HashMap Name ConstantInfo := Std.HashMap.emptyWithCapacity (capacity := numPrivateConsts)
   let mut publicConstantMap : Std.HashMap Name ConstantInfo := Std.HashMap.emptyWithCapacity (capacity := numPublicConsts)
   for h : modIdx in *...moduleData.size do

src/Lean/Linter/MissingDocs.lean

@@ -314,7 +314,7 @@ def checkRegisterSimpAttr : SimpleHandler := mkSimpleHandler "simp attr"
 @[builtin_missing_docs_handler «in»]
 def handleIn : Handler := fun _ stx => do
   if stx[0].getKind == ``«set_option» then
-    let opts ← Elab.elabSetOption stx[0][1] stx[0][3]
+    let (opts, _) ← Elab.elabSetOption stx[0][1] stx[0][3]
     withScope (fun scope => { scope with opts }) do
       missingDocs.run stx[2]
   else

src/Lean/Meta/Eqns.lean

@@ -19,6 +19,7 @@ namespace Lean.Meta
 register_builtin_option backward.eqns.nonrecursive : Bool := {
     defValue := true
     descr    := "Create fine-grained equational lemmas even for non-recursive definitions."
+    deprecation? := some { since := "2026-03-30" }
   }
 
 register_builtin_option backward.eqns.deepRecursiveSplit : Bool := {
@@ -28,6 +29,7 @@ register_builtin_option backward.eqns.deepRecursiveSplit : Bool := {
                 that do not contain recursive calls do not cause further splits in the \
                 equational lemmas. This was the behavior before Lean 4.12, and the purpose of \
                 this option is to help migrating old code."
+    deprecation? := some { since := "2026-03-30" }
   }
 
 

src/Lean/Meta/InferType.lean

@@ -180,12 +180,14 @@ private def inferFVarType (fvarId : FVarId) : MetaM Expr := do
 
 @[inline] private def checkInferTypeCache (e : Expr) (inferType : MetaM Expr) : MetaM Expr := do
   if !(← read).cacheInferType || e.hasMVar then
+    Core.checkInterrupted
     inferType
   else
     let key ← mkExprConfigCacheKey e
     match (← get).cache.inferType.find? key with
     | some type => return type
     | none =>
+      Core.checkInterrupted
       let type ← inferType
       unless type.hasMVar do
         modifyInferTypeCache fun c => c.insert key type

src/Lean/Meta/Match/Basic.lean

@@ -256,12 +256,12 @@ abbrev CounterExample := List Example
 def counterExampleToMessageData (cex : CounterExample) : MessageData :=
   examplesToMessageData cex
 
-def counterExamplesToMessageData (cexs : List CounterExample) : MessageData :=
-  MessageData.joinSep (cexs.map counterExampleToMessageData) Format.line
+def counterExamplesToMessageData (cexs : Array CounterExample) : MessageData :=
+  MessageData.joinSep (cexs.toList.map counterExampleToMessageData) Format.line
 
 structure MatcherResult where
   matcher         : Expr -- The matcher. It is not just `Expr.const matcherName` because the type of the major premises may contain free variables.
-  counterExamples : List CounterExample
+  counterExamples : Array CounterExample
   unusedAltIdxs   : List Nat
   addMatcher      : MetaM Unit
 

src/Lean/Meta/Match/Match.lean

@@ -78,6 +78,14 @@ register_builtin_option backward.match.rowMajor : Bool := {
     it splits them from left to right, which can lead to unnecessary code bloat."
 }
 
+register_builtin_option match.maxCounterExamples : Nat := {
+  defValue := 5
+  descr := "Maximum number of missing-case counter-examples to generate. \
+    When this limit is reached, the match compiler stops exploring further \
+    case splits for counter-example generation. Increase if you need to see \
+    all missing cases."
+}
+
 private def mkIncorrectNumberOfPatternsMsg [ToMessageData α]
     (discrepancyKind : String) (expected actual : Nat) (pats : List α) :=
   let patternsMsg := MessageData.joinSep (pats.map toMessageData) ", "
@@ -202,7 +210,7 @@ structure State where
   Used during splitter generation to avoid going through all pairs of patterns.
   -/
   overlaps        : Overlaps := {}
-  counterExamples : List (List Example) := []
+  counterExamples : Array (List Example) := #[]
 
 /-- Return true if the given (sub-)problem has been solved. -/
 private def isDone (p : Problem) : Bool :=
@@ -269,10 +277,16 @@ def isCurrVarInductive (p : Problem) : MetaM Bool := do
     let val? ← getInductiveVal? x
     return val?.isSome
 
-private def isConstructorTransition (p : Problem) : MetaM Bool := do
-  return (← isCurrVarInductive p)
-    && (hasCtorPattern p || p.alts.isEmpty)
-    && p.alts.all fun alt => match alt.patterns with
+private def isConstructorTransition (p : Problem) : StateRefT State MetaM Bool := do
+  if !(← isCurrVarInductive p) then return false
+  if p.alts.isEmpty then
+    /- When there are no alternatives left and we have already accumulated enough
+       counter-examples, stop exploring further case splits. This prevents
+       combinatorial explosion when generating "missing cases" diagnostics. -/
+    let maxCEx := match.maxCounterExamples.get (← getOptions)
+    return (← get).counterExamples.size < maxCEx
+  else
+    return hasCtorPattern p && p.alts.all fun alt => match alt.patterns with
       | .ctor .. :: _        => true
       | .inaccessible _ :: _ => true -- should be a done pattern by now
       | _                    => false
@@ -467,7 +481,7 @@ where
         trace[Meta.Match.match] "contradiction succeeded"
       else
         trace[Meta.Match.match] "contradiction failed, missing alternative"
-        modify fun s => { s with counterExamples := p.examples :: s.counterExamples }
+        modify fun s => { s with counterExamples := s.counterExamples.push p.examples }
     | alt :: overlapped =>
       solveCnstrs p.mvarId alt
       for otherAlt in overlapped do

src/Lean/Parser/Do.lean

@@ -67,9 +67,9 @@ def notFollowedByRedefinedTermToken :=
     "token at 'do' element"
 
 @[builtin_doElem_parser] def doLet      := leading_parser
-  "let " >> optional "mut " >> letDecl
+  "let " >> optional "mut " >> letConfig >> letDecl
 @[builtin_doElem_parser] def doLetElse  := leading_parser withPosition <|
-  "let " >> optional "mut " >> termParser >> " := " >> termParser >>
+  "let " >> optional "mut " >> letConfig >> termParser >> " := " >> termParser >>
   (checkColGe >> " | " >> doSeqIndent) >> optional (checkColGe >> doSeqIndent)
 
 @[builtin_doElem_parser] def doLetExpr  := leading_parser withPosition <|
@@ -89,7 +89,7 @@ def doPatDecl  := leading_parser
   atomic (termParser >> optType >> ppSpace >> leftArrow) >>
   doElemParser >> optional ((checkColGe >> " | " >> doSeqIndent) >> optional (checkColGe >> doSeqIndent))
 @[builtin_doElem_parser] def doLetArrow      := leading_parser withPosition <|
-  "let " >> optional "mut " >> (doIdDecl <|> doPatDecl)
+  "let " >> optional "mut " >> letConfig >> (doIdDecl <|> doPatDecl)
 
 /-
 We use `letIdDeclNoBinders` to define `doReassign`.
@@ -114,7 +114,7 @@ def letIdDeclNoBinders := leading_parser
 @[builtin_doElem_parser] def doReassignArrow := leading_parser
   notFollowedByRedefinedTermToken >> (doIdDecl <|> doPatDecl)
 @[builtin_doElem_parser] def doHave     := leading_parser
-  "have" >> Term.letDecl
+  "have" >> Term.letConfig >> Term.letDecl
 /-
 In `do` blocks, we support `if` without an `else`.
 Thus, we use indentation to prevent examples such as

src/Lean/Parser/Term.lean

@@ -882,13 +882,19 @@ the available context).
 -/
 def identProjKind := `Lean.Parser.Term.identProj
 
+@[builtin_term_parser] def dotIdent := leading_parser
+  "." >> checkNoWsBefore >> rawIdent
+
 def isIdent (stx : Syntax) : Bool :=
   -- antiquotations should also be allowed where an identifier is expected
   stx.isAntiquot || stx.isIdent
 
+def isIdentOrDotIdent (stx : Syntax) : Bool :=
+  isIdent stx || stx.isOfKind ``dotIdent
+
 /-- `x.{u, ...}` explicitly specifies the universes `u, ...` of the constant `x`. -/
 @[builtin_term_parser] def explicitUniv : TrailingParser := trailing_parser
-  checkStackTop isIdent "expected preceding identifier" >>
+  checkStackTop isIdentOrDotIdent "expected preceding identifier" >>
   checkNoWsBefore "no space before '.{'" >> ".{" >>
   sepBy1 levelParser ", " >> "}"
 /-- `x@e` or `x@h:e` matches the pattern `e` and binds its value to the identifier `x`.
@@ -976,9 +982,6 @@ appropriate parameter for the underlying monad's `ST` effects, then passes it to
 @[builtin_term_parser] def dynamicQuot := withoutPosition <| leading_parser
   "`(" >> ident >> "| " >> incQuotDepth (parserOfStack 1) >> ")"
 
-@[builtin_term_parser] def dotIdent := leading_parser
-  "." >> checkNoWsBefore >> rawIdent
-
 /--
 Implementation of the `show_term` term elaborator.
 -/

src/Lean/PrettyPrinter/Delaborator/Builtins.lean

@@ -619,8 +619,9 @@ private partial def collectStructFields
             if s'.induct == parentName then
               let (fieldValues, fields) ← collectStructFields structName levels params fields fieldValues s'
               return (i + 1, fieldValues, fields)
-      /- Does this field have a default value? and if so, can we omit the field? -/
-      unless ← getPPOption getPPStructureInstancesDefaults do
+      /- Does this field have a default value? and if so, can we omit the field?
+      We cannot omit fields for patterns, since default values do not apply for them. -/
+      unless ← pure (← read).inPattern <||> getPPOption getPPStructureInstancesDefaults do
         if let some defFn := getEffectiveDefaultFnForField? (← getEnv) structName fieldName then
           -- Use `withNewMCtxDepth` to prevent delaborator from solving metavariables.
           if let some (_, defValue) ← withNewMCtxDepth <| instantiateStructDefaultValueFn? defFn levels params (pure ∘ fieldValues.get?) then

src/Lean/Server/Test/Runner.lean

@@ -641,13 +641,13 @@ def processGenericRequest : RunnerM Unit := do
   let params := params.setObjVal! "position" (toJson s.pos)
   logResponse s.method params
 
-def processDirective (ws directive : String) (directiveTargetLineNo : Nat) : RunnerM Unit := do
+def processDirective (_ws directive : String) (directiveTargetLineNo : Nat)
+    (directiveTargetColumn : Nat) : RunnerM Unit := do
   let directive := directive.drop 1
   let colon := directive.find ':'
   let method := directive.sliceTo colon |>.trimAscii |>.copy
   -- TODO: correctly compute in presence of Unicode
-  let directiveTargetColumn := ws.rawEndPos + "--"
-  let pos : Lsp.Position := { line := directiveTargetLineNo, character := directiveTargetColumn.byteIdx }
+  let pos : Lsp.Position := { line := directiveTargetLineNo, character := directiveTargetColumn }
   let params :=
     if h : ¬colon.IsAtEnd then
       directive.sliceFrom (colon.next h) |>.trimAscii.copy
@@ -686,10 +686,15 @@ def processLine (line : String) : RunnerM Unit := do
     match directive.front with
     | 'v' => pure <| (← get).lineNo + 1  -- TODO: support subsequent 'v'... or not
     | '^' => pure <| (← get).lastActualLineNo
+    -- `⬑` is like `^` but targets the column of the `--` marker itself (i.e. column 0 when the
+    -- marker is at the start of the line), rather than the column after `--`.
+    | '⬑' => pure <| (← get).lastActualLineNo
     | _ =>
       skipLineWithoutDirective
       return
-  processDirective ws directive directiveTargetLineNo
+  let directiveTargetColumn :=
+    if directive.front == '⬑' then ws.rawEndPos.byteIdx else (ws.rawEndPos + "--").byteIdx
+  processDirective ws directive directiveTargetLineNo (directiveTargetColumn := directiveTargetColumn)
   skipLineWithDirective
 
 

src/Lean/Shell.lean

@@ -12,6 +12,7 @@ import Lean.Server.Watchdog
 import Lean.Server.FileWorker
 import Lean.Compiler.LCNF.EmitC
 import Init.System.Platform
+import Lean.Compiler.Options
 
 /-  Lean companion to  `shell.cpp` -/
 
@@ -340,7 +341,10 @@ def ShellOptions.process (opts : ShellOptions)
   | 'I' => -- `-I, --stdin`
     return {opts with useStdin := true}
   | 'r' => -- `--run`
-    return {opts with run := true}
+    return {opts with
+      run := true
+      -- can't get IR if it's postponed
+      leanOpts := Compiler.compiler.postponeCompile.set opts.leanOpts false }
   | 'o' => -- `--o, olean=fname`
     return {opts with oleanFileName? := ← checkOptArg "o" optArg?}
   | 'i' => -- `--i, ilean=fname`

src/LeanIR.lean

@@ -57,15 +57,19 @@ def setConfigOption (opts : Options) (arg : String) : IO Options := do
 
 public def main (args : List String) : IO UInt32 := do
   let setupFile::irFile::c::optArgs := args | do
-    IO.println s!"usage: leanir <setup.json> <module> <output.ir> <output.c> <-Dopt=val>..."
+    IO.println s!"usage: leanir <setup.json> <output.ir> <output.c> [--stat] <-Dopt=val>..."
     return 1
 
   let setup ← ModuleSetup.load setupFile
   let modName := setup.name
 
+  let mut printStats := false
   let mut opts := setup.options.toOptions
   for optArg in optArgs do
-    opts ← setConfigOption opts optArg
+    if optArg == "--stat" then
+      printStats := true
+    else
+      opts ← setConfigOption opts optArg
   opts := Compiler.compiler.inLeanIR.set opts true
   opts := maxHeartbeats.set opts 0
 
@@ -127,12 +131,15 @@ public def main (args : List String) : IO UInt32 := do
     modifyEnv (postponedCompileDeclsExt.setState · (decls.foldl (fun s e => e.declNames.foldl (·.insert · e) s) {}))
     for decl in decls do
       for decl in decl.declNames do
-        resumeCompilation decl
+        try
+          resumeCompilation decl (← getOptions)
+        finally
+          addTraceAsMessages
+      for msg in (← Core.getAndEmptyMessageLog).unreported do
+        IO.eprintln (← msg.toString)
   catch e =>
     unless e.isInterrupt do
       logError e.toMessageData
-  finally
-    addTraceAsMessages
 
   let .ok (_, s) := res? | unreachable!
   let env := s.env
@@ -155,4 +162,6 @@ public def main (args : List String) : IO UInt32 := do
     out.write data.toUTF8
 
   displayCumulativeProfilingTimes
+  if printStats then
+    env.displayStats
   return 0

src/Std/Internal/Async/Select.lean

@@ -10,6 +10,8 @@ public import Init.Data.Random
 public import Std.Internal.Async.Basic
 import Init.Data.ByteArray.Extra
 import Init.Data.Array.Lemmas
+public import Std.Sync.Mutex
+public import Std.Sync.Barrier
 import Init.Omega
 
 public section
@@ -132,6 +134,8 @@ partial def Selectable.one (selectables : Array (Selectable α)) : Async α := d
   let gen := mkStdGen seed
   let selectables := shuffleIt selectables gen
 
+  let gate ← IO.Promise.new
+
   for selectable in selectables do
     if let some val ← selectable.selector.tryFn then
       let result ← selectable.cont val
@@ -141,6 +145,9 @@ partial def Selectable.one (selectables : Array (Selectable α)) : Async α := d
   let promise ← IO.Promise.new
 
   for selectable in selectables do
+    if ← finished.get then
+      break
+
     let waiterPromise ← IO.Promise.new
     let waiter := Waiter.mk finished waiterPromise
     selectable.selector.registerFn waiter
@@ -157,18 +164,20 @@ partial def Selectable.one (selectables : Array (Selectable α)) : Async α := d
         let async : Async _ :=
           try
             let res ← IO.ofExcept res
+            discard <| await gate.result?
 
             for selectable in selectables do
               selectable.selector.unregisterFn
 
-            let contRes ← selectable.cont res
-            promise.resolve (.ok contRes)
+            promise.resolve (.ok (← selectable.cont res))
           catch e =>
             promise.resolve (.error e)
 
         async.toBaseIO
 
-  Async.ofPromise (pure promise)
+  gate.resolve ()
+  let result ← Async.ofPromise (pure promise)
+  return result
 
 /--
 Performs fair and data-loss free non-blocking multiplexing on the `Selectable`s in `selectables`.
@@ -224,6 +233,8 @@ def Selectable.combine (selectables : Array (Selectable α)) : IO (Selector α)
         let derivedWaiter := Waiter.mk waiter.finished waiterPromise
         selectable.selector.registerFn derivedWaiter
 
+        let barrier ← IO.Promise.new
+
         discard <| IO.bindTask (t := waiterPromise.result?) fun res? => do
           match res? with
           | none => return (Task.pure (.ok ()))
@@ -231,6 +242,7 @@ def Selectable.combine (selectables : Array (Selectable α)) : IO (Selector α)
             let async : Async _ := do
               let mainPromise := waiter.promise
 
