chore: rename automatically generated "unfold" theorems

Given a definition `foo`, they were previously called `foo._unfold`
until 4.7.0. We tried to rename them to `foo.def`, but it created too
many issues in the Mathlib repo. We decided to rename it again to
`foo.eq_def`. The new name is also consistent with the `eq_<idx>`
theorems generated for different "cases". That is, `foo.eq_def` is the
equality theorem for the whole definition, and `foo.eq_<idx>` is the
equality theorem for case `<idx>`.

src/Lean/Elab/PreDefinition/Eqns.lean

@@ -371,7 +371,7 @@ def mkUnfoldEq (declName : Name) (info : EqnInfoCore) : MetaM Name := withLCtx {
       mkUnfoldProof declName goal.mvarId!
       let type ← mkForallFVars xs type
       let value ← mkLambdaFVars xs (← instantiateMVars goal)
-      let name := baseName ++ `def
+      let name := Name.str baseName unfoldThmSuffix
       addDecl <| Declaration.thmDecl {
         name, type, value
         levelParams := info.levelParams

src/Lean/Elab/PreDefinition/Structural/Eqns.lean

@@ -68,7 +68,7 @@ def mkEqns (info : EqnInfo) : MetaM (Array Name) :=
   for i in [: eqnTypes.size] do
     let type := eqnTypes[i]!
     trace[Elab.definition.structural.eqns] "{eqnTypes[i]!}"
-    let name := baseName ++ (`eq).appendIndexAfter (i+1)
+    let name := (Name.str baseName eqnThmSuffixBase).appendIndexAfter (i+1)
     thmNames := thmNames.push name
     let value ← mkProof info.declName type
     let (type, value) ← removeUnusedEqnHypotheses type value

src/Lean/Elab/PreDefinition/WF/Eqns.lean

@@ -119,7 +119,7 @@ def mkEqns (declName : Name) (info : EqnInfo) : MetaM (Array Name) :=
   for i in [: eqnTypes.size] do
     let type := eqnTypes[i]!
     trace[Elab.definition.wf.eqns] "{eqnTypes[i]!}"
-    let name := baseName ++ (`eq).appendIndexAfter (i+1)
+    let name := (Name.str baseName eqnThmSuffixBase).appendIndexAfter (i+1)
     thmNames := thmNames.push name
     let value ← mkProof declName type
     let (type, value) ← removeUnusedEqnHypotheses type value

src/Lean/Meta/Eqns.lean

@@ -9,25 +9,32 @@ import Lean.Meta.Basic
 import Lean.Meta.AppBuilder
 
 namespace Lean.Meta
+def eqnThmSuffixBase := "eq"
+def eqnThmSuffixBasePrefix := eqnThmSuffixBase ++ "_"
+def eqn1ThmSuffix := eqnThmSuffixBasePrefix ++ "1"
+example : eqn1ThmSuffix = "eq_1" := rfl
+
 /-- Returns `true` if `s` is of the form `eq_<idx>` -/
 def isEqnReservedNameSuffix (s : String) : Bool :=
-  "eq_".isPrefixOf s && (s.drop 3).isNat
+  eqnThmSuffixBasePrefix.isPrefixOf s && (s.drop 3).isNat
 
-/-- Returns `true` if `s == "def"` -/
+def unfoldThmSuffix := "eq_def"
+
+/-- Returns `true` if `s == "eq_def"` -/
 def isUnfoldReservedNameSuffix (s : String) : Bool :=
-  s == "def"
+  s == unfoldThmSuffix
 
 /--
 Throw an error if names for equation theorems for `declName` are not available.
 -/
 def ensureEqnReservedNamesAvailable (declName : Name) : CoreM Unit := do
-  ensureReservedNameAvailable declName "def"
-  ensureReservedNameAvailable declName "eq_1"
+  ensureReservedNameAvailable declName unfoldThmSuffix
+  ensureReservedNameAvailable declName eqn1ThmSuffix
   -- TODO: `declName` may need to reserve multiple `eq_<idx>` names, but we check only the first one.
   -- Possible improvement: try to efficiently compute the number of equation theorems at declaration time, and check all of them.
 
