fix

This PR introduces date and time functionality to the Lean 4 Std.

Breaking Changes:
- `Lean.Data.Rat` is now `Std.Internal.Rat` because it's used by the
DateTime library.

---------

Co-authored-by: Markus Himmel <markus@himmel-villmar.de>
Co-authored-by: Mac Malone <tydeu@hatpress.net>

nix/bootstrap.nix

@@ -170,7 +170,7 @@ lib.warn "The Nix-based build is deprecated" rec {
           ln -sf ${lean-all}/* .
         '';
         buildPhase = ''
-          ctest --output-junit test-results.xml --output-on-failure -E 'leancomptest_(doc_example|foreign)|leanlaketest_reverse-ffi' -j$NIX_BUILD_CORES
+         ctest --output-junit test-results.xml --output-on-failure -E 'leancomptest_(doc_example|foreign)|leanlaketest_reverse-ffi|leanruntest_timeIO' -j$NIX_BUILD_CORES
         '';
         installPhase = ''
           mkdir $out

src/Init/Data.lean

@@ -42,3 +42,4 @@ import Init.Data.PLift
 import Init.Data.Zero
 import Init.Data.NeZero
 import Init.Data.Function
+import Init.Data.RArray

src/Init/Data/Array/Attach.lean

@@ -10,6 +10,16 @@ import Init.Data.List.Attach
 
 namespace Array
 
+/-- `O(n)`. Partial map. If `f : Π a, P a → β` is a partial function defined on
+  `a : α` satisfying `P`, then `pmap f l h` is essentially the same as `map f l`
+  but is defined only when all members of `l` satisfy `P`, using the proof
+  to apply `f`.
+
+We replace this at runtime with a more efficient version via
+-/
+def pmap {P : α → Prop} (f : ∀ a, P a → β) (l : Array α) (H : ∀ a ∈ l, P a) : Array β :=
+  (l.toList.pmap f (fun a m => H a (mem_def.mpr m))).toArray
+
 /--
 Unsafe implementation of `attachWith`, taking advantage of the fact that the representation of
 `Array {x // P x}` is the same as the input `Array α`.
@@ -35,6 +45,10 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
     l.toArray.attach = (l.attachWith (· ∈ l.toArray) (by simp)).toArray := by
   simp [attach]
 
+@[simp] theorem _root_.List.pmap_toArray {l : List α} {P : α → Prop} {f : ∀ a, P a → β} {H : ∀ a ∈ l.toArray, P a} :
+    l.toArray.pmap f H = (l.pmap f (by simpa using H)).toArray := by
+  simp [pmap]
+
 @[simp] theorem toList_attachWith {l : Array α} {P : α → Prop} {H : ∀ x ∈ l, P x} :
    (l.attachWith P H).toList = l.toList.attachWith P (by simpa [mem_toList] using H) := by
   simp [attachWith]
@@ -43,6 +57,22 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
     l.attach.toList = l.toList.attachWith (· ∈ l) (by simp [mem_toList]) := by
   simp [attach]
 
+@[simp] theorem toList_pmap {l : Array α} {P : α → Prop} {f : ∀ a, P a → β} {H : ∀ a ∈ l, P a} :
+    (l.pmap f H).toList = l.toList.pmap f (fun a m => H a (mem_def.mpr m)) := by
+  simp [pmap]
+
+/-- Implementation of `pmap` using the zero-copy version of `attach`. -/
+@[inline] private def pmapImpl {P : α → Prop} (f : ∀ a, P a → β) (l : Array α) (H : ∀ a ∈ l, P a) :
+    Array β := (l.attachWith _ H).map fun ⟨x, h'⟩ => f x h'
+
+@[csimp] private theorem pmap_eq_pmapImpl : @pmap = @pmapImpl := by
+  funext α β p f L h'
+  cases L
+  simp only [pmap, pmapImpl, List.attachWith_toArray, List.map_toArray, mk.injEq, List.map_attachWith]
+  apply List.pmap_congr_left
+  intro a m h₁ h₂
+  congr
+
 @[simp] theorem _root_.List.attachWith_mem_toArray {l : List α} :
     l.attachWith (fun x => x ∈ l.toArray) (fun x h => by simpa using h) =
       l.attach.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by

src/Init/Data/Nat/Linear.lean

@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
 prelude
 import Init.ByCases
 import Init.Data.Prod
+import Init.Data.RArray
 
 namespace Nat.Linear
 
@@ -15,7 +16,7 @@ namespace Nat.Linear
 
 abbrev Var := Nat
 
-abbrev Context := List Nat
+abbrev Context := Lean.RArray Nat
 
 /--
   When encoding polynomials. We use `fixedVar` for encoding numerals.
@@ -23,12 +24,7 @@ abbrev Context := List Nat
 def fixedVar := 100000000 -- Any big number should work here
 
 def Var.denote (ctx : Context) (v : Var) : Nat :=
-  bif v == fixedVar then 1 else go ctx v
-where
-  go : List Nat → Nat → Nat
-   | [],    _   => 0
-   | a::_,  0   => a
-   | _::as, i+1 => go as i
+  bif v == fixedVar then 1 else ctx.get v
 
 inductive Expr where
   | num  (v : Nat)

src/Init/Data/RArray.lean

@@ -0,0 +1,69 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Joachim Breitner
+-/
+
+prelude
+import Init.PropLemmas
+
+namespace Lean
+
+/--
+A `RArray` can model `Fin n → α` or `Array α`, but is optimized for a fast kernel-reducible `get`
+operation.
+
+The primary intended use case is the “denote” function of a typical proof by reflection proof, where
+only the `get` operation is necessary. It is not suitable as a general-purpose data structure.
+
+There is no well-formedness invariant attached to this data structure, to keep it concise; it's
+semantics is given through `RArray.get`. In that way one can also view an `RArray` as a decision
+tree implementing `Nat → α`.
+
+See `RArray.ofFn` and `RArray.ofArray` in module `Lean.Data.RArray` for functions that construct an
+`RArray`.
+
+It is not universe-polymorphic. ; smaller proof objects and no complication with the `ToExpr` type
+class.
+-/
+inductive RArray (α : Type) : Type where
+  | leaf : α → RArray α
+  | branch : Nat → RArray α → RArray α → RArray α
+
+variable {α : Type}
+
+/-- The crucial operation, written with very little abstractional overhead -/
+noncomputable def RArray.get (a : RArray α) (n : Nat) : α :=
+  RArray.rec (fun x => x) (fun p _ _ l r => (Nat.ble p n).rec l r) a
+
+private theorem RArray.get_eq_def (a : RArray α) (n : Nat) :
+  a.get n = match a with
+    | .leaf x => x
+    | .branch p l r => (Nat.ble p n).rec (l.get n) (r.get n) := by
+  conv => lhs; unfold RArray.get
+  split <;> rfl
+
+/-- `RArray.get`, implemented conventionally -/
+def RArray.getImpl (a : RArray α) (n : Nat) : α :=
+  match a with
+  | .leaf x => x
+  | .branch p l r => if n < p then l.getImpl n else r.getImpl n
+
+@[csimp]
+theorem RArray.get_eq_getImpl : @RArray.get = @RArray.getImpl := by
+  funext α a n
+  induction a with
+  | leaf _ => rfl
+  | branch p l r ihl ihr =>
+    rw [RArray.getImpl, RArray.get_eq_def]
+    simp only [ihl, ihr, ← Nat.not_le, ← Nat.ble_eq, ite_not]
+    cases hnp : Nat.ble p n <;> rfl
+
+instance : GetElem (RArray α) Nat α (fun _ _ => True) where
+  getElem a n _ := a.get n
+
+def RArray.size : RArray α → Nat
+  | leaf _ => 1
+  | branch _ l r => l.size + r.size
+
+end Lean

src/Lean/Data.lean

@@ -29,4 +29,4 @@ import Lean.Data.Xml
 import Lean.Data.NameTrie
 import Lean.Data.RBTree
 import Lean.Data.RBMap
-import Lean.Data.Rat
+import Lean.Data.RArray

src/Lean/Data/RArray.lean

@@ -0,0 +1,75 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Joachim Breitner
+-/
+
+prelude
+import Init.Data.RArray
+import Lean.ToExpr
+
+/-!
+Auxillary definitions related to `Lean.RArray` that are typically only used in meta-code, in
+particular the `ToExpr` instance.
+-/
+
+namespace Lean
+
+-- This function could live in Init/Data/RArray.lean, but without omega it's tedious to implement
+def RArray.ofFn {n : Nat} (f : Fin n → α) (h : 0 < n) : RArray α :=
+  go 0 n h (Nat.le_refl _)
+where
+  go (lb ub : Nat) (h1 : lb < ub) (h2 : ub ≤ n) : RArray α :=
+    if h : lb + 1 = ub then
+      .leaf (f ⟨lb, Nat.lt_of_lt_of_le h1 h2⟩)
+    else
+      let mid := (lb + ub)/2
+      .branch mid (go lb mid (by omega) (by omega)) (go mid ub (by omega) h2)
+
+def RArray.ofArray (xs : Array α) (h : 0 < xs.size) : RArray α :=
+  .ofFn (xs[·]) h
+
+/-- The correctness theorem for `ofFn` -/
+theorem RArray.get_ofFn {n : Nat} (f : Fin n → α) (h : 0 < n) (i : Fin n) :
+    (ofFn f h).get i = f i :=
+  go 0 n h (Nat.le_refl _) (Nat.zero_le _) i.2
+where
+  go lb ub h1 h2 (h3 : lb ≤ i.val) (h3 : i.val < ub) : (ofFn.go f lb ub h1 h2).get i = f i := by
+    induction lb, ub, h1, h2 using RArray.ofFn.go.induct (f := f) (n := n)
+    case case1 =>
+      simp [ofFn.go, RArray.get_eq_getImpl, RArray.getImpl]
+      congr
+      omega
+    case case2 ih1 ih2 hiu =>
+      rw [ofFn.go]; simp only [↓reduceDIte, *]
+      simp [RArray.get_eq_getImpl, RArray.getImpl] at *
+      split
+      · rw [ih1] <;> omega
+      · rw [ih2] <;> omega
+
+@[simp]
+theorem RArray.size_ofFn {n : Nat} (f : Fin n → α) (h : 0 < n) :
+    (ofFn f h).size = n :=
+  go 0 n h (Nat.le_refl _)
+where
+  go lb ub h1 h2 : (ofFn.go f lb ub h1 h2).size = ub - lb := by
+    induction lb, ub, h1, h2 using RArray.ofFn.go.induct (f := f) (n := n)
+    case case1 => simp [ofFn.go, size]; omega
+    case case2 ih1 ih2 hiu => rw [ofFn.go]; simp [size, *]; omega
+
+section Meta
+open Lean
+
+def RArray.toExpr (ty : Expr) (f : α → Expr) : RArray α → Expr
+  | .leaf x  =>
+    mkApp2 (mkConst ``RArray.leaf) ty (f x)
+  | .branch p l r =>
+    mkApp4 (mkConst ``RArray.branch) ty (mkRawNatLit p) (l.toExpr ty f) (r.toExpr ty f)
+
+instance [ToExpr α] : ToExpr (RArray α) where
+  toTypeExpr := mkApp (mkConst ``RArray) (toTypeExpr α)
+  toExpr a := a.toExpr (toTypeExpr α) toExpr
+
+end Meta
+
+end Lean

src/Lean/Elab/Syntax.lean

@@ -233,11 +233,14 @@ where
     return (← `((with_annotate_term $(stx[0]) @ParserDescr.sepBy1) $p $sep $psep $(quote allowTrailingSep)), 1)
 
   isValidAtom (s : String) : Bool :=
+    -- Pretty-printing instructions shouldn't affect validity
+    let s := s.trim
     !s.isEmpty &&
-    s.front != '\'' &&
+    (s.front != '\'' || s == "''") &&
     s.front != '\"' &&
     !(s.front == '`' && (s.endPos == ⟨1⟩ || isIdFirst (s.get ⟨1⟩) || isIdBeginEscape (s.get ⟨1⟩))) &&
-    !s.front.isDigit
+    !s.front.isDigit &&
+    !(s.any Char.isWhitespace)
 
   processAtom (stx : Syntax) := do
     match stx[0].isStrLit? with

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize.lean

@@ -216,35 +216,23 @@ Flatten out ands. That is look for hypotheses of the form `h : (x && y) = true`
 with `h.left : x = true` and `h.right : y = true`. This can enable more fine grained substitutions
 in embedded constraint substitution.
 -/
-def andFlatteningPass : Pass where
+partial def andFlatteningPass : Pass where
   name := `andFlattening
   run goal := do
     goal.withContext do
       let hyps ← goal.getNondepPropHyps
       let mut newHyps := #[]
       let mut oldHyps := #[]
-      for hyp in hyps do
-        let typ ← hyp.getType
-        let_expr Eq α eqLhs eqRhs := typ | continue
-        let_expr Bool.and lhs rhs := eqLhs | continue
-        let_expr Bool := α | continue
-        let_expr Bool.true := eqRhs | continue
-        let mkEqTrue (lhs : Expr) : Expr :=
-          mkApp3 (mkConst ``Eq [1]) (mkConst ``Bool) lhs (mkConst ``Bool.true)
-        let hypExpr := (← hyp.getDecl).toExpr
-        let leftHyp : Hypothesis := {
-          userName := (← hyp.getUserName) ++ `left,
-          type := mkEqTrue lhs,
-          value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_left) lhs rhs hypExpr
+      for fvar in hyps do
+        let hyp : Hypothesis := {
+          userName := (← fvar.getDecl).userName
+          type := ← fvar.getType
+          value := mkFVar fvar
         }
-        let rightHyp : Hypothesis := {
-          userName := (← hyp.getUserName) ++ `right,
-          type := mkEqTrue rhs,
-          value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_right) lhs rhs hypExpr
-        }
-        newHyps := newHyps.push leftHyp
-        newHyps := newHyps.push rightHyp
-        oldHyps := oldHyps.push hyp
+        let sizeBefore := newHyps.size
+        newHyps ← splitAnds hyp newHyps
+        if newHyps.size > sizeBefore then
+          oldHyps := oldHyps.push fvar
       if newHyps.size == 0 then
         return goal
       else
@@ -252,6 +240,38 @@ def andFlatteningPass : Pass where
         -- Given that we collected the hypotheses in the correct order above the invariant is given
         let goal ← goal.tryClearMany oldHyps
         return goal
+where
+  splitAnds (hyp : Hypothesis) (hyps : Array Hypothesis) (first : Bool := true) :
+      MetaM (Array Hypothesis) := do
+    match ← trySplit hyp with
+    | some (left, right) =>
+      let hyps ← splitAnds left hyps false
+      splitAnds right hyps false
+    | none =>
+      if first then
+        return hyps
+      else
+        return hyps.push hyp
+
+  trySplit (hyp : Hypothesis) : MetaM (Option (Hypothesis × Hypothesis)) := do
+    let typ := hyp.type
+    let_expr Eq α eqLhs eqRhs := typ | return none
+    let_expr Bool.and lhs rhs := eqLhs | return none
+    let_expr Bool.true := eqRhs | return none
+    let_expr Bool := α | return none
+    let mkEqTrue (lhs : Expr) : Expr :=
+      mkApp3 (mkConst ``Eq [1]) (mkConst ``Bool) lhs (mkConst ``Bool.true)
+    let leftHyp : Hypothesis := {
+      userName := hyp.userName,
+      type := mkEqTrue lhs,
+      value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_left) lhs rhs hyp.value
+    }
+    let rightHyp : Hypothesis := {
+      userName := hyp.userName,
+      type := mkEqTrue rhs,
+      value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_right) lhs rhs hyp.value
+    }
+    return some (leftHyp, rightHyp)
 
 /--
 Substitute embedded constraints. That is look for hypotheses of the form `h : x = true` and use
@@ -308,22 +328,18 @@ def acNormalizePass : Pass where
 
     return newGoal
 
-/--
-The normalization passes used by `bv_normalize` and thus `bv_decide`.
--/
-def defaultPipeline (cfg : BVDecideConfig ): List Pass :=
-  [
-    rewriteRulesPass cfg.maxSteps,
-    andFlatteningPass,
-    embeddedConstraintPass cfg.maxSteps
-  ]
-
 def passPipeline (cfg : BVDecideConfig) : List Pass := Id.run do
-  let mut passPipeline := defaultPipeline cfg
+  let mut passPipeline := [rewriteRulesPass cfg.maxSteps]
 
   if cfg.acNf then
     passPipeline := passPipeline ++ [acNormalizePass]
 
+  if cfg.andFlattening then
+    passPipeline := passPipeline ++ [andFlatteningPass]
+
+  if cfg.embeddedConstraintSubst then
+    passPipeline := passPipeline ++ [embeddedConstraintPass cfg.maxSteps]
+
   return passPipeline
 
 end Pass

src/Lean/Meta/Tactic/LinearArith/Nat/Basic.lean

@@ -8,6 +8,7 @@ import Lean.Meta.Check
 import Lean.Meta.Offset
 import Lean.Meta.AppBuilder
 import Lean.Meta.KExprMap
+import Lean.Data.RArray
 
 namespace Lean.Meta.Linear.Nat
 
@@ -141,8 +142,11 @@ end ToLinear
 
 export ToLinear (toLinearCnstr? toLinearExpr)
 
-def toContextExpr (ctx : Array Expr) : MetaM Expr := do
-  mkListLit (mkConst ``Nat) ctx.toList
+def toContextExpr (ctx : Array Expr) : Expr :=
+  if h : 0 < ctx.size then
+    RArray.toExpr (mkConst ``Nat) id (RArray.ofArray ctx h)
+  else
+    RArray.toExpr (mkConst ``Nat) id (RArray.leaf (mkNatLit 0))
 
 def reflTrue : Expr :=
   mkApp2 (mkConst ``Eq.refl [levelOne]) (mkConst ``Bool) (mkConst ``Bool.true)

src/Lean/Meta/Tactic/LinearArith/Nat/Simp.lean

@@ -31,17 +31,17 @@ def simpCnstrPos? (e : Expr) : MetaM (Option (Expr × Expr)) := do
     let c₂ := c₁.norm
     if c₂.isUnsat then
       let r := mkConst ``False
-      let p := mkApp3 (mkConst ``Nat.Linear.ExprCnstr.eq_false_of_isUnsat) (← toContextExpr ctx) (toExpr c) reflTrue
+      let p := mkApp3 (mkConst ``Nat.Linear.ExprCnstr.eq_false_of_isUnsat) (toContextExpr ctx) (toExpr c) reflTrue
       return some (r, ← mkExpectedTypeHint p (← mkEq lhs r))
     else if c₂.isValid then
       let r := mkConst ``True
-      let p := mkApp3 (mkConst ``Nat.Linear.ExprCnstr.eq_true_of_isValid) (← toContextExpr ctx) (toExpr c) reflTrue
+      let p := mkApp3 (mkConst ``Nat.Linear.ExprCnstr.eq_true_of_isValid) (toContextExpr ctx) (toExpr c) reflTrue
       return some (r, ← mkExpectedTypeHint p (← mkEq lhs r))
     else
       let c₂ : LinearCnstr := c₂.toExpr
       let r ← c₂.toArith ctx
       if r != lhs then
-        let p := mkApp4 (mkConst ``Nat.Linear.ExprCnstr.eq_of_toNormPoly_eq) (← toContextExpr ctx) (toExpr c) (toExpr c₂) reflTrue
+        let p := mkApp4 (mkConst ``Nat.Linear.ExprCnstr.eq_of_toNormPoly_eq) (toContextExpr ctx) (toExpr c) (toExpr c₂) reflTrue
         return some (r, ← mkExpectedTypeHint p (← mkEq lhs r))
       else
         return none
@@ -81,7 +81,7 @@ def simpExpr? (e : Expr) : MetaM (Option (Expr × Expr)) := do
   if p'.length < p.length then
     -- We only return some if monomials were fused
     let e' : LinearExpr := p'.toExpr
-    let p := mkApp4 (mkConst ``Nat.Linear.Expr.eq_of_toNormPoly_eq) (← toContextExpr ctx) (toExpr e) (toExpr e') reflTrue
+    let p := mkApp4 (mkConst ``Nat.Linear.Expr.eq_of_toNormPoly_eq) (toContextExpr ctx) (toExpr e) (toExpr e') reflTrue
     let r ← e'.toArith ctx
     return some (r, p)
   else

src/Lean/Meta/Tactic/LinearArith/Solver.lean

@@ -6,9 +6,10 @@ Authors: Leonardo de Moura
 prelude
 import Init.Data.Ord
 import Init.Data.Array.DecidableEq
-import Lean.Data.Rat
+import Std.Internal.Rat
 
 namespace Lean.Meta.Linear
+open Std.Internal
 
 structure Var where
   id : Nat

src/Std.lean

@@ -6,5 +6,6 @@ Authors: Sebastian Ullrich
 prelude
 import Std.Data
 import Std.Sat
+import Std.Time
 import Std.Tactic
 import Std.Internal

src/Std/Internal/Rat.lean

@@ -8,7 +8,8 @@ import Init.NotationExtra
 import Init.Data.ToString.Macro
 import Init.Data.Int.DivMod
 import Init.Data.Nat.Gcd
-namespace Lean
+namespace Std
+namespace Internal
 
 /-!
   Rational numbers for implementing decision procedures.
@@ -144,4 +145,5 @@ instance : Coe Int Rat where
   coe num := { num }
 
 end Rat
-end Lean
+end Internal
+end Std

src/Std/Tactic/BVDecide/Syntax.lean

@@ -29,6 +29,16 @@ structure BVDecideConfig where
   -/
   acNf : Bool := false
   /--
+  Split hypotheses of the form `h : (x && y) = true` into `h1 : x = true` and `h2 : y = true`.
+  This has synergy potential with embedded constraint substitution.
+  -/
+  andFlattening : Bool := true
+  /--
+  Look at all hypotheses of the form `h : x = true`, if `x` occurs in another hypothesis substitute
+  it with `true`.
+  -/
+  embeddedConstraintSubst : Bool := true
+  /--
   Output the AIG of bv_decide as graphviz into a file called aig.gv in the working directory of the
   Lean process.
   -/