+              await barrier
               for selectable in selectables do
                 selectable.selector.unregisterFn
 

src/Std/Internal/Http.lean

@@ -6,4 +6,188 @@ Authors: Sofia Rodrigues
 module
 
 prelude
-public import Std.Internal.Http.Data
+public import Std.Internal.Http.Server
+
+public section
+
+/-!
+# HTTP Library
+
+A low-level HTTP/1.1 server implementation for Lean. This library provides a pure,
+sans-I/O protocol implementation that can be used with the `Async` library or with
+custom connection handlers.
+
+## Overview
+
+This module provides a complete HTTP/1.1 server implementation with support for:
+
+- Request/response handling with directional streaming bodies
+- Keep-alive connections
+- Chunked transfer encoding
+- Header validation and management
+- Configurable timeouts and limits
+
+**Sans I/O Architecture**: The core protocol logic doesn't perform any actual I/O itself -
+it just defines how data should be processed. This separation allows the protocol implementation
+to remain pure and testable, while different transports (TCP sockets, mock clients) handle
+the actual reading and writing of bytes.
+
+## Quick Start
+
+The main entry point is `Server.serve`, which starts an HTTP/1.1 server. Implement the
+`Server.Handler` type class to define how the server handles requests, errors, and
+`Expect: 100-continue` headers:
+
+```lean
+import Std.Internal.Http
+
+open Std Internal IO Async
+open Std Http Server
+
+structure MyHandler
+
+instance : Handler MyHandler where
+  onRequest _ req := do
+    Response.ok |>.text "Hello, World!"
+
+def main : IO Unit := Async.block do
+  let addr : Net.SocketAddress := .v4 ⟨.ofParts 127 0 0 1, 8080⟩
+  let server ← Server.serve addr MyHandler.mk
+  server.waitShutdown
+```
+
+## Working with Requests
+
+Incoming requests are represented by `Request Body.Stream`, which bundles the request
+line, parsed headers, and a lazily-consumed body. Headers are available immediately,
+while the body can be streamed or collected on demand, allowing handlers to process both
+small and large payloads efficiently.
+
+### Reading Headers
+
+```lean
+def handler (req : Request Body.Stream) : ContextAsync (Response Body.Stream) := do
+  -- Access request method and URI
+  let method := req.head.method      -- Method.get, Method.post, etc.
+  let uri := req.head.uri            -- RequestTarget
+
+  -- Read a specific header
+  if let some contentType := req.head.headers.get? (.mk "content-type") then
+    IO.println s!"Content-Type: {contentType}"
+
+  Response.ok |>.text "OK"
+```
+
+### URI Query Semantics
+
+`RequestTarget.query` is parsed using form-style key/value conventions (`k=v&...`), and `+` is decoded as a
+space in query components. If you need RFC 3986 opaque query handling, use the raw request target string
+(`toString req.head.uri`) and parse it with custom logic.
+
+### Reading the Request Body
+
+The request body is exposed as `Body.Stream`, which can be consumed incrementally or
+collected into memory. The `readAll` method reads the entire body, with an optional size
+limit to protect against unbounded payloads.
+
+```lean
+def handler (req : Request Body.Stream) : ContextAsync (Response Body.Stream) := do
+  -- Collect entire body as a String
+  let bodyStr : String ← req.body.readAll
+
+  -- Or with a maximum size limit
+  let bodyStr : String ← req.body.readAll (maximumSize := some 1024)
+
+  Response.ok |>.text s!"Received: {bodyStr}"
+```
+
+## Building Responses
+
+Responses are constructed using a builder API that starts from a status code and adds
+headers and a body. Common helpers exist for text, HTML, JSON, and binary responses, while
+still allowing full control over status codes and header values.
+
+Response builders produce `Async (Response Body.Stream)`.
+
+```lean
+-- Text response
+Response.ok |>.text "Hello!"
+
+-- HTML response
+Response.ok |>.html "<h1>Hello!</h1>"
+
+-- JSON response
+Response.ok |>.json "{\"key\": \"value\"}"
+
+-- Binary response
+Response.ok |>.bytes someByteArray
+
+-- Custom status
+Response.new |>.status .created |>.text "Resource created"
+
+-- With custom headers
+Response.ok
+  |>.header! "X-Custom-Header" "value"
+  |>.header! "Cache-Control" "no-cache"
+  |>.text "Response with headers"
+```
+
+### Streaming Responses
+
+For large responses or server-sent events, use streaming:
+
+```lean
+def handler (req : Request Body.Stream) : ContextAsync (Response Body.Stream) := do
+  Response.ok
+    |>.header! "Content-Type" "text/plain"
+    |>.stream fun stream => do
+      for i in [0:10] do
+        stream.send { data := s!"chunk {i}\n".toUTF8 }
+        Async.sleep 1000
+      stream.close
+```
+
+## Server Configuration
+
+Configure server behavior with `Config`:
+
+```lean
+def config : Config := {
+  maxRequests := 10000000,
+  lingeringTimeout := 5000,
+}
+
+let server ← Server.serve addr MyHandler.mk config
+```
+
+## Handler Type Class
+
+Implement `Server.Handler` to define how the server processes events. The class has three
+methods, all with default implementations:
+
+- `onRequest` — called for each incoming request; returns a response inside `ContextAsync`
+- `onFailure` — called when an error occurs while processing a request
+- `onContinue` — called when a request includes an `Expect: 100-continue` header; return
+  `true` to accept the body or `false` to reject it
+
+```lean
+structure MyHandler where
+  greeting : String
+
+instance : Handler MyHandler where
+  onRequest self req := do
+    Response.ok |>.text self.greeting
+
+  onFailure self err := do
+    IO.eprintln s!"Error: {err}"
+```
+
+The handler methods operate in the following monads:
+
+- `onRequest` uses `ContextAsync` — an asynchronous monad (`ReaderT CancellationContext Async`) that provides:
+  - Full access to `Async` operations (spawning tasks, sleeping, concurrent I/O)
+  - A `CancellationContext` tied to the client connection — when the client disconnects, the
+    context is cancelled, allowing your handler to detect this and stop work early
+- `onFailure` uses `Async`
+- `onContinue` uses `Async`
+-/

src/Std/Internal/Http/Data/Extensions.lean

@@ -7,7 +7,7 @@ module
 
 prelude
 public import Init.Dynamic
-public import Init.Data.String
+public import Init.Data.String.Basic
 public import Std.Data.TreeMap
 
 open Lean

src/Std/Internal/Http/Data/Headers/Basic.lean

@@ -6,9 +6,11 @@ Authors: Sofia Rodrigues
 module
 
 prelude
+public import Std.Internal.Http.Data.URI
 public import Std.Internal.Http.Data.Headers.Name
 public import Std.Internal.Http.Data.Headers.Value
 public import Std.Internal.Parsec.Basic
+import Init.Data.String.Search
 
 public section
 
@@ -214,4 +216,97 @@ def serialize (connection : Connection) : Header.Name × Header.Value :=
 
 instance : Header Connection := ⟨parse, serialize⟩
 
-end Std.Http.Header.Connection
+end Connection
+
+/--
+The `Host` header.
+
+Represents the authority component of a URI:
+  host [ ":" port ]
+
+Reference: https://www.rfc-editor.org/rfc/rfc9110.html#name-host-and-authority
+-/
+structure Host where
+  /--
+  Host name (reg-name, IPv4, or IPv6 literal).
+  -/
+  host : URI.Host
+
+  /--
+  Optional port.
+  -/
+  port : URI.Port
+deriving Repr, BEq
+
+namespace Host
+
+/--
+Parses a `Host` header value.
+-/
+def parse (v : Value) : Option Host :=
+  let parsed := (Std.Http.URI.Parser.parseHostHeader <* Std.Internal.Parsec.eof).run v.value.toUTF8
+  match parsed with
+  | .ok ⟨host, port⟩ => some ⟨host, port⟩
+  | .error _ => none
+
+/--
+Serializes a `Host` header back to a name and a value.
+-/
+def serialize (host : Host) : Header.Name × Header.Value :=
+  let value := match host.port with
+    | .value port => Header.Value.ofString! s!"{host.host}:{port}"
+    | .empty => Header.Value.ofString! s!"{host.host}:"
+    | .omitted => Header.Value.ofString! <| toString host.host
+
+  (.mk "host", value)
+
+instance : Header Host := ⟨parse, serialize⟩
+
+end Host
+
+/--
+The `Expect` header.
+
+Represents an expectation token.
+The only standardized expectation is `100-continue`.
+
+Reference: https://www.rfc-editor.org/rfc/rfc9110.html#name-expect
+-/
+structure Expect where
+
+  /--
+  True if the client expects `100-continue`.
+  -/
+  expect : Bool
+deriving Repr, BEq
+
+namespace Expect
+
+/--
+Parses an `Expect` header.
+
+Succeeds only if the value is exactly `100-continue`
+(case-insensitive, trimmed).
+-/
+def parse (v : Value) : Option Expect :=
+  let normalized := v.value.trimAscii.toString.toLower
+
+  if normalized == "100-continue" then
+    some ⟨true⟩
+  else
+    none
+
+/--
+Serializes an `Expect` header.
+-/
+def serialize (e : Expect) : Header.Name × Header.Value :=
+  if e.expect then
+    (Header.Name.expect, Value.ofString! "100-continue")
+  else
+    (Header.Name.expect, Value.ofString! "")
+
+instance : Header Expect := ⟨parse, serialize⟩
+
+end Expect
+
+end Std.Http.Header

src/Std/Internal/Http/Data/Headers/Name.lean

@@ -8,6 +8,8 @@ module
 prelude
 public import Init.Data.ToString
 public import Std.Internal.Http.Internal
+import Init.Data.String.Search
+import Init.Data.String.Iter
 
 public section
 
@@ -107,10 +109,10 @@ but since HTTP header names are case-insensitive, this always uses simple capita
 -/
 @[inline]
 def toCanonical (name : Name) : String :=
-  let it := name.value.splitOn "-"
-    |>.map (·.capitalize)
+  let it := name.value.split '-'
+    |>.map (·.copy.capitalize)
 
-  String.intercalate "-" it
+  it.intercalateString "-"
 
 /--
 Performs a case-insensitive comparison between a `Name` and a `String`. Returns `true` if they match.

src/Std/Internal/Http/Data/URI/Basic.lean

@@ -10,6 +10,7 @@ import Init.Data.ToString
 public import Std.Net
 public import Std.Internal.Http.Internal
 public import Std.Internal.Http.Data.URI.Encoding
+public import Init.Data.String.Search
 
 public section
 
@@ -164,8 +165,8 @@ Proposition that asserts `s` is a valid dot-separated domain name.
 Each label must satisfy `IsValidDomainLabel`, and the full name must be at most 255 characters.
 -/
 abbrev IsValidDomainName (s : String) : Prop :=
-  let labels := s.splitOn "."
-  ¬labels.isEmpty ∧ labels.all isValidDomainLabel ∧ s.length ≤ 255
+  let labels := s.split '.'
+  ¬labels.isEmpty ∧ labels.all (fun s => isValidDomainLabel s.copy) ∧ s.length ≤ 255
 
 /--
 A domain name represented as a validated, lowercase-normalized string.

src/Std/Internal/Http/Data/URI/Encoding.lean

@@ -12,7 +12,7 @@ import Init.Data.SInt.Lemmas
 import Init.Data.UInt.Lemmas
 import Init.Data.UInt.Bitwise
 import Init.Data.Array.Lemmas
-public import Init.Data.String
+public import Init.Data.String.Basic
 public import Std.Internal.Http.Internal.Char
 
 public section

src/Std/Internal/Http/Data/URI/Parser.lean

@@ -7,11 +7,12 @@ module
 
 prelude
 import Init.While
-public import Init.Data.String
+public import Init.Data.String.Basic
 public import Std.Internal.Parsec
 public import Std.Internal.Parsec.ByteArray
 public import Std.Internal.Http.Data.URI.Basic
 public import Std.Internal.Http.Data.URI.Config
+import Init.Data.String.Search
 
 public section
 
@@ -51,13 +52,13 @@ private def parseScheme (config : URI.Config) : Parser URI.Scheme := do
   if config.maxSchemeLength = 0 then
     fail "scheme length limit is 0 (no scheme allowed)"
 
-  let first ← takeWhileUpTo1 isAlphaByte 1
-  let rest ← takeWhileUpTo
+  let first : UInt8 ← satisfy (fun b : UInt8 => Internal.Char.isAlphaByte b)
+  let rest ← takeWhileAtMost
     (fun c =>
       isAlphaNum c ∨
       c = '+'.toUInt8 ∨ c = '-'.toUInt8 ∨ c = '.'.toUInt8)
     (config.maxSchemeLength - 1)
-  let schemeBytes := first.toByteArray ++ rest.toByteArray
+  let schemeBytes := ByteArray.empty.push first ++ rest.toByteArray
   let str := String.fromUTF8! schemeBytes |>.toLower
 
   if h : URI.IsValidScheme str then
@@ -67,7 +68,7 @@ private def parseScheme (config : URI.Config) : Parser URI.Scheme := do
 
 -- port = 1*DIGIT
 private def parsePortNumber : Parser UInt16 := do
-  let portBytes ← takeWhileUpTo1 isDigitByte 5
+  let portBytes ← takeWhileAtMost isDigitByte 5
 
   let portStr := String.fromUTF8! portBytes.toByteArray
 
@@ -81,7 +82,7 @@ private def parsePortNumber : Parser UInt16 := do
 
 -- userinfo = *( unreserved / pct-encoded / sub-delims / ":" )
 private def parseUserInfo (config : URI.Config) : Parser URI.UserInfo := do
-  let userBytesName ← takeWhileUpTo
+  let userBytesName ← takeWhileAtMost
     (fun x =>
       x ≠ ':'.toUInt8 ∧
       (isUserInfoChar x ∨ x = '%'.toUInt8))
@@ -93,7 +94,7 @@ private def parseUserInfo (config : URI.Config) : Parser URI.UserInfo := do
   let userPassEncoded ← if ← peekIs (· == ':'.toUInt8) then
       skip
 
-      let userBytesPass ← takeWhileUpTo
+      let userBytesPass ← takeWhileAtMost
         (fun x => isUserInfoChar x ∨ x = '%'.toUInt8)
         config.maxUserInfoLength
 
@@ -112,7 +113,7 @@ private def parseUserInfo (config : URI.Config) : Parser URI.UserInfo := do
 private def parseIPv6 : Parser Net.IPv6Addr := do
   skipByte '['.toUInt8
 
-  let result ← takeWhileUpTo1
+  let result ← takeWhile1AtMost
     (fun x => x = ':'.toUInt8 ∨ x = '.'.toUInt8 ∨ isHexDigitByte x)
     256
 
@@ -126,7 +127,7 @@ private def parseIPv6 : Parser Net.IPv6Addr := do
 
 -- IPv4address = dec-octet "." dec-octet "." dec-octet "." dec-octet
 private def parseIPv4 : Parser Net.IPv4Addr := do
-  let result ← takeWhileUpTo1
+  let result ← takeWhile1AtMost
     (fun x => x = '.'.toUInt8 ∨ isDigitByte x)
     256
 
@@ -147,8 +148,8 @@ private def parseHost (config : URI.Config) : Parser URI.Host := do
       if let some ipv4 ← tryOpt parseIPv4 then
         return .ipv4 ipv4
 
-    -- We intentionally parse DNS names here (not full RFC 3986 reg-name).
-    let some str := String.fromUTF8? (← takeWhileUpTo1
+    -- It needs to be a legal DNS label, so it differs from reg-name.
+    let some str := String.fromUTF8? (← takeWhile1AtMost
       (fun x => isAlphaNum x ∨ x = '-'.toUInt8 ∨ x = '.'.toUInt8)
       config.maxHostLength).toByteArray
       | fail s!"invalid host"
@@ -186,7 +187,7 @@ private def parseAuthority (config : URI.Config) : Parser URI.Authority := do
 
 -- segment = *pchar
 private def parseSegment (config : URI.Config) : Parser ByteSlice := do
-  takeWhileUpTo (fun c => isPChar c ∨ c = '%'.toUInt8) config.maxSegmentLength
+  takeWhileAtMost (fun c => isPChar c ∨ c = '%'.toUInt8) config.maxSegmentLength
 
 /-
 path = path-abempty ; begins with "/" or is empty
@@ -271,7 +272,7 @@ def parsePath (config : URI.Config) (forceAbsolute : Bool) (allowEmpty : Bool) :
 -- query = *( pchar / "/" / "?" )
 private def parseQuery (config : URI.Config) : Parser URI.Query := do
   let queryBytes ←
-    takeWhileUpTo (fun c => isQueryChar c ∨ c = '%'.toUInt8) config.maxQueryLength
+    takeWhileAtMost (fun c => isQueryChar c ∨ c = '%'.toUInt8) config.maxQueryLength
 
   let some queryStr := String.fromUTF8? queryBytes.toByteArray
     | fail "invalid query string"
@@ -279,13 +280,13 @@ private def parseQuery (config : URI.Config) : Parser URI.Query := do
   if queryStr.isEmpty then
     return URI.Query.empty
 
-  let rawPairs := queryStr.splitOn "&"
+  let rawPairs := queryStr.split '&'
 
   if rawPairs.length > config.maxQueryParams then
     fail s!"too many query parameters (limit: {config.maxQueryParams})"
 
-  let pairs : Option URI.Query := rawPairs.foldlM (init := URI.Query.empty) fun acc pair => do
-    match pair.splitOn "=" with
+  let pairs : Option URI.Query := rawPairs.foldM (init := URI.Query.empty) fun acc pair => do
+    match pair.split '=' |>.toStringList with
     | [key] =>
       let key ← URI.EncodedQueryParam.fromString? key
       pure (acc.insertEncoded key none)
@@ -303,7 +304,7 @@ private def parseQuery (config : URI.Config) : Parser URI.Query := do
 --  fragment = *( pchar / "/" / "?" )
 private def parseFragment (config : URI.Config) : Parser URI.EncodedFragment := do
   let fragmentBytes ←
-    takeWhileUpTo (fun c => isFragmentChar c ∨ c = '%'.toUInt8) config.maxFragmentLength
+    takeWhileAtMost (fun c => isFragmentChar c ∨ c = '%'.toUInt8) config.maxFragmentLength
 
   let some fragmentStr := URI.EncodedFragment.ofByteArray? fragmentBytes.toByteArray
     | fail "invalid percent encoding in fragment"

src/Std/Internal/Http/Data/Version.lean

@@ -7,7 +7,7 @@ module
 
 prelude
 import Init.Data.ToString
-public import Init.Data.String
+public import Init.Data.String.Basic
 
 public section
 

src/Std/Internal/Http/Internal/Char.lean

@@ -7,7 +7,7 @@ module
 
 prelude
 public import Init.Data.Char
-public import Init.Data.String
+public import Init.Data.String.Basic
 public import Init.Data.Int
 public import Init.Grind
 

src/Std/Internal/Http/Internal/ChunkedBuffer.lean

@@ -8,7 +8,7 @@ module
 prelude
 import Init.Data.ToString
 import Init.Data.Array.Lemmas
-public import Init.Data.String
+public import Init.Data.String.Basic
 public import Init.Data.ByteArray
 
 public section

src/Std/Internal/Http/Internal/LowerCase.lean

@@ -9,7 +9,8 @@ prelude
 import Init.Grind
 import Init.Data.Int.OfNat
 import Init.Data.UInt.Lemmas
-public import Init.Data.String
+public import Init.Data.String.Modify
+import Init.Data.String.Lemmas.Modify
 