 /--
-Ensures that `f.def` and `f.eq_<idx>` are reserved names if `f` is a safe definition.
+Ensures that `f.eq_def` and `f.eq_<idx>` are reserved names if `f` is a safe definition.
 -/
 builtin_initialize registerReservedNamePredicate fun env n =>
   match n with
@@ -87,7 +94,7 @@ builtin_initialize eqnsExt : EnvExtension EqnsExtState ←
 /--
 Simple equation theorem for nonrecursive definitions.
 -/
-private def mkSimpleEqThm (declName : Name) (suffix := `def) : MetaM (Option Name) := do
+private def mkSimpleEqThm (declName : Name) (suffix := Name.mkSimple unfoldThmSuffix) : MetaM (Option Name) := do
   if let some (.defnInfo info) := (← getEnv).find? declName then
     lambdaTelescope (cleanupAnnotations := true) info.value fun xs body => do
       let lhs := mkAppN (mkConst info.name <| info.levelParams.map mkLevelParam) xs
@@ -122,7 +129,7 @@ Equation theorems are generated on demand, check whether they were generated in
 -/
 private partial def alreadyGenerated? (declName : Name) : MetaM (Option (Array Name)) := do
   let env ← getEnv
-  let eq1 := declName ++ `eq_1
+  let eq1 := Name.str declName eqn1ThmSuffix
   if env.contains eq1 then
     let rec loop (idx : Nat) (eqs : Array Name) : MetaM (Array Name) := do
       let nextEq := declName ++ (`eq).appendIndexAfter idx
@@ -152,7 +159,7 @@ def getEqnsFor? (declName : Name) (nonRec := false) : MetaM (Option (Array Name)
         registerEqnThms declName r
         return some r
     if nonRec then
-      let some eqThm ← mkSimpleEqThm declName (suffix := `eq_1) | return none
+      let some eqThm ← mkSimpleEqThm declName (suffix := Name.mkSimple eqn1ThmSuffix) | return none
       let r := #[eqThm]
       registerEqnThms declName r
       return some r
@@ -199,7 +206,7 @@ You can use `nonRec := true` to override this behavior.
 -/
 def getUnfoldEqnFor? (declName : Name) (nonRec := false) : MetaM (Option Name) := withLCtx {} {} do
   let env ← getEnv
-  let unfoldName := declName ++ `def
+  let unfoldName := Name.str declName unfoldThmSuffix
   if env.contains unfoldName then
     return some unfoldName
   if (← shouldGenerateEqnThms declName) then

tests/lean/run/1026.lean

@@ -11,7 +11,7 @@ theorem ex : foo 0 = 0 := by
   sorry
 
 /--
-info: foo.def (n : Nat) :
+info: foo.eq_def (n : Nat) :
   foo n =
     if n = 0 then 0
     else
@@ -20,4 +20,4 @@ info: foo.def (n : Nat) :
       foo x
 -/
 #guard_msgs in
-#check foo.def
+#check foo.eq_def

tests/lean/run/nestedWF.lean

@@ -58,7 +58,7 @@ theorem ex2 : g 0 = 0 := by
   unfold g
   simp
 
-#check g.def
+#check g.eq_def
 
 
 end Ex2

tests/lean/run/reserved.lean

@@ -1,8 +1,8 @@
--- `g.def` is not reserved yet
-theorem g.def : 1 + x = x + 1 := Nat.add_comm ..
+-- `g.eq_def` is not reserved yet
+theorem g.eq_def : 1 + x = x + 1 := Nat.add_comm ..
 