src/Std/Time.lean

@@ -0,0 +1,231 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Time
+import Std.Time.Date
+import Std.Time.Zoned
+import Std.Time.Format
+import Std.Time.DateTime
+import Std.Time.Notation
+import Std.Time.Duration
+import Std.Time.Zoned.Database
+
+namespace Std
+namespace Time
+
+/-!
+# Time
+
+The Lean API for date, time, and duration functionalities.
+
+# Overview
+
+This module of the standard library defines various concepts related to time, such as dates, times,
+time zones and durations. These types are designed to be strongly-typed and to avoid problems with
+conversion. It offers both unbounded and bounded variants to suit different use cases, like
+adding days to a date or representing ordinal values.
+
+# Date and Time Components
+
+Date and time components are classified into different types based how you SHOULD use them. These
+components are categorized as:
+
+## Offset
+
+Offsets represent unbounded shifts in specific date or time units. They are typically used in operations
+like `date.addDays` where a `Day.Offset` is the parameter. Some offsets, such as `Month.Offset`, do not
+correspond directly to a specific duration in seconds, as their value depends on the context (if
+the year is leap or the size of the month). Offsets with a clear correspondent to seconds can be
+converted because they use an internal type called `UnitVal`.
+
+- Types with a correspondence to seconds:
+  - `Day.Offset`
+  - `Hour.Offset`
+  - `Week.Offset`
+  - `Millisecond.Offset`
+  - `Nanosecond.Offset`
+  - `Second.Offset`
+
+- Types without a correspondence to seconds:
+  - `Month.Offset`
+  - `Year.Offset`
+
+## Ordinal
+
+Ordinal types represent specific bounded values in reference to another unit, e.g., `Day.Ordinal`
+represents a day in a month, ranging from 1 to 31. Some ordinal types like `Hour.Ordinal` and `Second.Ordinal`,
+allow for values beyond the normal range (e.g, 60 seconds) to accommodate special cases with leap seconds
+like `23:59:60` that is valid in ISO 8601.
+
+- Ordinal types:
+  - `Day.Ordinal`: Ranges from 1 to 31.
+  - `Day.Ordinal.OfYear`: Ranges from 1 to (365 or 366).
+  - `Month.Ordinal`: Ranges from 1 to 12.
+  - `WeekOfYear.Ordinal`: Ranges from 1 to 53.
+  - `Hour.Ordinal`: Ranges from 0 to 23.
+  - `Millisecond.Ordinal`: Ranges from 0 to 999.
+  - `Minute.Ordinal`: Ranges from 0 to 59.
+  - `Nanosecond.Ordinal`: Ranges from 0 to 999,999,999.
+  - `Second.Ordinal`: Ranges from 0 to 60.
+  - `Weekday`: That is a inductive type with all the seven days.
+
+## Span
+
+Span types are used as subcomponents of other types. They represent a range of values in the limits
+of the parent type, e.g, `Nanosecond.Span` ranges from -999,999,999 to 999,999,999, as 1,000,000,000
+nanoseconds corresponds to one second.
+
+- Span types:
+  - `Nanosecond.Span`: Ranges from -999,999,999 to 999,999,999.
+
+# Date and Time Types
+
+Dates and times are made up of different parts. An `Ordinal` is an absolute value, like a specific day in a month,
+while an `Offset` is a shift forward or backward in time, used in arithmetic operations to add or subtract days, months or years.
+Dates use components like `Year.Ordinal`, `Month.Ordinal`, and `Day.Ordinal` to ensure they represent
+valid points in time.
+
+Some types, like `Duration`, include a `Span` to represent ranges over other types, such as `Second.Offset`.
+This type can have a fractional nanosecond part that can be negative or positive that is represented as a `Nanosecond.Span`.
+
+## Date
+These types provide precision down to the day level, useful for representing and manipulating dates.
+
+- **`PlainDate`:** Represents a calendar date in the format `YYYY-MM-DD`.
+
+## Time
+These types offer precision down to the nanosecond level, useful for representing and manipulating time of day.
+
+- **`PlainTime`**: Represents a time of day in the format `HH:mm:ss,sssssssss`.
+
+## Date and time
+Combines date and time into a single representation, useful for precise timestamps and scheduling.
+
+- **`PlainDateTime`**: Represents both date and time in the format `YYYY-MM-DDTHH:mm:ss,sssssssss`.
+- **`Timestamp`**: Represents a specific point in time with nanosecond precision. Its zero value corresponds
+to the UNIX epoch. This type should be used when sending or receiving timestamps between systems.
+
+## Zoned date and times.
+Combines date, time and time zones.
+
+- **`DateTime`**: Represents both date and time but with a time zone in the type constructor.
+- **`ZonedDateTime`**: Is a way to represent date and time that includes `ZoneRules`, which consider
+Daylight Saving Time (DST). This means it can handle local time changes throughout the year better
+than a regular `DateTime`. If you want to use a specific time zone without worrying about DST, you can
+use the `ofTimestampWithZone` function, which gives you a `ZonedDateTime` based only on that time zone,
+without considering the zone rules, otherwise you can use `ofTimestamp` or `ofTimestampWithIdentifier`.
+
+## Duration
+Represents spans of time and the difference between two points in time.
+
+- **`Duration`**: Represents the time span or difference between two `Timestamp`s values with nanosecond precision.
+
+# Formats
+
+Format strings are used to convert between `String` representations and date/time types, like `yyyy-MM-dd'T'HH:mm:ss.sssZ`.
+The table below shows the available format specifiers. Some specifiers can be repeated to control truncation or offsets.
+When a character is repeated `n` times, it usually truncates the value to `n` characters.
+
+The supported formats include:
+- `G`: Represents the era, such as AD (Anno Domini) or BC (Before Christ).
+  - `G`, `GG`, `GGG` (short): Displays the era in a short format (e.g., "AD").
+  - `GGGG` (full): Displays the era in a full format (e.g., "Anno Domini").
+  - `GGGGG` (narrow): Displays the era in a narrow format (e.g., "A").
+- `y`: Represents the year of the era.
+  - `yy`: Displays the year in a two-digit format, showing the last two digits (e.g., "04" for 2004).
+  - `yyyy`: Displays the year in a four-digit format (e.g., "2004").
+  - `yyyy+`: Extended format for years with more than four digits.
+- `u`: Represents the year.
+  - `uu`: Two-digit year format, showing the last two digits (e.g., "04" for 2004).
+  - `uuuu`: Displays the year in a four-digit format (e.g., "2004" or "-1000").
+  - `uuuu+`: Extended format for handling years with more than four digits (e.g., "12345" or "-12345"). Useful for historical dates far into the past or future!
+- `D`: Represents the day of the year.
+- `M`: Represents the month of the year, displayed as either a number or text.
+  - `M`, `MM`: Displays the month as a number, with `MM` zero-padded (e.g., "7" for July, "07" for July with padding).
+  - `MMM`: Displays the abbreviated month name (e.g., "Jul").
+  - `MMMM`: Displays the full month name (e.g., "July").
+  - `MMMMM`: Displays the month in a narrow form (e.g., "J" for July).
+- `d`: Represents the day of the month.
+- `Q`: Represents the quarter of the year.
+  - `Q`, `QQ`: Displays the quarter as a number (e.g., "3", "03").
+  - `QQQ` (short): Displays the quarter as an abbreviated text (e.g., "Q3").
+  - `QQQQ` (full): Displays the full quarter text (e.g., "3rd quarter").
+  - `QQQQQ` (narrow): Displays the quarter as a short number (e.g., "3").
+- `w`: Represents the week of the week-based year, each week starts on Monday (e.g., "27").
+- `W`: Represents the week of the month, each week starts on Monday (e.g., "4").
+- `E`: Represents the day of the week as text.
+  - `E`, `EE`, `EEE`: Displays the abbreviated weekday name (e.g., "Tue").
+  - `EEEE`: Displays the full day name (e.g., "Tuesday").
+  - `EEEEE`: Displays the narrow day name (e.g., "T" for Tuesday).
+- `e`: Represents the weekday as number or text.
+  - `e`, `ee`: Displays the the as a number, starting from 1 (Monday) to 7 (Sunday).
+  - `eee`, `eeee`, `eeeee`: Displays the weekday as text (same format as `E`).
+- `F`: Represents the week of the month that the first week starts on the first day of the month (e.g., "3").
+- `a`: Represents the AM or PM designation of the day.
+  - `a`, `aa`, `aaa`: Displays AM or PM in a concise format (e.g., "PM").
+  - `aaaa`: Displays the full AM/PM designation (e.g., "Post Meridium").
+- `h`: Represents the hour of the AM/PM clock (1-12) (e.g., "12").
+  - One or more repetitions of the character indicates the truncation of the value to the specified number of characters.
+- `K`: Represents the hour of the AM/PM clock (0-11) (e.g., "0").
+  - One or more repetitions of the character indicates the truncation of the value to the specified number of characters.
+- `k`: Represents the hour of the day in a 1-24 format (e.g., "24").
+  - One or more repetitions of the character indicates the truncation of the value to the specified number of characters.
+- `H`: Represents the hour of the day in a 0-23 format (e.g., "0").
+  - One or more repetitions of the character indicates the truncation of the value to the specified number of characters.
+- `m`: Represents the minute of the hour (e.g., "30").
+  - One or more repetitions of the character indicates the truncation of the value to the specified number of characters.
+- `s`: Represents the second of the minute (e.g., "55").
+  - One or more repetitions of the character indicates the truncation of the value to the specified number of characters.
+- `S`: Represents a fraction of a second, typically displayed as a decimal number (e.g., "978" for milliseconds).
+  - One or more repetitions of the character indicates the truncation of the value to the specified number of characters.
+- `A`: Represents the millisecond of the day (e.g., "1234").
+  - One or more repetitions of the character indicates the truncation of the value to the specified number of characters.
+- `n`: Represents the nanosecond of the second (e.g., "987654321").
+  - One or more repetitions of the character indicates the truncation of the value to the specified number of characters.
+- `N`: Represents the nanosecond of the day (e.g., "1234000000").
+  - One or more repetitions of the character indicates the truncation of the value to the specified number of characters.
+- `VV`: Represents the time zone ID, which could be a city-based zone (e.g., "America/Los_Angeles"), a UTC marker (`"Z"`), or a specific offset (e.g., "-08:30").
+  - One or more repetitions of the character indicates the truncation of the value to the specified number of characters.
+- `z`: Represents the time zone name.
+  - `z`, `zz`, `zzz`: Shows an abbreviated time zone name (e.g., "PST" for Pacific Standard Time).
+  - `zzzz`: Displays the full time zone name (e.g., "Pacific Standard Time").
+- `O`: Represents the localized zone offset in the format "GMT" followed by the time difference from UTC.
+  - `O`: Displays the GMT offset in a simple format (e.g., "GMT+8").
+  - `OOOO`: Displays the full GMT offset, including hours and minutes (e.g., "GMT+08:00").
+- `X`: Represents the zone offset. It uses 'Z' for UTC and can represent any offset (positive or negative).
+  - `X`: Displays the hour offset (e.g., "-08").
+  - `XX`: Displays the hour and minute offset without a colon (e.g., "-0830").
+  - `XXX`: Displays the hour and minute offset with a colon (e.g., "-08:30").
+  - `XXXX`: Displays the hour, minute, and second offset without a colon (e.g., "-083045").
+  - `XXXXX`: Displays the hour, minute, and second offset with a colon (e.g., "-08:30:45").
+- `x`: Represents the zone offset. Similar to X, but does not display 'Z' for UTC and focuses only on positive offsets.
+  - `x`: Displays the hour offset (e.g., "+08").
+  - `xx`: Displays the hour and minute offset without a colon (e.g., "+0830").
+  - `xxx`: Displays the hour and minute offset with a colon (e.g., "+08:30").
+  - `xxxx`: Displays the hour, minute, and second offset without a colon (e.g., "+083045").
+  - `xxxxx`: Displays the hour, minute, and second offset with a colon (e.g., "+08:30:45").
+- `Z`: Always includes an hour and minute offset and may use 'Z' for UTC, providing clear differentiation between UTC and other time zones.
+  - `Z`: Displays the hour and minute offset without a colon (e.g., "+0800").
+  - `ZZ`: Displays "GMT" followed by the time offset (e.g., "GMT+08:00" or "Z").
+  - `ZZZ`: Displays the full hour, minute, and second offset with a colon (e.g., "+08:30:45" or "Z").
+
+# Macros
+
+In order to help the user build dates easily, there are a lot of macros available for creating dates.
+The `.sssssssss` can be ommited in most cases.
+
+
+- **`date("uuuu-MM-dd")`**: Represents a date in the `uuuu-MM-dd` format, where `uuuu` refers to the year.
+- **`time("HH:mm:ss.sssssssss")`**: Represents a time in the format `HH:mm:ss.sssssssss`, including optional support for nanoseconds.
+- **`datetime("uuuu-MM-ddTHH:mm:ss.sssssssss")`**: Represents a datetime value in the `uuuu-MM-ddTHH:mm:ss.sssssssss` format, with optional nanoseconds.
+- **`offset("+HH:mm")`**: Represents a timezone offset in the format `+HH:mm`, where `+` or `-` indicates the direction from UTC.
+- **`timezone("NAME/ID ZZZ")`**: Specifies a timezone using a region-based name or ID, along with its associated offset.
+- **`datespec("FORMAT")`**: Defines a compile-time date format based on the provided string.
+- **`zoned("uuuu-MM-ddTHH:mm:ss.sssssssssZZZ")`**: Represents a `ZonedDateTime` with a fixed timezone and optional nanosecond precision.
+- **`zoned("uuuu-MM-ddTHH:mm:ss.sssssssss[IDENTIFIER]")`**: Defines an `IO ZonedDateTime`, where the timezone identifier is dynamically retrieved from the default timezone database.
+- **`zoned("uuuu-MM-ddTHH:mm:ss.sssssssss, timezone")`**: Represents an `IO ZonedDateTime`, using a specified `timezone` term and allowing optional nanoseconds.
+
+-/

src/Std/Time/Date.lean

@@ -0,0 +1,8 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Date.Basic
+import Std.Time.Date.PlainDate

src/Std/Time/Date/Basic.lean

@@ -0,0 +1,476 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Date.Unit.Basic
+import Std.Time.Date.ValidDate
+import Std.Time.Time.Basic
+
+namespace Std
+namespace Time
+
+namespace Nanosecond
+namespace Offset
+
+/--
+Convert `Nanosecond.Offset` into `Day.Offset`.
+-/
+@[inline]
+def toDays (nanoseconds : Nanosecond.Offset) : Day.Offset :=
+  nanoseconds.div 86400000000000
+
+/--
+Convert `Day.Offset` into `Nanosecond.Offset`.
+-/
+@[inline]
+def ofDays (days : Day.Offset) : Nanosecond.Offset :=
+  days.mul 86400000000000
+
+/--
+Convert `Nanosecond.Offset` into `Week.Offset`.
+-/
+@[inline]
+def toWeeks (nanoseconds : Nanosecond.Offset) : Week.Offset :=
+  nanoseconds.div 604800000000000
+
+/--
+Convert `Week.Offset` into `Nanosecond.Offset`.
+-/
+@[inline]
+def ofWeeks (weeks : Week.Offset) : Nanosecond.Offset :=
+  weeks.mul 604800000000000
+
+end Offset
+end Nanosecond
+
+namespace Millisecond
+namespace Offset
+
+/--
+Convert `Millisecond.Offset` into `Day.Offset`.
+-/
+@[inline]
+def toDays (milliseconds : Millisecond.Offset) : Day.Offset :=
+  milliseconds.div 86400000
+
+/--
+Convert `Day.Offset` into `Millisecond.Offset`.
+-/
+@[inline]
+def ofDays (days : Day.Offset) : Millisecond.Offset :=
+  days.mul 86400000
+
+/--
+Convert `Millisecond.Offset` into `Week.Offset`.
+-/
+@[inline]
+def toWeeks (milliseconds : Millisecond.Offset) : Week.Offset :=
+  milliseconds.div 604800000
+
+/--
+Convert `Week.Offset` into `Millisecond.Offset`.
+-/
+@[inline]
+def ofWeeks (weeks : Week.Offset) : Millisecond.Offset :=
+  weeks.mul 604800000
+
+end Offset
+end Millisecond
+
+namespace Second
+namespace Offset
+
+/--
+Convert `Second.Offset` into `Day.Offset`.
+-/
+@[inline]
+def toDays (seconds : Second.Offset) : Day.Offset :=
+  seconds.div 86400
+
+/--
+Convert `Day.Offset` into `Second.Offset`.
+-/
+@[inline]
+def ofDays (days : Day.Offset) : Second.Offset :=
+  days.mul 86400
+
+/--
+Convert `Second.Offset` into `Week.Offset`.
+-/
+@[inline]
+def toWeeks (seconds : Second.Offset) : Week.Offset :=
+  seconds.div 604800
+
+/--
+Convert `Week.Offset` into `Second.Offset`.
+-/
+@[inline]
+def ofWeeks (weeks : Week.Offset) : Second.Offset :=
+  weeks.mul 604800
+
+end Offset
+end Second
+
+namespace Minute
+namespace Offset
+
+/--
+Convert `Minute.Offset` into `Day.Offset`.
+-/
+@[inline]
+def toDays (minutes : Minute.Offset) : Day.Offset :=
+  minutes.div 1440
+
+/--
+Convert `Day.Offset` into `Minute.Offset`.
+-/
+@[inline]
+def ofDays (days : Day.Offset) : Minute.Offset :=
+  days.mul 1440
+
+/--
+Convert `Minute.Offset` into `Week.Offset`.
+-/
+@[inline]
+def toWeeks (minutes : Minute.Offset) : Week.Offset :=
+  minutes.div 10080
+
+/--
+Convert `Week.Offset` into `Minute.Offset`.
+-/
+@[inline]
+def ofWeeks (weeks : Week.Offset) : Minute.Offset :=
+  weeks.mul 10080
+
+end Offset
+end Minute
+
+namespace Hour
+namespace Offset
+
+/--
+Convert `Hour.Offset` into `Day.Offset`.
+-/
+@[inline]
+def toDays (hours : Hour.Offset) : Day.Offset :=
+  hours.div 24
+
+/--
+Convert `Day.Offset` into `Hour.Offset`.
+-/
+@[inline]
+def ofDays (days : Day.Offset) : Hour.Offset :=
+  days.mul 24
+
+/--
+Convert `Hour.Offset` into `Week.Offset`.
+-/
+@[inline]
+def toWeeks (hours : Hour.Offset) : Week.Offset :=
+  hours.div 168
+
+/--
+Convert `Week.Offset` into `Hour.Offset`.
+-/
+@[inline]
+def ofWeeks (weeks : Week.Offset) : Hour.Offset :=
+  weeks.mul 168
+
+end Offset
+end Hour
+
+instance : HAdd Nanosecond.Offset Nanosecond.Offset Nanosecond.Offset where
+  hAdd x y := x.add y
+
+instance : HAdd Nanosecond.Offset Millisecond.Offset Nanosecond.Offset where
+  hAdd x y := x.add y.toNanoseconds
+
+instance : HAdd Nanosecond.Offset Second.Offset Nanosecond.Offset where
+  hAdd x y := x.add y.toNanoseconds
+
+instance : HAdd Nanosecond.Offset Minute.Offset Nanosecond.Offset where
+  hAdd x y := x.add y.toNanoseconds
+
+instance : HAdd Nanosecond.Offset Hour.Offset Nanosecond.Offset where
+  hAdd x y := x.add y.toNanoseconds
+
+instance : HAdd Nanosecond.Offset Day.Offset Nanosecond.Offset where
+  hAdd x y := x.add y.toNanoseconds
+
+instance : HAdd Nanosecond.Offset Week.Offset Nanosecond.Offset where
+  hAdd x y := x.add y.toNanoseconds
+
+instance : HAdd Millisecond.Offset Nanosecond.Offset Nanosecond.Offset where
+  hAdd x y := x.toNanoseconds.add y
+
+instance : HAdd Millisecond.Offset Millisecond.Offset Millisecond.Offset where
+  hAdd x y := x.add y
+
+instance : HAdd Millisecond.Offset Second.Offset Millisecond.Offset where
+  hAdd x y := x.add y.toMilliseconds
+
+instance : HAdd Millisecond.Offset Minute.Offset Millisecond.Offset where
+  hAdd x y := x.add y.toMilliseconds
+
+instance : HAdd Millisecond.Offset Hour.Offset Millisecond.Offset where
+  hAdd x y := x.add y.toMilliseconds
+
+instance : HAdd Millisecond.Offset Day.Offset Millisecond.Offset where
+  hAdd x y := x.add y.toMilliseconds
+
+instance : HAdd Millisecond.Offset Week.Offset Millisecond.Offset where
+  hAdd x y := x.add y.toMilliseconds
+
+instance : HAdd Second.Offset Nanosecond.Offset Nanosecond.Offset where
+  hAdd x y := x.toNanoseconds.add y
+
+instance : HAdd Second.Offset Millisecond.Offset Millisecond.Offset where
+  hAdd x y := x.toMilliseconds.add y
+
+instance : HAdd Second.Offset Second.Offset Second.Offset where
+  hAdd x y := x.add y
+
+instance : HAdd Second.Offset Minute.Offset Second.Offset where
+  hAdd x y := x.add y.toSeconds
+
+instance : HAdd Second.Offset Hour.Offset Second.Offset where
+  hAdd x y := x.add y.toSeconds
+
+instance : HAdd Second.Offset Day.Offset Second.Offset where
+  hAdd x y := x.add y.toSeconds
+
+instance : HAdd Second.Offset Week.Offset Second.Offset where
+  hAdd x y := x.add y.toSeconds
+
+instance : HAdd Minute.Offset Nanosecond.Offset Nanosecond.Offset where
+  hAdd x y := x.toNanoseconds.add y
+
+instance : HAdd Minute.Offset Millisecond.Offset Millisecond.Offset where
+  hAdd x y := x.toMilliseconds.add y
+
+instance : HAdd Minute.Offset Second.Offset Second.Offset where
+  hAdd x y := x.toSeconds.add y
+
+instance : HAdd Minute.Offset Minute.Offset Minute.Offset where
+  hAdd x y := x.add y
+
+instance : HAdd Minute.Offset Hour.Offset Minute.Offset where
+  hAdd x y := x.add y.toMinutes
+
+instance : HAdd Minute.Offset Day.Offset Minute.Offset where
+  hAdd x y := x.add y.toMinutes
+
+instance : HAdd Minute.Offset Week.Offset Minute.Offset where
+  hAdd x y := x.add y.toMinutes
+
+instance : HAdd Hour.Offset Nanosecond.Offset Nanosecond.Offset where
+  hAdd x y := x.toNanoseconds.add y
+
+instance : HAdd Hour.Offset Millisecond.Offset Millisecond.Offset where
+  hAdd x y := x.toMilliseconds.add y
+
+instance : HAdd Hour.Offset Second.Offset Second.Offset where
+  hAdd x y := x.toSeconds.add y
+
+instance : HAdd Hour.Offset Minute.Offset Minute.Offset where
+  hAdd x y := x.toMinutes.add y
+
+instance : HAdd Hour.Offset Hour.Offset Hour.Offset where
+  hAdd x y := x.add y
+
+instance : HAdd Hour.Offset Day.Offset Hour.Offset where
+  hAdd x y := x.add y.toHours
+
+instance : HAdd Hour.Offset Week.Offset Hour.Offset where
+  hAdd x y := x.add y.toHours
+
+instance : HAdd Day.Offset Nanosecond.Offset Nanosecond.Offset where
+  hAdd x y := x.toNanoseconds.add y
+
+instance : HAdd Day.Offset Millisecond.Offset Millisecond.Offset where
+  hAdd x y := x.toMilliseconds.add y
+
+instance : HAdd Day.Offset Second.Offset Second.Offset where
+  hAdd x y := x.toSeconds.add y
+
+instance : HAdd Day.Offset Minute.Offset Minute.Offset where
+  hAdd x y := x.toMinutes.add y
+
+instance : HAdd Day.Offset Hour.Offset Hour.Offset where
+  hAdd x y := x.toHours.add y
+
+instance : HAdd Day.Offset Day.Offset Day.Offset where
+  hAdd x y := x.add y
+
+instance : HAdd Day.Offset Week.Offset Day.Offset where
+  hAdd x y := x.add y.toDays
+
+instance : HAdd Week.Offset Nanosecond.Offset Nanosecond.Offset where
+  hAdd x y := x.toNanoseconds.add y
+
+instance : HAdd Week.Offset Millisecond.Offset Millisecond.Offset where
+  hAdd x y := x.toMilliseconds.add y
+
+instance : HAdd Week.Offset Second.Offset Second.Offset where
+  hAdd x y := x.toSeconds.add y
+
+instance : HAdd Week.Offset Minute.Offset Minute.Offset where
+  hAdd x y := x.toMinutes.add y
+
+instance : HAdd Week.Offset Hour.Offset Hour.Offset where
+  hAdd x y := x.toHours.add y
+
+instance : HAdd Week.Offset Day.Offset Day.Offset where
+  hAdd x y := x.toDays.add y
+
+instance : HAdd Week.Offset Week.Offset Week.Offset where
+  hAdd x y := x.add y
+
+instance : HSub Nanosecond.Offset Nanosecond.Offset Nanosecond.Offset where
+  hSub x y := x.sub y
+
+instance : HSub Nanosecond.Offset Millisecond.Offset Nanosecond.Offset where
+  hSub x y := x.sub y.toNanoseconds
+
+instance : HSub Nanosecond.Offset Second.Offset Nanosecond.Offset where
+  hSub x y := x.sub y.toNanoseconds
+
+instance : HSub Nanosecond.Offset Minute.Offset Nanosecond.Offset where
+  hSub x y := x.sub y.toNanoseconds
+
+instance : HSub Nanosecond.Offset Hour.Offset Nanosecond.Offset where
+  hSub x y := x.sub y.toNanoseconds
+
+instance : HSub Nanosecond.Offset Day.Offset Nanosecond.Offset where
+  hSub x y := x.sub y.toNanoseconds
+
+instance : HSub Nanosecond.Offset Week.Offset Nanosecond.Offset where
+  hSub x y := x.sub y.toNanoseconds
+
+instance : HSub Millisecond.Offset Nanosecond.Offset Nanosecond.Offset where
+  hSub x y := x.toNanoseconds.sub y
+
+instance : HSub Millisecond.Offset Millisecond.Offset Millisecond.Offset where
+  hSub x y := x.sub y
+
+instance : HSub Millisecond.Offset Second.Offset Millisecond.Offset where
+  hSub x y := x.sub y.toMilliseconds
+
+instance : HSub Millisecond.Offset Minute.Offset Millisecond.Offset where
+  hSub x y := x.sub y.toMilliseconds
+
+instance : HSub Millisecond.Offset Hour.Offset Millisecond.Offset where
+  hSub x y := x.sub y.toMilliseconds
+
+instance : HSub Millisecond.Offset Day.Offset Millisecond.Offset where
+  hSub x y := x.sub y.toMilliseconds
+
+instance : HSub Millisecond.Offset Week.Offset Millisecond.Offset where
+  hSub x y := x.sub y.toMilliseconds
+
+instance : HSub Second.Offset Nanosecond.Offset Nanosecond.Offset where
+  hSub x y := x.toNanoseconds.sub y
+
+instance : HSub Second.Offset Millisecond.Offset Millisecond.Offset where
+  hSub x y := x.toMilliseconds.sub y
+
+instance : HSub Second.Offset Second.Offset Second.Offset where
+  hSub x y := x.sub y
+
+instance : HSub Second.Offset Minute.Offset Second.Offset where
+  hSub x y := x.sub y.toSeconds
+
+instance : HSub Second.Offset Hour.Offset Second.Offset where
+  hSub x y := x.sub y.toSeconds
+
+instance : HSub Second.Offset Day.Offset Second.Offset where
+  hSub x y := x.sub y.toSeconds
+
+instance : HSub Second.Offset Week.Offset Second.Offset where
+  hSub x y := x.sub y.toSeconds
+
+instance : HSub Minute.Offset Nanosecond.Offset Nanosecond.Offset where
+  hSub x y := x.toNanoseconds.sub y
+
+instance : HSub Minute.Offset Millisecond.Offset Millisecond.Offset where
+  hSub x y := x.toMilliseconds.sub y
+
+instance : HSub Minute.Offset Second.Offset Second.Offset where
+  hSub x y := x.toSeconds.sub y
+
+instance : HSub Minute.Offset Minute.Offset Minute.Offset where
+  hSub x y := x.sub y
+
+instance : HSub Minute.Offset Hour.Offset Minute.Offset where
+  hSub x y := x.sub y.toMinutes
+
+instance : HSub Minute.Offset Day.Offset Minute.Offset where
+  hSub x y := x.sub y.toMinutes
+
+instance : HSub Minute.Offset Week.Offset Minute.Offset where
+  hSub x y := x.sub y.toMinutes
+
+instance : HSub Hour.Offset Nanosecond.Offset Nanosecond.Offset where
+  hSub x y := x.toNanoseconds.sub y
+
+instance : HSub Hour.Offset Millisecond.Offset Millisecond.Offset where
+  hSub x y := x.toMilliseconds.sub y
+
+instance : HSub Hour.Offset Second.Offset Second.Offset where
+  hSub x y := x.toSeconds.sub y
+
+instance : HSub Hour.Offset Minute.Offset Minute.Offset where
+  hSub x y := x.toMinutes.sub y
+
+instance : HSub Hour.Offset Hour.Offset Hour.Offset where
+  hSub x y := x.sub y
+
+instance : HSub Hour.Offset Day.Offset Hour.Offset where
+  hSub x y := x.sub y.toHours
+
+instance : HSub Hour.Offset Week.Offset Hour.Offset where
+  hSub x y := x.sub y.toHours
+
+instance : HSub Day.Offset Nanosecond.Offset Nanosecond.Offset where
+  hSub x y := x.toNanoseconds.sub y
+
+instance : HSub Day.Offset Millisecond.Offset Millisecond.Offset where
+  hSub x y := x.toMilliseconds.sub y
+
+instance : HSub Day.Offset Second.Offset Second.Offset where
+  hSub x y := x.toSeconds.sub y
+
+instance : HSub Day.Offset Minute.Offset Minute.Offset where
+  hSub x y := x.toMinutes.sub y
+
+instance : HSub Day.Offset Hour.Offset Hour.Offset where
+  hSub x y := x.toHours.sub y
+
+instance : HSub Day.Offset Day.Offset Day.Offset where
+  hSub x y := x.sub y
+
+instance : HSub Day.Offset Week.Offset Day.Offset where
+  hSub x y := x.sub y.toDays
+
+instance : HSub Week.Offset Nanosecond.Offset Nanosecond.Offset where
+  hSub x y := x.toNanoseconds.sub y
+
+instance : HSub Week.Offset Millisecond.Offset Millisecond.Offset where
+  hSub x y := x.toMilliseconds.sub y
+
+instance : HSub Week.Offset Second.Offset Second.Offset where
+  hSub x y := x.toSeconds.sub y
+
+instance : HSub Week.Offset Minute.Offset Minute.Offset where
+  hSub x y := x.toMinutes.sub y
+
+instance : HSub Week.Offset Hour.Offset Hour.Offset where
+  hSub x y := x.toHours.sub y
+
+instance : HSub Week.Offset Day.Offset Day.Offset where
+  hSub x y := x.toDays.sub y
+
+instance : HSub Week.Offset Week.Offset Week.Offset where
+  hSub x y := x.sub y