 @[expose]
 public section

src/Std/Internal/Http/Internal/String.lean

@@ -7,7 +7,7 @@ module
 
 prelude
 import Init.Grind
-public import Init.Data.String
+public import Init.Data.String.TakeDrop
 public import Std.Internal.Http.Internal.Char
 
 public section

src/Std/Internal/Http/Protocol/H1/Config.lean

@@ -0,0 +1,134 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+module
+
+prelude
+public import Std.Internal.Http.Data
+public import Std.Internal.Http.Internal
+
+public section
+
+/-!
+# HTTP/1.1 Configuration
+
+This module defines the configuration options for HTTP/1.1 protocol processing,
+including connection limits, header constraints, and various size limits.
+-/
+
+namespace Std.Http.Protocol.H1
+
+set_option linter.all true
+
+open Std Internal Parsec ByteArray
+open Internal
+
+/--
+Connection limits and parser bounds configuration.
+-/
+structure Config where
+  /--
+  Maximum number of requests (server) or responses (client) per connection.
+  -/
+  maxMessages : Nat := 100
+
+  /--
+  Maximum number of headers allowed per message.
+  -/
+  maxHeaders : Nat := 100
+
+  /--
+  Maximum aggregate byte size of all header field lines in a single message
+  (name + value bytes plus 4 bytes per line for `: ` and `\r\n`). Default: 64 KiB.
+  -/
+  maxHeaderBytes : Nat := 65536
+
+  /--
+  Whether to enable keep-alive connections by default.
+  -/
+  enableKeepAlive : Bool := true
+
+  /--
+  The `Server` header value injected into outgoing responses (receiving mode) or the
+  `User-Agent` header value injected into outgoing requests (sending mode).
+  `none` suppresses the header entirely.
+  -/
+  agentName : Option Header.Value := none
+
+  /--
+  Maximum length of request URI (default: 8192 bytes).
+  -/
+  maxUriLength : Nat := 8192
+
+  /--
+  Maximum number of bytes consumed while parsing request/status start-lines (default: 8192 bytes).
+  -/
+  maxStartLineLength : Nat := 8192
+
+  /--
+  Maximum length of header field name (default: 256 bytes).
+  -/
+  maxHeaderNameLength : Nat := 256
+
+  /--
+  Maximum length of header field value (default: 8192 bytes).
+  -/
+  maxHeaderValueLength : Nat := 8192
+
+  /--
+  Maximum number of spaces in delimiter sequences (default: 16).
+  -/
+  maxSpaceSequence : Nat := 16
+
+  /--
+  Maximum number of leading empty lines (bare CRLF) to skip before a request-line
+  (RFC 9112 §2.2 robustness). Default: 8.
+  -/
+  maxLeadingEmptyLines : Nat := 8
+
+  /--
+  Maximum number of extensions on a single chunk-size line (default: 16).
+  -/
+  maxChunkExtensions : Nat := 16
+
+  /--
+  Maximum length of chunk extension name (default: 256 bytes).
+  -/
+  maxChunkExtNameLength : Nat := 256
+
+  /--
+  Maximum length of chunk extension value (default: 256 bytes).
+  -/
+  maxChunkExtValueLength : Nat := 256
+
+  /--
+  Maximum number of bytes consumed while parsing one chunk-size line with extensions (default: 8192 bytes).
+  -/
+  maxChunkLineLength : Nat := 8192
+
+  /--
+  Maximum allowed chunk payload size in bytes (default: 8 MiB).
+  -/
+  maxChunkSize : Nat := 8 * 1024 * 1024
+
+  /--
+  Maximum allowed total body size per message in bytes (default: 64 MiB).
+  This limit applies across all body framing modes. For chunked transfer encoding,
+  chunk-size lines (including extensions) and the trailer section also count toward
+  this limit, so the total wire bytes consumed by the body cannot exceed this value.
+  -/
+  maxBodySize : Nat := 64 * 1024 * 1024
+
+  /--
+  Maximum length of reason phrase (default: 512 bytes).
+  -/
+  maxReasonPhraseLength : Nat := 512
+
+  /--
+  Maximum number of trailer headers (default: 20).
+  -/
+  maxTrailerHeaders : Nat := 20
+
+end Std.Http.Protocol.H1

src/Std/Internal/Http/Protocol/H1/Error.lean

@@ -0,0 +1,110 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+module
+
+prelude
+public import Std.Time
+public import Std.Internal.Http.Data
+public import Std.Internal.Http.Internal
+public import Std.Internal.Http.Protocol.H1.Parser
+public import Std.Internal.Http.Protocol.H1.Config
+public import Std.Internal.Http.Protocol.H1.Message
+
+public section
+
+/-!
+# HTTP/1.1 Errors
+
+This module defines the error types for HTTP/1.1 protocol processing,
+including parsing errors, timeout errors, and connection errors.
+-/
+
+namespace Std.Http.Protocol.H1
+
+set_option linter.all true
+
+/--
+Specific HTTP processing errors with detailed information.
+-/
+inductive Error
+  /--
+  Malformed start line (request-line or status-line).
+  -/
+  | invalidStatusLine
+
+  /--
+  Invalid or malformed header.
+  -/
+  | invalidHeader
+
+  /--
+  Request timeout occurred.
+  -/
+  | timeout
+
+  /--
+  Request entity too large.
+  -/
+  | entityTooLarge
+
+  /--
+  Request URI is too long.
+  -/
+  | uriTooLong
+
+  /--
+  Unsupported HTTP version.
+  -/
+  | unsupportedVersion
+
+  /--
+  Invalid chunk encoding.
+  -/
+  | invalidChunk
+
+  /--
+  Connection closed.
+  -/
+  | connectionClosed
+
+  /--
+  Bad request or response message.
+  -/
+  | badMessage
+
+  /--
+  The number of header fields in the message exceeds the configured limit.
+  Maps to HTTP 431 Request Header Fields Too Large.
+  -/
+  | tooManyHeaders
+
+  /--
+  The aggregate byte size of all header fields exceeds the configured limit.
+  Maps to HTTP 431 Request Header Fields Too Large.
+  -/
+  | headersTooLarge
+
+  /--
+  Generic error with message.
+  -/
+  | other (message : String)
+deriving Repr, BEq
+
+instance : ToString Error where
+  toString
+  | .invalidStatusLine => "Invalid status line"
+  | .invalidHeader => "Invalid header"
+  | .timeout => "Timeout"
+  | .entityTooLarge => "Entity too large"
+  | .uriTooLong => "URI too long"
+  | .unsupportedVersion => "Unsupported version"
+  | .invalidChunk => "Invalid chunk"
+  | .connectionClosed => "Connection closed"
+  | .badMessage => "Bad message"
+  | .tooManyHeaders => "Too many headers"
+  | .headersTooLarge => "Headers too large"
+  | .other msg => s!"Other error: {msg}"
+

src/Std/Internal/Http/Protocol/H1/Event.lean

@@ -0,0 +1,73 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+module
+
+prelude
+public import Std.Time
+public import Std.Internal.Http.Data
+public import Std.Internal.Http.Internal
+public import Std.Internal.Http.Protocol.H1.Parser
+public import Std.Internal.Http.Protocol.H1.Config
+public import Std.Internal.Http.Protocol.H1.Message
+public import Std.Internal.Http.Protocol.H1.Error
+
+public section
+
+/-!
+# HTTP/1.1 Events
+
+This module defines the events that can occur during HTTP/1.1 message processing,
+including header completion and control/error signals.
+-/
+
+namespace Std.Http.Protocol.H1
+
+set_option linter.all true
+
+/--
+Events emitted during HTTP message processing.
+-/
+inductive Event (dir : Direction)
+  /--
+  Indicates that all headers have been successfully parsed.
+  -/
+  | endHeaders (head : Message.Head dir)
+
+  /--
+  Signals that additional input data is required to continue processing.
+  -/
+  | needMoreData (size : Option Nat)
+
+  /--
+  Indicates a failure during parsing or processing.
+  -/
+  | failed (err : Error)
+
+  /--
+  Requests that the connection be closed.
+  -/
+  | close
+
+  /--
+  The body should be closed.
+  -/
+  | closeBody
+
+  /--
+  Indicates that a response is required.
+  -/
+  | needAnswer
+
+  /--
+  Indicates readiness to process the next message.
+  -/
+  | next
+
+  /--
+  Signals that an `Expect: 100-continue` decision is pending.
+  -/
+  | «continue»
+deriving Inhabited, Repr

src/Std/Internal/Http/Protocol/H1/Message.lean

@@ -0,0 +1,139 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+module
+
+prelude
+import Init.Data.Array
+public import Std.Internal.Http.Data
+
+public section
+
+/-!
+# Message
+
+This module provides types and operations for HTTP/1.1 messages, centered around the `Direction`
+type which models the server's role in message exchange: `Direction.receiving` for parsing incoming
+requests from clients, and `Direction.sending` for generating outgoing responses to clients.
+The `Message.Head` type is parameterized by `Direction` and resolves to `Request.Head` or
+`Response.Head` accordingly, enabling generic code that works uniformly across both phases
+while exposing common operations such as headers, version, and `shouldKeepAlive`
+-/
+
+namespace Std.Http.Protocol.H1
+
+set_option linter.all true
+
+/--
+Direction of message flow from the server's perspective.
+-/
+inductive Direction
+  /--
+  Receiving and parsing incoming requests from clients.
+  -/
+  | receiving
+
+  /--
+  Client perspective: writing outgoing requests and reading incoming responses.
+  -/
+  | sending
+deriving BEq
+
+/--
+Inverts the message direction.
+-/
+@[expose]
+abbrev Direction.swap : Direction → Direction
+  | .receiving => .sending
+  | .sending => .receiving
+
+/--
+Gets the message head type based on direction.
+-/
+@[expose]
+def Message.Head : Direction → Type
+  | .receiving => Request.Head
+  | .sending => Response.Head
+
+/--
+Gets the headers of a `Message`.
+-/
+def Message.Head.headers (m : Message.Head dir) : Headers :=
+  match dir with
+  | .receiving => Request.Head.headers m
+  | .sending => Response.Head.headers m
+
+/--
+Gets the version of a `Message`.
+-/
+def Message.Head.version (m : Message.Head dir) : Version :=
+  match dir with
+  | .receiving => Request.Head.version m
+  | .sending => Response.Head.version m
+
+/--
+Determines the message body size based on the `Content-Length` header and the `Transfer-Encoding` (chunked) flag.
+-/
+def Message.Head.getSize (message : Message.Head dir) (allowEOFBody : Bool) : Option Body.Length :=
+  let contentLength := message.headers.getAll? .contentLength
+
+  match message.headers.getAll? .transferEncoding with
+  | none =>
+      match contentLength with
+      | some #[cl] => .fixed <$> cl.value.toNat?
+      | some _ => none -- To avoid request smuggling with malformed/multiple content-length headers.
+      | none => if allowEOFBody then some (.fixed 0) else none
+
+  -- Single transfer-encoding header.
+  | some #[header] =>
+    let te := Header.TransferEncoding.parse header
+
+    match Header.TransferEncoding.isChunked <$> te, contentLength with
+    | some true, none =>
+        -- HTTP/1.0 does not define chunked transfer encoding (RFC 2068 §19.4.6).
+        -- A server MUST NOT use chunked with an HTTP/1.0 peer; likewise, an
+        -- HTTP/1.0 request carrying Transfer-Encoding: chunked is malformed.
+        if message.version == .v10 then none else some .chunked
+    | _, _ => none -- To avoid request smuggling when TE and CL are mixed.
+
+  -- We disallow multiple transfer-encoding headers.
+  | some _ => none
+/--
+Checks whether the message indicates that the connection should be kept alive.
+-/
+def Message.Head.shouldKeepAlive (message : Message.Head dir) : Bool :=
+  let tokens? : Option (Array String) :=
+    match message.headers.getAll? .connection with
+    | none => some #[]
+    | some values =>
+        values.foldl (fun acc raw => do
+          let acc ← acc
+          let parsed ← Header.Connection.parse raw
+          pure (acc ++ parsed.tokens)
+        ) (some #[])
+
+  match tokens? with
+  | none =>false
+  | some tokens =>
+      if message.version == .v11 then
+        !tokens.any (· == "close")
+      else
+        tokens.any (· == "keep-alive")
+
+instance : Repr (Message.Head dir) :=
+  match dir with
+  | .receiving => inferInstanceAs (Repr Request.Head)
+  | .sending => inferInstanceAs (Repr Response.Head)
+
+instance : Internal.Encode .v11 (Message.Head dir) :=
+  match dir with
+  | .receiving => inferInstanceAs (Internal.Encode .v11 Request.Head)
+  | .sending => inferInstanceAs (Internal.Encode .v11 Response.Head)
+
+instance : EmptyCollection (Message.Head dir) where
+  emptyCollection :=
+    match dir with
+    | .receiving => { method := .get, version := .v11 }
+    | .sending => {}