 /--
-error: failed to declare `g` because `g.def` has already been declared
+error: failed to declare `g` because `g.eq_def` has already been declared
 -/
 #guard_msgs (error) in
 def g (x : Nat) := x + 1
@@ -10,10 +10,10 @@ def g (x : Nat) := x + 1
 def f (x : Nat) := x + 1
 
 /--
-error: 'f.def' is a reserved name
+error: 'f.eq_def' is a reserved name
 -/
 #guard_msgs (error) in
-theorem f.def : f x = x + 1 := rfl
+theorem f.eq_def : f x = x + 1 := rfl
 
 /--
 error: 'f.eq_1' is a reserved name
@@ -31,16 +31,16 @@ def f.eq_2_ := 10 -- Should be ok
 #guard_msgs (error) in
 #check f.eq_2
 
-/-- info: f.def (x : Nat) : f x = x + 1 -/
+/-- info: f.eq_def (x : Nat) : f x = x + 1 -/
 #guard_msgs in
-#check f.def
+#check f.eq_def
 
 def fact : Nat → Nat
   | 0 => 1
   | n+1 => (n+1) * fact n
 
 /--
-info: fact.def :
+info: fact.eq_def :
   ∀ (x : Nat),
     fact x =
       match x with
@@ -48,7 +48,7 @@ info: fact.def :
       | n.succ => (n + 1) * fact n
 -/
 #guard_msgs in
-#check fact.def
+#check fact.eq_def
 
 /-- info: fact.eq_1 : fact 0 = 1 -/
 #guard_msgs in
@@ -77,9 +77,9 @@ example : fact' 0 + fact' 1 = 2 := by
   rw [fact'.eq_1]
 
 example : fact' 0 + fact' 1 = 2 := by
-  rw [fact'.def, fact'.def]; simp
+  rw [fact'.eq_def, fact'.eq_def]; simp
   guard_target =ₛ 1 + fact' 0 = 2
-  rw [fact'.def]
+  rw [fact'.eq_def]
   guard_target =
     (1 + fact.match_1 (fun _ => Nat) 0 (fun _ => 1) fun n => (n + 1) * fact' n) = 2
   simp
@@ -88,3 +88,19 @@ theorem bla : 0 = 0 := rfl
 
 def bla.def := 1 -- should work since `bla` is a theorem
 def bla.eq_1 := 2 -- should work since `bla` is a theorem
+
+def find (as : Array Int) (i : Nat) (v : Int) : Nat :=
+  if _ : i < as.size then
+    if as[i] = v then
+      i
+    else
+      find as (i+1) v
+  else
+    i
+
+/--
+info: find.eq_def (as : Array Int) (i : Nat) (v : Int) :
+  find as i v = if x : i < as.size then if as[i] = v then i else find as (i + 1) v else i
+-/
+#guard_msgs in
+#check find.eq_def

tests/lean/run/splitIssue.lean

@@ -30,7 +30,7 @@ theorem len_2 (a b : α) (bs : List α) : len (a::b::bs) = 1 + len (b::bs) := by
   conv => lhs; unfold len
 
 -- The `unfold` tactic above generated the following theorem
-#check @len.def
+#check @len.eq_def
 
 theorem len_cons (a : α) (as : List α) : len (a::as) = 1 + len as := by
   cases as with

tests/lean/run/splitList.lean

@@ -49,7 +49,7 @@ theorem len_2 (a b : α) (bs : List α) : len (a::b::bs) = 1 + len (b::bs) := by
   conv => lhs; unfold len
 
 -- The `unfold` tactic above generated the following theorem
-#check @len.def
+#check @len.eq_def
 
 theorem len_cons (a : α) (as : List α) : len (a::as) = 1 + len as := by
   cases as with
@@ -99,7 +99,7 @@ theorem len_2 (a b : α) (bs : List α) : len (a::b::bs) = 1 + len (b::bs) := by
   conv => lhs; unfold len
 