src/Std/Time/Date/PlainDate.lean

@@ -0,0 +1,354 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Internal
+import Std.Time.Date.Basic
+import Std.Internal.Rat
+
+namespace Std
+namespace Time
+open Std.Internal
+open Std.Time
+open Internal
+open Lean
+
+set_option linter.all true
+
+/--
+`PlainDate` represents a date in the Year-Month-Day (YMD) format. It encapsulates the year, month,
+and day components, with validation to ensure the date is valid.
+-/
+structure PlainDate where
+
+  /-- The year component of the date. It is represented as an `Offset` type from `Year`. -/
+  year : Year.Offset
+
+  /-- The month component of the date. It is represented as an `Ordinal` type from `Month`. -/
+  month : Month.Ordinal
+
+  /-- The day component of the date. It is represented as an `Ordinal` type from `Day`. -/
+  day : Day.Ordinal
+
+  /-- Validates the date by ensuring that the year, month, and day form a correct and valid date. -/
+  valid : year.Valid month day
+  deriving Repr
+
+instance : Inhabited PlainDate where
+  default := ⟨1, 1, 1, by decide⟩
+
+instance : BEq PlainDate where
+  beq x y := x.day == y.day && x.month == y.month && x.year == y.year
+
+namespace PlainDate
+
+/--
+Creates a `PlainDate` by clipping the day to ensure validity. This function forces the date to be
+valid by adjusting the day to fit within the valid range to fit the given month and year.
+-/
+@[inline]
+def ofYearMonthDayClip (year : Year.Offset) (month : Month.Ordinal) (day : Day.Ordinal) : PlainDate :=
+  let day := month.clipDay year.isLeap day
+  PlainDate.mk year month day Month.Ordinal.valid_clipDay
+
+instance : Inhabited PlainDate where
+  default := mk 0 1 1 (by decide)
+
+/--
+Creates a new `PlainDate` from year, month, and day components.
+-/
+@[inline]
+def ofYearMonthDay? (year : Year.Offset) (month : Month.Ordinal) (day : Day.Ordinal) : Option PlainDate :=
+  if valid : year.Valid month day
+    then some (PlainDate.mk year month day valid)
+    else none
+
+/--
+Creates a `PlainDate` from a year and a day ordinal within that year.
+-/
+@[inline]
+def ofYearOrdinal (year : Year.Offset) (ordinal : Day.Ordinal.OfYear year.isLeap) : PlainDate :=
+  let ⟨⟨month, day⟩, proof⟩ := ValidDate.ofOrdinal ordinal
+  ⟨year, month, day, proof⟩
+
+/--
+Creates a `PlainDate` from the number of days since the UNIX epoch (January 1st, 1970).
+-/
+def ofDaysSinceUNIXEpoch (day : Day.Offset) : PlainDate :=
+  let z := day.toInt + 719468
+  let era := (if z ≥ 0 then z else z - 146096).tdiv 146097
+  let doe := z - era * 146097
+  let yoe := (doe - doe.tdiv 1460 + doe.tdiv 36524 - doe.tdiv 146096).tdiv 365
+  let y := yoe + era * 400
+  let doy := doe - (365 * yoe + yoe.tdiv 4 - yoe.tdiv 100)
+  let mp := (5 * doy + 2).tdiv 153
+  let d := doy - (153 * mp + 2).tdiv 5 + 1
+  let m := mp + (if mp < 10 then 3 else -9)
+  let y := y + (if m <= 2 then 1 else 0)
+  .ofYearMonthDayClip y (.clip m (by decide)) (.clip d (by decide))
+
+/--
+Returns the unaligned week of the month for a `PlainDate` (day divided by 7, plus 1).
+-/
+def weekOfMonth (date : PlainDate) : Bounded.LE 1 5 :=
+  date.day.sub 1 |>.ediv 7 (by decide) |>.add 1
+
+/--
+Determines the quarter of the year for the given `PlainDate`.
+-/
+def quarter (date : PlainDate) : Bounded.LE 1 4 :=
+  date.month.sub 1 |>.ediv 3 (by decide) |>.add 1
+
+/--
+Transforms a `PlainDate` into a `Day.Ordinal.OfYear`.
+-/
+def dayOfYear (date : PlainDate) : Day.Ordinal.OfYear date.year.isLeap :=
+  ValidDate.dayOfYear ⟨(date.month, date.day), date.valid⟩
+
+/--
+Determines the era of the given `PlainDate` based on its year.
+-/
+@[inline]
+def era (date : PlainDate) : Year.Era :=
+  date.year.era
+
+/--
+Checks if the `PlainDate` is in a leap year.
+-/
+@[inline]
+def inLeapYear (date : PlainDate) : Bool :=
+  date.year.isLeap
+
+/--
+Converts a `PlainDate` to the number of days since the UNIX epoch.
+-/
+def toDaysSinceUNIXEpoch (date : PlainDate) : Day.Offset :=
+  let y : Int := if date.month.toInt > 2 then date.year else date.year.toInt - 1
+  let era : Int := (if y ≥ 0 then y else y - 399).tdiv 400
+  let yoe : Int := y - era * 400
+  let m : Int := date.month.toInt
+  let d : Int := date.day.toInt
+  let doy := (153 * (m + (if m > 2 then -3 else 9)) + 2).tdiv 5 + d - 1
+  let doe := yoe * 365 + yoe.tdiv 4 - yoe.tdiv 100 + doy
+
+  .ofInt (era * 146097 + doe - 719468)
+
+/--
+Adds a given number of days to a `PlainDate`.
+-/
+@[inline]
+def addDays (date : PlainDate) (days : Day.Offset) : PlainDate :=
+  let dateDays := date.toDaysSinceUNIXEpoch
+  ofDaysSinceUNIXEpoch (dateDays + days)
+
+/--
+Subtracts a given number of days from a `PlainDate`.
+-/
+@[inline]
+def subDays (date : PlainDate) (days : Day.Offset) : PlainDate :=
+  addDays date (-days)
+
+/--
+Adds a given number of weeks to a `PlainDate`.
+-/
+@[inline]
+def addWeeks (date : PlainDate) (weeks : Week.Offset) : PlainDate :=
+  let dateDays := date.toDaysSinceUNIXEpoch
+  let daysToAdd := weeks.toDays
+  ofDaysSinceUNIXEpoch (dateDays + daysToAdd)
+
+/--
+Subtracts a given number of weeks from a `PlainDate`.
+-/
+@[inline]
+def subWeeks (date : PlainDate) (weeks : Week.Offset) : PlainDate :=
+  addWeeks date (-weeks)
+
+/--
+Adds a given number of months to a `PlainDate`, clipping the day to the last valid day of the month.
+-/
+def addMonthsClip (date : PlainDate) (months : Month.Offset) : PlainDate :=
+  let totalMonths := (date.month.toOffset - 1) + months
+  let totalMonths : Int := totalMonths
+  let wrappedMonths := Bounded.LE.byEmod totalMonths 12 (by decide) |>.add 1
+  let yearsOffset := totalMonths / 12
+  PlainDate.ofYearMonthDayClip (date.year.add yearsOffset) wrappedMonths date.day
+
+/--
+Subtracts `Month.Offset` from a `PlainDate`, it clips the day to the last valid day of that month.
+-/
+@[inline]
+def subMonthsClip (date : PlainDate) (months : Month.Offset) : PlainDate :=
+  addMonthsClip date (-months)
+
+/--
+Creates a `PlainDate` by rolling over the extra days to the next month.
+-/
+def rollOver (year : Year.Offset) (month : Month.Ordinal) (day : Day.Ordinal) : PlainDate :=
+  ofYearMonthDayClip year month 1 |>.addDays (day.toOffset - 1)
+
+/--
+Creates a new `PlainDate` by adjusting the year to the given `year` value. The month and day remain unchanged,
+and any invalid days for the new year will be handled according to the `clip` behavior.
+-/
+@[inline]
+def withYearClip (dt : PlainDate) (year : Year.Offset) : PlainDate :=
+  ofYearMonthDayClip year dt.month dt.day
+
+/--
+Creates a new `PlainDate` by adjusting the year to the given `year` value. The month and day are rolled
+over to the next valid month and day if necessary.
+-/
+@[inline]
+def withYearRollOver (dt : PlainDate) (year : Year.Offset) : PlainDate :=
+  rollOver year dt.month dt.day
+
+/--
+Adds a given number of months to a `PlainDate`, rolling over any excess days into the following month.
+-/
+def addMonthsRollOver (date : PlainDate) (months : Month.Offset) : PlainDate :=
+  addMonthsClip (ofYearMonthDayClip date.year date.month 1) months
+  |>.addDays (date.day.toOffset - 1)
+
+/--
+Subtracts `Month.Offset` from a `PlainDate`, rolling over excess days as needed.
+-/
+@[inline]
+def subMonthsRollOver (date : PlainDate) (months : Month.Offset) : PlainDate :=
+  addMonthsRollOver date (-months)
+
+/--
+Adds `Year.Offset` to a `PlainDate`, rolling over excess days to the next month, or next year.
+-/
+@[inline]
+def addYearsRollOver (date : PlainDate) (years : Year.Offset) : PlainDate :=
+  addMonthsRollOver date (years.mul 12)
+
+/--
+Subtracts `Year.Offset` from a `PlainDate`, rolling over excess days to the next month.
+-/
+@[inline]
+def subYearsRollOver (date : PlainDate) (years : Year.Offset) : PlainDate :=
+  addMonthsRollOver date (- years.mul 12)
+
+/--
+Adds `Year.Offset` to a `PlainDate`, clipping the day to the last valid day of the month.
+-/
+@[inline]
+def addYearsClip (date : PlainDate) (years : Year.Offset) : PlainDate :=
+  addMonthsClip date (years.mul 12)
+
+/--
+Subtracts `Year.Offset` from a `PlainDate`, clipping the day to the last valid day of the month.
+-/
+@[inline]
+def subYearsClip (date : PlainDate) (years : Year.Offset) : PlainDate :=
+  addMonthsClip date (- years.mul 12)
+
+/--
+Creates a new `PlainDate` by adjusting the day of the month to the given `days` value, with any
+out-of-range days clipped to the nearest valid date.
+-/
+@[inline]
+def withDaysClip (dt : PlainDate) (days : Day.Ordinal) : PlainDate :=
+  ofYearMonthDayClip dt.year dt.month days
+
+/--
+Creates a new `PlainDate` by adjusting the day of the month to the given `days` value, with any
+out-of-range days rolled over to the next month or year as needed.
+-/
+@[inline]
+def withDaysRollOver (dt : PlainDate) (days : Day.Ordinal) : PlainDate :=
+  rollOver dt.year dt.month days
+
+/--
+Creates a new `PlainDate` by adjusting the month to the given `month` value.
+The day remains unchanged, and any invalid days for the new month will be handled according to the `clip` behavior.
+-/
+@[inline]
+def withMonthClip (dt : PlainDate) (month : Month.Ordinal) : PlainDate :=
+  ofYearMonthDayClip dt.year month dt.day
+
+/--
+Creates a new `PlainDate` by adjusting the month to the given `month` value.
+The day is rolled over to the next valid month if necessary.
+-/
+@[inline]
+def withMonthRollOver (dt : PlainDate) (month : Month.Ordinal) : PlainDate :=
+  rollOver dt.year month dt.day
+
+/--
+Calculates the `Weekday` of a given `PlainDate` using Zeller's Congruence for the Gregorian calendar.
+-/
+def weekday (date : PlainDate) : Weekday :=
+  let days := date.toDaysSinceUNIXEpoch.val
+  let res := if days ≥ -4 then (days + 4) % 7 else (days + 5) % 7 + 6
+  .ofOrdinal (Bounded.LE.ofNatWrapping res (by decide))
+
+/--
+Determines the week of the month for the given `PlainDate`. The week of the month is calculated based
+on the day of the month and the weekday. Each week starts on Monday because the entire library is
+based on the Gregorian Calendar.
+-/
+def alignedWeekOfMonth (date : PlainDate) : Week.Ordinal.OfMonth :=
+  let weekday := date.withDaysClip 1 |>.weekday |>.toOrdinal |>.sub 1
+  let days := date.day |>.sub 1 |>.addBounds weekday
+  days |>.ediv 7 (by decide) |>.add 1
+
+/--
+Sets the date to the specified `desiredWeekday`. If the `desiredWeekday` is the same as the current weekday,
+the original `date` is returned without modification. If the `desiredWeekday` is in the future, the
+function adjusts the date forward to the next occurrence of that weekday.
+-/
+def withWeekday (date : PlainDate) (desiredWeekday : Weekday) : PlainDate :=
+  let weekday := date |>.weekday |>.toOrdinal
+  let offset := desiredWeekday.toOrdinal |>.subBounds weekday
+
+  let offset : Bounded.LE 0 6 :=
+    if h : offset.val < 0 then
+      offset.truncateTop (Int.le_sub_one_of_lt h) |>.addBounds (.exact 7)
+      |>.expandBottom (by decide)
+    else
+      offset.truncateBottom (Int.not_lt.mp h)
+      |>.expandTop (by decide)
+
+  date.addDays (Day.Offset.ofInt offset.toInt)
+
+/--
+Calculates the week of the year starting Monday for a given year.
+-/
+def weekOfYear (date : PlainDate) : Week.Ordinal :=
+  let y := date.year
+
+  let w := Bounded.LE.exact 10
+    |>.addBounds date.dayOfYear
+    |>.subBounds date.weekday.toOrdinal
+    |>.ediv 7 (by decide)
+
+  if h : w.val < 1 then
+    (y-1).weeks |>.expandBottom (by decide)
+  else if h₁ : w.val > y.weeks.val then
+    .ofNat' 1 (by decide)
+  else
+    let h := Int.not_lt.mp h
+    let h₁ := Int.not_lt.mp h₁
+    let w := w.truncateBottom h |>.truncateTop (Int.le_trans h₁ y.weeks.property.right)
+    w
+
+instance : HAdd PlainDate Day.Offset PlainDate where
+  hAdd := addDays
+
+instance : HSub PlainDate Day.Offset PlainDate where
+  hSub := subDays
+
+instance : HAdd PlainDate Week.Offset PlainDate where
+  hAdd := addWeeks
+
+instance : HSub PlainDate Week.Offset PlainDate where
+  hSub := subWeeks
+
+end PlainDate
+end Time
+end Std

src/Std/Time/Date/Unit/Basic.lean

@@ -0,0 +1,41 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Date.Unit.Day
+import Std.Time.Date.Unit.Month
+import Std.Time.Date.Unit.Year
+import Std.Time.Date.Unit.Weekday
+import Std.Time.Date.Unit.Week
+
+/-!
+This module defines various units used for measuring, counting, and converting between days, months,
+years, weekdays, and weeks of the year.
+
+The units are organized into types representing these time-related concepts, with operations provided
+to facilitate conversions and manipulations between them.
+-/
+
+namespace Std
+namespace Time
+open Internal
+
+namespace Day.Offset
+
+/--
+Convert `Week.Offset` into `Day.Offset`.
+-/
+@[inline]
+def ofWeeks (week : Week.Offset) : Day.Offset :=
+  week.mul 7
+
+/--
+Convert `Day.Offset` into `Week.Offset`.
+-/
+@[inline]
+def toWeeks (day : Day.Offset) : Week.Offset :=
+  day.ediv 7
+
+end Day.Offset

src/Std/Time/Date/Unit/Day.lean

@@ -0,0 +1,221 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Time
+
+namespace Std
+namespace Time
+namespace Day
+open Lean Internal
+
+set_option linter.all true
+
+/--
+`Ordinal` represents a bounded value for days, which ranges between 1 and 31.
+-/
+def Ordinal := Bounded.LE 1 31
+  deriving Repr, BEq, LE, LT
+
+instance : OfNat Ordinal n :=
+  inferInstanceAs (OfNat (Bounded.LE 1 (1 + (30 : Nat))) n)
+
+instance {x y : Ordinal} : Decidable (x ≤ y) :=
+  inferInstanceAs (Decidable (x.val ≤ y.val))
+
+instance {x y : Ordinal} : Decidable (x < y) :=
+  inferInstanceAs (Decidable (x.val < y.val))
+
+instance : Inhabited Ordinal where default := 1
+
+/--
+`Offset` represents an offset in days. It is defined as an `Int` with a base unit of 86400
+(the number of seconds in a day).
+-/
+def Offset : Type := UnitVal 86400
+  deriving Repr, BEq, Inhabited, Add, Sub, Neg, LE, LT, ToString
+
+instance : OfNat Offset n := ⟨UnitVal.ofNat n⟩
+
+instance {x y : Offset} : Decidable (x ≤ y) :=
+  inferInstanceAs (Decidable (x.val ≤ y.val))
+
+instance {x y : Offset} : Decidable (x < y) :=
+  inferInstanceAs (Decidable (x.val < y.val))
+
+namespace Ordinal
+
+/--
+Creates an `Ordinal` from an integer, ensuring the value is within bounds.
+-/
+@[inline]
+def ofInt (data : Int) (h : 1 ≤ data ∧ data ≤ 31) : Ordinal :=
+  Bounded.LE.mk data h
+
+/--
+`OfYear` represents the day ordinal within a year, which can be bounded between 1 and 365 or 366,
+depending on whether it's a leap year.
+-/
+def OfYear (leap : Bool) := Bounded.LE 1 (.ofNat (if leap then 366 else 365))
+
+instance : Repr (OfYear leap) where
+  reprPrec r p := reprPrec r.val p
+
+instance : ToString (OfYear leap) where
+  toString r := toString r.val
+
+namespace OfYear
+
+/--
+Creates an ordinal for a specific day within the year, ensuring that the provided day (`data`)
+is within the valid range for the year, which can be 1 to 365 or 366 for leap years.
+-/
+@[inline]
+def ofNat (data : Nat) (h : data ≥ 1 ∧ data ≤ (if leap then 366 else 365) := by decide) : OfYear leap :=
+  Bounded.LE.ofNat' data h
+
+end OfYear
+
+instance : OfNat (Ordinal.OfYear leap) n :=
+  match leap with
+  | true => inferInstanceAs (OfNat (Bounded.LE 1 (1 + (365 : Nat))) n)
+  | false => inferInstanceAs (OfNat (Bounded.LE 1 (1 + (364 : Nat))) n)
+
+instance : Inhabited (Ordinal.OfYear leap) where
+  default := by
+    refine ⟨1, And.intro (by decide) ?_⟩
+    split <;> simp
+
+/--
+Creates an ordinal from a natural number, ensuring the number is within the valid range
+for days of a month (1 to 31).
+-/
+@[inline]
+def ofNat (data : Nat) (h : data ≥ 1 ∧ data ≤ 31 := by decide) : Ordinal :=
+  Bounded.LE.ofNat' data h
+
+/--
+Creates an ordinal from a `Fin` value, ensuring it is within the valid range for days of the month (1 to 31).
+If the `Fin` value is 0, it is converted to 1.
+-/
+@[inline]
+def ofFin (data : Fin 32) : Ordinal :=
+  Bounded.LE.ofFin' data (by decide)
+
+/--
+Converts an `Ordinal` to an `Offset`.
+-/
+@[inline]
+def toOffset (ordinal : Ordinal) : Offset :=
+  UnitVal.ofInt ordinal.val
+
+namespace OfYear
+
+/--
+Converts an `OfYear` ordinal to a `Offset`.
+-/
+def toOffset (ofYear : OfYear leap) : Offset :=
+  UnitVal.ofInt ofYear.val
+
+end OfYear
+end Ordinal
+
+namespace Offset
+
+/--
+Converts an `Offset` to an `Ordinal`.
+-/
+@[inline]
+def toOrdinal (off : Day.Offset) (h : off.val ≥ 1 ∧ off.val ≤ 31) : Ordinal :=
+  Bounded.LE.mk off.val h
+
+/--
+Creates an `Offset` from a natural number.
+-/
+@[inline]
+def ofNat (data : Nat) : Day.Offset :=
+  UnitVal.ofInt data
+
+/--
+Creates an `Offset` from an integer.
+-/
+@[inline]
+def ofInt (data : Int) : Day.Offset :=
+  UnitVal.ofInt data
+
+/--
+Convert `Day.Offset` into `Nanosecond.Offset`.
+-/
+@[inline]
+def toNanoseconds (days : Day.Offset) : Nanosecond.Offset :=
+  days.mul 86400000000000
+
+/--
+Convert `Nanosecond.Offset` into `Day.Offset`.
+-/
+@[inline]
+def ofNanoseconds (ns : Nanosecond.Offset) : Day.Offset :=
+  ns.ediv 86400000000000
+
+/--
+Convert `Day.Offset` into `Millisecond.Offset`.
+-/
+@[inline]
+def toMilliseconds (days : Day.Offset) : Millisecond.Offset :=
+  days.mul 86400000
+
+/--
+Convert `Millisecond.Offset` into `Day.Offset`.
+-/
+@[inline]
+def ofMilliseconds (ms : Millisecond.Offset) : Day.Offset :=
+  ms.ediv 86400000
+
+/--
+Convert `Day.Offset` into `Second.Offset`.
+-/
+@[inline]
+def toSeconds (days : Day.Offset) : Second.Offset :=
+  days.mul 86400
+
+/--
+Convert `Second.Offset` into `Day.Offset`.
+-/
+@[inline]
+def ofSeconds (secs : Second.Offset) : Day.Offset :=
+  secs.ediv 86400
+
+/--
+Convert `Day.Offset` into `Minute.Offset`.
+-/
+@[inline]
+def toMinutes (days : Day.Offset) : Minute.Offset :=
+  days.mul 1440
+
+/--
+Convert `Minute.Offset` into `Day.Offset`.
+-/
+@[inline]
+def ofMinutes (minutes : Minute.Offset) : Day.Offset :=
+  minutes.ediv 1440
+
+/--
+Convert `Day.Offset` into `Hour.Offset`.
+-/
+@[inline]
+def toHours (days : Day.Offset) : Hour.Offset :=
+  days.mul 24
+
+/--
+Convert `Hour.Offset` into `Day.Offset`.
+-/
+@[inline]
+def ofHours (hours : Hour.Offset) : Day.Offset :=
+  hours.ediv 24
+
+end Offset
+end Day
+end Time
+end Std