src/Std/Internal/Http/Protocol/H1/Parser.lean

@@ -0,0 +1,548 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+module
+
+prelude
+public import Std.Internal.Parsec
+public import Std.Internal.Http.Data
+public import Std.Internal.Parsec.ByteArray
+public import Std.Internal.Http.Protocol.H1.Config
+
+/-!
+This module defines parsers for HTTP/1.1 request and response lines, headers, and body framing. The
+reference used is https://httpwg.org/specs/rfc9112.html.
+-/
+
+namespace Std.Http.Protocol.H1
+
+open Std Internal Parsec ByteArray Internal Internal.Char
+
+set_option linter.all true
+
+/--
+Checks if a byte may appear inside a field value.
+
+This parser enforces strict ASCII-only field values and allows only `field-content`
+(`HTAB / SP / VCHAR`).
+-/
+@[inline]
+def isFieldVChar (c : UInt8) : Bool :=
+  fieldContent (Char.ofUInt8 c)
+
+/--
+Checks if a byte may appear unescaped inside a quoted-string value.
+
+Allows `HTAB / SP / %x21 / %x23-5B / %x5D-7E` (strict ASCII-only; no obs-text).
+-/
+@[inline]
+def isQdText (c : UInt8) : Bool :=
+  qdtext (Char.ofUInt8 c)
+
+/--
+Checks if a byte is optional whitespace (`OWS = SP / HTAB`, RFC 9110 §5.6.3).
+-/
+@[inline]
+def isOwsByte (c : UInt8) : Bool :=
+  ows (Char.ofUInt8 c)
+
+-- Parser blocks
+
+/--
+Repeatedly applies `parser` until it returns `none` or the `maxCount` limit is
+exceeded. Returns the collected results as an array.
+-/
+partial def manyItems {α : Type} (parser : Parser (Option α)) (maxCount : Nat) : Parser (Array α) := do
+  let rec go (acc : Array α) : Parser (Array α) := do
+    let step ← optional <| attempt do
+      match ← parser with
+      | none => fail "end of items"
+      | some x => return x
+
+    match step with
+    | none =>
+      return acc
+    | some x =>
+      let acc := acc.push x
+
+      if acc.size > maxCount then
+        fail s!"too many items: {acc.size} > {maxCount}"
+
+      go acc
+  go #[]
+
+
+/--
+Lifts an `Option` into the parser monad, failing with a generic message if the value is `none`.
+-/
+def liftOption (x : Option α) : Parser α :=
+  if let some res := x then
+    return res
+  else
+    fail "expected value but got none"
+
+/--
+Parses an HTTP token (RFC 9110 §5.6.2): one or more token characters, up to `limit` bytes.
+Fails if the input starts with a non-token character or is empty.
+-/
+@[inline]
+def parseToken (limit : Nat) : Parser ByteSlice :=
+  takeWhileUpTo1 (fun c => tchar (Char.ofUInt8 c)) limit
+
+/--
+Parses a line terminator.
+-/
+@[inline]
+def crlf : Parser Unit := do
+  skipBytes "\r\n".toUTF8
+
+/--
+Consumes and ignores empty lines (`CRLF`) that appear before a request-line.
+
+https://httpwg.org/specs/rfc9112.html#rfc.section.2.2:
+
+"In the interest of robustness, a server that is expecting to receive and parse a request-line SHOULD
+ignore at least one empty line (CRLF) received prior to the request-line."
+-/
+def skipLeadingRequestEmptyLines (limits : H1.Config) : Parser Unit := do
+  let mut count := 0
+  while (← peekWhen? (· == '\r'.toUInt8)).isSome do
+    if count >= limits.maxLeadingEmptyLines then
+      fail "too many leading empty lines"
+    crlf
+    count := count + 1
+
+/--
+Parses a single space (SP, 0x20).
+-/
+@[inline]
+def sp : Parser Unit :=
+  skipByte ' '.toUInt8
+
+/--
+Parses optional whitespace (OWS = *(SP / HTAB), RFC 9110 §5.6.3), bounded by
+`limits.maxSpaceSequence`. Fails if more whitespace follows the limit, so oversized
+padding is rejected rather than silently truncated.
+-/
+@[inline]
+def ows (limits : H1.Config) : Parser Unit := do
+  discard <| takeWhileUpTo isOwsByte limits.maxSpaceSequence
+
+  if (← peekWhen? isOwsByte) |>.isSome then
+    fail "invalid space sequence"
+  else
+    pure ()
+
+/--
+Parses a single ASCII hex digit and returns its numeric value (`0`–`15`).
+-/
+def hexDigit : Parser UInt8 := do
+  let b ← any
+  if isHexDigitByte b then
+    if b ≥ '0'.toUInt8 && b ≤ '9'.toUInt8 then return b - '0'.toUInt8
+    else if b ≥ 'A'.toUInt8 && b ≤ 'F'.toUInt8 then return b - 'A'.toUInt8 + 10
+    else return b - 'a'.toUInt8 + 10
+  else fail s!"invalid hex digit {Char.ofUInt8 b |>.quote}"
+
+/--
+Parses a hexadecimal integer (one or more hex digits, up to 16 digits).
+Used for chunk-size lines in chunked transfer encoding.
+-/
+partial def hex : Parser Nat := do
+  let rec go (acc : Nat) (count : Nat) : Parser Nat := do
+    match ← optional (attempt hexDigit) with
+    | some d =>
+        if count + 1 > 16 then
+          fail "chunk size too large"
+        else
+          go (acc * 16 + d.toNat) (count + 1)
+    | none =>
+        if count = 0 then
+          -- Preserve EOF as incremental chunk-size parsing can request more data.
+          -- For non-EOF invalid bytes, keep the specific parse failure.
+          let _ ← peek!
+          fail "expected hex digit"
+        else
+          return acc
+  go 0 0
+
+-- Actual parsers
+
+/--
+Parses `HTTP-version = HTTP-name "/" DIGIT "." DIGIT` and returns the major and
+minor version numbers as a pair.
+-/
+def parseHttpVersionNumber : Parser (Nat × Nat) := do
+  skipBytes "HTTP/".toUTF8
+  let major ← digit
+  skipByte '.'.toUInt8
+  let minor ← digit
+  pure ((major.toNat - 48), (minor.toNat - 48))
+
+/--
+Parses an HTTP version string and returns the corresponding `Version` value.
+Fails if the version is not recognized by `Version.ofNumber?`.
+-/
+def parseHttpVersion : Parser Version := do
+  let (major, minor) ← parseHttpVersionNumber
+  liftOption <| Version.ofNumber? major minor
+
+/-
+method         = token
+
+Every branch is wrapped in `attempt` so that `<|>` always backtracks on
+failure, even after consuming bytes. This is strictly necessary only for the
+P-group (POST / PUT / PATCH) which share a common first byte, but wrapping
+all alternatives keeps the parser defensively correct if new methods are
+added in the future.
+-/
+def parseMethod : Parser Method :=
+  (attempt <| skipBytes "GET".toUTF8 <&> fun _ => Method.get)
+  <|> (attempt <| skipBytes "HEAD".toUTF8 <&> fun _ => Method.head)
+  <|> (attempt <| skipBytes "DELETE".toUTF8 <&> fun _ => Method.delete)
+  <|> (attempt <| skipBytes "TRACE".toUTF8 <&> fun _ => Method.trace)
+  <|> (attempt <| skipBytes "ACL".toUTF8 <&> fun _ => Method.acl)
+  <|> (attempt <| skipBytes "QUERY".toUTF8 <&> fun _ => Method.query)
+  <|> (attempt <| skipBytes "SEARCH".toUTF8 <&> fun _ => Method.search)
+  <|> (attempt <| skipBytes "BASELINE-CONTROL".toUTF8 <&> fun _ => Method.baselineControl)
+  <|> (attempt <| skipBytes "BIND".toUTF8 <&> fun _ => Method.bind)
+  <|> (attempt <| skipBytes "CONNECT".toUTF8 <&> fun _ => Method.connect)
+  <|> (attempt <| skipBytes "CHECKIN".toUTF8 <&> fun _ => Method.checkin)
+  <|> (attempt <| skipBytes "CHECKOUT".toUTF8 <&> fun _ => Method.checkout)
+  <|> (attempt <| skipBytes "COPY".toUTF8 <&> fun _ => Method.copy)
+  <|> (attempt <| skipBytes "LABEL".toUTF8 <&> fun _ => Method.label)
+  <|> (attempt <| skipBytes "LINK".toUTF8 <&> fun _ => Method.link)
+  <|> (attempt <| skipBytes "LOCK".toUTF8 <&> fun _ => Method.lock)
+  <|> (attempt <| skipBytes "MERGE".toUTF8 <&> fun _ => Method.merge)
+  <|> (attempt <| skipBytes "MKACTIVITY".toUTF8 <&> fun _ => Method.mkactivity)
+  <|> (attempt <| skipBytes "MKCALENDAR".toUTF8 <&> fun _ => Method.mkcalendar)
+  <|> (attempt <| skipBytes "MKCOL".toUTF8 <&> fun _ => Method.mkcol)
+  <|> (attempt <| skipBytes "MKREDIRECTREF".toUTF8 <&> fun _ => Method.mkredirectref)
+  <|> (attempt <| skipBytes "MKWORKSPACE".toUTF8 <&> fun _ => Method.mkworkspace)
+  <|> (attempt <| skipBytes "MOVE".toUTF8 <&> fun _ => Method.move)
+  <|> (attempt <| skipBytes "OPTIONS".toUTF8 <&> fun _ => Method.options)
+  <|> (attempt <| skipBytes "ORDERPATCH".toUTF8 <&> fun _ => Method.orderpatch)
+  <|> (attempt <| skipBytes "POST".toUTF8 <&> fun _ => Method.post)
+  <|> (attempt <| skipBytes "PUT".toUTF8 <&> fun _ => Method.put)
+  <|> (attempt <| skipBytes "PATCH".toUTF8 <&> fun _ => Method.patch)
+  <|> (attempt <| skipBytes "PRI".toUTF8 <&> fun _ => Method.pri)
+  <|> (attempt <| skipBytes "PROPFIND".toUTF8 <&> fun _ => Method.propfind)
+  <|> (attempt <| skipBytes "PROPPATCH".toUTF8 <&> fun _ => Method.proppatch)
+  <|> (attempt <| skipBytes "REBIND".toUTF8 <&> fun _ => Method.rebind)
+  <|> (attempt <| skipBytes "REPORT".toUTF8 <&> fun _ => Method.report)
+  <|> (attempt <| skipBytes "UNBIND".toUTF8 <&> fun _ => Method.unbind)
+  <|> (attempt <| skipBytes "UNCHECKOUT".toUTF8 <&> fun _ => Method.uncheckout)
+  <|> (attempt <| skipBytes "UNLINK".toUTF8 <&> fun _ => Method.unlink)
+  <|> (attempt <| skipBytes "UNLOCK".toUTF8 <&> fun _ => Method.unlock)
+  <|> (attempt <| skipBytes "UPDATEREDIRECTREF".toUTF8 <&> fun _ => Method.updateredirectref)
+  <|> (attempt <| skipBytes "UPDATE".toUTF8 <&> fun _ => Method.update)
+  <|> (attempt <| skipBytes "VERSION-CONTROL".toUTF8 <&> fun _ => Method.versionControl)
+  <|> (parseToken 64 *> fail "unrecognized method")
+
+/--
+Parses a request-target URI, up to `limits.maxUriLength` bytes.
+Fails with `"uri too long"` if the target exceeds the configured limit.
+-/
+def parseURI (limits : H1.Config) : Parser ByteArray := do
+  let uri ← takeUntilUpTo (· == ' '.toUInt8) limits.maxUriLength
+  if uri.size == limits.maxUriLength then
+    if (← peekWhen? (· != ' '.toUInt8)) |>.isSome then
+      fail "uri too long"
+
+  return uri.toByteArray
+
+/--
+Shared core for request-line parsing: parses `request-target SP HTTP-version CRLF`
+and returns the `RequestTarget` together with the raw major/minor version numbers.
+
+Both `parseRequestLine` and `parseRequestLineRawVersion` call this after consuming
+the method token, keeping URI validation and version parsing in one place.
+-/
+private def parseRequestLineBody (limits : H1.Config) : Parser (RequestTarget × Nat × Nat) := do
+  let rawUri ← parseURI limits <* sp
+  let uri ← match (Std.Http.URI.Parser.parseRequestTarget <* eof).run rawUri with
+  | .ok res => pure res
+  | .error res => fail res
+  let versionPair ← parseHttpVersionNumber <* crlf
+  return (uri, versionPair)
+
+/--
+Parses a request line and returns a fully-typed `Request.Head`.
+`request-line = method SP request-target SP HTTP-version`
+-/
+public def parseRequestLine (limits : H1.Config) : Parser Request.Head := do
+  skipLeadingRequestEmptyLines limits
+  let method ← parseMethod <* sp
+  let (uri, (major, minor)) ← parseRequestLineBody limits
+  if major == 1 ∧ minor == 1 then
+    return ⟨method, .v11, uri, .empty⟩
+  else if major == 1 ∧ minor == 0 then
+    return ⟨method, .v10, uri, .empty⟩
+  else
+    fail "unsupported HTTP version"
+
+/--
+Parses a request line and returns the recognized HTTP method and version when available.
+
+request-line = method SP request-target SP HTTP-version
+-/
+public def parseRequestLineRawVersion (limits : H1.Config) : Parser (Method × RequestTarget × Option Version) := do
+  skipLeadingRequestEmptyLines limits
+  let method ← parseMethod <* sp
+  let (uri, (major, minor)) ← parseRequestLineBody limits
+  return (method, uri, Version.ofNumber? major minor)
+
+/--
+Parses a single header field line.
+
+`field-line = field-name ":" OWS field-value OWS`
+-/
+def parseFieldLine (limits : H1.Config) : Parser (String × String) := do
+  let name ← parseToken limits.maxHeaderNameLength
+  let value ← skipByte ':'.toUInt8 *> ows limits *> optional (takeWhileUpTo isFieldVChar limits.maxHeaderValueLength) <* ows limits
+
+  let name ← liftOption <| String.fromUTF8? name.toByteArray
+  let value ← liftOption <| String.fromUTF8? <| value.map (·.toByteArray) |>.getD .empty
+  let value := value.trimAsciiEnd.toString
+
+  return (name, value)
+
+/--
+Parses a single header field line, or returns `none` when it sees the blank line that
+terminates the header section.
+
+```
+field-line = field-name ":" OWS field-value OWS CRLF
+```
+-/
+public def parseSingleHeader (limits : H1.Config) : Parser (Option (String × String)) := do
+  let next ← peek?
+  if next == some '\r'.toUInt8 ∨ next == some '\n'.toUInt8 then
+    crlf
+    pure none
+  else
+    some <$> (parseFieldLine limits <* crlf)
+
+/--
+Parses a backslash-escaped character inside a quoted-string.
+
+`quoted-pair = "\" ( HTAB / SP / VCHAR )` — strict ASCII-only (no obs-text).
+-/
+def parseQuotedPair : Parser UInt8 := do
+  skipByte '\\'.toUInt8
+  let b ← any
+
+  if quotedPairChar (Char.ofUInt8 b) then
+    return b
+  else
+    fail s!"invalid quoted-pair byte: {Char.ofUInt8 b |>.quote}"
+
+/--
+Parses a quoted-string value, unescaping quoted-pairs.
+
+`quoted-string = DQUOTE *( qdtext / quoted-pair ) DQUOTE`
+-/
+partial def parseQuotedString (maxLength : Nat) : Parser String := do
+  skipByte '"'.toUInt8
+
+  let rec loop (buf : ByteArray) (length : Nat) : Parser ByteArray := do
+    let b ← any
+
+    if b == '"'.toUInt8 then
+      return buf
+    else if b == '\\'.toUInt8 then
+      let next ← any
+      if quotedPairChar (Char.ofUInt8 next)
+        then
+          let length := length + 1
+          if length > maxLength then
+            fail "quoted-string too long"
+          else
+            loop (buf.push next) length
+        else fail s!"invalid quoted-pair byte: {Char.ofUInt8 next |>.quote}"
+    else if isQdText b then
+      let length := length + 1
+      if length > maxLength then
+        fail "quoted-string too long"
+      else
+        loop (buf.push b) length
+    else
+      fail s!"invalid qdtext byte: {Char.ofUInt8 b |>.quote}"
+
+  liftOption <| String.fromUTF8? (← loop .empty 0)
+
+-- chunk-ext = *( BWS ";" BWS chunk-ext-name [ BWS "=" BWS chunk-ext-val] )
+def parseChunkExt (limits : H1.Config) : Parser (Chunk.ExtensionName × Option Chunk.ExtensionValue) := do
+  ows limits *> skipByte ';'.toUInt8 *> ows limits
+  let name ← (liftOption =<< String.fromUTF8? <$> ByteSlice.toByteArray <$> parseToken limits.maxChunkExtNameLength) <* ows limits
+
+  let some name := Chunk.ExtensionName.ofString? name
+    | fail "invalid extension name"
+
+  if (← peekWhen? (· == '='.toUInt8)) |>.isSome then
+    -- RFC 9112 §7.1.1: BWS is allowed around "=".
+    -- The `<* ows limits` after the name already consumed any trailing whitespace,
+    -- so these ows calls are no-ops in practice, but kept for explicit grammar correspondence.
+    ows limits *> skipByte '='.toUInt8 *> ows limits
+    let value ← ows limits *> (parseQuotedString limits.maxChunkExtValueLength <|> liftOption =<< (String.fromUTF8? <$> ByteSlice.toByteArray <$> parseToken limits.maxChunkExtValueLength))
+
+    let some value := Chunk.ExtensionValue.ofString? value
+      | fail "invalid extension value"
+
+    return (name, some value)
+
+  return (name, none)
+
+/--
+Parses the size and extensions of a chunk.
+-/
+public def parseChunkSize (limits : H1.Config) : Parser (Nat × Array (Chunk.ExtensionName × Option Chunk.ExtensionValue)) := do
+  let size ← hex
+  let ext ← manyItems (optional (attempt (parseChunkExt limits))) limits.maxChunkExtensions
+  crlf
+  return (size, ext)
+
+/--
+Result of parsing partial or complete information.
+-/
+public inductive TakeResult
+  | complete (data : ByteSlice)
+  | incomplete (data : ByteSlice) (remaining : Nat)
+
+/--
+Parses a single chunk in chunked transfer encoding.
+-/
+public def parseChunkPartial (limits : H1.Config) : Parser (Option (Nat × Array (Chunk.ExtensionName × Option Chunk.ExtensionValue) × ByteSlice)) := do
+  let (size, ext) ← parseChunkSize limits
+  if size == 0 then
+    return none
+  else
+    let data ← take size
+    return some ⟨size, ext, data⟩
+
+/--
+Parses fixed-size data that can be incomplete.
+-/
+public def parseFixedSizeData (size : Nat) : Parser TakeResult := fun it =>
+  if it.remainingBytes = 0 then
+    .error it .eof
+  else if it.remainingBytes < size then
+    .success (it.forward it.remainingBytes) (.incomplete it.array[it.idx...(it.idx+it.remainingBytes)] (size - it.remainingBytes))
+  else
+    .success (it.forward size) (.complete (it.array[it.idx...(it.idx+size)]))
+
+/--
+Parses fixed-size chunk data that can be incomplete.
+-/
+public def parseChunkSizedData (size : Nat) : Parser TakeResult := do
+  match ← parseFixedSizeData size with
+  | .complete data => crlf *> return .complete data
+  | .incomplete data res => return .incomplete data res
+
+/--
+Returns `true` if `name` (compared case-insensitively) is a field that MUST NOT appear in HTTP/1.1
+trailer sections per RFC 9112 §6.5. Forbidden fields are those required for message framing
+(`content-length`, `transfer-encoding`), routing (`host`), or connection management (`connection`).
+-/
+private def isForbiddenTrailerField (name : String) : Bool :=
+  let n := name.toLower
+  n == "content-length" || n == "transfer-encoding" || n == "host" ||
+  n == "connection" || n == "expect" || n == "te" ||
+  n == "authorization" || n == "max-forwards" || n == "cache-control" ||
+  n == "content-encoding" || n == "upgrade" || n == "trailer"
+
+/--
+Parses a trailer header (used after a chunked body), rejecting forbidden field names per RFC 9112
+§6.5. Fields used for message framing (`content-length`, `transfer-encoding`), routing (`host`),
+or connection management (`connection`, `te`, `upgrade`) are rejected to prevent trailer injection
+attacks where a downstream proxy might re-interpret them.
+-/
+def parseTrailerHeader (limits : H1.Config) : Parser (Option (String × String)) := do
+  let result ← parseSingleHeader limits
+  if let some (name, _) := result then
+    if isForbiddenTrailerField name then
+      fail s!"forbidden trailer field: {name}"
+  return result
+
+/--
+Parses trailer headers after a chunked body and returns them as an array of name-value pairs.
+
+This is exposed for callers that need the trailer values directly (e.g. clients). The
+internal protocol machine uses `parseLastChunkBody` instead, which discards trailer values.
+-/
+public def parseTrailers (limits : H1.Config) : Parser (Array (String × String)) := do
+  let trailers ← manyItems (parseTrailerHeader limits) limits.maxTrailerHeaders
+  crlf
+  return trailers
+
+/--
+Returns `true` if `c` is a valid reason-phrase byte (`HTAB / SP / VCHAR`, strict ASCII-only).
+-/
+@[inline]
+def isReasonPhraseByte (c : UInt8) : Bool :=
+  fieldContent (Char.ofUInt8 c)
+
+/--
+Parses a reason phrase (text after status code).
+
+Allows only `HTAB / SP / VCHAR` bytes (strict ASCII-only).
+-/
+def parseReasonPhrase (limits : H1.Config) : Parser String := do
+  let bytes ← takeWhileUpTo isReasonPhraseByte limits.maxReasonPhraseLength
+  liftOption <| String.fromUTF8? bytes.toByteArray
+
+/--
+Parses a status-code (3 decimal digits), the following reason phrase, and the
+terminating CRLF; returns a typed `Status`.
+-/
+def parseStatusCode (limits : H1.Config) : Parser Status := do
+  let d1 ← digit
+  let d2 ← digit
+  let d3 ← digit
+  let code := (d1.toNat - 48) * 100 + (d2.toNat - 48) * 10 + (d3.toNat - 48)
+  sp
+  let phrase ← parseReasonPhrase limits <* crlf
+
+  if h : IsValidReasonPhrase phrase then
+    if let some status := Status.ofCode (some ⟨phrase, h⟩) code.toUInt16 then
+      return status
+
+  fail "invalid status code"
+
+/--
+Parses a status line and returns a fully-typed `Response.Head`.
+`status-line = HTTP-version SP status-code SP [ reason-phrase ]`
+Accepts only HTTP/1.1. For parsing where the version may be unrecognized and must be
+mapped to an error event, use `parseStatusLineRawVersion`.
+-/
+public def parseStatusLine (limits : H1.Config) : Parser Response.Head := do
+  let (major, minor) ← parseHttpVersionNumber <* sp
+  let status ← parseStatusCode limits
+  if major == 1 ∧ minor == 1 then
+    return { status, version := .v11, headers := .empty }
+  else if major == 1 ∧ minor == 0 then
+    return { status, version := .v10, headers := .empty }
+  else
+    fail "unsupported HTTP version"
+
+/--
+Parses a status line and returns the status code plus recognized HTTP version when available.
+Consumes and discards the reason phrase.
+
+status-line = HTTP-version SP status-code SP [ reason-phrase ] CRLF
+-/
+public def parseStatusLineRawVersion (limits : H1.Config) : Parser (Status × Option Version) := do
+  let (major, minor) ← parseHttpVersionNumber <* sp
+  let status ← parseStatusCode limits
+  return (status, Version.ofNumber? major minor)
+
+/--
+Parses the trailer section that follows the last chunk size line (`0\r\n`).
+-/
+public def parseLastChunkBody (limits : H1.Config) : Parser Unit := do
+  discard <| manyItems (parseTrailerHeader limits) limits.maxTrailerHeaders
+  crlf
+
+end Std.Http.Protocol.H1