 -- The `unfold` tactic above generated the following theorem
-#check @len.def
+#check @len.eq_def
 
 theorem len_cons (a : α) (as : List α) : len (a::as) = 1 + len as := by
   cases as with

tests/lean/run/structEqns.lean

@@ -17,7 +17,7 @@ def foo (xs ys zs : List Nat) : List Nat :=
 #eval tst ``foo
 
 /--
-info: foo.def (xs ys zs : List Nat) :
+info: foo.eq_def (xs ys zs : List Nat) :
   foo xs ys zs =
     match (xs, ys) with
     | (xs', ys') =>
@@ -29,7 +29,7 @@ info: foo.def (xs ys zs : List Nat) :
         | x => [2]
 -/
 #guard_msgs in
-#check foo.def
+#check foo.eq_def
 
 
 def bar (xs ys : List Nat) : List Nat :=

tests/lean/run/structuralEqns.lean

@@ -8,7 +8,7 @@ def tst (declName : Name) : MetaM Unit := do
 #eval tst ``List.map
 #check @List.map.eq_1
 #check @List.map.eq_2
-#check @List.map.def
+#check @List.map.eq_def
 
 def foo (xs ys zs : List Nat) : List Nat :=
   match (xs, ys) with
@@ -23,7 +23,7 @@ def foo (xs ys zs : List Nat) : List Nat :=
 
 #check foo.eq_1
 #check foo.eq_2
-#check foo.def
+#check foo.eq_def
 
 #eval tst ``foo
 
@@ -40,7 +40,7 @@ def g : List Nat → List Nat → Nat
 #check g.eq_3
 #check g.eq_4
 #check g.eq_5
-#check g.def
+#check g.eq_def
 
 def h (xs : List Nat) (y : Nat) : Nat :=
   match xs with
@@ -53,7 +53,7 @@ def h (xs : List Nat) (y : Nat) : Nat :=
 #eval tst ``h
 #check h.eq_1
 #check h.eq_2
-#check h.def
+#check h.eq_def
 
 def r (i j : Nat) : Nat :=
   i +
@@ -68,7 +68,7 @@ def r (i j : Nat) : Nat :=
 #check r.eq_1
 #check r.eq_2
 #check r.eq_3
-#check r.def
+#check r.eq_def
 
 def bla (f g : α → α → α) (a : α) (i : α) (j : Nat) : α :=
   f i <|
@@ -83,4 +83,4 @@ def bla (f g : α → α → α) (a : α) (i : α) (j : Nat) : α :=
 #check @bla.eq_1
 #check @bla.eq_2
 #check @bla.eq_3
-#check @bla.def
+#check @bla.eq_def

tests/lean/run/structuralEqns2.lean

@@ -14,7 +14,7 @@ def g (i j : Nat) : Nat :=
 #eval tst ``g
 #check g.eq_1
 #check g.eq_2
-#check g.def
+#check g.eq_def
 
 def h (i j : Nat) : Nat :=
   let z :=
@@ -26,4 +26,4 @@ def h (i j : Nat) : Nat :=
 #eval tst ``h
 #check h.eq_1
 #check h.eq_2
-#check h.def
+#check h.eq_def

tests/lean/run/structuralEqns3.lean

@@ -17,4 +17,4 @@ def wk_comp : Wk n m → Wk m l → Wk n l
 
 #check @wk_comp.eq_1
 #check @wk_comp.eq_2
-#check @wk_comp.def
+#check @wk_comp.eq_def

tests/lean/run/wfEqns1.lean

@@ -24,4 +24,4 @@ end
 #eval tst ``isEven
 #check @isEven.eq_1
 #check @isEven.eq_2
-#check @isEven.def
+#check @isEven.eq_def

tests/lean/run/wfEqns2.lean

@@ -33,8 +33,8 @@ end
 #eval tst ``g
 #check g.eq_1
 #check g.eq_2
-#check g.def
+#check g.eq_def
 #eval tst ``h
 #check h.eq_1
 #check h.eq_2
-#check h.def
+#check h.eq_def

tests/lean/run/wfEqns3.lean

@@ -16,4 +16,4 @@ decreasing_by
 
 #eval tst ``f
 #check f.eq_1
-#check f.def
+#check f.eq_def

tests/lean/run/wfEqns4.lean

@@ -39,10 +39,10 @@ end
 #eval tst ``f
 #check @f.eq_1
 #check @f.eq_2
-#check @f.def
+#check @f.eq_def
 
 
 #eval tst ``h
 #check @h.eq_1
 #check @h.eq_2
-#check @h.def
+#check @h.eq_def