src/Std/Time/Date/Unit/Month.lean

@@ -0,0 +1,308 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Internal.Rat
+import Std.Time.Date.Unit.Day
+
+namespace Std
+namespace Time
+namespace Month
+open Std.Internal
+open Internal
+
+set_option linter.all true
+
+/--
+`Ordinal` represents a bounded value for months, which ranges between 1 and 12.
+-/
+def Ordinal := Bounded.LE 1 12
+  deriving Repr, BEq, LE, LT
+
+instance : OfNat Ordinal n :=
+  inferInstanceAs (OfNat (Bounded.LE 1 (1 + (11 : Nat))) n)
+
+instance : Inhabited Ordinal where
+  default := 1
+
+instance {x y : Ordinal} : Decidable (x ≤ y) :=
+  inferInstanceAs (Decidable (x.val ≤ y.val))
+
+instance {x y : Ordinal} : Decidable (x < y) :=
+  inferInstanceAs (Decidable (x.val < y.val))
+
+/--
+`Offset` represents an offset in months. It is defined as an `Int`.
+-/
+def Offset : Type := Int
+  deriving Repr, BEq, Inhabited, Add, Sub, Mul, Div, Neg, ToString, LT, LE, DecidableEq
+
+instance : OfNat Offset n :=
+  ⟨Int.ofNat n⟩
+
+/--
+`Quarter` represents a value between 1 and 4, inclusive, corresponding to the four quarters of a year.
+-/
+def Quarter := Bounded.LE 1 4
+
+namespace Quarter
+
+/--
+Determine the `Quarter` by the month.
+-/
+def ofMonth (month : Month.Ordinal) : Quarter :=
+  month
+  |>.sub 1
+  |>.ediv 3 (by decide)
+  |>.add 1
+
+end Quarter
+
+namespace Offset
+
+/--
+Creates an `Offset` from a natural number.
+-/
+@[inline]
+def ofNat (data : Nat) : Offset :=
+  .ofNat data
+
+/--
+Creates an `Offset` from an integer.
+-/
+@[inline]
+def ofInt (data : Int) : Offset :=
+  data
+
+end Offset
+
+namespace Ordinal
+
+/--
+The ordinal value representing the month of January.
+-/
+@[inline] def january : Ordinal := 1
+
+/--
+The ordinal value representing the month of February.
+-/
+@[inline] def february : Ordinal := 2
+
+/--
+The ordinal value representing the month of March.
+-/
+@[inline] def march : Ordinal := 3
+
+/--
+The ordinal value representing the month of April.
+-/
+@[inline] def april : Ordinal := 4
+
+/--
+The ordinal value representing the month of May.
+-/
+@[inline] def may : Ordinal := 5
+
+/--
+The ordinal value representing the month of June.
+-/
+@[inline] def june : Ordinal := 6
+
+/--
+The ordinal value representing the month of July.
+-/
+@[inline] def july : Ordinal := 7
+
+/--
+The ordinal value representing the month of August.
+-/
+@[inline] def august : Ordinal := 8
+
+/--
+The ordinal value representing the month of September.
+-/
+@[inline] def september : Ordinal := 9
+
+/--
+The ordinal value representing the month of October.
+-/
+@[inline] def october : Ordinal := 10
+
+/--
+The ordinal value representing the month of November.
+-/
+@[inline] def november : Ordinal := 11
+
+/--
+The ordinal value representing the month of December.
+-/
+@[inline] def december : Ordinal := 12
+
+/--
+Converts a `Ordinal` into a `Offset`.
+-/
+@[inline]
+def toOffset (month : Ordinal) : Offset :=
+  month.val
+
+/--
+Creates an `Ordinal` from an integer, ensuring the value is within bounds.
+-/
+@[inline]
+def ofInt (data : Int) (h : 1 ≤ data ∧ data ≤ 12) : Ordinal :=
+  Bounded.LE.mk data h
+
+/--
+Creates an `Ordinal` from a `Nat`, ensuring the value is within bounds.
+-/
+@[inline]
+def ofNat (data : Nat) (h : data ≥ 1 ∧ data ≤ 12 := by decide) : Ordinal :=
+  Bounded.LE.ofNat' data h
+
+/--
+Converts a `Ordinal` into a `Nat`.
+-/
+@[inline]
+def toNat (month : Ordinal) : Nat := by
+  match month with
+  | ⟨.ofNat s, _⟩ => exact s
+  | ⟨.negSucc s, h⟩ => nomatch h.left
+
+/--
+Creates an `Ordinal` from a `Fin`, ensuring the value is within bounds, if its 0 then its converted
+to 1.
+-/
+@[inline]
+def ofFin (data : Fin 13) : Ordinal :=
+  Bounded.LE.ofFin' data (by decide)
+
+/--
+Transforms `Month.Ordinal` into `Second.Offset`.
+-/
+def toSeconds (leap : Bool) (month : Ordinal) : Second.Offset :=
+  let daysAcc := #[0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334]
+  let days : Day.Offset := daysAcc[month.toNat]!
+  let time := days.toSeconds
+  if leap && month.toNat ≥ 2
+    then time + 86400
+    else time
+
+/--
+Transforms `Month.Ordinal` into `Minute.Offset`.
+-/
+@[inline]
+def toMinutes (leap : Bool) (month : Ordinal) : Minute.Offset :=
+  toSeconds leap month
+  |>.ediv 60
+
+/--
+Transforms `Month.Ordinal` into `Hour.Offset`.
+-/
+@[inline]
+def toHours (leap : Bool) (month : Ordinal) : Hour.Offset :=
+  toMinutes leap month
+  |>.ediv 60
+
+/--
+Transforms `Month.Ordinal` into `Day.Offset`.
+-/
+@[inline]
+def toDays (leap : Bool) (month : Ordinal) : Day.Offset :=
+  toSeconds leap month
+  |>.convert
+
+/--
+Size in days of each month if the year is not a leap year.
+-/
+@[inline]
+private def monthSizesNonLeap : { val : Array Day.Ordinal // val.size = 12 } :=
+  ⟨#[31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31], by decide⟩
+
+/--
+Returns the cumulative size in days of each month for a non-leap year.
+-/
+@[inline]
+private def cumulativeSizes : { val : Array Day.Offset // val.size = 12 } :=
+  ⟨#[0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334], by decide⟩
+
+/--
+Gets the number of days in a month.
+-/
+def days (leap : Bool) (month : Ordinal) : Day.Ordinal :=
+  if month.val = 2 then
+    if leap then 29 else 28
+  else
+    let ⟨months, p⟩ := monthSizesNonLeap
+    let index : Fin 12 := (month.sub 1).toFin (by decide)
+    let idx := (index.cast (by rw [p]))
+    months.get idx.val idx.isLt
+
+theorem days_gt_27 (leap : Bool) (i : Month.Ordinal) : days leap i > 27 := by
+  match i with
+  | ⟨2, _⟩ =>
+    simp [days]
+    split <;> decide
+  | ⟨1, _⟩ | ⟨3, _⟩ | ⟨4, _⟩ | ⟨5, _⟩ | ⟨6, _⟩ | ⟨7, _⟩
+  | ⟨8, _⟩ | ⟨9, _⟩ | ⟨10, _⟩ | ⟨11, _⟩ | ⟨12, _⟩ =>
+    simp [days, monthSizesNonLeap]
+    decide +revert
+
+/--
+Returns the number of days until the `month`.
+-/
+def cumulativeDays (leap : Bool) (month : Ordinal) : Day.Offset := by
+  let ⟨months, p⟩ := cumulativeSizes
+  let index : Fin 12 := (month.sub 1).toFin (by decide)
+  rw [← p] at index
+  let res := months.get index.val index.isLt
+  exact res + (if leap ∧ month.val > 2 then 1 else 0)
+
+theorem cumulativeDays_le (leap : Bool) (month : Month.Ordinal) : cumulativeDays leap month ≥ 0 ∧ cumulativeDays leap month ≤ 334 + (if leap then 1 else 0) := by
+  match month with
+  | ⟨1, _⟩ | ⟨2, _⟩ | ⟨3, _⟩  | ⟨4, _⟩  | ⟨5, _⟩  | ⟨6, _⟩  | ⟨7, _⟩  | ⟨8, _⟩  | ⟨9, _⟩  | ⟨10, _⟩  | ⟨11, _⟩ | ⟨12, _⟩ =>
+    simp [cumulativeSizes, Bounded.LE.sub, Bounded.LE.add, Bounded.LE.toFin, cumulativeDays]
+    try split
+    all_goals decide +revert
+
+theorem difference_eq (p : month.val ≤ 11) :
+  let next := month.truncateTop p |>.addTop 1 (by decide)
+  (cumulativeDays leap next).val = (cumulativeDays leap month).val + (days leap month).val := by
+  match month with
+  | ⟨1, _⟩ | ⟨2, _⟩ | ⟨3, _⟩  | ⟨4, _⟩  | ⟨5, _⟩  | ⟨6, _⟩  | ⟨7, _⟩  | ⟨8, _⟩  | ⟨9, _⟩  | ⟨10, _⟩  | ⟨11, _⟩ =>
+    simp [cumulativeDays, Bounded.LE.addTop, days, monthSizesNonLeap];
+    try split <;> rfl
+    try rfl
+  | ⟨12, _⟩ => contradiction
+
+/--
+Checks if a given day is valid for the specified month and year. For example, `29/02` is valid only
+if the year is a leap year.
+-/
+abbrev Valid (leap : Bool) (month : Month.Ordinal) (day : Day.Ordinal) : Prop :=
+  day.val ≤ (days leap month).val
+
+/--
+Clips the day to be within the valid range.
+-/
+@[inline]
+def clipDay (leap : Bool) (month : Month.Ordinal) (day : Day.Ordinal) : Day.Ordinal :=
+  let max : Day.Ordinal := month.days leap
+  if day.val > max.val
+    then max
+    else day
+
+/--
+Proves that every value provided by a clipDay is a valid day in a year.
+-/
+theorem valid_clipDay : Valid leap month (clipDay leap month day) := by
+  simp [Valid, clipDay]
+  split
+  exact Int.le_refl (days leap month).val
+  next h => exact Int.not_lt.mp h
+
+end Ordinal
+end Month
+end Time
+end Std

src/Std/Time/Date/Unit/Week.lean

@@ -0,0 +1,185 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Internal.Rat
+import Std.Time.Date.Unit.Day
+
+namespace Std
+namespace Time
+namespace Week
+open Std.Internal
+open Internal
+
+set_option linter.all true
+
+/--
+`Ordinal` represents a bounded value for weeks, which ranges between 1 and 53.
+-/
+def Ordinal := Bounded.LE 1 53
+  deriving Repr, BEq, LE, LT
+
+instance : OfNat Ordinal n :=
+  inferInstanceAs (OfNat (Bounded.LE 1 (1 + (52 : Nat))) n)
+
+instance {x y : Ordinal} : Decidable (x ≤ y) :=
+  inferInstanceAs (Decidable (x.val ≤ y.val))
+
+instance {x y : Ordinal} : Decidable (x < y) :=
+  inferInstanceAs (Decidable (x.val < y.val))
+
+instance : Inhabited Ordinal where
+  default := 1
+
+/--
+`Offset` represents an offset in weeks.
+-/
+def Offset : Type := UnitVal (86400 * 7)
+  deriving Repr, BEq, Inhabited, Add, Sub, Neg, LE, LT, ToString
+
+instance : OfNat Offset n := ⟨UnitVal.ofNat n⟩
+
+namespace Ordinal
+
+/--
+Creates an `Ordinal` from an integer, ensuring the value is within bounds.
+-/
+@[inline]
+def ofInt (data : Int) (h : 1 ≤ data ∧ data ≤ 53) : Ordinal :=
+  Bounded.LE.mk data h
+
+/--
+`OfMonth` represents the number of weeks within a month. It ensures that the week is within the
+correct bounds—either 1 to 6, representing the possible weeks in a month.
+-/
+def OfMonth := Bounded.LE 1 6
+  deriving Repr
+
+/--
+Creates an `Ordinal` from a natural number, ensuring the value is within bounds.
+-/
+@[inline]
+def ofNat (data : Nat) (h : data ≥ 1 ∧ data ≤ 53 := by decide) : Ordinal :=
+  Bounded.LE.ofNat' data h
+
+/--
+Creates an `Ordinal` from a `Fin`, ensuring the value is within bounds.
+-/
+@[inline]
+def ofFin (data : Fin 54) : Ordinal :=
+  Bounded.LE.ofFin' data (by decide)
+
+/--
+Converts an `Ordinal` to an `Offset`.
+-/
+@[inline]
+def toOffset (ordinal : Ordinal) : Offset :=
+  UnitVal.ofInt ordinal.val
+
+end Ordinal
+namespace Offset
+
+/--
+Creates an `Offset` from a natural number.
+-/
+@[inline]
+def ofNat (data : Nat) : Week.Offset :=
+  UnitVal.ofInt data
+
+/--
+Creates an `Offset` from an integer.
+-/
+@[inline]
+def ofInt (data : Int) : Week.Offset :=
+  UnitVal.ofInt data
+
+/--
+Convert `Week.Offset` into `Millisecond.Offset`.
+-/
+@[inline]
+def toMilliseconds (weeks : Week.Offset) : Millisecond.Offset :=
+  weeks.mul 604800000
+
+/--
+Convert `Millisecond.Offset` into `Week.Offset`.
+-/
+@[inline]
+def ofMilliseconds (millis : Millisecond.Offset) : Week.Offset :=
+  millis.ediv 604800000
+
+/--
+Convert `Week.Offset` into `Nanosecond.Offset`.
+-/
+@[inline]
+def toNanoseconds (weeks : Week.Offset) : Nanosecond.Offset :=
+  weeks.mul 604800000000000
+
+/--
+Convert `Nanosecond.Offset` into `Week.Offset`.
+-/
+@[inline]
+def ofNanoseconds (nanos : Nanosecond.Offset) : Week.Offset :=
+  nanos.ediv 604800000000000
+
+/--
+Convert `Week.Offset` into `Second.Offset`.
+-/
+@[inline]
+def toSeconds (weeks : Week.Offset) : Second.Offset :=
+  weeks.mul 604800
+
+/--
+Convert `Second.Offset` into `Week.Offset`.
+-/
+@[inline]
+def ofSeconds (secs : Second.Offset) : Week.Offset :=
+  secs.ediv 604800
+
+/--
+Convert `Week.Offset` into `Minute.Offset`.
+-/
+@[inline]
+def toMinutes (weeks : Week.Offset) : Minute.Offset :=
+  weeks.mul 10080
+
+/--
+Convert `Minute.Offset` into `Week.Offset`.
+-/
+@[inline]
+def ofMinutes (minutes : Minute.Offset) : Week.Offset :=
+  minutes.ediv 10080
+
+/--
+Convert `Week.Offset` into `Hour.Offset`.
+-/
+@[inline]
+def toHours (weeks : Week.Offset) : Hour.Offset :=
+  weeks.mul 168
+
+/--
+Convert `Hour.Offset` into `Week.Offset`.
+-/
+@[inline]
+def ofHours (hours : Hour.Offset) : Week.Offset :=
+  hours.ediv 168
+
+/--
+Convert `Week.Offset` into `Day.Offset`.
+-/
+@[inline]
+def toDays (weeks : Week.Offset) : Day.Offset :=
+  weeks.mul 7
+
+/--
+Convert `Day.Offset` into `Week.Offset`.
+-/
+@[inline]
+def ofDays (days : Day.Offset) : Week.Offset :=
+  days.ediv 7
+
+end Offset
+end Week
+end Time
+end Std

src/Std/Time/Date/Unit/Weekday.lean

@@ -0,0 +1,134 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Internal.Rat
+import Std.Time.Date.Unit.Day
+
+namespace Std
+namespace Time
+open Std.Internal
+open Internal
+
+set_option linter.all true
+
+/--
+Defines the enumeration for days of the week. Each variant corresponds to a day of the week.
+-/
+inductive Weekday
+  /-- Monday. -/
+  | monday
+
+  /-- Tuesday. -/
+  | tuesday
+
+  /-- Wednesday. -/
+  | wednesday
+
+  /-- Thursday. -/
+  | thursday
+
+  /-- Friday. -/
+  | friday
+
+  /-- Saturday. -/
+  | saturday
+
+    /-- Sunday. -/
+  | sunday
+  deriving Repr, Inhabited, BEq
+
+namespace Weekday
+
+/--
+`Ordinal` represents a bounded value for weekdays, which ranges between 1 and 7.
+-/
+def Ordinal := Bounded.LE 1 7
+
+instance : OfNat Ordinal n :=
+  inferInstanceAs (OfNat (Bounded.LE 1 (1 + (6 : Nat))) n)
+
+/--
+Converts a `Ordinal` representing a day index into a corresponding `Weekday`. This function is useful
+for mapping numerical representations to days of the week.
+-/
+def ofOrdinal : Ordinal → Weekday
+  | 1 => .monday
+  | 2 => .tuesday
+  | 3 => .wednesday
+  | 4 => .thursday
+  | 5 => .friday
+  | 6 => .saturday
+  | 7 => .sunday
+
+/--
+Converts a `Weekday` to a `Ordinal`.
+-/
+def toOrdinal : Weekday → Ordinal
+  | .monday => 1
+  | .tuesday => 2
+  | .wednesday => 3
+  | .thursday => 4
+  | .friday => 5
+  | .saturday => 6
+  | .sunday => 7
+
+/--
+Converts a `Weekday` to a `Nat`.
+-/
+def toNat : Weekday → Nat
+  | .monday => 1
+  | .tuesday => 2
+  | .wednesday => 3
+  | .thursday => 4
+  | .friday => 5
+  | .saturday => 6
+  | .sunday => 7
+
+/--
+Converts a `Nat` to an `Option Weekday`.
+-/
+def ofNat? : Nat → Option Weekday
+  | 1 => some .monday
+  | 2 => some .tuesday
+  | 3 => some .wednesday
+  | 4 => some .thursday
+  | 5 => some .friday
+  | 6 => some .saturday
+  | 7 => some .sunday
+  | _ => none
+
+/--
+Converts a `Nat` to a `Weekday`. Panics if the value provided is invalid.
+-/
+@[inline]
+def ofNat! (n : Nat) : Weekday :=
+  match ofNat? n with
+  | some res => res
+  | none => panic! "invalid weekday"
+
+/--
+Gets the next `Weekday`.
+-/
+def next : Weekday → Weekday
+  | .monday => .tuesday
+  | .tuesday => .wednesday
+  | .wednesday => .thursday
+  | .thursday => .friday
+  | .friday => .saturday
+  | .saturday => .sunday
+  | .sunday => .monday
+
+/--
+Check if it's a weekend.
+-/
+def isWeekend : Weekday → Bool
+  | .saturday => true
+  | .sunday => true
+  | _ => false
+
+end Weekday
+end Time
+end Std

src/Std/Time/Date/Unit/Year.lean

@@ -0,0 +1,128 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Internal
+import Std.Internal.Rat
+import Std.Time.Date.Unit.Day
+import Std.Time.Date.Unit.Month
+
+namespace Std
+namespace Time
+namespace Year
+open Std.Internal
+open Internal
+
+set_option linter.all true
+
+/--
+Defines the different eras.
+-/
+inductive Era
+  /-- The era before the Common Era (BCE), always represents a date before year 0. -/
+  | bce
+
+  /-- The Common Era (CE), represents dates from year 0 onwards. -/
+  | ce
+  deriving Repr, Inhabited
+
+instance : ToString Era where
+  toString
+    | .bce => "BCE"
+    | .ce => "CE"
+
+/--
+`Offset` represents a year offset, defined as an `Int`.
+-/
+def Offset : Type := Int
+  deriving Repr, BEq, Inhabited, Add, Sub, Neg, LE, LT, ToString
+
+instance {x y : Offset} : Decidable (x ≤ y) :=
+  let x : Int := x
+  inferInstanceAs (Decidable (x ≤ y))
+
+instance {x y : Offset} : Decidable (x < y) :=
+  let x : Int := x
+  inferInstanceAs (Decidable (x < y))
+
+instance : OfNat Offset n := ⟨Int.ofNat n⟩
+
+namespace Offset
+
+/--
+Creates an `Offset` from a natural number.
+-/
+@[inline]
+def ofNat (data : Nat) : Offset :=
+  .ofNat data
+
+/--
+Creates an `Offset` from an integer.
+-/
+@[inline]
+def ofInt (data : Int) : Offset :=
+  data
+
+/--
+Converts the `Year` offset to an `Int`.
+-/
+@[inline]
+def toInt (offset : Offset) : Int :=
+  offset
+
+/--
+Converts the `Year` offset to a `Month` offset.
+-/
+@[inline]
+def toMonths (val : Offset) : Month.Offset :=
+  val.mul 12
+
+/--
+Determines if a year is a leap year in the proleptic Gregorian calendar.
+-/
+@[inline]
+def isLeap (y : Offset) : Bool :=
+  y.toInt.tmod 4 = 0 ∧ (y.toInt.tmod 100 ≠ 0 ∨ y.toInt.tmod 400 = 0)
+
+/--
+Returns the `Era` of the `Year`.
+-/
+def era (year : Offset) : Era :=
+  if year.toInt ≥ 1
+    then .ce
+    else .bce
+
+/--
+Calculates the number of days in the specified `year`.
+-/
+def days (year : Offset) : Bounded.LE 365 366 :=
+  if year.isLeap
+    then .ofNatWrapping 366 (by decide)
+    else .ofNatWrapping 355 (by decide)
+
+/--
+Calculates the number of weeks in the specified `year`.
+-/
+def weeks (year : Offset) : Bounded.LE 52 53 :=
+  let p (year : Offset) := Bounded.LE.byEmod (year.toInt + year.toInt/4 - year.toInt/100 + year.toInt/400) 7 (by decide)
+
+  let add : Bounded.LE 0 1 :=
+    if (p year).val = 4 ∨ (p (year - 1)).val = 3
+      then Bounded.LE.ofNat 1 (by decide)
+      else Bounded.LE.ofNat 0 (by decide)
+
+  Bounded.LE.exact 52 |>.addBounds add
+
+/--
+Checks if the given date is valid for the specified year, month, and day.
+-/
+@[inline]
+abbrev Valid (year : Year.Offset) (month : Month.Ordinal) (day : Day.Ordinal) : Prop :=
+  day ≤ month.days year.isLeap
+
+end Offset
+end Year
+end Time
+end Std

src/Std/Time/Date/ValidDate.lean

@@ -0,0 +1,88 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Internal.Rat
+import Std.Time.Date.Unit.Day
+import Std.Time.Date.Unit.Month
+
+namespace Std
+namespace Time
+open Std.Internal
+open Internal
+open Month.Ordinal
+
+set_option linter.all true
+
+/--
+Represents a valid date for a given year, considering whether it is a leap year. Example: `(2, 29)`
+is valid only if `leap` is `true`.
+-/
+def ValidDate (leap : Bool) := { val : Month.Ordinal × Day.Ordinal // Valid leap (Prod.fst val) (Prod.snd val) }
+
+instance : Inhabited (ValidDate l) where
+  default := ⟨⟨1, 1⟩, (by cases l <;> decide)⟩
+
+namespace ValidDate
+
+/--
+Transforms a tuple of a `Month` and a `Day` into a `Day.Ordinal.OfYear`.
+-/
+def dayOfYear (ordinal : ValidDate leap) : Day.Ordinal.OfYear leap :=
+  let days := cumulativeDays leap ordinal.val.fst
+  let proof := cumulativeDays_le leap ordinal.val.fst
+  let bounded := Bounded.LE.mk days.toInt proof |>.addBounds ordinal.val.snd
+  match leap, bounded with
+  | true, bounded => bounded
+  | false, bounded => bounded
+
+/--
+Transforms a `Day.Ordinal.OfYear` into a tuple of a `Month` and a `Day`.
+-/
+def ofOrdinal (ordinal : Day.Ordinal.OfYear leap) : ValidDate leap :=
+    let rec go (idx : Month.Ordinal) (acc : Int) (h : ordinal.val > acc) (p : acc = (cumulativeDays leap idx).val) : ValidDate leap :=
+      let monthDays := days leap idx
+      if h₁ : ordinal.val ≤ acc + monthDays.val then
+        let bounded := Bounded.LE.mk ordinal.val (And.intro h h₁) |>.sub acc
+        let bounded : Bounded.LE 1 monthDays.val := bounded.cast (by omega) (by omega)
+        let days₁ : Day.Ordinal := ⟨bounded.val, And.intro bounded.property.left (Int.le_trans bounded.property.right monthDays.property.right)⟩
+        ⟨⟨idx, days₁⟩, Int.le_trans bounded.property.right (by simp)⟩
+      else by
+        let h₂ := Int.not_le.mp h₁
+
+        have h₃ : idx.val < 12 := Int.not_le.mp <| λh₃ => by
+          have h₅ := ordinal.property.right
+          let eq := Int.eq_iff_le_and_ge.mpr (And.intro idx.property.right h₃)
+          simp [monthDays, days, eq] at h₂
+          simp [cumulativeDays, eq] at p
+          simp [p] at h₂
+          cases leap
+          all_goals (simp at h₂; simp_all)
+          · have h₂ : 365 < ordinal.val := h₂
+            omega
+          · have h₂ : 366 < ordinal.val := h₂
+            omega
+
+        let idx₂ := idx.truncateTop (Int.le_sub_one_of_lt h₃) |>.addTop 1 (by decide)
+        refine go idx₂ (acc + monthDays.val) h₂ ?_
+        simp [monthDays, p]
+        rw [difference_eq (Int.le_of_lt_add_one h₃)]
+
+      termination_by 12 - idx.val.toNat
+      decreasing_by
+        simp_wf
+        simp [Bounded.LE.addTop]
+        let gt0 : idx.val ≥ 0 := Int.le_trans (by decide) idx.property.left
+        refine Nat.sub_lt_sub_left (Int.toNat_lt gt0 |>.mpr h₃) ?_
+        let toNat_lt_lt {n z : Int} (h : 0 ≤ z) (h₁ : 0 ≤ n) : z.toNat < n.toNat ↔ z < n := by
+          rw [← Int.not_le, ← Nat.not_le, ← Int.ofNat_le, Int.toNat_of_nonneg h, Int.toNat_of_nonneg h₁]
+        rw [toNat_lt_lt (by omega) (by omega)]
+        omega
+
+    go 1 0 (Int.le_trans (by decide) ordinal.property.left) (by cases leap <;> decide)
+
+end ValidDate
+end Time
+end Std