src/Std/Internal/Http/Protocol/H1/Reader.lean

@@ -0,0 +1,319 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+module
+
+prelude
+public import Std.Time
+public import Std.Internal.Http.Data
+public import Std.Internal.Http.Internal
+public import Std.Internal.Http.Protocol.H1.Parser
+public import Std.Internal.Http.Protocol.H1.Config
+public import Std.Internal.Http.Protocol.H1.Message
+public import Std.Internal.Http.Protocol.H1.Error
+
+public section
+
+/-!
+# HTTP/1.1 Reader
+
+This module defines the reader state machine for parsing incoming HTTP/1.1 messages.
+It tracks the parsing state including start line, headers, and body handling for
+both fixed-length and chunked transfer encodings.
+-/
+
+namespace Std.Http.Protocol.H1
+
+set_option linter.all true
+
+/--
+The body-framing sub-state of the `Reader` state machine.
+-/
+inductive Reader.BodyState where
+  /--
+  Parse fixed-length body bytes, tracking the number of bytes remaining.
+  -/
+  | fixed (remaining : Nat)
+
+  /--
+  Parse the next chunk-size line in chunked transfer encoding.
+  -/
+  | chunkedSize
+
+  /--
+  Parse chunk data for the current chunk.
+  -/
+  | chunkedBody (ext : Array (Chunk.ExtensionName × Option Chunk.ExtensionValue)) (remaining : Nat)
+
+  /--
+  Parse body bytes until EOF (connection close).
+  -/
+  | closeDelimited
+deriving Inhabited, Repr, BEq
+
+/--
+The state of the `Reader` state machine.
+-/
+inductive Reader.State (dir : Direction) : Type
+  /--
+  Initial state waiting for HTTP start line.
+  -/
+  | needStartLine : State dir
+
+  /--
+  State waiting for HTTP headers, tracking number of headers parsed.
+  -/
+  | needHeader : Nat → State dir
+
+  /--
+  Unified body-reading state.
+  -/
+  | readBody : Reader.BodyState → State dir
+
+  /--
+  Paused waiting for a `canContinue` decision, carrying the next state.
+  -/
+  | continue : State dir → State dir
+
+  /--
+  State waiting to be able to read new data.
+  -/
+  | pending : State dir
+
+  /--
+  State that it completed a single request or response and can go to the next one
+  -/
+  | complete
+
+  /--
+  State that it has completed and cannot process more data.
+  -/
+  | closed
+
+  /--
+  The input is malformed.
+  -/
+  | failed (error : Error) : State dir
+deriving Inhabited, Repr, BEq
+
+/--
+Manages the reading state of the HTTP parsing and processing machine.
+-/
+structure Reader (dir : Direction) where
+  /--
+  The current state of the machine.
+  -/
+  state : Reader.State dir := match dir with | .receiving => .needStartLine | .sending => .pending
+
+  /--
+  The input byte array.
+  -/
+  input : ByteArray.Iterator := ByteArray.emptyWithCapacity 4096 |>.iter
+
+  /--
+  The incoming message head.
+  -/
+  messageHead : Message.Head dir := {}
+
+  /--
+  Count of messages that this connection has already parsed.
+  -/
+  messageCount : Nat := 0
+
+  /--
+  Number of body bytes read for the current message.
+  -/
+  bodyBytesRead : Nat := 0
+
+  /--
+  Number of header bytes accumulated for the current message.
+  Counts name + value bytes plus 4 bytes per line for `: ` and `\r\n`.
+  -/
+  headerBytesRead : Nat := 0
+
+  /--
+  Set when no further input bytes will arrive (the remote end has closed the connection).
+  -/
+  noMoreInput : Bool := false
+
+namespace Reader
+
+/--
+Checks if the reader is in a closed state and cannot process more messages.
+-/
+@[inline]
+def isClosed (reader : Reader dir) : Bool :=
+  match reader.state with
+  | .closed => true
+  | _ => false
+
+/--
+Checks if the reader has completed parsing the current message.
+-/
+@[inline]
+def isComplete (reader : Reader dir) : Bool :=
+  match reader.state with
+  | .complete => true
+  | _ => false
+
+/--
+Checks if the reader has encountered an error.
+-/
+@[inline]
+def hasFailed (reader : Reader dir) : Bool :=
+  match reader.state with
+  | .failed _ => true
+  | _ => false
+
+/--
+Feeds new data into the reader's input buffer.
+If the current input is exhausted, replaces it; otherwise compacts the buffer
+by discarding already-parsed bytes before appending.
+-/
+@[inline]
+def feed (data : ByteArray) (reader : Reader dir) : Reader dir :=
+  { reader with input :=
+    if reader.input.atEnd
+      then data.iter
+      else (reader.input.array.extract reader.input.pos reader.input.array.size ++ data).iter }
+
+/--
+Replaces the reader's input iterator with a new one.
+-/
+@[inline]
+def setInput (input : ByteArray.Iterator) (reader : Reader dir) : Reader dir :=
+  { reader with input }
+
+/--
+Updates the message head being constructed.
+-/
+@[inline]
+def setMessageHead (messageHead : Message.Head dir) (reader : Reader dir) : Reader dir :=
+  { reader with messageHead }
+
+/--
+Adds a header to the current message head.
+-/
+@[inline]
+def addHeader (name : Header.Name) (value : Header.Value) (reader : Reader dir) : Reader dir :=
+  match dir with
+  | .sending | .receiving => { reader with messageHead := { reader.messageHead with headers := reader.messageHead.headers.insert name value } }
+
+/--
+Closes the reader, transitioning to the closed state.
+-/
+@[inline]
+def close (reader : Reader dir) : Reader dir :=
+  { reader with state := .closed, noMoreInput := true }
+
+/--
+Marks the current message as complete and prepares for the next message.
+-/
+@[inline]
+def markComplete (reader : Reader dir) : Reader dir :=
+  { reader with
+    state := .complete
+    messageCount := reader.messageCount + 1 }
+
+/--
+Transitions the reader to a failed state with the given error.
+-/
+@[inline]
+def fail (error : Error) (reader : Reader dir) : Reader dir :=
+  { reader with state := .failed error }
+
+/--
+Resets the reader to parse a new message on the same connection.
+-/
+@[inline]
+def reset (reader : Reader dir) : Reader dir :=
+  { reader with
+    state := .needStartLine
+    bodyBytesRead := 0
+    headerBytesRead := 0
+    messageHead := {} }
+
+/--
+Checks if more input is needed to continue parsing.
+-/
+@[inline]
+def needsMoreInput (reader : Reader dir) : Bool :=
+  reader.input.atEnd && !reader.noMoreInput &&
+  match reader.state with
+  | .complete | .closed | .failed _ | .«continue» _ => false
+  | _ => true
+
+/--
+Returns the current parse error if the reader has failed.
+-/
+@[inline]
+def getError (reader : Reader dir) : Option Error :=
+  match reader.state with
+  | .failed err => some err
+  | _ => none
+
+/--
+Gets the number of bytes remaining in the input buffer.
+-/
+@[inline]
+def remainingBytes (reader : Reader dir) : Nat :=
+  reader.input.array.size - reader.input.pos
+
+/--
+Advances the input iterator by n bytes.
+-/
+@[inline]
+def advance (n : Nat) (reader : Reader dir) : Reader dir :=
+  { reader with input := reader.input.forward n }
+
+/--
+Transitions to the state for reading headers.
+-/
+@[inline]
+def startHeaders (reader : Reader dir) : Reader dir :=
+  { reader with state := .needHeader 0, bodyBytesRead := 0, headerBytesRead := 0 }
+
+/--
+Adds body bytes parsed for the current message.
+-/
+@[inline]
+def addBodyBytes (n : Nat) (reader : Reader dir) : Reader dir :=
+  { reader with bodyBytesRead := reader.bodyBytesRead + n }
+
+/--
+Adds header bytes accumulated for the current message.
+-/
+@[inline]
+def addHeaderBytes (n : Nat) (reader : Reader dir) : Reader dir :=
+  { reader with headerBytesRead := reader.headerBytesRead + n }
+
+/--
+Transitions to the state for reading a fixed-length body.
+-/
+@[inline]
+def startFixedBody (size : Nat) (reader : Reader dir) : Reader dir :=
+  { reader with state := .readBody (.fixed size) }
+
+/--
+Transitions to the state for reading chunked transfer encoding.
+-/
+@[inline]
+def startChunkedBody (reader : Reader dir) : Reader dir :=
+  { reader with state := .readBody .chunkedSize }
+
+/--
+Marks that no more input will be provided (connection closed).
+-/
+@[inline]
+def markNoMoreInput (reader : Reader dir) : Reader dir :=
+  { reader with noMoreInput := true }
+
+/--
+Checks if the connection should be kept alive for the next message.
+-/
+def shouldKeepAlive (reader : Reader dir) : Bool :=
+  reader.messageHead.shouldKeepAlive
+
+end Reader

src/Std/Internal/Http/Protocol/H1/Writer.lean

@@ -0,0 +1,280 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+module
+
+prelude
+public import Std.Time
+public import Std.Internal.Http.Data
+public import Std.Internal.Http.Internal
+public import Std.Internal.Http.Protocol.H1.Parser
+public import Std.Internal.Http.Protocol.H1.Config
+public import Std.Internal.Http.Protocol.H1.Message
+public import Std.Internal.Http.Protocol.H1.Error
+
+public section
+
+/-!
+# HTTP/1.1 Writer
+
+This module defines the writer state machine for generating outgoing HTTP/1.1 messages.
+It handles encoding headers and body content for both fixed-length and chunked
+transfer encodings.
+-/
+
+namespace Std.Http.Protocol.H1
+
+set_option linter.all true
+
+open Internal
+
+/--
+The state of the `Writer` state machine.
+-/
+inductive Writer.State
+  /--
+  Initial state before any outgoing message has been prepared.
+  -/
+  | pending
+
+  /--
+  Waiting for the application to provide the outgoing message head via `send`.
+  -/
+  | waitingHeaders
+
+  /--
+  The message head has been provided; waiting for `shouldFlush` to become true before
+  serializing headers to output.
+  -/
+  | waitingForFlush
+
+  /--
+  Writing the body output (either fixed-length or chunked).
+  -/
+  | writingBody (mode : Body.Length)
+
+  /--
+  Completed writing a single message and ready to begin the next one.
+  -/
+  | complete
+
+  /--
+  Closed; no further data can be written.
+  -/
+  | closed
+deriving Inhabited, Repr, BEq
+
+/--
+Manages the writing state of the HTTP generating and writing machine.
+-/
+structure Writer (dir : Direction) where
+  /--
+  Body chunks supplied by the user, accumulated before being flushed to output.
+  -/
+  userData : Array Chunk := .empty
+
+  /--
+  All the data produced by the writer, ready to be sent to the socket.
+  -/
+  outputData : ChunkedBuffer := .empty
+
+  /--
+  The state of the writer machine.
+  -/
+  state : Writer.State := match dir with | .receiving => .pending | .sending => .waitingHeaders
+
+  /--
+  When the user specifies the exact body size upfront, `Content-Length` framing is
+  used instead of chunked transfer encoding.
+  -/
+  knownSize : Option Body.Length := none
+
+  /--
+  The outgoing message that will be written to the output.
+  -/
+  messageHead : Message.Head dir.swap := {}
+
+  /--
+  Whether the user has called `send` to provide the outgoing message head.
+  -/
+  sentMessage : Bool := false
+
+  /--
+  Set when the user has finished sending body data, allowing fixed-size framing
+  to be determined upfront.
+  -/
+  userClosedBody : Bool := false
+
+  /--
+  When `true`, body bytes are intentionally omitted from the wire for this message
+  (e.g. HEAD responses), while headers/framing metadata may still describe the
+  hypothetical representation.
+  -/
+  omitBody : Bool := false
+
+  /--
+  Running total of bytes across all `userData` chunks, maintained incrementally
+  to avoid an O(n) fold on every fixed-length write step.
+  -/
+  userDataBytes : Nat := 0
+
+namespace Writer
+
+/--
+Returns `true` when no more user body data will arrive: either the user called
+`closeBody`, or the writer has already transitioned to `complete` or `closed`.
+
+Note: this does **not** mean the wire is ready to accept new bytes — a `closed`
+writer cannot send anything. Use this to decide whether to flush pending body
+data rather than to check writability.
+-/
+@[inline]
+def noMoreUserData {dir} (writer : Writer dir) : Bool :=
+  match writer.state with
+  | .closed | .complete => true
+  | _ => writer.userClosedBody
+
+/--
+Checks if the writer is closed (cannot process more data).
+-/
+@[inline]
+def isClosed (writer : Writer dir) : Bool :=
+  match writer.state with
+  | .closed => true
+  | _ => false
+
+/--
+Checks if the writer has completed processing a request.
+-/
+@[inline]
+def isComplete (writer : Writer dir) : Bool :=
+  match writer.state with
+  | .complete => true
+  | _ => false
+
+/--
+Checks if the writer can accept more data from the user.
+-/
+@[inline]
+def canAcceptData (writer : Writer dir) : Bool :=
+  match writer.state with
+  | .waitingHeaders => true
+  | .waitingForFlush => true
+  | .writingBody _ => !writer.userClosedBody
+  | _ => false
+
+/--
+Marks the body as closed, indicating no more user data will be added.
+-/
+@[inline]
+def closeBody (writer : Writer dir) : Writer dir :=
+  { writer with userClosedBody := true }
+
+/--
+Determines the transfer encoding mode based on explicit setting, body closure state, or defaults to chunked.
+-/
+def determineTransferMode (writer : Writer dir) : Body.Length :=
+  if let some mode := writer.knownSize then
+    mode
+  else if writer.userClosedBody then
+    .fixed writer.userDataBytes
+  else
+    .chunked
+
+/--
+Adds user data chunks to the writer's buffer if the writer can accept data.
+-/
+@[inline]
+def addUserData (data : Array Chunk) (writer : Writer dir) : Writer dir :=
+  if writer.canAcceptData then
+    let extraBytes := data.foldl (fun acc c => acc + c.data.size) 0
+    { writer with userData := writer.userData ++ data, userDataBytes := writer.userDataBytes + extraBytes }
+  else
+    writer
+
+/--
+Writes accumulated user data to output using fixed-size encoding.
+-/
+def writeFixedBody (writer : Writer dir) (limitSize : Nat) : Writer dir × Nat :=
+  if writer.userData.size = 0 then
+    (writer, limitSize)
+  else
+    let (chunks, pending, totalSize) := writer.userData.foldl (fun (state : Array ByteArray × Array Chunk × Nat) chunk =>
+      let (acc, pending, size) := state
+      if size >= limitSize then
+        (acc, pending.push chunk, size)
+      else
+        let remaining := limitSize - size
+        let takeSize := min chunk.data.size remaining
+        let dataPart := chunk.data.extract 0 takeSize
+        let acc := if takeSize = 0 then acc else acc.push dataPart
+        let size := size + takeSize
+        if takeSize < chunk.data.size then
+          let pendingChunk : Chunk := { chunk with data := chunk.data.extract takeSize chunk.data.size }
+          (acc, pending.push pendingChunk, size)
+        else
+          (acc, pending, size)
+    ) (#[], #[], 0)
+    let outputData := writer.outputData.append (ChunkedBuffer.ofArray chunks)
+    let remaining := limitSize - totalSize
+    ({ writer with userData := pending, outputData, userDataBytes := writer.userDataBytes - totalSize }, remaining)
+
+/--
+Writes accumulated user data to output using chunked transfer encoding.
+-/
+def writeChunkedBody (writer : Writer dir) : Writer dir :=
+  if writer.userData.size = 0 then
+    writer
+  else
+    let data := writer.userData
+    { writer with userData := #[], userDataBytes := 0, outputData := data.foldl (Encode.encode .v11) writer.outputData }
+
+/--
+Writes the final chunk terminator (0\r\n\r\n) and transitions to complete state.
+-/
+def writeFinalChunk (writer : Writer dir) : Writer dir :=
+  let writer := writer.writeChunkedBody
+  { writer with
+    outputData := writer.outputData.write "0\r\n\r\n".toUTF8
+    state := .complete
+  }
+
+/--
+Extracts all accumulated output data and returns it with a cleared output buffer.
+-/
+@[inline]
+def takeOutput (writer : Writer dir) : Option (Writer dir × ByteArray) :=
+  let output := writer.outputData.toByteArray
+  some ({ writer with outputData := ChunkedBuffer.empty }, output)
+
+/--
+Updates the writer's state machine to a new state.
+-/
+@[inline]
+def setState (state : Writer.State) (writer : Writer dir) : Writer dir :=
+  { writer with state }
+
+/--
+Writes the message headers to the output buffer.
+-/
+private def writeHeaders (messageHead : Message.Head dir.swap) (writer : Writer dir) : Writer dir :=
+  { writer with outputData := Internal.Encode.encode (v := .v11) writer.outputData messageHead }
+
+/--
+Checks if the connection should be kept alive based on the Connection header.
+-/
+def shouldKeepAlive (writer : Writer dir) : Bool :=
+  writer.messageHead.headers.get? .connection
+  |>.map (fun v => v.value.toLower != "close")
+  |>.getD true
+
+/--
+Closes the writer, transitioning to the closed state.
+-/
+@[inline]
+def close (writer : Writer dir) : Writer dir :=
+  { writer with state := .closed }
+
+end Writer