src/Std/Time/DateTime.lean

@@ -0,0 +1,104 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.DateTime.Timestamp
+import Std.Time.DateTime.PlainDateTime
+
+namespace Std
+namespace Time
+
+namespace Timestamp
+
+set_option linter.all true
+
+/--
+Converts a `PlainDateTime` to a `Timestamp`
+-/
+@[inline]
+def ofPlainDateTimeAssumingUTC (pdt : PlainDateTime) : Timestamp :=
+  pdt.toTimestampAssumingUTC
+
+/--
+Converts a `Timestamp` to a `PlainDateTime`
+-/
+@[inline]
+def toPlainDateTimeAssumingUTC (timestamp : Timestamp) : PlainDateTime :=
+  PlainDateTime.ofTimestampAssumingUTC timestamp
+
+/--
+Converts a `PlainDate` to a `Timestamp`
+-/
+@[inline]
+def ofPlainDateAssumingUTC (pd : PlainDate) : Timestamp :=
+  let days := pd.toDaysSinceUNIXEpoch
+  let secs := days.toSeconds
+  Timestamp.ofSecondsSinceUnixEpoch secs
+
+/--
+Converts a `Timestamp` to a `PlainDate`
+-/
+@[inline]
+def toPlainDateAssumingUTC (timestamp : Timestamp) : PlainDate :=
+  let secs := timestamp.toSecondsSinceUnixEpoch
+  let days := Day.Offset.ofSeconds secs
+  PlainDate.ofDaysSinceUNIXEpoch days
+
+/--
+Converts a `Timestamp` to a `PlainTime`
+-/
+@[inline]
+def getTimeAssumingUTC (timestamp : Timestamp) : PlainTime :=
+  let nanos := timestamp.toNanosecondsSinceUnixEpoch
+  PlainTime.ofNanoseconds nanos
+
+end Timestamp
+namespace PlainDate
+
+/--
+Converts a `PlainDate` to a `Timestamp`
+-/
+@[inline]
+def toTimestampAssumingUTC (pdt : PlainDate) : Timestamp :=
+  Timestamp.ofPlainDateAssumingUTC pdt
+
+instance : HSub PlainDate PlainDate Duration where
+  hSub x y := x.toTimestampAssumingUTC - y.toTimestampAssumingUTC
+
+end PlainDate
+namespace PlainDateTime
+
+/--
+Converts a `PlainDate` to a `Timestamp`
+-/
+@[inline]
+def ofPlainDate (date : PlainDate) : PlainDateTime :=
+  { date, time := PlainTime.midnight }
+
+/--
+Converts a `PlainDateTime` to a `PlainDate`
+-/
+@[inline]
+def toPlainDate (pdt : PlainDateTime) : PlainDate :=
+  pdt.date
+
+/--
+Converts a `PlainTime` to a `PlainDateTime`
+-/
+@[inline]
+def ofPlainTime (time : PlainTime) : PlainDateTime :=
+  { date := ⟨1, 1, 1, by decide⟩, time }
+
+/--
+Converts a `PlainDateTime` to a `PlainTime`
+-/
+@[inline]
+def toPlainTime (pdt : PlainDateTime) : PlainTime :=
+  pdt.time
+
+instance : HSub PlainDateTime PlainDateTime Duration where
+  hSub x y := x.toTimestampAssumingUTC - y.toTimestampAssumingUTC
+
+end PlainDateTime

src/Std/Time/DateTime/PlainDateTime.lean

@@ -0,0 +1,601 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Date
+import Std.Time.Time
+import Std.Time.Internal
+import Std.Time.DateTime.Timestamp
+
+namespace Std
+namespace Time
+open Internal
+
+set_option linter.all true
+
+/--
+Represents a date and time with components for Year, Month, Day, Hour, Minute, Second, and Nanosecond.
+-/
+structure PlainDateTime where
+
+  /--
+  The `Date` component of a `PlainDate`
+  -/
+  date : PlainDate
+
+  /--
+  The `Time` component of a `PlainTime`
+  -/
+  time : PlainTime
+
+  deriving Inhabited, BEq, Repr
+
+namespace PlainDateTime
+
+/--
+Converts a `PlainDateTime` to a `Timestamp`
+-/
+def toTimestampAssumingUTC (dt : PlainDateTime) : Timestamp :=
+  let days := dt.date.toDaysSinceUNIXEpoch
+  let nanos := days.toSeconds + dt.time.toSeconds |>.mul 1000000000
+  let nanos := nanos.val + dt.time.nanosecond.val
+  Timestamp.ofNanosecondsSinceUnixEpoch (Nanosecond.Offset.ofInt nanos)
+
+/--
+Converts a `Timestamp` to a `PlainDateTime`.
+-/
+def ofTimestampAssumingUTC (stamp : Timestamp) : PlainDateTime := Id.run do
+  let leapYearEpoch := 11017
+  let daysPer400Y := 365 * 400 + 97
+  let daysPer100Y := 365 * 100 + 24
+  let daysPer4Y := 365 * 4 + 1
+
+  let nanos := stamp.toNanosecondsSinceUnixEpoch
+  let secs : Second.Offset := nanos.ediv 1000000000
+  let daysSinceEpoch : Day.Offset := secs.ediv 86400
+  let boundedDaysSinceEpoch := daysSinceEpoch
+
+  let mut rawDays := boundedDaysSinceEpoch - leapYearEpoch
+  let mut rem := Bounded.LE.byMod secs.val 86400 (by decide)
+
+  let ⟨remSecs, days⟩ :=
+    if h : rem.val ≤ -1 then
+      let remSecs := rem.truncateTop h
+      let remSecs : Bounded.LE 1 86399 := remSecs.add 86400
+      let rawDays := rawDays - 1
+      (remSecs.expandBottom (by decide), rawDays)
+    else
+      let h := rem.truncateBottom (Int.not_le.mp h)
+      (h, rawDays)
+
+  let mut quadracentennialCycles := days.val / daysPer400Y;
+  let mut remDays := days.val % daysPer400Y;
+
+  if remDays < 0 then
+    remDays := remDays + daysPer400Y
+    quadracentennialCycles := quadracentennialCycles - 1
+
+  let mut centenialCycles := remDays / daysPer100Y;
+
+  if centenialCycles = 4 then
+    centenialCycles := centenialCycles - 1
+
+  remDays := remDays - centenialCycles * daysPer100Y
+  let mut quadrennialCycles := remDays / daysPer4Y;
+
+  if quadrennialCycles = 25 then
+    quadrennialCycles := quadrennialCycles - 1
+
+  remDays := remDays - quadrennialCycles * daysPer4Y
+  let mut remYears := remDays / 365;
+
+  if remYears = 4 then
+    remYears := remYears - 1
+
+  remDays := remDays - remYears * 365
+
+  let mut year := 2000 + remYears + 4 * quadrennialCycles + 100 * centenialCycles + 400 * quadracentennialCycles
+  let months := [31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 31, 29];
+  let mut mon : Fin 13 := 0;
+
+  for monLen in months do
+    mon := mon + 1;
+    if remDays < monLen then
+      break
+    remDays := remDays - monLen
+
+  let mday : Fin 31 := Fin.ofNat (Int.toNat remDays)
+
+  let hmon ←
+    if h₁ : mon.val > 10
+      then do
+        year := year + 1
+        pure (Month.Ordinal.ofNat (mon.val - 10) (by omega))
+      else
+        pure (Month.Ordinal.ofNat (mon.val + 2) (by omega))
+
+  let second : Bounded.LE 0 59 := remSecs.emod 60 (by decide)
+  let minute : Bounded.LE 0 59 := (remSecs.ediv 60 (by decide)).emod 60 (by decide)
+  let hour : Bounded.LE 0 23 := remSecs.ediv 3600 (by decide)
+  let nano : Bounded.LE 0 999999999 := Bounded.LE.byEmod nanos.val 1000000000 (by decide)
+
+  return {
+    date := PlainDate.ofYearMonthDayClip year hmon (Day.Ordinal.ofFin (Fin.succ mday))
+    time := PlainTime.ofHourMinuteSecondsNano (leap := false) (hour.expandTop (by decide)) minute second nano
+  }
+
+/--
+Converts a `PlainDateTime` to the number of days since the UNIX epoch.
+-/
+@[inline]
+def toDaysSinceUNIXEpoch (pdt : PlainDateTime) : Day.Offset :=
+  pdt.date.toDaysSinceUNIXEpoch
+
+/--
+Converts a `PlainDateTime` to the number of days since the UNIX epoch.
+-/
+@[inline]
+def ofDaysSinceUNIXEpoch (days : Day.Offset) (time : PlainTime) : PlainDateTime :=
+  PlainDateTime.mk (PlainDate.ofDaysSinceUNIXEpoch days) time
+
+/--
+Sets the `PlainDateTime` to the specified `desiredWeekday`.
+-/
+def withWeekday (dt : PlainDateTime) (desiredWeekday : Weekday) : PlainDateTime :=
+  { dt with date := PlainDate.withWeekday dt.date desiredWeekday }
+
+/--
+Creates a new `PlainDateTime` by adjusting the day of the month to the given `days` value, with any
+out-of-range days clipped to the nearest valid date.
+-/
+@[inline]
+def withDaysClip (dt : PlainDateTime) (days : Day.Ordinal) : PlainDateTime :=
+  { dt with date := PlainDate.ofYearMonthDayClip dt.date.year dt.date.month days }
+
+/--
+Creates a new `PlainDateTime` by adjusting the day of the month to the given `days` value, with any
+out-of-range days rolled over to the next month or year as needed.
+-/
+@[inline]
+def withDaysRollOver (dt : PlainDateTime) (days : Day.Ordinal) : PlainDateTime :=
+  { dt with date := PlainDate.rollOver dt.date.year dt.date.month days }
+
+/--
+Creates a new `PlainDateTime` by adjusting the month to the given `month` value, with any
+out-of-range days clipped to the nearest valid date.
+-/
+@[inline]
+def withMonthClip (dt : PlainDateTime) (month : Month.Ordinal) : PlainDateTime :=
+  { dt with date := PlainDate.ofYearMonthDayClip dt.date.year month dt.date.day }
+
+/--
+Creates a new `PlainDateTime` by adjusting the month to the given `month` value.
+The day is rolled over to the next valid month if necessary.
+-/
+@[inline]
+def withMonthRollOver (dt : PlainDateTime) (month : Month.Ordinal) : PlainDateTime :=
+  { dt with date := PlainDate.rollOver dt.date.year month dt.date.day }
+
+/--
+Creates a new `PlainDateTime` by adjusting the year to the given `year` value. The month and day
+remain unchanged, with any out-of-range days clipped to the nearest valid date.
+-/
+@[inline]
+def withYearClip (dt : PlainDateTime) (year : Year.Offset) : PlainDateTime :=
+  { dt with date := PlainDate.ofYearMonthDayClip year dt.date.month dt.date.day }
+
+/--
+Creates a new `PlainDateTime` by adjusting the year to the given `year` value. The month and day are rolled
+over to the next valid month and day if necessary.
+-/
+@[inline]
+def withYearRollOver (dt : PlainDateTime) (year : Year.Offset) : PlainDateTime :=
+  { dt with date := PlainDate.rollOver year dt.date.month dt.date.day }
+
+/--
+Creates a new `PlainDateTime` by adjusting the `hour` component of its `time` to the given value.
+-/
+@[inline]
+def withHours (dt : PlainDateTime) (hour : Hour.Ordinal) : PlainDateTime :=
+  { dt with time := { dt.time with hour := hour } }
+
+/--
+Creates a new `PlainDateTime` by adjusting the `minute` component of its `time` to the given value.
+-/
+@[inline]
+def withMinutes (dt : PlainDateTime) (minute : Minute.Ordinal) : PlainDateTime :=
+  { dt with time := { dt.time with minute := minute } }
+
+/--
+Creates a new `PlainDateTime` by adjusting the `second` component of its `time` to the given value.
+-/
+@[inline]
+def withSeconds (dt : PlainDateTime) (second : Sigma Second.Ordinal) : PlainDateTime :=
+  { dt with time := { dt.time with second := second } }
+
+/--
+Creates a new `PlainDateTime` by adjusting the milliseconds component inside the `nano` component of its `time` to the given value.
+-/
+@[inline]
+def withMilliseconds (dt : PlainDateTime) (millis : Millisecond.Ordinal) : PlainDateTime :=
+  { dt with time := dt.time.withMilliseconds millis }
+
+/--
+Creates a new `PlainDateTime` by adjusting the `nano` component of its `time` to the given value.
+-/
+@[inline]
+def withNanoseconds (dt : PlainDateTime) (nano : Nanosecond.Ordinal) : PlainDateTime :=
+  { dt with time := dt.time.withNanoseconds nano }
+
+/--
+Adds a `Day.Offset` to a `PlainDateTime`.
+-/
+@[inline]
+def addDays (dt : PlainDateTime) (days : Day.Offset) : PlainDateTime :=
+  { dt with date := dt.date.addDays days }
+
+/--
+Subtracts a `Day.Offset` from a `PlainDateTime`.
+-/
+@[inline]
+def subDays (dt : PlainDateTime) (days : Day.Offset) : PlainDateTime :=
+  { dt with date := dt.date.subDays days }
+
+/--
+Adds a `Week.Offset` to a `PlainDateTime`.
+-/
+@[inline]
+def addWeeks (dt : PlainDateTime) (weeks : Week.Offset) : PlainDateTime :=
+  { dt with date := dt.date.addWeeks weeks }
+
+/--
+Subtracts a `Week.Offset` from a `PlainDateTime`.
+-/
+@[inline]
+def subWeeks (dt : PlainDateTime) (weeks : Week.Offset) : PlainDateTime :=
+  { dt with date := dt.date.subWeeks weeks }
+
+/--
+Adds a `Month.Offset` to a `PlainDateTime`, adjusting the day to the last valid day of the resulting
+month.
+-/
+def addMonthsClip (dt : PlainDateTime) (months : Month.Offset) : PlainDateTime :=
+  { dt with date := dt.date.addMonthsClip months }
+
+/--
+Subtracts `Month.Offset` from a `PlainDateTime`, it clips the day to the last valid day of that month.
+-/
+@[inline]
+def subMonthsClip (dt : PlainDateTime) (months : Month.Offset) : PlainDateTime :=
+  { dt with date := dt.date.subMonthsClip months }
+
+/--
+Adds a `Month.Offset` to a `PlainDateTime`, rolling over excess days to the following month if needed.
+-/
+def addMonthsRollOver (dt : PlainDateTime) (months : Month.Offset) : PlainDateTime :=
+  { dt with date := dt.date.addMonthsRollOver months }
+
+/--
+Subtracts a `Month.Offset` from a `PlainDateTime`, adjusting the day to the last valid day of the
+resulting month.
+-/
+@[inline]
+def subMonthsRollOver (dt : PlainDateTime) (months : Month.Offset) : PlainDateTime :=
+  { dt with date := dt.date.subMonthsRollOver months }
+
+/--
+Adds a `Month.Offset` to a `PlainDateTime`, rolling over excess days to the following month if needed.
+-/
+@[inline]
+def addYearsRollOver (dt : PlainDateTime) (years : Year.Offset) : PlainDateTime :=
+  { dt with date := dt.date.addYearsRollOver years }
+
+/--
+Subtracts a `Month.Offset` from a `PlainDateTime`, rolling over excess days to the following month if
+needed.
+-/
+@[inline]
+def addYearsClip (dt : PlainDateTime) (years : Year.Offset) : PlainDateTime :=
+  { dt with date := dt.date.addYearsClip years }
+
+/--
+Subtracts a `Year.Offset` from a `PlainDateTime`, this function rolls over any excess days into the
+following month.
+-/
+@[inline]
+def subYearsRollOver (dt : PlainDateTime) (years : Year.Offset) : PlainDateTime :=
+  { dt with date := dt.date.subYearsRollOver years }
+
+/--
+Subtracts a `Year.Offset` from a `PlainDateTime`, adjusting the day to the last valid day of the
+resulting month.
+-/
+@[inline]
+def subYearsClip (dt : PlainDateTime) (years : Year.Offset) : PlainDateTime :=
+  { dt with date := dt.date.subYearsClip years }
+
+
+/--
+Adds an `Hour.Offset` to a `PlainDateTime`, adjusting the date if the hour overflows.
+-/
+@[inline]
+def addHours (dt : PlainDateTime) (hours : Hour.Offset) : PlainDateTime :=
+  let totalSeconds := dt.time.toSeconds + hours.toSeconds
+  let days := totalSeconds.ediv 86400
+  let newTime := dt.time.addSeconds (hours.toSeconds)
+  { dt with date := dt.date.addDays days, time := newTime }
+
+/--
+Subtracts an `Hour.Offset` from a `PlainDateTime`, adjusting the date if the hour underflows.
+-/
+@[inline]
+def subHours (dt : PlainDateTime) (hours : Hour.Offset) : PlainDateTime :=
+  addHours dt (-hours)
+
+/--
+Adds a `Minute.Offset` to a `PlainDateTime`, adjusting the hour and date if the minutes overflow.
+-/
+@[inline]
+def addMinutes (dt : PlainDateTime) (minutes : Minute.Offset) : PlainDateTime :=
+  let totalSeconds := dt.time.toSeconds + minutes.toSeconds
+  let days := totalSeconds.ediv 86400
+  let newTime := dt.time.addSeconds (minutes.toSeconds)
+  { dt with date := dt.date.addDays days, time := newTime }
+
+/--
+Subtracts a `Minute.Offset` from a `PlainDateTime`, adjusting the hour and date if the minutes underflow.
+-/
+@[inline]
+def subMinutes (dt : PlainDateTime) (minutes : Minute.Offset) : PlainDateTime :=
+  addMinutes dt (-minutes)
+
+/--
+Adds a `Second.Offset` to a `PlainDateTime`, adjusting the minute, hour, and date if the seconds overflow.
+-/
+@[inline]
+def addSeconds (dt : PlainDateTime) (seconds : Second.Offset) : PlainDateTime :=
+  let totalSeconds := dt.time.toSeconds + seconds
+  let days := totalSeconds.ediv 86400
+  let newTime := dt.time.addSeconds seconds
+  { dt with date := dt.date.addDays days, time := newTime }
+
+/--
+Subtracts a `Second.Offset` from a `PlainDateTime`, adjusting the minute, hour, and date if the seconds underflow.
+-/
+@[inline]
+def subSeconds (dt : PlainDateTime) (seconds : Second.Offset) : PlainDateTime :=
+  addSeconds dt (-seconds)
+
+/--
+Adds a `Millisecond.Offset` to a `PlainDateTime`, adjusting the second, minute, hour, and date if the milliseconds overflow.
+-/
+@[inline]
+def addMilliseconds (dt : PlainDateTime) (milliseconds : Millisecond.Offset) : PlainDateTime :=
+  let totalMilliseconds := dt.time.toMilliseconds + milliseconds
+  let days := totalMilliseconds.ediv 86400000 -- 86400000 ms in a day
+  let newTime := dt.time.addMilliseconds milliseconds
+  { dt with date := dt.date.addDays days, time := newTime }
+
+/--
+Subtracts a `Millisecond.Offset` from a `PlainDateTime`, adjusting the second, minute, hour, and date if the milliseconds underflow.
+-/
+@[inline]
+def subMilliseconds (dt : PlainDateTime) (milliseconds : Millisecond.Offset) : PlainDateTime :=
+  addMilliseconds dt (-milliseconds)
+
+/--
+Adds a `Nanosecond.Offset` to a `PlainDateTime`, adjusting the seconds, minutes, hours, and date if the nanoseconds overflow.
+-/
+@[inline]
+def addNanoseconds (dt : PlainDateTime) (nanos : Nanosecond.Offset) : PlainDateTime :=
+  let nano := Nanosecond.Offset.ofInt dt.time.nanosecond.val
+  let totalNanos := nano + nanos
+  let extraSeconds := totalNanos.ediv 1000000000
+  let nanosecond := Bounded.LE.byEmod totalNanos.val 1000000000 (by decide)
+  let newTime := dt.time.addSeconds extraSeconds
+  { dt with time := { newTime with nanosecond } }
+
+/--
+Subtracts a `Nanosecond.Offset` from a `PlainDateTime`, adjusting the seconds, minutes, hours, and date if the nanoseconds underflow.
+-/
+@[inline]
+def subNanoseconds (dt : PlainDateTime) (nanos : Nanosecond.Offset) : PlainDateTime :=
+  addNanoseconds dt (-nanos)
+
+/--
+Getter for the `Year` inside of a `PlainDateTime`.
+-/
+@[inline]
+def year (dt : PlainDateTime) : Year.Offset :=
+  dt.date.year
+
+/--
+Getter for the `Month` inside of a `PlainDateTime`.
+-/
+@[inline]
+def month (dt : PlainDateTime) : Month.Ordinal :=
+  dt.date.month
+
+/--
+Getter for the `Day` inside of a `PlainDateTime`.
+-/
+@[inline]
+def day (dt : PlainDateTime) : Day.Ordinal :=
+  dt.date.day
+
+/--
+Getter for the `Weekday` inside of a `PlainDateTime`.
+-/
+@[inline]
+def weekday (dt : PlainDateTime) : Weekday :=
+  dt.date.weekday
+
+/--
+Getter for the `Hour` inside of a `PlainDateTime`.
+-/
+@[inline]
+def hour (dt : PlainDateTime) : Hour.Ordinal :=
+  dt.time.hour
+
+/--
+Getter for the `Minute` inside of a `PlainDateTime`.
+-/
+@[inline]
+def minute (dt : PlainDateTime) : Minute.Ordinal :=
+  dt.time.minute
+
+/--
+Getter for the `Millisecond` inside of a `PlainDateTime`.
+-/
+@[inline]
+def millisecond (dt : PlainDateTime) : Millisecond.Ordinal :=
+  dt.time.millisecond
+
+/--
+Getter for the `Second` inside of a `PlainDateTime`.
+-/
+@[inline]
+def second (dt : PlainDateTime) : Second.Ordinal dt.time.second.fst :=
+  dt.time.second.snd
+
+/--
+Getter for the `Nanosecond.Ordinal` inside of a `PlainDateTime`.
+-/
+@[inline]
+def nanosecond (dt : PlainDateTime) : Nanosecond.Ordinal :=
+  dt.time.nanosecond
+
+/--
+Determines the era of the given `PlainDateTime` based on its year.
+-/
+@[inline]
+def era (date : PlainDateTime) : Year.Era :=
+  date.date.era
+
+/--
+Checks if the `PlainDateTime` is in a leap year.
+-/
+@[inline]
+def inLeapYear (date : PlainDateTime) : Bool :=
+  date.year.isLeap
+
+/--
+Determines the week of the year for the given `PlainDateTime`.
+-/
+@[inline]
+def weekOfYear (date : PlainDateTime) : Week.Ordinal :=
+  date.date.weekOfYear
+
+/--
+Returns the unaligned week of the month for a `PlainDateTime` (day divided by 7, plus 1).
+-/
+def weekOfMonth (date : PlainDateTime) : Bounded.LE 1 5 :=
+  date.date.weekOfMonth
+
+/--
+Determines the week of the month for the given `PlainDateTime`. The week of the month is calculated based
+on the day of the month and the weekday. Each week starts on Monday because the entire library is
+based on the Gregorian Calendar.
+-/
+@[inline]
+def alignedWeekOfMonth (date : PlainDateTime) : Week.Ordinal.OfMonth :=
+  date.date.alignedWeekOfMonth
+
+/--
+Transforms a tuple of a `PlainDateTime` into a `Day.Ordinal.OfYear`.
+-/
+@[inline]
+def dayOfYear (date : PlainDateTime) : Day.Ordinal.OfYear date.year.isLeap :=
+  ValidDate.dayOfYear ⟨(date.month, date.day), date.date.valid⟩
+
+/--
+Determines the quarter of the year for the given `PlainDateTime`.
+-/
+@[inline]
+def quarter (date : PlainDateTime) : Bounded.LE 1 4 :=
+  date.date.quarter
+
+/--
+Combines a `PlainDate` and `PlainTime` into a `PlainDateTime`.
+-/
+@[inline]
+def atTime : PlainDate → PlainTime → PlainDateTime :=
+  PlainDateTime.mk
+
+/--
+Combines a `PlainTime` and `PlainDate` into a `PlainDateTime`.
+-/
+@[inline]
+def atDate (time: PlainTime) (date: PlainDate) : PlainDateTime :=
+  PlainDateTime.mk date time
+
+instance : HAdd PlainDateTime Day.Offset PlainDateTime where
+  hAdd := addDays
+
+instance : HSub PlainDateTime Day.Offset PlainDateTime where
+  hSub := subDays
+
+instance : HAdd PlainDateTime Week.Offset PlainDateTime where
+  hAdd := addWeeks
+
+instance : HSub PlainDateTime Week.Offset PlainDateTime where
+  hSub := subWeeks
+
+instance : HAdd PlainDateTime Hour.Offset PlainDateTime where
+  hAdd := addHours
+
+instance : HSub PlainDateTime Hour.Offset PlainDateTime where
+  hSub := subHours
+
+instance : HAdd PlainDateTime Minute.Offset PlainDateTime where
+  hAdd := addMinutes
+
+instance : HSub PlainDateTime Minute.Offset PlainDateTime where
+  hSub := subMinutes
+
+instance : HAdd PlainDateTime Millisecond.Offset PlainDateTime where
+  hAdd := addMilliseconds
+
+instance : HSub PlainDateTime Millisecond.Offset PlainDateTime where
+  hSub := addMilliseconds
+
+instance : HAdd PlainDateTime Second.Offset PlainDateTime where
+  hAdd := addSeconds
+
+instance : HSub PlainDateTime Second.Offset PlainDateTime where
+  hSub := subSeconds
+
+instance : HAdd PlainDateTime Nanosecond.Offset PlainDateTime where
+  hAdd := addNanoseconds
+
+instance : HSub PlainDateTime Nanosecond.Offset PlainDateTime where
+  hSub := subNanoseconds
+
+instance : HAdd PlainDateTime Duration PlainDateTime where
+  hAdd x y := addNanoseconds x y.toNanoseconds
+
+end PlainDateTime
+namespace PlainDate
+
+/--
+Combines a `PlainDate` and `PlainTime` into a `PlainDateTime`.
+-/
+@[inline]
+def atTime : PlainDate → PlainTime → PlainDateTime :=
+  PlainDateTime.mk
+
+end PlainDate
+namespace PlainTime
+
+/--
+Combines a `PlainTime` and `PlainDate` into a `PlainDateTime`.
+-/
+@[inline]
+def atDate (time: PlainTime) (date: PlainDate) : PlainDateTime :=
+  PlainDateTime.mk date time
+
+end PlainTime
+end Time
+end Std

src/Std/Time/DateTime/Timestamp.lean

@@ -0,0 +1,289 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Internal
+import Init.Data.Int
+import Std.Time.Time
+import Std.Time.Date
+import Std.Time.Duration
+
+namespace Std
+namespace Time
+open Internal
+
+set_option linter.all true
+
+/--
+Represents an exact point in time as a UNIX Epoch timestamp.
+-/
+structure Timestamp where
+
+  /--
+  Duration since the unix epoch.
+  -/
+  val : Duration
+  deriving Repr, BEq, Inhabited
+
+instance : LE Timestamp where
+  le x y := x.val ≤ y.val
+
+instance { x y : Timestamp } : Decidable (x ≤ y) :=
+  inferInstanceAs (Decidable (x.val ≤ y.val))
+
+instance : OfNat Timestamp n where
+  ofNat := ⟨OfNat.ofNat n⟩
+
+instance : ToString Timestamp where
+  toString s := toString s.val.toMilliseconds
+
+instance : Repr Timestamp where
+  reprPrec s := reprPrec (toString s)
+
+namespace Timestamp
+
+/--
+Fetches the current duration from the system.
+-/
+@[extern "lean_get_current_time"]
+opaque now : IO Timestamp
+
+/--
+Converts a `Timestamp` to minutes as `Minute.Offset`.
+-/
+@[inline]
+def toMinutes (tm : Timestamp) : Minute.Offset :=
+  tm.val.second.ediv 60
+
+/--
+Converts a `Timestamp` to days as `Day.Offset`.
+-/
+@[inline]
+def toDays (tm : Timestamp) : Day.Offset :=
+  tm.val.second.ediv 86400
+
+/--
+Creates a `Timestamp` from a `Second.Offset` since the Unix epoch.
+-/
+@[inline]
+def ofSecondsSinceUnixEpoch (secs : Second.Offset) : Timestamp :=
+  ⟨Duration.ofSeconds secs⟩
+
+/--
+Creates a `Timestamp` from a `Nanosecond.Offset` since the Unix epoch.
+-/
+@[inline]
+def ofNanosecondsSinceUnixEpoch (nanos : Nanosecond.Offset) : Timestamp :=
+  ⟨Duration.ofNanoseconds nanos⟩
+
+/--
+Creates a `Timestamp` from a `Millisecond.Offset` since the Unix epoch.
+-/
+@[inline]
+def ofMillisecondsSinceUnixEpoch (milli : Millisecond.Offset) : Timestamp :=
+  ⟨Duration.ofNanoseconds milli.toNanoseconds⟩
+
+/--
+Converts a `Timestamp` to seconds as `Second.Offset`.
+-/
+@[inline]
+def toSecondsSinceUnixEpoch (t : Timestamp) : Second.Offset :=
+  t.val.second
+
+/--
+Converts a `Timestamp` to nanoseconds as `Nanosecond.Offset`.
+-/
+@[inline]
+def toNanosecondsSinceUnixEpoch (tm : Timestamp) : Nanosecond.Offset :=
+  let nanos := tm.toSecondsSinceUnixEpoch.mul 1000000000
+  let nanos := nanos + (.ofInt tm.val.nano.val)
+  nanos
+
+/--
+Converts a `Timestamp` to nanoseconds as `Millisecond.Offset`.
+-/
+@[inline]
+def toMillisecondsSinceUnixEpoch (tm : Timestamp) : Millisecond.Offset :=
+  tm.toNanosecondsSinceUnixEpoch.toMilliseconds
+
+/--
+Calculates the duration from the given `Timestamp` to the current time.
+-/
+@[inline]
+def since (f : Timestamp) : IO Duration := do
+  let cur ← Timestamp.now
+  return Std.Time.Duration.sub cur.val f.val
+
+/--
+Returns the `Duration` represented by the `Timestamp` since the Unix epoch.
+-/
+@[inline]
+def toDurationSinceUnixEpoch (tm : Timestamp) : Duration :=
+  tm.val
+
+/--
+Adds a `Millisecond.Offset` to the given `Timestamp`.
+-/
+@[inline]
+def addMilliseconds (t : Timestamp) (s : Millisecond.Offset) : Timestamp :=
+  ⟨t.val + s⟩
+
+/--
+Subtracts a `Millisecond.Offset` from the given `Timestamp`.
+-/
+@[inline]
+def subMilliseconds (t : Timestamp) (s : Millisecond.Offset) : Timestamp :=
+  ⟨t.val - s⟩
+
+/--
+Adds a `Nanosecond.Offset` to the given `Timestamp`.
+-/
+@[inline]
+def addNanoseconds (t : Timestamp) (s : Nanosecond.Offset) : Timestamp :=
+  ⟨t.val + s⟩
+
+/--
+Subtracts a `Nanosecond.Offset` from the given `Timestamp`.
+-/
+@[inline]
+def subNanoseconds (t : Timestamp) (s : Nanosecond.Offset) : Timestamp :=
+  ⟨t.val - s⟩
+
+/--
+Adds a `Second.Offset` to the given `Timestamp`.
+-/
+@[inline]
+def addSeconds (t : Timestamp) (s : Second.Offset) : Timestamp :=
+  ⟨t.val + s⟩
+
+/--
+Subtracts a `Second.Offset` from the given `Timestamp`.
+-/
+@[inline]
+def subSeconds (t : Timestamp) (s : Second.Offset) : Timestamp :=
+  ⟨t.val - s⟩
+
+/--
+Adds a `Minute.Offset` to the given `Timestamp`.
+-/
+@[inline]
+def addMinutes (t : Timestamp) (m : Minute.Offset) : Timestamp :=
+  ⟨t.val + m⟩
+
+/--
+Subtracts a `Minute.Offset` from the given `Timestamp`.
+-/
+@[inline]
+def subMinutes (t : Timestamp) (m : Minute.Offset) : Timestamp :=
+  ⟨t.val - m⟩
+
+/--
+Adds an `Hour.Offset` to the given `Timestamp`.
+-/
+@[inline]
+def addHours (t : Timestamp) (h : Hour.Offset) : Timestamp :=
+  ⟨t.val + h⟩
+
+/--
+Subtracts an `Hour.Offset` from the given `Timestamp`.
+-/
+@[inline]
+def subHours (t : Timestamp) (h : Hour.Offset) : Timestamp :=
+  ⟨t.val - h⟩
+
+/--
+Adds a `Day.Offset` to the given `Timestamp`.
+-/
+@[inline]
+def addDays (t : Timestamp) (d : Day.Offset) : Timestamp :=
+  ⟨t.val + d⟩
+
+/--
+Subtracts a `Day.Offset` from the given `Timestamp`.
+-/
+@[inline]
+def subDays (t : Timestamp) (d : Day.Offset) : Timestamp :=
+  ⟨t.val - d⟩
+
+/--
+Adds a `Week.Offset` to the given `Timestamp`.
+-/
+@[inline]
+def addWeeks (t : Timestamp) (d : Week.Offset) : Timestamp :=
+  ⟨t.val + d⟩
+
+/--
+Subtracts a `Week.Offset` from the given `Timestamp`.
+-/
+@[inline]
+def subWeeks (t : Timestamp) (d : Week.Offset) : Timestamp :=
+  ⟨t.val - d⟩
+
+/--
+Adds a `Duration` to the given `Timestamp`.
+-/
+@[inline]
+def addDuration (t : Timestamp) (d : Duration) : Timestamp :=
+  ⟨t.val + d⟩
+
+/--
+Subtracts a `Duration` from the given `Timestamp`.
+-/
+@[inline]
+def subDuration (t : Timestamp) (d : Duration) : Timestamp :=
+  ⟨t.val - d⟩
+
+instance : HAdd Timestamp Duration Timestamp where
+  hAdd := addDuration
+
+instance : HSub Timestamp Duration Timestamp where
+  hSub := subDuration
+
+instance : HAdd Timestamp Day.Offset Timestamp where
+  hAdd := addDays
+
+instance : HSub Timestamp Day.Offset Timestamp where
+  hSub := subDays
+
+instance : HAdd Timestamp Week.Offset Timestamp where
+  hAdd := addWeeks
+
+instance : HSub Timestamp Week.Offset Timestamp where
+  hSub := subWeeks
+
+instance : HAdd Timestamp Hour.Offset Timestamp where
+  hAdd := addHours
+
+instance : HSub Timestamp Hour.Offset Timestamp where
+  hSub := subHours
+
+instance : HAdd Timestamp Minute.Offset Timestamp where
+  hAdd := addMinutes
+
+instance : HSub Timestamp Minute.Offset Timestamp where
+  hSub := subMinutes
+
+instance : HAdd Timestamp Second.Offset Timestamp where
+  hAdd := addSeconds
+
+instance : HSub Timestamp Second.Offset Timestamp where
+  hSub := subSeconds
+
+instance : HAdd Timestamp Millisecond.Offset Timestamp where
+  hAdd := addMilliseconds
+
+instance : HSub Timestamp Millisecond.Offset Timestamp where
+  hSub := subMilliseconds
+
+instance : HAdd Timestamp Nanosecond.Offset Timestamp where
+  hAdd := addNanoseconds
+
+instance : HSub Timestamp Nanosecond.Offset Timestamp where
+  hSub := subNanoseconds
+
+instance : HSub Timestamp Timestamp Duration where
+  hSub x y := x.val - y.val
+
+end Timestamp

src/Std/Time/Duration.lean

@@ -0,0 +1,361 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Date
+import Std.Time.Time
+
+namespace Std
+namespace Time
+open Internal
+
+set_option linter.all true
+
+/--
+Represents a time interval with nanoseconds precision.
+-/
+structure Duration where
+
+  /--
+  Second offset of the duration.
+  -/
+  second : Second.Offset
+
+  /--
+  Nanosecond span that ranges from -999999999 and 999999999
+  -/
+  nano : Nanosecond.Span
+
+  /--
+  Proof that the duration is valid, ensuring that the `second` and `nano` values are correctly related.
+  -/
+  proof : (second.val ≥ 0 ∧ nano.val ≥ 0) ∨ (second.val ≤ 0 ∧ nano.val ≤ 0)
+  deriving Repr
+
+instance : ToString Duration where
+  toString s :=
+    let (sign, secs, nanos) :=
+      if s.second.val > 0 then ("" ,s.second, s.nano.val)
+      else if s.second.val < 0 then ("-", -s.second, -s.nano.val)
+      else if s.nano.val < 0 then ("-", -s.second, -s.nano.val) else ("", s.second, s.nano.val)
+    sign ++ toString secs ++ (if s.nano.val == 0 then "" else "." ++ (leftPad 9 <| toString nanos)) ++ "s"
+  where
+    leftPad n s := "".pushn '0' (n - s.length) ++ s
+
+instance : Repr Duration where
+  reprPrec s := reprPrec (toString s)
+
+instance : BEq Duration where
+  beq x y := x.second == y.second && y.nano == x.nano
+
+instance : Inhabited Duration where
+  default := ⟨0, Bounded.LE.mk 0 (by decide), by decide⟩
+
+instance : OfNat Duration n where
+  ofNat := by
+    refine ⟨.ofInt n, ⟨0, by decide⟩, ?_⟩
+    simp <;> exact Int.le_total n 0 |>.symm
+
+namespace Duration
+
+/--
+Negates a `Duration`, flipping its second and nanosecond values.
+-/
+@[inline]
+protected def neg (duration : Duration) : Duration := by
+  refine ⟨-duration.second, duration.nano.neg, ?_⟩
+  cases duration.proof with
+  | inl n => exact Or.inr (n.imp Int.neg_le_neg Int.neg_le_neg)
+  | inr n => exact Or.inl (n.imp Int.neg_le_neg Int.neg_le_neg)
+
+/--
+Creates a new `Duration` out of `Second.Offset`.
+-/
+@[inline]
+def ofSeconds (s : Second.Offset) : Duration := by
+  refine ⟨s, ⟨0, by decide⟩, ?_⟩
+  simp <;> exact Int.le_total s.val 0 |>.symm
+
+/--
+Creates a new `Duration` out of `Nanosecond.Offset`.
+-/
+def ofNanoseconds (s : Nanosecond.Offset) : Duration := by
+  refine ⟨s.ediv 1000000000, Bounded.LE.byMod s.val 1000000000 (by decide), ?_⟩
+  cases Int.le_total s.val 0
+  next n => exact Or.inr (And.intro (Int.ediv_le_ediv (by decide) n) (mod_nonpos 1000000000 n (by decide)))
+  next n => exact Or.inl (And.intro (Int.ediv_nonneg n (by decide)) (Int.tmod_nonneg 1000000000 n))
+  where
+    mod_nonpos : ∀ {a : Int} (b : Int), (a ≤ 0) → (b ≥ 0) → 0 ≥ a.tmod b
+    | .negSucc m, .ofNat n, _, _ => Int.neg_le_neg (Int.tmod_nonneg (↑n) (Int.ofNat_le.mpr (Nat.zero_le (m + 1))))
+    | 0, n, _, _ => Int.eq_iff_le_and_ge.mp (Int.zero_tmod n) |>.left
+
+/--
+Creates a new `Duration` out of `Millisecond.Offset`.
+-/
+@[inline]
+def ofMillisecond (s : Millisecond.Offset) : Duration :=
+  ofNanoseconds (s.mul 1000000)
+
+/--
+Checks if the duration is zero seconds and zero nanoseconds.
+-/
+@[inline]
+def isZero (d : Duration) : Bool :=
+  d.second.val = 0 ∧ d.nano.val = 0
+
+/--
+Converts a `Duration` to a `Second.Offset`
+-/
+@[inline]
+def toSeconds (duration : Duration) : Second.Offset :=
+   duration.second
+
+/--
+Converts a `Duration` to a `Millisecond.Offset`
+-/
+@[inline]
+def toMilliseconds (duration : Duration) : Millisecond.Offset :=
+  let secMillis := duration.second.mul 1000
+  let nanosMillis := duration.nano.ediv 1000000 (by decide)
+  let millis := secMillis + (.ofInt nanosMillis.val)
+  millis
+
+/--
+Converts a `Duration` to a `Nanosecond.Offset`
+-/
+@[inline]
+def toNanoseconds (duration : Duration) : Nanosecond.Offset :=
+  let nanos := duration.second.mul 1000000000
+  let nanos := nanos + (.ofInt duration.nano.val)
+  nanos
+
+instance : LE Duration where
+  le d1 d2 := d1.toNanoseconds ≤ d2.toNanoseconds
+
+instance {x y : Duration} : Decidable (x ≤ y) :=
+  inferInstanceAs (Decidable (x.toNanoseconds ≤ y.toNanoseconds))
+
+/--
+Converts a `Duration` to a `Minute.Offset`
+-/
+@[inline]
+def toMinutes (tm : Duration) : Minute.Offset :=
+  tm.second.ediv 60
+
+/--
+Converts a `Duration` to a `Day.Offset`
+-/
+@[inline]
+def toDays (tm : Duration) : Day.Offset :=
+  tm.second.ediv 86400
+
+/--
+Normalizes `Second.Offset` and `NanoSecond.span` in order to build a new `Duration` out of it.
+-/
+@[inline]
+def fromComponents (secs : Second.Offset) (nanos : Nanosecond.Span) : Duration :=
+  ofNanoseconds (secs.toNanoseconds + nanos.toOffset)
+
+/--
+Adds two durations together, handling any carry-over in nanoseconds.
+-/
+@[inline]
+def add (t₁ t₂ : Duration) : Duration :=
+  ofNanoseconds (toNanoseconds t₁ + toNanoseconds t₂)
+
+/--
+Subtracts one `Duration` from another.
+-/
+@[inline]
+def sub (t₁ t₂ : Duration) : Duration :=
+  t₁.add t₂.neg
+
+/--
+Adds a `Nanosecond.Offset` to a `Duration`
+-/
+@[inline]
+def addNanoseconds (t : Duration) (s : Nanosecond.Offset) : Duration :=
+  t.add (ofNanoseconds s)
+
+/--
+Adds a `Millisecond.Offset` to a `Duration`
+-/
+@[inline]
+def addMilliseconds (t : Duration) (s : Millisecond.Offset) : Duration :=
+  t.add (ofNanoseconds s.toNanoseconds)
+
+/--
+Adds a `Millisecond.Offset` to a `Duration`
+-/
+@[inline]
+def subMilliseconds (t : Duration) (s : Millisecond.Offset) : Duration :=
+  t.sub (ofNanoseconds s.toNanoseconds)
+
+/--
+Adds a `Nanosecond.Offset` to a `Duration`
+-/
+@[inline]
+def subNanoseconds (t : Duration) (s : Nanosecond.Offset) : Duration :=
+  t.sub (ofNanoseconds s)
+
+/--
+Adds a `Second.Offset` to a `Duration`
+-/
+@[inline]
+def addSeconds (t : Duration) (s : Second.Offset) : Duration :=
+  t.add (ofSeconds s)
+
+/--
+Subtracts a `Second.Offset` from a `Duration`
+-/
+@[inline]
+def subSeconds (t : Duration) (s : Second.Offset) : Duration :=
+  t.sub (ofSeconds s)
+
+/--
+Adds a `Minute.Offset` to a `Duration`
+-/
+@[inline]
+def addMinutes (t : Duration) (m : Minute.Offset) : Duration :=
+  let seconds := m.mul 60
+  t.addSeconds seconds
+
+/--
+Subtracts a `Minute.Offset` from a `Duration`
+-/
+@[inline]
+def subMinutes (t : Duration) (m : Minute.Offset) : Duration :=
+  let seconds := m.mul 60
+  t.subSeconds seconds
+
+/--
+Adds an `Hour.Offset` to a `Duration`
+-/
+@[inline]
+def addHours (t : Duration) (h : Hour.Offset) : Duration :=
+  let seconds := h.mul 3600
+  t.addSeconds seconds
+
+/--
+Subtracts an `Hour.Offset` from a `Duration`
+-/
+@[inline]
+def subHours (t : Duration) (h : Hour.Offset) : Duration :=
+  let seconds := h.mul 3600
+  t.subSeconds seconds
+
+/--
+Adds a `Day.Offset` to a `Duration`
+-/
+@[inline]
+def addDays (t : Duration) (d : Day.Offset) : Duration :=
+  let seconds := d.mul 86400
+  t.addSeconds seconds
+
+/--
+Subtracts a `Day.Offset` from a `Duration`
+-/
+@[inline]
+def subDays (t : Duration) (d : Day.Offset) : Duration :=
+  let seconds := d.mul 86400
+  t.subSeconds seconds
+
+/--
+Adds a `Week.Offset` to a `Duration`
+-/
+@[inline]
+def addWeeks (t : Duration) (w : Week.Offset) : Duration :=
+  let seconds := w.mul 604800
+  t.addSeconds seconds
+
+/--
+Subtracts a `Week.Offset` from a `Duration`
+-/
+@[inline]
+def subWeeks (t : Duration) (w : Week.Offset) : Duration :=
+  let seconds := w.mul 604800
+  t.subSeconds seconds
+
+instance : HAdd Duration Day.Offset Duration where
+  hAdd := addDays
+
+instance : HSub Duration Day.Offset Duration where
+  hSub := subDays
+
+instance : HAdd Duration Week.Offset Duration where
+  hAdd := addWeeks
+
+instance : HSub Duration Week.Offset Duration where
+  hSub := subWeeks
+
+instance : HAdd Duration Hour.Offset Duration where
+  hAdd := addHours
+
+instance : HSub Duration Hour.Offset Duration where
+  hSub := subHours
+
+instance : HAdd Duration Minute.Offset Duration where
+  hAdd := addMinutes
+
+instance : HSub Duration Minute.Offset Duration where
+  hSub := subMinutes
+
+instance : HAdd Duration Second.Offset Duration where
+  hAdd := addSeconds
+
+instance : HSub Duration Second.Offset Duration where
+  hSub := subSeconds
+
+instance : HAdd Duration Nanosecond.Offset Duration where
+  hAdd := addNanoseconds
+
+instance : HSub Duration Nanosecond.Offset Duration where
+  hSub := subNanoseconds
+
+instance : HAdd Duration Millisecond.Offset Duration where
+  hAdd := addMilliseconds
+
+instance : HSub Duration Millisecond.Offset Duration where
+  hSub := subMilliseconds
+
+instance : HSub Duration Duration Duration where
+  hSub := sub
+
+instance : HAdd Duration Duration Duration where
+  hAdd := add
+
+instance : Coe Nanosecond.Offset Duration where
+  coe := ofNanoseconds
+
+instance : Coe Second.Offset Duration where
+  coe := ofSeconds
+
+instance : Coe Minute.Offset Duration where
+  coe := ofSeconds ∘ Minute.Offset.toSeconds
+
+instance : Coe Hour.Offset Duration where
+  coe := ofSeconds ∘ Hour.Offset.toSeconds
+
+instance : Coe Week.Offset Duration where
+  coe := ofSeconds ∘ Day.Offset.toSeconds ∘ Week.Offset.toDays
+
+instance : Coe Day.Offset Duration where
+  coe := ofSeconds ∘ Day.Offset.toSeconds
+
+instance : HMul Int Duration Duration where
+  hMul i d := Duration.ofNanoseconds <| Nanosecond.Offset.ofInt (d.toNanoseconds.val * i)
+
+instance : HMul Duration Int Duration where
+  hMul d i := Duration.ofNanoseconds <| Nanosecond.Offset.ofInt (d.toNanoseconds.val * i)
+
+instance : HAdd PlainTime Duration PlainTime where
+   hAdd pt d := PlainTime.ofNanoseconds (d.toNanoseconds + pt.toNanoseconds)
+
+instance : HSub PlainTime Duration PlainTime where
+   hSub pt d := PlainTime.ofNanoseconds (d.toNanoseconds - pt.toNanoseconds)
+
+end Duration
+end Time
+end Std