src/Std/Internal/Http/Server.lean

@@ -0,0 +1,188 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+module
+
+prelude
+public import Std.Internal.Async
+public import Std.Internal.Async.TCP
+public import Std.Sync.CancellationToken
+public import Std.Sync.Semaphore
+public import Std.Internal.Http.Server.Config
+public import Std.Internal.Http.Server.Handler
+public import Std.Internal.Http.Server.Connection
+
+public section
+
+/-!
+# HTTP Server
+
+This module defines a simple, asynchronous HTTP/1.1 server implementation.
+
+It provides the `Std.Http.Server` structure, which encapsulates all server state, and functions for
+starting, managing, and gracefully shutting down the server.
+
+The server runs entirely using `Async` and uses a shared `CancellationContext` to signal shutdowns.
+Each active client connection is tracked, and the server automatically resolves its shutdown
+promise once all connections have closed.
+-/
+
+namespace Std.Http
+open Std.Internal.IO.Async TCP
+
+set_option linter.all true
+
+/--
+The `Server` structure holds all state required to manage the lifecycle of an HTTP server, including
+connection tracking and shutdown coordination.
+-/
+structure Server where
+
+  /--
+  The context used for shutting down all connections and the server.
+  -/
+  context : Std.CancellationContext
+
+  /--
+  Active HTTP connections
+  -/
+  activeConnections : Std.Mutex UInt64
+
+  /--
+  Semaphore used to enforce the maximum number of simultaneous active connections.
+  `none` means no connection limit.
+  -/
+  connectionLimit : Option Std.Semaphore
+
+  /--
+  Indicates when the server has successfully shut down.
+  -/
+  shutdownPromise : Std.Channel Unit
+
+  /--
+  Configuration of the server
+  -/
+  config : Std.Http.Config
+
+namespace Server
+
+/--
+Create a new `Server` structure with an optional configuration.
+-/
+def new (config : Std.Http.Config := {}) : IO Server := do
+  let context ← Std.CancellationContext.new
+  let activeConnections ← Std.Mutex.new 0
+  let connectionLimit ←
+    if config.maxConnections = 0 then
+      pure none
+    else
+      some <$> Std.Semaphore.new config.maxConnections
+  let shutdownPromise ← Std.Channel.new
+
+  return { context, activeConnections, connectionLimit, shutdownPromise, config }
+
+/--
+Triggers cancellation of all requests and the accept loop in the server. This function should be used
+in conjunction with `waitShutdown` to properly coordinate the shutdown sequence.
+-/
+@[inline]
+def shutdown (s : Server) : Async Unit :=
+  s.context.cancel .shutdown
+
+/--
+Waits for the server to shut down. Blocks until another task or async operation calls the `shutdown` function.
+-/
+@[inline]
+def waitShutdown (s : Server) : Async Unit := do
+  Async.ofAsyncTask ((← s.shutdownPromise.recv).map Except.ok)
+
+/--
+Returns a `Selector` that waits for the server to shut down.
+-/
+@[inline]
+def waitShutdownSelector (s : Server) : Selector Unit :=
+  s.shutdownPromise.recvSelector
+
+/--
+Triggers cancellation of all requests and the accept loop, then waits for the server to fully shut down.
+This is a convenience function combining `shutdown` and then `waitShutdown`.
+-/
+@[inline]
+def shutdownAndWait (s : Server) : Async Unit := do
+  s.context.cancel .shutdown
+  s.waitShutdown
+
+@[inline]
+private def frameCancellation (s : Server) (releaseConnectionPermit : Bool := false)
+    (action : ContextAsync α) : ContextAsync α := do
+  s.activeConnections.atomically (modify (· + 1))
+  try
+    action
+  finally
+    if releaseConnectionPermit then
+      if let some limit := s.connectionLimit then
+        limit.release
+
+    s.activeConnections.atomically do
+      modify (· - 1)
+
+      if (← get) = 0 ∧ (← s.context.isCancelled) then
+        discard <| s.shutdownPromise.send ()
+
+/--
+Start a new HTTP/1.1 server on the given socket address. This function uses `Async` to handle tasks
+and TCP connections, and returns a `Server` structure that can be used to cancel the server.
+-/
+def serve {σ : Type} [Handler σ]
+    (addr : Net.SocketAddress)
+    (handler : σ)
+    (config : Config := {}) (backlog : UInt32 := 1024) : Async Server := do
+
+  let httpServer ← Server.new config
+
+  let server ← Socket.Server.mk
+  server.bind addr
+  server.listen backlog
+  server.noDelay
+
+  let runServer := do
+    frameCancellation httpServer (action := do
+      while true do
+        let permitAcquired ←
+          if let some limit := httpServer.connectionLimit then
+            let permit ← limit.acquire
+            await permit
+            pure true
+          else
+            pure false
+
+        let result ← Selectable.one #[
+          .case (server.acceptSelector) (fun x => pure <| some x),
+          .case (← ContextAsync.doneSelector) (fun _ => pure none)
+        ]
+
+        match result with
+        | some client =>
+          let extensions ← do
+            match (← EIO.toBaseIO client.getPeerName) with
+            | .ok addr => pure <| Extensions.empty.insert (Server.RemoteAddr.mk addr)
+            | .error _ => pure Extensions.empty
+
+          ContextAsync.background
+            (frameCancellation httpServer (releaseConnectionPermit := permitAcquired)
+              (action := do
+                serveConnection client handler config extensions))
+        | none =>
+          if permitAcquired then
+            if let some limit := httpServer.connectionLimit then
+              limit.release
+          break
+    )
+
+  background (runServer httpServer.context)
+
+  return httpServer
+
+end Std.Http.Server

src/Std/Internal/Http/Server/Config.lean

@@ -0,0 +1,196 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+module
+
+prelude
+public import Std.Time
+public import Std.Internal.Http.Protocol.H1
+
+public section
+
+/-!
+# Config
+
+This module exposes the `Config`, a structure that describes timeout, request and headers
+configuration of an HTTP Server.
+-/
+
+namespace Std.Http
+
+set_option linter.all true
+
+/--
+Connection limits configuration with validation.
+-/
+structure Config where
+  /--
+  Maximum number of simultaneous active connections (default: 1024).
+  Setting this to `0` disables the limit entirely: the server will accept any number of
+  concurrent connections and no semaphore-based cap is enforced. Use with care — an
+  unconstrained server may exhaust file descriptors or memory under adversarial load.
+  -/
+  maxConnections : Nat := 1024
+
+  /--
+  Maximum number of requests per connection.
+  -/
+  maxRequests : Nat := 100
+
+  /--
+  Maximum number of headers allowed per request.
+  -/
+  maxHeaders : Nat := 50
+
+  /--
+  Maximum aggregate byte size of all header field lines in a single message
+  (name + value bytes plus 4 bytes per line for `: ` and `\r\n`). Default: 64 KiB.
+  -/
+  maxHeaderBytes : Nat := 65536
+
+  /--
+  Timeout (in milliseconds) for receiving additional data while a request is actively being
+  processed (e.g. reading the request body). Applies after the request headers have been parsed
+  and replaces the keep-alive timeout for the duration of the request.
+  -/
+  lingeringTimeout : Time.Millisecond.Offset := 10000
+
+  /--
+  Timeout for keep-alive connections
+  -/
+  keepAliveTimeout : { x : Time.Millisecond.Offset // 0 < x } :=  ⟨12000, by decide⟩
+
+  /--
+  Maximum time (in milliseconds) allowed to receive the complete request headers after the first
+  byte of a new request arrives. This prevents Slowloris-style attacks where a client sends bytes
+  at a slow rate to hold a connection slot open without completing a request. Once a request starts,
+  each individual read must complete within this window. Default: 5 seconds.
+  -/
+  headerTimeout : Time.Millisecond.Offset := 5000
+
+  /--
+  Whether to enable keep-alive connections by default.
+  -/
+  enableKeepAlive : Bool := true
+
+  /--
+  The maximum size that the connection can receive in a single recv call.
+  -/
+  maximumRecvSize : Nat := 8192
+
+  /--
+  Default buffer size for the connection
+  -/
+  defaultPayloadBytes : Nat := 8192
+
+  /--
+  Whether to automatically generate the `Date` header in responses.
+  -/
+  generateDate : Bool := true
+
+  /--
+  The `Server` header value injected into outgoing responses.
+  `none` suppresses the header entirely.
+  -/
+  serverName : Option Header.Value := some (.mk "LeanHTTP/1.1")
+
+  /--
+  Maximum length of request URI (default: 8192 bytes)
+  -/
+  maxUriLength : Nat := 8192
+
+  /--
+  Maximum number of bytes consumed while parsing request start-lines (default: 8192 bytes).
+  -/
+  maxStartLineLength : Nat := 8192
+
+  /--
+  Maximum length of header field name (default: 256 bytes)
+  -/
+  maxHeaderNameLength : Nat := 256
+
+  /--
+  Maximum length of header field value (default: 8192 bytes)
+  -/
+  maxHeaderValueLength : Nat := 8192
+
+  /--
+  Maximum number of spaces in delimiter sequences (default: 16)
+  -/
+  maxSpaceSequence : Nat := 16
+
+  /--
+  Maximum number of leading empty lines (bare CRLF) to skip before a request-line
+  (RFC 9112 §2.2 robustness). Default: 8.
+  -/
+  maxLeadingEmptyLines : Nat := 8
+
+  /--
+  Maximum length of chunk extension name (default: 256 bytes)
+  -/
+  maxChunkExtNameLength : Nat := 256
+
+  /--
+  Maximum length of chunk extension value (default: 256 bytes)
+  -/
+  maxChunkExtValueLength : Nat := 256
+
+  /--
+  Maximum number of bytes consumed while parsing one chunk-size line with extensions (default: 8192 bytes).
+  -/
+  maxChunkLineLength : Nat := 8192
+
+  /--
+  Maximum allowed chunk payload size in bytes (default: 8 MiB).
+  -/
+  maxChunkSize : Nat := 8 * 1024 * 1024
+
+  /--
+  Maximum allowed total body size per request in bytes (default: 64 MiB).
+  -/
+  maxBodySize : Nat := 64 * 1024 * 1024
+
+  /--
+  Maximum length of reason phrase (default: 512 bytes)
+  -/
+  maxReasonPhraseLength : Nat := 512
+
+  /--
+  Maximum number of trailer headers (default: 20)
+  -/
+  maxTrailerHeaders : Nat := 20
+
+  /--
+  Maximum number of extensions on a single chunk-size line (default: 16).
+  -/
+  maxChunkExtensions : Nat := 16
+
+namespace Config
+
+/--
+Converts to HTTP/1.1 config.
+-/
+def toH1Config (config : Config) : Protocol.H1.Config where
+  maxMessages := config.maxRequests
+  maxHeaders := config.maxHeaders
+  maxHeaderBytes := config.maxHeaderBytes
+  enableKeepAlive := config.enableKeepAlive
+  agentName := config.serverName
+  maxUriLength := config.maxUriLength
+  maxStartLineLength := config.maxStartLineLength
+  maxHeaderNameLength := config.maxHeaderNameLength
+  maxHeaderValueLength := config.maxHeaderValueLength
+  maxSpaceSequence := config.maxSpaceSequence
+  maxLeadingEmptyLines := config.maxLeadingEmptyLines
+  maxChunkExtensions := config.maxChunkExtensions
+  maxChunkExtNameLength := config.maxChunkExtNameLength
+  maxChunkExtValueLength := config.maxChunkExtValueLength
+  maxChunkLineLength := config.maxChunkLineLength
+  maxChunkSize := config.maxChunkSize
+  maxBodySize := config.maxBodySize
+  maxReasonPhraseLength := config.maxReasonPhraseLength
+  maxTrailerHeaders := config.maxTrailerHeaders
+
+end Std.Http.Config