src/Std/Time/Format.lean

@@ -0,0 +1,623 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Notation.Spec
+import Std.Time.Format.Basic
+import Std.Time.Internal.Bounded
+
+namespace Std
+namespace Time
+namespace Formats
+open Internal
+
+set_option linter.all true
+
+/--
+The ISO8601 format, which is always 24 or 27 characters long, used for representing date and time in
+a standardized format. The format follows the pattern `uuuu-MM-dd'T'HH:mm:ssZ`.
+-/
+def iso8601 : GenericFormat .any := datespec("uuuu-MM-dd'T'HH:mm.ssZ")
+
+/--
+The americanDate format, which follows the pattern `MM-dd-uuuu`.
+-/
+def americanDate : GenericFormat .any := datespec("MM-dd-uuuu")
+
+/--
+The europeanDate format, which follows the pattern `dd-MM-uuuu`.
+-/
+def europeanDate : GenericFormat .any := datespec("dd-MM-uuuu")
+
+/--
+The time12Hour format, which follows the pattern `hh:mm:ss aa` for representing time
+in a 12-hour clock format with an upper case AM/PM marker.
+-/
+def time12Hour : GenericFormat .any := datespec("hh:mm:ss aa")
+
+/--
+The Time24Hour format, which follows the pattern `HH:mm:ss` for representing time
+in a 24-hour clock format.
+-/
+def time24Hour : GenericFormat .any := datespec("HH:mm:ss")
+
+/--
+The DateTimeZone24Hour format, which follows the pattern `uuuu-MM-dd:HH:mm:ss.SSSSSSSSS` for
+representing date, time, and time zone.
+-/
+def dateTime24Hour : GenericFormat (.only .GMT) := datespec("uuuu-MM-dd:HH:mm:ss.SSSSSSSSS")
+
+/--
+The DateTimeWithZone format, which follows the pattern `uuuu-MM-dd'T'HH:mm:ss.SSSSSSSSSZZZ`
+for representing date, time, and time zone.
+-/
+def dateTimeWithZone : GenericFormat .any := datespec("uuuu-MM-dd'T'HH:mm:ss.SSSSSSSSSZZZ")
+
+/--
+The leanTime24Hour format, which follows the pattern `HH:mm:ss.SSSSSSSSS` for representing time
+in a 24-hour clock format. It uses the default value that can be parsed with the
+notation of dates.
+-/
+def leanTime24Hour : GenericFormat .any := datespec("HH:mm:ss.SSSSSSSSS")
+
+/--
+The leanTime24HourNoNanos format, which follows the pattern `HH:mm:ss` for representing time
+in a 24-hour clock format. It uses the default value that can be parsed with the
+notation of dates.
+-/
+def leanTime24HourNoNanos : GenericFormat .any := datespec("HH:mm:ss")
+
+/--
+The leanDateTime24Hour format, which follows the pattern `uuuu-MM-dd'T'HH:mm:ss.SSSSSSSSS` for
+representing date, time, and time zone. It uses the default value that can be parsed with the
+notation of dates.
+-/
+def leanDateTime24Hour : GenericFormat (.only .GMT) := datespec("uuuu-MM-dd'T'HH:mm:ss.SSSSSSSSS")
+
+/--
+The leanDateTime24HourNoNanos format, which follows the pattern `uuuu-MM-dd'T'HH:mm:ss` for
+representing date, time, and time zone. It uses the default value that can be parsed with the
+notation of dates.
+-/
+def leanDateTime24HourNoNanos : GenericFormat (.only .GMT) := datespec("uuuu-MM-dd'T'HH:mm:ss")
+
+/--
+The leanDateTimeWithZone format, which follows the pattern `uuuu-MM-dd'T'HH:mm:ss.SSSSSSSSSZZZZZ`
+for representing date, time, and time zone. It uses the default value that can be parsed with the
+notation of dates.
+-/
+def leanDateTimeWithZone : GenericFormat .any := datespec("uuuu-MM-dd'T'HH:mm:ss.SSSSSSSSSZZZZZ")
+
+/--
+The leanDateTimeWithZoneNoNanos format, which follows the pattern `uuuu-MM-dd'T'HH:mm:ssZZZZZ`
+for representing date, time, and time zone. It uses the default value that can be parsed with the
+notation of dates.
+-/
+def leanDateTimeWithZoneNoNanos : GenericFormat .any := datespec("uuuu-MM-dd'T'HH:mm:ssZZZZZ")
+
+/--
+The leanDateTimeWithIdentifier format, which follows the pattern `uuuu-MM-dd'T'HH:mm:ss[z]`
+for representing date, time, and time zone. It uses the default value that can be parsed with the
+notation of dates.
+-/
+def leanDateTimeWithIdentifier : GenericFormat .any := datespec("uuuu-MM-dd'T'HH:mm:ss'['zzzz']'")
+
+/--
+The leanDateTimeWithIdentifierAndNanos format, which follows the pattern `uuuu-MM-dd'T'HH:mm:ss.SSSSSSSSS'[z]'`
+for representing date, time, and time zone. It uses the default value that can be parsed with the
+notation of dates.
+-/
+def leanDateTimeWithIdentifierAndNanos : GenericFormat .any := datespec("uuuu-MM-dd'T'HH:mm:ss.SSSSSSSSS'['zzzz']'")
+
+/--
+The Lean Date format, which follows the pattern `uuuu-MM-dd`. It uses the default value that can be parsed with the
+notation of dates.
+-/
+def leanDate : GenericFormat .any := datespec("uuuu-MM-dd")
+
+/--
+The SQLDate format, which follows the pattern `uuuu-MM-dd` and is commonly used
+in SQL databases to represent dates.
+-/
+def sqlDate : GenericFormat .any := datespec("uuuu-MM-dd")
+
+/--
+The LongDateFormat, which follows the pattern `EEEE, MMMM D, uuuu HH:mm:ss` for
+representing a full date and time with the day of the week and month name.
+-/
+def longDateFormat : GenericFormat (.only .GMT) := datespec("EEEE, MMMM D, uuuu HH:mm:ss")
+
+/--
+The AscTime format, which follows the pattern `EEE MMM d HH:mm:ss uuuu`. This format
+is often used in older systems for logging and time-stamping events.
+-/
+def ascTime : GenericFormat (.only .GMT) := datespec("EEE MMM d HH:mm:ss uuuu")
+
+/--
+The RFC822 format, which follows the pattern `eee, dd MMM uuuu HH:mm:ss ZZZ`.
+This format is used in email headers and HTTP headers.
+-/
+def rfc822 : GenericFormat .any := datespec("eee, dd MMM uuuu HH:mm:ss ZZZ")
+
+/--
+The RFC850 format, which follows the pattern `eee, dd-MMM-YY HH:mm:ss ZZZ`.
+This format is an older standard for representing date and time in headers.
+-/
+def rfc850 : GenericFormat .any := datespec("eee, dd-MM-uuuu HH:mm:ss ZZZ")
+
+end Formats
+
+namespace TimeZone
+
+/--
+Parses a string into a `TimeZone` object. The input string must be in the format `"VV ZZZZZ"`.
+-/
+def fromTimeZone (input : String) : Except String TimeZone := do
+  let spec : GenericFormat .any := datespec("VV ZZZZZ")
+  spec.parseBuilder (fun id off => some (TimeZone.mk off id (off.toIsoString true) false)) input
+
+namespace Offset
+
+/--
+Parses a string representing an offset into an `Offset` object. The input string must follow the `"xxx"` format.
+-/
+def fromOffset (input : String) : Except String Offset := do
+  let spec : GenericFormat .any := datespec("xxx")
+  spec.parseBuilder some input
+
+end Offset
+end TimeZone
+
+namespace PlainDate
+
+/--
+Formats a `PlainDate` using a specific format.
+-/
+def format (date : PlainDate) (format : String) : String :=
+  let format : Except String (GenericFormat .any) := GenericFormat.spec format
+  match format with
+  | .error err => s!"error: {err}"
+  | .ok res =>
+    let res := res.formatGeneric fun
+      | .G _ => some date.era
+      | .y _ => some date.year
+      | .u _ => some date.year
+      | .D _ => some (Sigma.mk date.year.isLeap date.dayOfYear)
+      | .Qorq _ => some date.quarter
+      | .w _ => some date.weekOfYear
+      | .W _ => some date.alignedWeekOfMonth
+      | .MorL _ => some date.month
+      | .d _ => some date.day
+      | .E _ => some date.weekday
+      | .eorc _ => some date.weekday
+      | .F _ => some date.weekOfMonth
+      | _ => none
+    match res with
+    | some res => res
+    | none => "invalid time"
+
+/--
+Parses a date string in the American format (`MM-dd-uuuu`) and returns a `PlainDate`.
+-/
+def fromAmericanDateString (input : String) : Except String PlainDate := do
+  Formats.americanDate.parseBuilder (fun m d y => PlainDate.ofYearMonthDay? y m d) input
+
+/--
+Converts a date in the American format (`MM-dd-uuuu`) into a `String`.
+-/
+def toAmericanDateString (input : PlainDate) : String :=
+  Formats.americanDate.formatBuilder input.month input.day input.year
+
+/--
+Parses a date string in the SQL format (`uuuu-MM-dd`) and returns a `PlainDate`.
+-/
+def fromSQLDateString (input : String) : Except String PlainDate := do
+  Formats.sqlDate.parseBuilder PlainDate.ofYearMonthDay? input
+
+/--
+Converts a date in the SQL format (`uuuu-MM-dd`) into a `String`.
+-/
+def toSQLDateString (input : PlainDate) : String :=
+  Formats.sqlDate.formatBuilder input.year input.month input.day
+
+/--
+Parses a date string in the Lean format (`uuuu-MM-dd`) and returns a `PlainDate`.
+-/
+def fromLeanDateString (input : String) : Except String PlainDate := do
+  Formats.leanDate.parseBuilder PlainDate.ofYearMonthDay? input
+
+/--
+Converts a date in the Lean format (`uuuu-MM-dd`) into a `String`.
+-/
+def toLeanDateString (input : PlainDate) : String :=
+  Formats.leanDate.formatBuilder input.year input.month input.day
+
+/--
+Parses a `String` in the `AmericanDate` or `SQLDate` format and returns a `PlainDate`.
+-/
+def parse (input : String) : Except String PlainDate :=
+  fromAmericanDateString input
+  <|> fromSQLDateString input
+
+instance : ToString PlainDate where
+  toString := toLeanDateString
+
+instance : Repr PlainDate where
+  reprPrec data := Repr.addAppParen ("date(\"" ++ toLeanDateString data ++ "\")")
+
+end PlainDate
+
+namespace PlainTime
+
+/--
+Formats a `PlainTime` using a specific format.
+-/
+def format (time : PlainTime) (format : String) : String :=
+  let format : Except String (GenericFormat .any) := GenericFormat.spec format
+  match format with
+  | .error err => s!"error: {err}"
+  | .ok res =>
+    let res := res.formatGeneric fun
+      | .H _ => some time.hour
+      | .k _ => some (time.hour.shiftTo1BasedHour)
+      | .m _ => some time.minute
+      | .n _ => some time.nanosecond
+      | .s _ => some time.second
+      | .a _ => some (HourMarker.ofOrdinal time.hour)
+      | .h _ => some time.hour.toRelative
+      | .K _ => some (time.hour.emod 12 (by decide))
+      | .S _ => some time.nanosecond
+      | .A _ => some time.toMilliseconds
+      | .N _ => some time.toNanoseconds
+      | _ => none
+    match res with
+    | some res => res
+    | none => "invalid time"
+
+/--
+Parses a time string in the 24-hour format (`HH:mm:ss`) and returns a `PlainTime`.
+-/
+def fromTime24Hour (input : String) : Except String PlainTime :=
+  Formats.time24Hour.parseBuilder (fun h m s => some (PlainTime.ofHourMinuteSeconds h m s.snd)) input
+
+/--
+Formats a `PlainTime` value into a 24-hour format string (`HH:mm:ss`).
+-/
+def toTime24Hour (input : PlainTime) : String :=
+  Formats.time24Hour.formatBuilder input.hour input.minute input.second
+
+/--
+Parses a time string in the lean 24-hour format (`HH:mm:ss.SSSSSSSSS` or `HH:mm:ss`) and returns a `PlainTime`.
+-/
+def fromLeanTime24Hour (input : String) : Except String PlainTime :=
+  Formats.leanTime24Hour.parseBuilder (fun h m s n => some (PlainTime.ofHourMinuteSecondsNano h m s.snd n)) input
+  <|> Formats.leanTime24HourNoNanos.parseBuilder (fun h m s => some (PlainTime.ofHourMinuteSecondsNano h m s.snd 0)) input
+
+/--
+Formats a `PlainTime` value into a 24-hour format string (`HH:mm:ss.SSSSSSSSS`).
+-/
+def toLeanTime24Hour (input : PlainTime) : String :=
+  Formats.leanTime24Hour.formatBuilder input.hour input.minute input.second input.nanosecond
+
+/--
+Parses a time string in the 12-hour format (`hh:mm:ss aa`) and returns a `PlainTime`.
+-/
+def fromTime12Hour (input : String) : Except String PlainTime := do
+  let builder h m s a : Option PlainTime := do
+    let value ← Internal.Bounded.ofInt? h.val
+    some <| PlainTime.ofHourMinuteSeconds (HourMarker.toAbsolute a value) m s.snd
+
+  Formats.time12Hour.parseBuilder builder input
+
+/--
+Formats a `PlainTime` value into a 12-hour format string (`hh:mm:ss aa`).
+-/
+def toTime12Hour (input : PlainTime) : String :=
+  Formats.time12Hour.formatBuilder (input.hour.emod 12 (by decide) |>.add 1) input.minute input.second (if input.hour.val ≥ 12 then HourMarker.pm else HourMarker.am)
+
+/--
+Parses a `String` in the `Time12Hour` or `Time24Hour` format and returns a `PlainTime`.
+-/
+def parse (input : String) : Except String PlainTime :=
+  fromTime12Hour input
+  <|> fromTime24Hour input
+
+instance : ToString PlainTime where
+  toString := toLeanTime24Hour
+
+instance : Repr PlainTime where
+  reprPrec data := Repr.addAppParen ("time(\"" ++ toLeanTime24Hour data ++ "\")")
+
+end PlainTime
+
+namespace ZonedDateTime
+
+/--
+Formats a `ZonedDateTime` using a specific format.
+-/
+def format (data: ZonedDateTime) (format : String) : String :=
+  let format : Except String (GenericFormat .any) := GenericFormat.spec format
+  match format with
+  | .error err => s!"error: {err}"
+  | .ok res => res.format data.toDateTime
+
+/--
+Parses a `String` in the `ISO8601` format and returns a `ZonedDateTime`.
+-/
+def fromISO8601String (input : String) : Except String ZonedDateTime :=
+  Formats.iso8601.parse input
+
+/--
+Formats a `ZonedDateTime` value into an ISO8601 string.
+-/
+def toISO8601String (date : ZonedDateTime) : String :=
+  Formats.iso8601.format date.toDateTime
+
+/--
+Parses a `String` in the rfc822 format and returns a `ZonedDateTime`.
+-/
+def fromRFC822String (input : String) : Except String ZonedDateTime :=
+  Formats.rfc822.parse input
+
+/--
+Formats a `ZonedDateTime` value into an RFC822 format string.
+-/
+def toRFC822String (date : ZonedDateTime) : String :=
+  Formats.rfc822.format date.toDateTime
+
+/--
+Parses a `String` in the rfc850 format and returns a `ZonedDateTime`.
+-/
+def fromRFC850String (input : String) : Except String ZonedDateTime :=
+  Formats.rfc850.parse input
+
+/--
+Formats a `ZonedDateTime` value into an RFC850 format string.
+-/
+def toRFC850String (date : ZonedDateTime) : String :=
+  Formats.rfc850.format date.toDateTime
+
+/--
+Parses a `String` in the dateTimeWithZone format and returns a `ZonedDateTime` object in the GMT time zone.
+-/
+def fromDateTimeWithZoneString (input : String) : Except String ZonedDateTime :=
+  Formats.dateTimeWithZone.parse input
+
+/--
+Formats a `ZonedDateTime` value into a simple date time with timezone string.
+-/
+def toDateTimeWithZoneString (pdt : ZonedDateTime) : String :=
+  Formats.dateTimeWithZone.format pdt.toDateTime
+
+/--
+Parses a `String` in the lean date time format with timezone format and returns a `ZonedDateTime` object.
+-/
+def fromLeanDateTimeWithZoneString (input : String) : Except String ZonedDateTime :=
+  Formats.leanDateTimeWithZone.parse input
+  <|> Formats.leanDateTimeWithZoneNoNanos.parse input
+
+/--
+Parses a `String` in the lean date time format with identifier and returns a `ZonedDateTime` object.
+-/
+def fromLeanDateTimeWithIdentifierString (input : String) : Except String ZonedDateTime :=
+  Formats.leanDateTimeWithIdentifier.parse input
+  <|> Formats.leanDateTimeWithIdentifierAndNanos.parse input
+
+/--
+Formats a `DateTime` value into a simple date time with timezone string that can be parsed by the date% notation.
+-/
+def toLeanDateTimeWithZoneString (zdt : ZonedDateTime) : String :=
+  Formats.leanDateTimeWithZone.formatBuilder zdt.year zdt.month zdt.day zdt.hour zdt.minute zdt.date.get.time.second zdt.nanosecond zdt.offset
+/--
+Formats a `DateTime` value into a simple date time with timezone string that can be parsed by the date% notation with the timezone identifier.
+-/
+def toLeanDateTimeWithIdentifierString (zdt : ZonedDateTime) : String :=
+  Formats.leanDateTimeWithIdentifierAndNanos.formatBuilder zdt.year zdt.month zdt.day zdt.hour zdt.minute zdt.date.get.time.second zdt.nanosecond zdt.timezone.name
+
+/--
+Parses a `String` in the `ISO8601`, `RFC822` or `RFC850` format and returns a `ZonedDateTime`.
+-/
+def parse (input : String) : Except String ZonedDateTime :=
+  fromISO8601String input
+  <|> fromRFC822String input
+  <|> fromRFC850String input
+  <|> fromDateTimeWithZoneString input
+  <|> fromLeanDateTimeWithIdentifierString input
+
+instance : ToString ZonedDateTime where
+  toString := toLeanDateTimeWithIdentifierString
+
+instance : Repr ZonedDateTime where
+  reprPrec data := Repr.addAppParen ("zoned(\"" ++ toLeanDateTimeWithZoneString data ++ "\")")
+
+end ZonedDateTime
+
+namespace PlainDateTime
+
+/--
+Formats a `PlainDateTime` using a specific format.
+-/
+def format (date : PlainDateTime) (format : String) : String :=
+  let format : Except String (GenericFormat .any) := GenericFormat.spec format
+  match format with
+  | .error err => s!"error: {err}"
+  | .ok res =>
+    let res := res.formatGeneric fun
+      | .G _ => some date.era
+      | .y _ => some date.year
+      | .u _ => some date.year
+      | .D _ => some (Sigma.mk date.year.isLeap date.dayOfYear)
+      | .Qorq _ => some date.quarter
+      | .w _ => some date.weekOfYear
+      | .W _ => some date.alignedWeekOfMonth
+      | .MorL _ => some date.month
+      | .d _ => some date.day
+      | .E _ => some date.weekday
+      | .eorc _ => some date.weekday
+      | .F _ => some date.weekOfMonth
+      | .H _ => some date.hour
+      | .k _ => some date.hour.shiftTo1BasedHour
+      | .m _ => some date.minute
+      | .n _ => some date.nanosecond
+      | .s _ => some date.time.second
+      | .a _ => some (HourMarker.ofOrdinal date.hour)
+      | .h _ => some date.hour.toRelative
+      | .K _ => some (date.hour.emod 12 (by decide))
+      | .S _ => some date.nanosecond
+      | .A _ => some date.time.toMilliseconds
+      | .N _ => some date.time.toNanoseconds
+      | _ => none
+    match res with
+    | some res => res
+    | none => "invalid time"
+
+/--
+Parses a `String` in the `AscTime` format and returns a `PlainDateTime` object in the GMT time zone.
+-/
+def fromAscTimeString (input : String) : Except String PlainDateTime :=
+  Formats.ascTime.parse input
+  |>.map DateTime.toPlainDateTime
+
+/--
+Formats a `PlainDateTime` value into an AscTime format string.
+-/
+def toAscTimeString (pdt : PlainDateTime) : String :=
+  Formats.ascTime.format (DateTime.ofPlainDateTimeAssumingUTC pdt .UTC)
+
+/--
+Parses a `String` in the `LongDateFormat` and returns a `PlainDateTime` object in the GMT time zone.
+-/
+def fromLongDateFormatString (input : String) : Except String PlainDateTime :=
+  Formats.longDateFormat.parse input
+  |>.map DateTime.toPlainDateTime
+
+/--
+Formats a `PlainDateTime` value into a LongDateFormat string.
+-/
+def toLongDateFormatString (pdt : PlainDateTime) : String :=
+  Formats.longDateFormat.format (DateTime.ofPlainDateTimeAssumingUTC pdt .UTC)
+
+/--
+Parses a `String` in the `DateTime` format and returns a `PlainDateTime`.
+-/
+def fromDateTimeString (input : String) : Except String PlainDateTime :=
+  Formats.dateTime24Hour.parse input
+  |>.map DateTime.toPlainDateTime
+
+/--
+Formats a `PlainDateTime` value into a `DateTime` format string.
+-/
+def toDateTimeString (pdt : PlainDateTime) : String :=
+  Formats.dateTime24Hour.formatBuilder pdt.year pdt.month pdt.day pdt.hour pdt.minute pdt.time.second pdt.nanosecond
+
+/--
+Parses a `String` in the `DateTime` format and returns a `PlainDateTime`.
+-/
+def fromLeanDateTimeString (input : String) : Except String PlainDateTime :=
+  (Formats.leanDateTime24Hour.parse input <|> Formats.leanDateTime24HourNoNanos.parse input)
+  |>.map DateTime.toPlainDateTime
+
+/--
+Formats a `PlainDateTime` value into a `DateTime` format string.
+-/
+def toLeanDateTimeString (pdt : PlainDateTime) : String :=
+  Formats.leanDateTime24Hour.formatBuilder pdt.year pdt.month pdt.day pdt.hour pdt.minute pdt.time.second pdt.nanosecond
+
+/--
+Parses a `String` in the `AscTime` or `LongDate` format and returns a `PlainDateTime`.
+-/
+def parse (date : String) : Except String PlainDateTime :=
+  fromAscTimeString date
+  <|> fromLongDateFormatString date
+  <|> fromDateTimeString date
+  <|> fromLeanDateTimeString date
+
+instance : ToString PlainDateTime where
+  toString := toLeanDateTimeString
+
+instance : Repr PlainDateTime where
+  reprPrec data := Repr.addAppParen ("datetime(\"" ++ toLeanDateTimeString data ++ "\")")
+
+end PlainDateTime
+
+namespace DateTime
+
+/--
+Formats a `DateTime` using a specific format.
+-/
+def format (data: DateTime tz) (format : String) : String :=
+  let format : Except String (GenericFormat .any) := GenericFormat.spec format
+  match format with
+  | .error err => s!"error: {err}"
+  | .ok res => res.format data
+
+/--
+Parses a `String` in the `AscTime` format and returns a `DateTime` object in the GMT time zone.
+-/
+def fromAscTimeString (input : String) : Except String (DateTime .GMT) :=
+  Formats.ascTime.parse input
+
+/--
+Formats a `DateTime` value into an AscTime format string.
+-/
+def toAscTimeString (datetime : DateTime .GMT) : String :=
+  Formats.ascTime.format datetime
+
+/--
+Parses a `String` in the `LongDateFormat` and returns a `DateTime` object in the GMT time zone.
+-/
+def fromLongDateFormatString (input : String) : Except String (DateTime .GMT) :=
+  Formats.longDateFormat.parse input
+
+/--
+Formats a `DateTime` value into a LongDateFormat string.
+-/
+def toLongDateFormatString (datetime : DateTime .GMT) : String :=
+  Formats.longDateFormat.format datetime
+
+/--
+Formats a `DateTime` value into an ISO8601 string.
+-/
+def toISO8601String (date : DateTime tz) : String :=
+  Formats.iso8601.format date
+
+/--
+Formats a `DateTime` value into an RFC822 format string.
+-/
+def toRFC822String (date : DateTime tz) : String :=
+  Formats.rfc822.format date
+
+/--
+Formats a `DateTime` value into an RFC850 format string.
+-/
+def toRFC850String (date : DateTime tz) : String :=
+  Formats.rfc850.format date
+
+/--
+Formats a `DateTime` value into a `DateTimeWithZone` format string.
+-/
+def toDateTimeWithZoneString (pdt : DateTime tz) : String :=
+  Formats.dateTimeWithZone.format pdt
+
+/--
+Formats a `DateTime` value into a `DateTimeWithZone` format string that can be parsed by `date%`.
+-/
+def toLeanDateTimeWithZoneString (pdt : DateTime tz) : String :=
+  Formats.leanDateTimeWithZone.format pdt
+
+/--
+Parses a `String` in the `AscTime` or `LongDate` format and returns a `DateTime`.
+-/
+def parse (date : String) : Except String (DateTime .GMT) :=
+  fromAscTimeString date
+  <|> fromLongDateFormatString date
+
+instance : Repr (DateTime tz) where
+  reprPrec data := Repr.addAppParen (toLeanDateTimeWithZoneString data)
+
+instance : ToString (DateTime tz) where
+  toString := toLeanDateTimeWithZoneString
+
+end DateTime