src/Std/Internal/Http/Server/Connection.lean

@@ -0,0 +1,530 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+module
+
+prelude
+public import Std.Internal.Async.TCP
+public import Std.Internal.Async.ContextAsync
+public import Std.Internal.Http.Transport
+public import Std.Internal.Http.Protocol.H1
+public import Std.Internal.Http.Server.Config
+public import Std.Internal.Http.Server.Handler
+
+public section
+
+namespace Std
+namespace Http
+namespace Server
+
+open Std Internal IO Async TCP Protocol
+open Time
+
+/-!
+# Connection
+
+This module defines `Server.Connection`, a structure used to handle a single HTTP connection with
+possibly multiple requests.
+-/
+
+set_option linter.all true
+
+/--
+Represents the remote address of a client connection.
+-/
+public structure RemoteAddr where
+  /--
+  The socket address of the remote client.
+  -/
+  addr : Net.SocketAddress
+deriving TypeName
+
+instance : ToString RemoteAddr where
+  toString addr := toString addr.addr.ipAddr ++ ":" ++ toString addr.addr.port
+
+/--
+A single HTTP connection.
+-/
+public structure Connection (α : Type) where
+  /--
+  The client connection.
+  -/
+  socket : α
+
+  /--
+  The processing machine for HTTP/1.1.
+  -/
+  machine : H1.Machine .receiving
+
+  /--
+  Extensions to attach to each request (e.g., remote address).
+  -/
+  extensions : Extensions := .empty
+
+namespace Connection
+
+/--
+Events produced by the async select loop in `receiveWithTimeout`.
+Each variant corresponds to one possible outcome of waiting for I/O.
+-/
+private inductive Recv (β : Type)
+  | bytes (x : Option ByteArray)
+  | responseBody (x : Option Chunk)
+  | bodyInterest (x : Bool)
+  | response (x : (Except Error (Response β)))
+  | timeout
+  | keepAliveTimeout
+  | shutdown
+  | close
+
+/--
+The set of I/O sources to wait on during a single poll iteration.
+Each `Option` field is `none` when that source is not currently active.
+-/
+private structure PollSources (α β : Type) where
+  socket : Option α
+  expect : Option Nat
+  response : Option (Std.Channel (Except Error (Response β)))
+  responseBody : Option β
+  requestBody : Option Body.Stream
+  timeout : Millisecond.Offset
+  keepAliveTimeout : Option Millisecond.Offset
+  headerTimeout : Option Timestamp
+  connectionContext : CancellationContext
+
+/--
+Waits for the next I/O event across all active sources described by `sources`.
+Computes the socket recv size from `config`, then races all active selectables.
+Calls `Handler.onFailure` and returns `.close` on transport errors.
+-/
+private def pollNextEvent
+    {σ β : Type} [Transport α] [Handler σ] [Body β]
+    (config : Config) (handler : σ) (sources : PollSources α β)
+    : Async (Recv β) := do
+  let expectedBytes := sources.expect
+    |>.getD config.defaultPayloadBytes
+    |>.min config.maximumRecvSize
+    |>.toUInt64
+
+  let mut selectables : Array (Selectable (Recv β)) := #[
+    .case sources.connectionContext.doneSelector (fun _ => do
+      let reason ← sources.connectionContext.getCancellationReason
+      match reason with
+      | some .deadline => pure .timeout
+      | _ => pure .shutdown)
+  ]
+
+  if let some socket := sources.socket then
+    selectables := selectables.push (.case (Transport.recvSelector socket expectedBytes) (Recv.bytes · |> pure))
+
+    if let some keepAliveTimeout := sources.keepAliveTimeout then
+      selectables := selectables.push (.case (← Selector.sleep keepAliveTimeout) (fun _ => pure .keepAliveTimeout))
+    else if let some timeout := sources.headerTimeout then
+      selectables := selectables.push (.case (← Selector.sleep (timeout - (← Timestamp.now)).toMilliseconds) (fun _ => pure .timeout))
+    else
+      selectables := selectables.push (.case (← Selector.sleep sources.timeout) (fun _ => pure .timeout))
+
+  if let some responseBody := sources.responseBody then
+    selectables := selectables.push (.case (Body.recvSelector responseBody) (Recv.responseBody · |> pure))
+
+  if let some requestBody := sources.requestBody then
+    selectables := selectables.push (.case (requestBody.interestSelector) (Recv.bodyInterest · |> pure))
+
+  if let some response := sources.response then
+    selectables := selectables.push (.case response.recvSelector (Recv.response · |> pure))
+
+  try Selectable.one selectables
+  catch e =>
+    Handler.onFailure handler e
+    pure .close
+
+/--
+Handles the `Expect: 100-continue` protocol for a pending request head.
+Races between the handler's decision (`Handler.onContinue`), the connection being
+cancelled, and a lingering timeout. Returns the updated machine and whether
+`pendingHead` should be cleared (i.e. when the request is rejected).
+-/
+private def handleContinueEvent
+    {σ : Type} [Handler σ]
+    (handler : σ) (machine : H1.Machine .receiving) (head : Request.Head)
+    (config : Config) (connectionContext : CancellationContext)
+    : Async (H1.Machine .receiving × Bool) := do
+
+  let continueChannel : Std.Channel Bool ← Std.Channel.new
+  let continueTask ← Handler.onContinue handler head |>.asTask
+
+  BaseIO.chainTask continueTask fun
+    | .ok v => discard <| continueChannel.send v
+    | .error _ => discard <| continueChannel.send false
+
+  let canContinue ← Selectable.one #[
+    .case continueChannel.recvSelector pure,
+    .case connectionContext.doneSelector (fun _ => pure false),
+    .case (← Selector.sleep config.lingeringTimeout) (fun _ => pure false)
+  ]
+
+  let status := if canContinue then Status.«continue» else Status.expectationFailed
+  return (machine.canContinue status, !canContinue)
+
+/--
+Injects a `Date` header into a response head if `Config.generateDate` is set
+and the response does not already include one.
+-/
+private def prepareResponseHead (config : Config) (head : Response.Head) : Async Response.Head := do
+  if config.generateDate ∧ ¬head.headers.contains Header.Name.date then
+    let now ← Std.Time.DateTime.now (tz := .UTC)
+    return { head with headers := head.headers.insert Header.Name.date (Header.Value.ofString! now.toRFC822String) }
+  else
+    return head
+
+/--
+Applies a successful handler response to the machine.
+Optionally injects a `Date` header, records the known body size, and sends the
+response head. Returns the updated machine and the body stream to drain, or `none`
+when the body should be omitted (e.g., for HEAD requests).
+-/
+private def applyResponse
+    {β : Type} [Body β]
+    (config : Config) (machine : H1.Machine .receiving) (res : Response β)
+    : Async (H1.Machine .receiving × Option β) := do
+  let size ← Body.getKnownSize res.body
+  let machineSized :=
+    if let some knownSize := size then machine.setKnownSize knownSize
+    else machine
+  let responseHead ← prepareResponseHead config res.line
+  let machineWithHead := machineSized.send responseHead
+  if machineWithHead.writer.omitBody then
+    if ¬(← Body.isClosed res.body) then
+      Body.close res.body
+    return (machineWithHead, none)
+  else
+    return (machineWithHead, some res.body)
+
+/--
+All mutable state carried through the connection processing loop.
+Bundled into a struct so it can be passed to and returned from helper functions.
+-/
+private structure ConnectionState (β : Type) where
+  machine : H1.Machine .receiving
+  requestStream : Body.Stream
+  keepAliveTimeout : Option Millisecond.Offset
+  currentTimeout : Millisecond.Offset
+  headerTimeout : Option Timestamp
+  response : Std.Channel (Except Error (Response β))
+  respStream : Option β
+  requiresData : Bool
+  expectData : Option Nat
+  handlerDispatched : Bool
+  pendingHead : Option Request.Head
+
+/--
+Processes all H1 events from a single machine step, updating the connection state.
+Handles keep-alive resets, body-size tracking, `Expect: 100-continue`, and parse errors.
+Returns the updated state; stops early on `.failed`.
+-/
+private def processH1Events
+    {σ β : Type} [Handler σ] [Body β]
+    (handler : σ) (config : Config) (connectionContext : CancellationContext)
+    (events : Array (H1.Event .receiving))
+    (state : ConnectionState β)
+    : Async (ConnectionState β) := do
+
+  let mut st := state
+
+  for event in events do
+    match event with
+    | .needMoreData expect =>
+      st := { st with requiresData := true, expectData := expect }
+
+    | .needAnswer => pure ()
+
+    | .endHeaders head =>
+
+      -- Sets the pending head and removes the KeepAlive or Header timeout.
+      st := { st with
+        currentTimeout := config.lingeringTimeout
+        keepAliveTimeout := none
+        headerTimeout := none
+        pendingHead := some head
+      }
+
+      if let some length := head.getSize true then
+        -- Sets the size of the body that is going out of the connection.
+        Body.setKnownSize st.requestStream (some length)
+
+    | .«continue» =>
+      if let some head := st.pendingHead then
+        let (newMachine, clearPending) ← handleContinueEvent handler st.machine head config connectionContext
+        st := { st with machine := newMachine }
+        if clearPending then
+          st := { st with pendingHead := none }
+
+    | .next =>
+      -- Reset all per-request state for the next pipelined request.
+      if ¬(← Body.isClosed st.requestStream) then
+        Body.close st.requestStream
+
+      if let some res := st.respStream then
+        if ¬(← Body.isClosed res) then
+          Body.close res
+
+      let newStream ← Body.mkStream
+
+      st := { st with
+        requestStream := newStream
+        response := ← Std.Channel.new
+        respStream := none
+        keepAliveTimeout := some config.keepAliveTimeout.val
+        currentTimeout := config.keepAliveTimeout.val
+        headerTimeout := none
+        handlerDispatched := false
+      }
+
+    | .failed err =>
+      Handler.onFailure handler (toString err)
+
+      if ¬(← Body.isClosed st.requestStream) then
+        Body.close st.requestStream
+
+      st := { st with requiresData := false, pendingHead := none }
+      break
+
+    | .closeBody =>
+      if ¬(← Body.isClosed st.requestStream) then
+        Body.close st.requestStream
+
+    | .close => pure ()
+
+  return st
+
+/--
+Dispatches a pending request head to the handler if one is waiting.
+Spawns the handler as an async task and routes its result back through `state.response`.
+Returns the updated state with `pendingHead` cleared and `handlerDispatched` set.
+-/
+private def dispatchPendingRequest
+    {σ : Type} [Handler σ]
+    (handler : σ) (extensions : Extensions) (connectionContext : CancellationContext)
+    (state : ConnectionState (Handler.ResponseBody σ))
+    : Async (ConnectionState (Handler.ResponseBody σ)) := do
+  if let some line := state.pendingHead then
+
+    let task ← Handler.onRequest handler { line, body := state.requestStream, extensions } connectionContext
+      |>.asTask
+
+    BaseIO.chainTask task (discard ∘ state.response.send)
+    return { state with pendingHead := none, handlerDispatched := true }
+  else
+    return state
+
+/--
+Processes a single async I/O event and updates the connection state.
+Returns the updated state and `true` if the connection should be closed immediately.
+-/
+private def handleRecvEvent
+    {σ β : Type} [Handler σ] [Body β]
+    (handler : σ) (config : Config)
+    (event : Recv β) (state : ConnectionState β)
+    : Async (ConnectionState β × Bool) := do
+
+  match event with
+  | .bytes (some bs) =>
+
+    let mut st := state
+
+    -- After the first byte after idle we switch from keep-alive timeout to per-request header timeout.
+    if st.keepAliveTimeout.isSome then
+      st := { st with
+        keepAliveTimeout := none
+        headerTimeout := some <| (← Timestamp.now) + config.headerTimeout
+      }
+
+    return ({ st with machine := st.machine.feed bs }, false)
+
+  | .bytes none =>
+    return ({ state with machine := state.machine.noMoreInput }, false)
+
+  | .responseBody (some chunk) =>
+    return ({ state with machine := state.machine.sendData #[chunk] }, false)
+
+  | .responseBody none =>
+    if let some res := state.respStream then
+      if ¬(← Body.isClosed res) then Body.close res
+    return ({ state with machine := state.machine.userClosedBody, respStream := none }, false)
+
+  | .bodyInterest interested =>
+    if interested then
+      let (newMachine, pulledChunk) := state.machine.pullBody
+      let mut st := { state with machine := newMachine }
+
+      if let some pulled := pulledChunk then
+        try st.requestStream.send pulled.chunk pulled.incomplete
+        catch e => Handler.onFailure handler e
+        if pulled.final then
+          if ¬(← Body.isClosed st.requestStream) then
+            Body.close st.requestStream
+
+      return (st, false)
+    else
+      return (state, false)
+
+  | .close => return (state, true)
+
+  | .timeout =>
+    Handler.onFailure handler "request header timeout"
+    return ({ state with machine := state.machine.closeWithError .requestTimeout, handlerDispatched := false }, false)
+
+  | .keepAliveTimeout =>
+    return ({ state with machine := state.machine.closeWithError .requestTimeout, handlerDispatched := false }, false)
+
+  | .shutdown =>
+    return ({ state with machine := state.machine.closeWithError .serviceUnavailable, handlerDispatched := false }, false)
+
+  | .response (.error err) =>
+    Handler.onFailure handler err
+    return ({ state with machine := state.machine.closeWithError .internalServerError, handlerDispatched := false }, false)
+
+  | .response (.ok res) =>
+    if state.machine.failed then
+      if ¬(← Body.isClosed res.body) then Body.close res.body
+      return ({ state with handlerDispatched := false }, false)
+    else
+      let (newMachine, newRespStream) ← applyResponse config state.machine res
+      return ({ state with machine := newMachine, handlerDispatched := false, respStream := newRespStream }, false)
+
+/--
+Computes the active `PollSources` for the current connection state.
+Determines which IO sources need attention and whether to include the socket.
+-/
+private def buildPollSources
+    {α β : Type} [Transport α]
+    (socket : α) (connectionContext : CancellationContext) (state : ConnectionState β)
+    : Async (PollSources α β) := do
+  let requestBodyOpen ←
+    if state.machine.canPullBody then pure !(← Body.isClosed state.requestStream)
+    else pure false
+
+  let requestBodyInterested ←
+    if state.machine.canPullBody ∧ requestBodyOpen then state.requestStream.hasInterest
+    else pure false
+
+  let requestBody ←
+    if state.machine.canPullBodyNow ∧ requestBodyOpen then pure (some state.requestStream)
+    else pure none
+
+  -- Include the socket only when there is more to do than waiting for the handler alone.
+  let pollSocket :=
+    state.requiresData ∨ !state.handlerDispatched ∨ state.respStream.isSome ∨
+    state.machine.writer.sentMessage ∨ (state.machine.canPullBody ∧ requestBodyInterested)
+
+  return {
+    socket := if pollSocket then some socket else none
+    expect := state.expectData
+    response := if state.handlerDispatched then some state.response else none
+    responseBody := state.respStream
+    requestBody := requestBody
+    timeout := state.currentTimeout
+    keepAliveTimeout := state.keepAliveTimeout
+    headerTimeout := state.headerTimeout
+    connectionContext := connectionContext
+  }
+
+/--
+Runs the main request/response processing loop for a single connection.
+Drives the HTTP/1.1 state machine through four phases each iteration:
+send buffered output, process H1 events, dispatch pending requests, poll for I/O.
+-/
+private def handle
+    {σ : Type} [Transport α] [h : Handler σ]
+    (connection : Connection α)
+    (config : Config)
+    (connectionContext : CancellationContext)
+    (handler : σ) : Async Unit := do
+
+  let _ : Body (Handler.ResponseBody σ) := Handler.responseBodyInstance
+
+  let socket := connection.socket
+  let initStream ← Body.mkStream
+
+  let mut state : ConnectionState (Handler.ResponseBody σ) := {
+    machine := connection.machine
+    requestStream := initStream
+    keepAliveTimeout := some config.keepAliveTimeout.val
+    currentTimeout := config.keepAliveTimeout.val
+    headerTimeout := none
+    response := ← Std.Channel.new
+    respStream := none
+    requiresData := false
+    expectData := none
+    handlerDispatched := false
+    pendingHead := none
+  }
+
+  while ¬state.machine.halted do
+
+    -- Phase 1: advance the state machine and flush any output.
+    let (newMachine, step) := state.machine.step
+    state := { state with machine := newMachine }
+
+    if step.output.size > 0 then
+      try Transport.sendAll socket step.output.data
+      catch e =>
+        Handler.onFailure handler e
+        break
+
+    -- Phase 2: process all events emitted by this step.
+    state ← processH1Events handler config connectionContext step.events state
+
+    -- Phase 3: dispatch any newly parsed request to the handler.
+    state ← dispatchPendingRequest handler connection.extensions connectionContext state
+
+    -- Phase 4: wait for the next IO event when any source needs attention.
+    if state.requiresData ∨ state.handlerDispatched ∨ state.respStream.isSome ∨ state.machine.canPullBody then
+      state := { state with requiresData := false }
+      let sources ← buildPollSources socket connectionContext state
+      let event ← pollNextEvent config handler sources
+      let (newState, shouldClose) ← handleRecvEvent handler config event state
+      state := newState
+      if shouldClose then break
+
+  -- Clean up: close all open streams and the socket.
+  if ¬(← Body.isClosed state.requestStream) then
+    Body.close state.requestStream
+
+  if let some res := state.respStream then
+    if ¬(← Body.isClosed res) then Body.close res
+
+  Transport.close socket
+
+end Connection
+
+/--
+Handles request/response processing for a single connection using an `Async` handler.
+The library-level entry point for running a server is `Server.serve`.
+This function can be used with a `TCP.Socket` or any other type that implements
+`Transport` to build custom server loops.
+
+# Example
+
+```lean
+-- Create a TCP socket server instance
+let server ← Socket.Server.mk
+server.bind addr
+server.listen backlog
+
+-- Enter an infinite loop to handle incoming client connections
+while true do
+  let client ← server.accept
+  background (serveConnection client handler config)
+```
+-/
+def serveConnection
+    {σ : Type} [Transport t] [Handler σ]
+    (client : t) (handler : σ)
+    (config : Config) (extensions : Extensions := .empty) : ContextAsync Unit := do
+  (Connection.mk client { config := config.toH1Config } extensions)
+  |>.handle config (← ContextAsync.getContext) handler
+
+end Std.Http.Server

src/Std/Internal/Http/Server/Handler.lean

@@ -0,0 +1,60 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+module
+
+prelude
+public import Std.Internal.Async
+public import Std.Internal.Http.Data
+public import Std.Internal.Async.ContextAsync
+
+public section
+
+namespace Std.Http.Server
+
+open Std.Internal.IO.Async
+
+set_option linter.all true
+
+/--
+A type class for handling HTTP server requests. Implement this class to define how the server
+responds to incoming requests, failures, and `Expect: 100-continue` headers.
+-/
+class Handler (σ : Type) where
+  /--
+  Concrete body type produced by `onRequest`.
+  Defaults to `Body.Any`, but handlers may override it with any reader/writer-compatible body.
+  -/
+  ResponseBody : Type := Body.Any
+
+  /--
+  Body instance required by the connection loop for receiving response chunks.
+  -/
+  [responseBodyInstance : Body ResponseBody]
+
+  /--
+  Called for each incoming HTTP request.
+  -/
+  onRequest (self : σ) (request : Request Body.Stream) : ContextAsync (Response ResponseBody)
+
+  /--
+  Called when an I/O or transport error occurs while processing a request (e.g. broken socket,
+  handler exception). This is a **notification only**: the connection will close regardless of
+  the handler's response. Use this for logging and metrics. The default implementation does nothing.
+  -/
+  onFailure (self : σ) (error : IO.Error) : Async Unit :=
+    pure ()
+
+  /--
+  Called when a request includes an `Expect: 100-continue` header. Return `true` to send a
+  `100 Continue` response and accept the body. If `false` is returned the server sends
+  `417 Expectation Failed`, disables keep-alive, and closes the request body reader.
+  This function is guarded by `Config.lingeringTimeout` and may be cancelled on server shutdown.
+  The default implementation always returns `true`.
+  -/
+  onContinue (self : σ) (request : Request.Head) : Async Bool :=
+    pure true
+
+end Std.Http.Server

src/Std/Internal/Http/Transport.lean

@@ -0,0 +1,249 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+module
+
+prelude
+public import Std.Internal.Http.Protocol.H1
+
+public section
+
+/-!
+# Transport
+
+This module exposes a `Transport` type class that is used to represent different transport mechanisms
+that can be used with an HTTP connection.
+-/
+
+namespace Std.Http
+open Std Internal IO Async TCP
+
+set_option linter.all true
+
+/--
+Generic HTTP interface that abstracts over different transport mechanisms.
+-/
+class Transport (α : Type) where
+  /--
+  Receive data from the client connection, up to the expected size.
+  Returns None if the connection is closed or no data is available.
+  -/
+  recv : α → UInt64 → Async (Option ByteArray)
+
+  /--
+  Send all data through the client connection.
+  -/
+  sendAll : α → Array ByteArray → Async Unit
+
+  /--
+  Get a selector for receiving data asynchronously.
+  -/
+  recvSelector : α → UInt64 → Selector (Option ByteArray)
+
+  /--
+  Close the transport connection.
+  The default implementation is a no-op; override this for transports that require explicit teardown.
+  For `Socket.Client`, the runtime closes the file descriptor when the object is finalized.
+  -/
+  close : α → IO Unit := fun _ => pure ()
+
+instance : Transport Socket.Client where
+  recv client expect := client.recv? expect
+  sendAll client data := client.sendAll data
+  recvSelector client expect := client.recvSelector expect
+
+open Internal.IO.Async in
+
+/--
+Shared state for a bidirectional mock connection.
+-/
+private structure MockLink.SharedState where
+  /--
+  Client to server direction.
+  -/
+  clientToServer : Std.CloseableChannel ByteArray
+
+  /--
+  Server to client direction.
+  -/
+  serverToClient : Std.CloseableChannel ByteArray
+
+/--
+Mock client endpoint for testing.
+-/
+structure Mock.Client where
+  private shared : MockLink.SharedState
+
+/--
+Mock server endpoint for testing.
+-/
+structure Mock.Server where
+  private shared : MockLink.SharedState
+
+namespace Mock
+
+/--
+Creates a mock server and client that are connected to each other and share the
+same underlying state, enabling bidirectional communication.
+-/
+def new : BaseIO (Mock.Client × Mock.Server) := do
+  let first ← Std.CloseableChannel.new
+  let second ← Std.CloseableChannel.new
+
+  return (⟨⟨first, second⟩⟩, ⟨⟨first, second⟩⟩)
+
+/--
+Receives data from a channel, joining all available data up to the expected size. First does a
+blocking recv, then greedily consumes available data with tryRecv until `expect` bytes are reached.
+-/
+def recvJoined (recvChan : Std.CloseableChannel ByteArray) (expect : Option UInt64) : Async (Option ByteArray) := do
+  match ← await (← recvChan.recv) with
+  | none => return none
+  | some first =>
+    let mut result := first
+    repeat
+      if let some expect := expect then
+        if result.size.toUInt64 ≥ expect then break
+
+      match ← recvChan.tryRecv with
+      | none => break
+      | some chunk => result := result ++ chunk
+    return some result
+
+/--
+Sends a single ByteArray through a channel.
+-/
+def send (sendChan : Std.CloseableChannel ByteArray) (data : ByteArray) : Async Unit := do
+  Async.ofAsyncTask ((← sendChan.send data) |>.map (Except.mapError (IO.userError ∘ toString)))
+
+/--
+Sends ByteArrays through a channel.
+-/
+def sendAll (sendChan : Std.CloseableChannel ByteArray) (data : Array ByteArray) : Async Unit := do
+  for chunk in data do
+    send sendChan chunk
+
+/--
+Creates a selector for receiving from a channel.
+-/
+def recvSelector (recvChan : Std.CloseableChannel ByteArray) : Selector (Option ByteArray) :=
+  recvChan.recvSelector
+
+end Mock
+
+namespace Mock.Client
+
+/--
+Gets the receive channel for a client (server to client direction).
+-/
+def getRecvChan (client : Mock.Client) : Std.CloseableChannel ByteArray :=
+  client.shared.serverToClient
+
+/--
+Gets the send channel for a client (client to server direction).
+-/
+def getSendChan (client : Mock.Client) : Std.CloseableChannel ByteArray :=
+  client.shared.clientToServer
+
+/--
+Sends a single ByteArray.
+-/
+def send (client : Mock.Client) (data : ByteArray) : Async Unit :=
+  Mock.send (getSendChan client) data
+
+/--
+Receives data, joining all available chunks.
+-/
+def recv? (client : Mock.Client) (expect : Option UInt64 := none) : Async (Option ByteArray) :=
+  Mock.recvJoined (getRecvChan client) expect
+
+/--
+Tries to receive data without blocking, joining all immediately available chunks.
+Returns `none` if no data is available.
+-/
+def tryRecv? (client : Mock.Client) (_expect : UInt64 := 0) : BaseIO (Option ByteArray) := do
+  match ← (getRecvChan client).tryRecv with
+  | none => return none
+  | some first =>
+    let mut result := first
+    repeat
+      match ← (getRecvChan client).tryRecv with
+      | none => break
+      | some chunk => result := result ++ chunk
+    return some result
+
+/--
+Closes the mock server and client.
+-/
+def close (client : Mock.Client) : IO Unit := do
+  if !(← client.shared.clientToServer.isClosed) then client.shared.clientToServer.close
+  if !(← client.shared.serverToClient.isClosed) then client.shared.serverToClient.close
+
+end Mock.Client
+
+namespace Mock.Server
+
+/--
+Gets the receive channel for a server (client to server direction).
+-/
+def getRecvChan (server : Mock.Server) : Std.CloseableChannel ByteArray :=
+  server.shared.clientToServer
+
+/--
+Gets the send channel for a server (server to client direction).
+-/
+def getSendChan (server : Mock.Server) : Std.CloseableChannel ByteArray :=
+  server.shared.serverToClient
+
+/--
+Sends a single ByteArray.
+-/
+def send (server : Mock.Server) (data : ByteArray) : Async Unit :=
+  Mock.send (getSendChan server) data
+
+/--
+Receives data, joining all available chunks.
+-/
+def recv? (server : Mock.Server) (expect : Option UInt64 := none) : Async (Option ByteArray) :=
+  Mock.recvJoined (getRecvChan server) expect
+
+/--
+Tries to receive data without blocking, joining all immediately available chunks. Returns `none` if no
+data is available.
+-/
+def tryRecv? (server : Mock.Server) (_expect : UInt64 := 0) : BaseIO (Option ByteArray) := do
+  match ← (getRecvChan server).tryRecv with
+  | none => return none
+  | some first =>
+    let mut result := first
+    repeat
+      match ← (getRecvChan server).tryRecv with
+      | none => break
+      | some chunk => result := result ++ chunk
+    return some result
+
+/--
+Closes the mock server and client.
+-/
+def close (server : Mock.Server) : IO Unit := do
+  if !(← server.shared.clientToServer.isClosed) then server.shared.clientToServer.close
+  if !(← server.shared.serverToClient.isClosed) then server.shared.serverToClient.close
+
+
+end Mock.Server
+
+instance : Transport Mock.Client where
+  recv client expect := Mock.recvJoined (Mock.Client.getRecvChan client) (some expect)
+  sendAll client data := Mock.sendAll (Mock.Client.getSendChan client) data
+  recvSelector client _ := Mock.recvSelector (Mock.Client.getRecvChan client)
+  close client := client.close
+
+instance : Transport Mock.Server where
+  recv server expect := Mock.recvJoined (Mock.Server.getRecvChan server) (some expect)
+  sendAll server data := Mock.sendAll (Mock.Server.getSendChan server) data
+  recvSelector server _ := Mock.recvSelector (Mock.Server.getRecvChan server)
+  close server := server.close
+
+end Std.Http

src/Std/Internal/Parsec/ByteArray.lean

@@ -44,8 +44,15 @@ protected def Parser.run (p : Parser α) (arr : ByteArray) : Except String α :=
 Parse a single byte equal to `b`, fails if different.
 -/
 @[inline]
-def pbyte (b : UInt8) : Parser UInt8 := attempt do
-  if (← any) = b then pure b else fail s!"expected: '{b}'"
+def pbyte (b : UInt8) : Parser UInt8 := fun it =>
+  if h : it.hasNext then
+    let got := it.curr' h
+    if got = b then
+      .success (it.next' h) got
+    else
+      .error it (.other s!"expected: '{b}'")
+  else
+    .error it .eof
 
 /--
 Skip a single byte equal to `b`, fails if different.
@@ -57,16 +64,29 @@ def skipByte (b : UInt8) : Parser Unit :=
 /--
 Skip a sequence of bytes equal to the given `ByteArray`.
 -/
-def skipBytes (arr : ByteArray) : Parser Unit := do
-  for b in arr do
-    skipByte b
+def skipBytes (arr : ByteArray) : Parser Unit := fun it =>
+  let rec go (idx : Nat) (it : ByteArray.Iterator) : ParseResult Unit ByteArray.Iterator :=
+    if h : idx < arr.size then
+      if hnext : it.hasNext then
+        let got := it.curr' hnext
+        let want := arr[idx]
+        if got = want then
+          go (idx + 1) (it.next' hnext)
+        else
+          .error it (.other s!"expected byte {want}, got {got}")
+      else
+        .error it .eof
+    else
+      .success it ()
+  go 0 it
 
 /--
 Parse a string by matching its UTF-8 bytes, returns the string on success.
 -/
 @[inline]
 def pstring (s : String) : Parser String := do
-  skipBytes s.toUTF8
+  let utf8 := s.toUTF8
+  skipBytes utf8
   return s
 
 /--
@@ -193,19 +213,47 @@ def take (n : Nat) : Parser ByteSlice := fun it =>
   else
     .success (it.forward n) (it.array[it.idx...(it.idx+n)])
 
+/--
+Scans while `pred` is satisfied. Returns `(count, iterator, hitEof)`.
+-/
+private partial def scanWhile (pred : UInt8 → Bool) (count : Nat) (iter : ByteArray.Iterator) :
+    Nat × ByteArray.Iterator × Bool :=
+  if h : iter.hasNext then
+    if pred (iter.curr' h) then
+      scanWhile pred (count + 1) (iter.next' h)
+    else
+      (count, iter, false)
+  else
+    (count, iter, true)
+
+/--
+Scans while `pred` is satisfied, bounded by `limit`.
+Returns `(count, iterator, hitEof)`.
+-/
+private partial def scanWhileUpTo (pred : UInt8 → Bool) (limit : Nat) (count : Nat)
+    (iter : ByteArray.Iterator) : Nat × ByteArray.Iterator × Bool :=
+  if count ≥ limit then
+    (count, iter, false)
+  else if h : iter.hasNext then
+    if pred (iter.curr' h) then
+      scanWhileUpTo pred limit (count + 1) (iter.next' h)
+    else
+      (count, iter, false)
+  else
+    (count, iter, true)
+
 /--
 Parses while a predicate is satisfied.
+Fails with `.eof` if input ends while the predicate still holds.
 -/
 @[inline]
 partial def takeWhile (pred : UInt8 → Bool) : Parser ByteSlice :=
   fun it =>
-    let rec findEnd (count : Nat) (iter : ByteArray.Iterator) : Nat × ByteArray.Iterator :=
-      if ¬iter.hasNext then (count, iter)
-      else if pred iter.curr then findEnd (count + 1) iter.next
-      else (count, iter)
-
-    let (length, newIt) := findEnd 0 it
-    .success newIt (it.array[it.idx...(it.idx + length)])
+    let (length, newIt, hitEof) := scanWhile pred 0 it
+    if hitEof then
+      .error newIt .eof
+    else
+      .success newIt (it.array[it.idx...(it.idx + length)])
 
 /--
 Parses until a predicate is satisfied (exclusive).
@@ -216,16 +264,16 @@ def takeUntil (pred : UInt8 → Bool) : Parser ByteSlice :=
 
 /--
 Skips while a predicate is satisfied.
+Fails with `.eof` if input ends while the predicate still holds.
 -/
 @[inline]
 partial def skipWhile (pred : UInt8 → Bool) : Parser Unit :=
   fun it =>
-    let rec findEnd (count : Nat) (iter : ByteArray.Iterator) : ByteArray.Iterator :=
-      if ¬iter.hasNext then iter
-      else if pred iter.curr then findEnd (count + 1) iter.next
-      else iter
-
-    .success (findEnd 0 it) ()
+    let (_, newIt, hitEof) := scanWhile pred 0 it
+    if hitEof then
+      .error newIt .eof
+    else
+      .success newIt ()
 
 /--
 Skips until a predicate is satisfied.
@@ -236,34 +284,31 @@ def skipUntil (pred : UInt8 → Bool) : Parser Unit :=
 
 /--
 Parses while a predicate is satisfied, up to a given limit.
+Fails with `.eof` if input ends before stopping or reaching the limit.
 -/
 @[inline]
 partial def takeWhileUpTo (pred : UInt8 → Bool) (limit : Nat) : Parser ByteSlice :=
   fun it =>
-    let rec findEnd (count : Nat) (iter : ByteArray.Iterator) : Nat × ByteArray.Iterator :=
-      if count ≥ limit then (count, iter)
-      else if ¬iter.hasNext then (count, iter)
-      else if pred iter.curr then findEnd (count + 1) iter.next
-      else (count, iter)
+    let (length, newIt, hitEof) := scanWhileUpTo pred limit 0 it
 
-    let (length, newIt) := findEnd 0 it
-    .success newIt (it.array[it.idx...(it.idx + length)])
+    if hitEof then
+      .error newIt .eof
+    else
+      .success newIt (it.array[it.idx...(it.idx + length)])
 
 /--
 Parses while a predicate is satisfied, up to a given limit, requiring at least one byte.
+Fails with `.eof` if input ends before stopping or reaching the limit.
 -/
 @[inline]
 def takeWhileUpTo1 (pred : UInt8 → Bool) (limit : Nat) : Parser ByteSlice :=
   fun it =>
-    let rec findEnd (count : Nat) (iter : ByteArray.Iterator) : Nat × ByteArray.Iterator :=
-      if count ≥ limit then (count, iter)
-      else if ¬iter.hasNext then (count, iter)
-      else if pred iter.curr then findEnd (count + 1) iter.next
-      else (count, iter)
+    let (length, newIt, hitEof) := scanWhileUpTo pred limit 0 it
 
-    let (length, newIt) := findEnd 0 it
-    if length = 0 then
-      .error it (if newIt.atEnd then .eof else .other "expected at least one char")
+    if hitEof then
+      .error newIt .eof
+    else if length = 0 then
+      .error it (.other "expected at least one char")
     else
       .success newIt (it.array[it.idx...(it.idx + length)])
 
@@ -274,19 +319,42 @@ Parses until a predicate is satisfied (exclusive), up to a given limit.
 def takeUntilUpTo (pred : UInt8 → Bool) (limit : Nat) : Parser ByteSlice :=
   takeWhileUpTo (fun b => ¬pred b) limit
 
+/--
+Parses while a predicate is satisfied, consuming at most `limit` bytes.
+Unlike `takeWhileUpTo`, succeeds even if input ends before the predicate stops holding.
+-/
+@[inline]
+def takeWhileAtMost (pred : UInt8 → Bool) (limit : Nat) : Parser ByteSlice :=
+  fun it =>
+    let (length, newIt, _) := scanWhileUpTo pred limit 0 it
+    .success newIt (it.array[it.idx...(it.idx + length)])
+
+/--
+Parses while a predicate is satisfied, consuming at most `limit` bytes, requiring at least one.
+Unlike `takeWhileUpTo1`, succeeds even if input ends before the predicate stops holding.
+-/
+@[inline]
+def takeWhile1AtMost (pred : UInt8 → Bool) (limit : Nat) : Parser ByteSlice :=
+  fun it =>
+    let (length, newIt, _) := scanWhileUpTo pred limit 0 it
+    if length = 0 then
+      .error it (.other "expected at least one char")
+    else
+      .success newIt (it.array[it.idx...(it.idx + length)])
+
 /--
 Skips while a predicate is satisfied, up to a given limit.
+Fails with `.eof` if input ends before stopping or reaching the limit.
 -/
 @[inline]
 partial def skipWhileUpTo (pred : UInt8 → Bool) (limit : Nat) : Parser Unit :=
   fun it =>
-    let rec findEnd (count : Nat) (iter : ByteArray.Iterator) : ByteArray.Iterator :=
-      if count ≥ limit then iter
-      else if ¬iter.hasNext then iter
-      else if pred iter.curr then findEnd (count + 1) iter.next
-      else iter
+    let (_, newIt, hitEof) := scanWhileUpTo pred limit 0 it
 
-    .success (findEnd 0 it) ()
+    if hitEof then
+      .error newIt .eof
+    else
+      .success newIt ()
 
 /--
 Skips until a predicate is satisfied, up to a given limit.

src/Std/Sync.lean

@@ -11,6 +11,7 @@ public import Std.Sync.Channel
 public import Std.Sync.Mutex
 public import Std.Sync.RecursiveMutex
 public import Std.Sync.Barrier
+public import Std.Sync.Semaphore
 public import Std.Sync.SharedMutex
 public import Std.Sync.Notify
 public import Std.Sync.Broadcast

src/Std/Sync/Semaphore.lean

@@ -0,0 +1,96 @@
+/-
+Copyright (c) 2026 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Lean FRO Contributors
+-/
+module
+
+prelude
+public import Init.Data.Queue
+public import Init.System.Promise
+public import Std.Sync.Mutex
+
+public section
+
+namespace Std
+
+private structure SemaphoreState where
+  permits : Nat
+  waiters : Std.Queue (IO.Promise Unit) := ∅
+deriving Nonempty
+
+/--
+Counting semaphore.
+
+`Semaphore.acquire` returns a promise that is resolved once a permit is available.
+If a permit is currently available, the returned promise is already resolved.
+`Semaphore.release` either resolves one waiting promise or increments the available permits.
+-/
+structure Semaphore where private mk ::
+  private lock : Mutex SemaphoreState
+
+/--
+Creates a resolved promise.
+-/
+private def mkResolvedPromise [Nonempty α] (a : α) : BaseIO (IO.Promise α) := do
+  let promise ← IO.Promise.new
+  promise.resolve a
+  return promise
+
+/--
+Creates a new semaphore with `permits` initially available permits.
+-/
+def Semaphore.new (permits : Nat) : BaseIO Semaphore := do
+  return { lock := ← Mutex.new { permits } }
+
+/--
+Requests one permit.
+Returns a promise that resolves once the permit is acquired.
+-/
+def Semaphore.acquire (sem : Semaphore) : BaseIO (IO.Promise Unit) := do
+  sem.lock.atomically do
+    let st ← get
+    if st.permits > 0 then
+      set { st with permits := st.permits - 1 }
+      mkResolvedPromise ()
+    else
+      let promise ← IO.Promise.new
+      set { st with waiters := st.waiters.enqueue promise }
+      return promise
+
+/--
+Tries to acquire a permit without blocking. Returns `true` on success.
+-/
+def Semaphore.tryAcquire (sem : Semaphore) : BaseIO Bool := do
+  sem.lock.atomically do
+    let st ← get
+    if st.permits > 0 then
+      set { st with permits := st.permits - 1 }
+      return true
+    else
+      return false
+
+/--
+Releases one permit and resolves one waiting acquirer, if any.
+-/
+def Semaphore.release (sem : Semaphore) : BaseIO Unit := do
+  let waiter? ← sem.lock.atomically do
+    let st ← get
+    match st.waiters.dequeue? with
+    | some (waiter, waiters) =>
+      set { st with waiters }
+      return some waiter
+    | none =>
+      set { st with permits := st.permits + 1 }
+      return none
+  if let some waiter := waiter? then
+    waiter.resolve ()
+
+/--
+Returns the number of currently available permits.
+-/
+def Semaphore.availablePermits (sem : Semaphore) : BaseIO Nat :=
+  sem.lock.atomically do
+    return (← get).permits
+
+end Std

src/util/option_declarations.cpp

@@ -49,7 +49,7 @@ data_value mk_data_value(data_value_kind k, char const * val) {
 extern "C" object * lean_register_option(obj_arg name, obj_arg decl);
 
 void register_option(name const & n, name const & decl_name, data_value_kind k, char const * default_value, char const * description) {
-    object_ref decl = mk_cnstr(0, n, decl_name, mk_data_value(k, default_value), string_ref(description));
+    object_ref decl = mk_cnstr(0, n, decl_name, mk_data_value(k, default_value), string_ref(description), object_ref(lean_box(0)));
     consume_io_result(lean_register_option(n.to_obj_arg(), decl.to_obj_arg()));
 }
 }