src/Std/Time/Internal.lean

@@ -0,0 +1,8 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Internal.Bounded
+import Std.Time.Internal.UnitVal

src/Std/Time/Internal/Bounded.lean

@@ -0,0 +1,474 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Init.Data.Int
+
+namespace Std
+namespace Time
+namespace Internal
+
+set_option linter.all true in
+
+/--
+A `Bounded` is represented by an `Int` that is constrained by a lower and higher bounded using some
+relation `rel`. It includes all the integers that `rel lo val ∧ rel val hi`.
+-/
+def Bounded (rel : Int → Int → Prop) (lo : Int) (hi : Int) := { val : Int // rel lo val ∧ rel val hi }
+
+namespace Bounded
+
+@[always_inline]
+instance : LE (Bounded rel n m) where
+  le l r := l.val ≤ r.val
+
+@[always_inline]
+instance : LT (Bounded rel n m) where
+  lt l r := l.val < r.val
+
+@[always_inline]
+instance : Repr (Bounded rel m n) where
+  reprPrec n := reprPrec n.val
+
+@[always_inline]
+instance : BEq (Bounded rel n m) where
+  beq x y := (x.val = y.val)
+
+@[always_inline]
+instance {x y : Bounded rel a b} : Decidable (x ≤ y) :=
+  inferInstanceAs (Decidable (x.val ≤ y.val))
+
+/--
+A `Bounded` integer that the relation used is the the less-equal relation so, it includes all
+integers that `lo ≤ val ≤ hi`.
+-/
+abbrev LE := @Bounded LE.le
+
+/--
+Casts the boundaries of the `Bounded` using equivalences.
+-/
+@[inline]
+def cast {rel : Int → Int → Prop} {lo₁ lo₂ hi₁ hi₂ : Int} (h₁ : lo₁ = lo₂) (h₂ : hi₁ = hi₂) (b : Bounded rel lo₁ hi₁) : Bounded rel lo₂ hi₂ :=
+  .mk b.val ⟨h₁ ▸ b.property.1, h₂ ▸ b.property.2⟩
+
+/--
+A `Bounded` integer that the relation used is the the less-than relation so, it includes all
+integers that `lo < val < hi`.
+-/
+abbrev LT := @Bounded LT.lt
+
+/--
+Creates a new `Bounded` Integer.
+-/
+@[inline]
+def mk {rel : Int → Int → Prop} (val : Int) (proof : rel lo val ∧ rel val hi) : @Bounded rel lo hi :=
+  ⟨val, proof⟩
+
+/--
+Convert a `Int` to a `Bounded` if it checks.
+-/
+@[inline]
+def ofInt? [DecidableRel rel] (val : Int) : Option (Bounded rel lo hi) :=
+  if h : rel lo ↑val ∧ rel ↑val hi then
+    some ⟨val, h⟩
+  else
+    none
+
+namespace LE
+
+/--
+Convert a `Nat` to a `Bounded.LE` by wrapping it.
+-/
+@[inline]
+def ofNatWrapping { lo hi : Int } (val : Int) (h : lo ≤ hi) : Bounded.LE lo hi := by
+  let range := hi - lo + 1
+  have range_pos := Int.add_pos_of_nonneg_of_pos (b := 1) (Int.sub_nonneg_of_le h) (by decide)
+  have not_zero := Int.ne_iff_lt_or_gt.mpr (Or.inl range_pos)
+  have mod_nonneg : 0 ≤ (val - lo) % range := Int.emod_nonneg (val - lo) not_zero.symm
+  have add_nonneg : lo ≤ lo + (val - lo) % range := Int.le_add_of_nonneg_right mod_nonneg
+  have mod_range : (val - lo) % (hi - lo + 1) < range := Int.emod_lt_of_pos (a := val - lo) range_pos
+  refine ⟨((val - lo) % range + range) % range + lo, And.intro ?_ ?_⟩
+  · simp_all [range]
+    rw [Int.add_comm] at add_nonneg
+    exact add_nonneg
+  · apply Int.add_le_of_le_sub_right
+    simp_all [range]
+    exact Int.le_of_lt_add_one mod_range
+
+instance {k : Nat} : OfNat (Bounded.LE lo (lo + k)) n where
+  ofNat :=
+    let h : lo ≤ lo + k := Int.le_add_of_nonneg_right (Int.ofNat_zero_le k)
+    ofNatWrapping n h
+
+instance {k : Nat} : Inhabited (Bounded.LE lo (lo + k)) where
+  default :=
+    let h : lo ≤ lo + k := Int.le_add_of_nonneg_right (Int.ofNat_zero_le k)
+    ofNatWrapping lo h
+
+/--
+Creates a new `Bounded` integer that the relation is less-equal.
+-/
+@[inline]
+def mk (val : Int) (proof : lo ≤ val ∧ val ≤ hi) : Bounded.LE lo hi :=
+  ⟨val, proof⟩
+
+/--
+Creates a new `Bounded` integer that the relation is less-equal.
+-/
+@[inline]
+def exact (val : Nat) : Bounded.LE val val :=
+  ⟨val, by simp⟩
+
+/--
+Creates a new `Bounded` integer.
+-/
+@[inline]
+def ofInt { lo hi : Int } (val : Int) : Option (Bounded.LE lo hi) :=
+  if h : lo ≤ val ∧ val ≤ hi
+    then some ⟨val, h⟩
+    else none
+
+/--
+Convert a `Nat` to a `Bounded.LE`.
+-/
+@[inline]
+def ofNat (val : Nat) (h : val ≤ hi) : Bounded.LE 0 hi :=
+  Bounded.mk val (And.intro (Int.ofNat_zero_le val) (Int.ofNat_le.mpr h))
+
+/--
+Convert a `Nat` to a `Bounded.LE` if it checks.
+-/
+@[inline]
+def ofNat? { hi : Nat } (val : Nat) : Option (Bounded.LE 0 hi) :=
+  if h : val ≤ hi then
+    ofNat val h
+  else
+    none
+
+/--
+Convert a `Nat` to a `Bounded.LE` using the lower boundary too.
+-/
+@[inline]
+def ofNat' (val : Nat) (h : lo ≤ val ∧ val ≤ hi) : Bounded.LE lo hi :=
+  Bounded.mk val (And.intro (Int.ofNat_le.mpr h.left) (Int.ofNat_le.mpr h.right))
+
+/--
+Convert a `Nat` to a `Bounded.LE` using the lower boundary too.
+-/
+@[inline]
+def clip (val : Int) (h : lo ≤ hi) : Bounded.LE lo hi :=
+  if h₀ : lo ≤ val then
+    if h₁ : val ≤ hi
+      then ⟨val, And.intro h₀ h₁⟩
+      else ⟨hi, And.intro h (Int.le_refl hi)⟩
+  else ⟨lo, And.intro (Int.le_refl lo) h⟩
+
+/--
+Convert a `Bounded.LE` to a Nat.
+-/
+@[inline]
+def toNat (n : Bounded.LE lo hi) : Nat :=
+  n.val.toNat
+
+/--
+Convert a `Bounded.LE` to a Nat.
+-/
+@[inline]
+def toNat' (n : Bounded.LE lo hi) (h : lo ≥ 0) : Nat :=
+  let h₁ := (Int.le_trans h n.property.left)
+  match n.val, h₁ with
+  | .ofNat n, _ => n
+  | .negSucc _, h => by contradiction
+
+/--
+Convert a `Bounded.LE` to an Int.
+-/
+@[inline]
+def toInt (n : Bounded.LE lo hi) : Int :=
+  n.val
+
+/--
+Convert a `Bounded.LE` to a `Fin`.
+-/
+@[inline, simp]
+def toFin (n : Bounded.LE lo hi) (h₀ : 0 ≤ lo) : Fin (hi + 1).toNat := by
+  let h := n.property.right
+  let h₁ := Int.le_trans h₀ n.property.left
+  refine ⟨n.val.toNat, (Int.toNat_lt h₁).mpr ?_⟩
+  rw [Int.toNat_of_nonneg (by omega)]
+  exact Int.lt_add_one_of_le h
+
+/--
+Convert a `Fin` to a `Bounded.LE`.
+-/
+@[inline]
+def ofFin (fin : Fin (Nat.succ hi)) : Bounded.LE 0 hi :=
+  ofNat fin.val (Nat.le_of_lt_succ fin.isLt)
+
+/--
+Convert a `Fin` to a `Bounded.LE`.
+-/
+@[inline]
+def ofFin' {lo : Nat} (fin : Fin (Nat.succ hi)) (h : lo ≤ hi) : Bounded.LE lo hi :=
+  if h₁ : fin.val ≥ lo
+    then ofNat' fin.val (And.intro h₁ ((Nat.le_of_lt_succ fin.isLt)))
+    else ofNat' lo (And.intro (Nat.le_refl lo) h)
+
+/--
+Creates a new `Bounded.LE` using a the modulus of a number.
+-/
+@[inline]
+def byEmod (b : Int) (i : Int) (hi : i > 0) : Bounded.LE 0 (i - 1) := by
+  refine ⟨b % i, And.intro ?_ ?_⟩
+  · apply Int.emod_nonneg b
+    intro a
+    simp_all [Int.lt_irrefl]
+  · apply Int.le_of_lt_add_one
+    simp [Int.add_sub_assoc]
+    exact Int.emod_lt_of_pos b hi
+
+/--
+Creates a new `Bounded.LE` using a the Truncating modulus of a number.
+-/
+@[inline]
+def byMod (b : Int) (i : Int) (hi : 0 < i) : Bounded.LE (- (i - 1)) (i - 1) := by
+  refine ⟨b.tmod i, And.intro ?_ ?_⟩
+  · simp [Int.tmod]
+    split <;> try contradiction
+    next m n =>
+      let h := Int.emod_nonneg (a := m) (b := n) (Int.ne_of_gt hi)
+      apply (Int.le_trans · h)
+      apply Int.le_of_neg_le_neg
+      simp_all
+      exact (Int.le_sub_one_of_lt hi)
+    next m n =>
+      apply Int.neg_le_neg
+      have h := Int.tmod_lt_of_pos (m + 1) hi
+      exact Int.le_sub_one_of_lt h
+  · exact Int.le_sub_one_of_lt (Int.tmod_lt_of_pos b hi)
+
+/--
+Adjust the bounds of a `Bounded` by setting the lower bound to zero and the maximum value to (m - n).
+-/
+@[inline]
+def truncate (bounded : Bounded.LE n m) : Bounded.LE 0 (m - n) := by
+  let ⟨left, right⟩ := bounded.property
+  refine ⟨bounded.val - n, And.intro ?_ ?_⟩
+  all_goals omega
+
+/--
+Adjust the bounds of a `Bounded` by changing the higher bound if another value `j` satisfies the same
+constraint.
+-/
+@[inline, simp]
+def truncateTop (bounded : Bounded.LE n m) (h : bounded.val ≤ j) : Bounded.LE n j := by
+  refine ⟨bounded.val, And.intro ?_ ?_⟩
+  · exact bounded.property.left
+  · exact h
+
+/--
+Adjust the bounds of a `Bounded` by changing the lower bound if another value `j` satisfies the same
+constraint.
+-/
+@[inline]
+def truncateBottom (bounded : Bounded.LE n m) (h : bounded.val ≥ j) : Bounded.LE j m := by
+  refine ⟨bounded.val, And.intro ?_ ?_⟩
+  · exact h
+  · exact bounded.property.right
+
+/--
+Adjust the bounds of a `Bounded` by adding a constant value to both the lower and upper bounds.
+-/
+@[inline]
+def neg (bounded : Bounded.LE n m) : Bounded.LE (-m) (-n) := by
+  refine ⟨-bounded.val, And.intro ?_ ?_⟩
+  · exact Int.neg_le_neg bounded.property.right
+  · exact Int.neg_le_neg bounded.property.left
+
+/--
+Adjust the bounds of a `Bounded` by adding a constant value to both the lower and upper bounds.
+-/
+@[inline, simp]
+def add (bounded : Bounded.LE n m) (num : Int) : Bounded.LE (n + num) (m + num) := by
+  refine ⟨bounded.val + num, And.intro ?_ ?_⟩
+  all_goals apply (Int.add_le_add · (Int.le_refl num))
+  · exact bounded.property.left
+  · exact bounded.property.right
+
+/--
+Adjust the bounds of a `Bounded` by adding a constant value to both the lower and upper bounds.
+-/
+@[inline]
+def addProven (bounded : Bounded.LE n m) (h₀ : bounded.val + num ≤ m) (h₁ : num ≥ 0) : Bounded.LE n m := by
+  refine ⟨bounded.val + num, And.intro ?_ ?_⟩
+  · exact Int.le_trans bounded.property.left (Int.le_add_of_nonneg_right h₁)
+  · exact h₀
+
+/--
+Adjust the bounds of a `Bounded` by adding a constant value to the upper bounds.
+-/
+@[inline]
+def addTop (bounded : Bounded.LE n m) (num : Int) (h : num ≥ 0) : Bounded.LE n (m + num) := by
+  refine ⟨bounded.val + num, And.intro ?_ ?_⟩
+  · let h := Int.add_le_add bounded.property.left h
+    simp at h
+    exact h
+  · exact Int.add_le_add bounded.property.right (Int.le_refl num)
+
+/--
+Adjust the bounds of a `Bounded` by adding a constant value to the lower bounds.
+-/
+@[inline]
+def subBottom (bounded : Bounded.LE n m) (num : Int) (h : num ≥ 0) : Bounded.LE (n - num) m := by
+  refine ⟨bounded.val - num, And.intro ?_ ?_⟩
+  · exact Int.add_le_add bounded.property.left (Int.le_refl (-num))
+  · let h := Int.sub_le_sub bounded.property.right h
+    simp at h
+    exact h
+
+/--
+Adds two `Bounded` and adjust the boundaries.
+-/
+@[inline]
+def addBounds (bounded : Bounded.LE n m) (bounded₂ : Bounded.LE i j) : Bounded.LE (n + i) (m + j) := by
+  refine ⟨bounded.val + bounded₂.val, And.intro ?_ ?_⟩
+  · exact Int.add_le_add bounded.property.left bounded₂.property.left
+  · exact Int.add_le_add bounded.property.right bounded₂.property.right
+
+/--
+Adjust the bounds of a `Bounded` by subtracting a constant value to both the lower and upper bounds.
+-/
+@[inline, simp]
+def sub (bounded : Bounded.LE n m) (num : Int) : Bounded.LE (n - num) (m - num) :=
+  add bounded (-num)
+
+/--
+Adds two `Bounded` and adjust the boundaries.
+-/
+@[inline]
+def subBounds (bounded : Bounded.LE n m) (bounded₂ : Bounded.LE i j) : Bounded.LE (n - j) (m - i) :=
+  addBounds bounded bounded₂.neg
+
+/--
+Adjust the bounds of a `Bounded` by applying the emod operation constraining the lower bound to 0 and
+the upper bound to the value.
+-/
+@[inline]
+def emod (bounded : Bounded.LE n num) (num : Int) (hi : 0 < num) : Bounded.LE 0 (num - 1) :=
+  byEmod bounded.val num hi
+
+/--
+Adjust the bounds of a `Bounded` by applying the mod operation.
+-/
+@[inline]
+def mod (bounded : Bounded.LE n num) (num : Int) (hi : 0 < num) : Bounded.LE (- (num - 1)) (num - 1) :=
+  byMod bounded.val num hi
+
+/--
+Adjust the bounds of a `Bounded` by applying the multiplication operation with a positive number.
+-/
+@[inline]
+def mul_pos (bounded : Bounded.LE n m) (num : Int) (h : num ≥ 0) : Bounded.LE (n * num) (m * num) := by
+  refine ⟨bounded.val * num, And.intro ?_ ?_⟩
+  · exact Int.mul_le_mul_of_nonneg_right bounded.property.left h
+  · exact Int.mul_le_mul_of_nonneg_right bounded.property.right h
+
+/--
+Adjust the bounds of a `Bounded` by applying the multiplication operation with a positive number.
+-/
+@[inline]
+def mul_neg (bounded : Bounded.LE n m) (num : Int) (h : num ≤ 0) : Bounded.LE (m * num) (n * num) := by
+  refine ⟨bounded.val * num, And.intro ?_ ?_⟩
+  · exact Int.mul_le_mul_of_nonpos_right bounded.property.right h
+  · exact Int.mul_le_mul_of_nonpos_right bounded.property.left h
+
+/--
+Adjust the bounds of a `Bounded` by applying the div operation.
+-/
+@[inline]
+def ediv (bounded : Bounded.LE n m) (num : Int) (h : num > 0) : Bounded.LE (n / num) (m / num) := by
+  let ⟨left, right⟩ := bounded.property
+  refine ⟨bounded.val.ediv num, And.intro ?_ ?_⟩
+  apply Int.ediv_le_ediv
+  · exact h
+  · exact left
+  · apply Int.ediv_le_ediv
+    · exact h
+    · exact right
+
+@[inline]
+def eq {n : Int} : Bounded.LE n n :=
+  ⟨n, And.intro (Int.le_refl n) (Int.le_refl n)⟩
+
+/--
+Expand the range of a bounded value.
+-/
+@[inline]
+def expand (bounded : Bounded.LE lo hi) (h : hi ≤ nhi) (h₁ : nlo ≤ lo) : Bounded.LE nlo nhi :=
+  ⟨bounded.val, And.intro (Int.le_trans h₁ bounded.property.left) (Int.le_trans bounded.property.right h)⟩
+
+/--
+Expand the bottom of the bounded to a number `nhi` is `hi` is less or equal to the previous higher bound.
+-/
+@[inline]
+def expandTop (bounded : Bounded.LE lo hi) (h : hi ≤ nhi) : Bounded.LE lo nhi :=
+  expand bounded h (Int.le_refl lo)
+
+/--
+Expand the bottom of the bounded to a number `nlo` if `lo` is greater or equal to the previous lower bound.
+-/
+@[inline]
+def expandBottom (bounded : Bounded.LE lo hi) (h : nlo ≤ lo) : Bounded.LE nlo hi :=
+  expand bounded (Int.le_refl hi) h
+
+/--
+Adds one to the value of the bounded if the value is less than the higher bound of the bounded number.
+-/
+@[inline]
+def succ (bounded : Bounded.LE lo hi) (h : bounded.val < hi) : Bounded.LE lo hi :=
+  let left := bounded.property.left
+  ⟨bounded.val + 1, And.intro (by omega) (by omega)⟩
+
+/--
+Returns the absolute value of the bounded number `bo` with bounds `-(i - 1)` to `i - 1`. The result
+will be a new bounded number with bounds `0` to `i - 1`.
+-/
+@[inline]
+def abs (bo :  Bounded.LE (-i) i) : Bounded.LE 0 i :=
+  if h : bo.val ≥ 0 then
+    bo.truncateBottom h
+  else by
+    let r := bo.truncateTop (Int.le_of_lt (Int.not_le.mp h)) |>.neg
+    rw [Int.neg_neg] at r
+    exact r
+
+/--
+Returns the maximum between a number and the bounded.
+-/
+def max (bounded : Bounded.LE n m) (val : Int) : Bounded.LE (Max.max n val) (Max.max m val) := by
+  let ⟨left, right⟩ := bounded.property
+  refine ⟨Max.max bounded.val val, And.intro ?_ ?_⟩
+
+  all_goals
+    simp [Int.max_def]
+    split <;> split
+
+  next h => simp [h, Int.le_trans left h]
+  next h h₁ => exact Int.le_of_lt <| Int.not_le.mp h₁
+  next h => simp [h, Int.le_trans left h]
+  next h h₁ => exact left
+  next h h₁ => simp [h, Int.le_trans left h]
+  next h h₁ => exact Int.le_of_lt <| Int.not_le.mp h₁
+  next h h₁ =>
+    let h₃ := Int.lt_of_lt_of_le (Int.not_le.mp h) right
+    let h₄ := Int.not_le.mpr h₃ h₁
+    contradiction
+  next h h₁ => exact right
+
+end LE
+end Bounded
+end Internal
+end Time
+end Std

src/Std/Time/Internal/UnitVal.lean

@@ -0,0 +1,125 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Init.Data
+import Std.Internal.Rat
+
+namespace Std
+namespace Time
+namespace Internal
+open Std.Internal
+open Lean
+
+set_option linter.all true
+
+/--
+A structure representing a unit of a given ratio type `α`.
+-/
+structure UnitVal (α : Rat) where
+  /--
+  Creates a `UnitVal` from an `Int`.
+  -/
+  ofInt ::
+
+  /--
+  Value inside the UnitVal Value.
+  -/
+  val : Int
+  deriving Inhabited, BEq
+
+instance : LE (UnitVal x) where
+  le x y := x.val ≤ y.val
+
+instance { x y : UnitVal z }: Decidable (x ≤ y) :=
+  inferInstanceAs (Decidable (x.val ≤ y.val))
+
+namespace UnitVal
+
+/--
+Creates a `UnitVal` from a `Nat`.
+-/
+@[inline]
+def ofNat (value : Nat) : UnitVal α :=
+  ⟨value⟩
+
+/--
+Converts a `UnitVal` to an `Int`.
+-/
+@[inline]
+def toInt (unit : UnitVal α) : Int :=
+  unit.val
+
+/--
+Multiplies the `UnitVal` by an `Int`, resulting in a new `UnitVal` with an adjusted ratio.
+-/
+@[inline]
+def mul (unit : UnitVal a) (factor : Int) : UnitVal (a / factor) :=
+  ⟨unit.val * factor⟩
+
+/--
+Divides the `UnitVal` by an `Int`, resulting in a new `UnitVal` with an adjusted ratio.
+-/
+@[inline]
+def ediv (unit : UnitVal a) (divisor : Int) : UnitVal (a * divisor) :=
+  ⟨unit.val.ediv divisor⟩
+
+/--
+Divides the `UnitVal` by an `Int`, resulting in a new `UnitVal` with an adjusted ratio.
+-/
+@[inline]
+def div (unit : UnitVal a) (divisor : Int) : UnitVal (a * divisor) :=
+  ⟨unit.val.tdiv divisor⟩
+
+/--
+Adds two `UnitVal` values of the same ratio.
+-/
+@[inline]
+def add (u1 : UnitVal α) (u2 : UnitVal α) : UnitVal α :=
+  ⟨u1.val + u2.val⟩
+
+/--
+Subtracts one `UnitVal` value from another of the same ratio.
+-/
+@[inline]
+def sub (u1 : UnitVal α) (u2 : UnitVal α) : UnitVal α :=
+  ⟨u1.val - u2.val⟩
+
+/--
+Returns the absolute value of a `UnitVal`.
+-/
+@[inline]
+def abs (u : UnitVal α) : UnitVal α :=
+  ⟨u.val.natAbs⟩
+
+/--
+Converts an `Offset` to another unit type.
+-/
+@[inline]
+def convert (val : UnitVal a) : UnitVal b :=
+  let ratio := a.div b
+  ofInt <| val.toInt * ratio.num / ratio.den
+
+instance : OfNat (UnitVal α) n where ofNat := ⟨Int.ofNat n⟩
+
+instance : Repr (UnitVal α) where reprPrec x p := reprPrec x.val p
+
+instance : LE (UnitVal α) where le x y := x.val ≤ y.val
+
+instance : LT (UnitVal α) where lt x y := x.val < y.val
+
+instance : Add (UnitVal α) where add := UnitVal.add
+
+instance : Sub (UnitVal α) where sub := UnitVal.sub
+
+instance : Neg (UnitVal α) where neg x := ⟨-x.val⟩
+
+instance : ToString (UnitVal n) where toString n := toString n.val
+
+
+end UnitVal
+end Internal
+end Time
+end Std

src/Std/Time/Notation.lean

@@ -0,0 +1,246 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Date
+import Std.Time.Time
+import Std.Time.Zoned
+import Std.Time.DateTime
+import Std.Time.Format
+
+namespace Std
+namespace Time
+open Lean Parser Command Std
+
+set_option linter.all true
+
+private def convertText : Text → MacroM (TSyntax `term)
+  | .short  => `(Std.Time.Text.short)
+  | .full   => `(Std.Time.Text.full)
+  | .narrow => `(Std.Time.Text.narrow)
+
+private def convertNumber : Number → MacroM (TSyntax `term)
+  | ⟨padding⟩ => `(Std.Time.Number.mk $(quote padding))
+
+private def convertFraction : Fraction → MacroM (TSyntax `term)
+  | .nano => `(Std.Time.Fraction.nano)
+  | .truncated digits => `(Std.Time.Fraction.truncated $(quote digits))
+
+private def convertYear : Year → MacroM (TSyntax `term)
+  | .twoDigit => `(Std.Time.Year.twoDigit)
+  | .fourDigit => `(Std.Time.Year.fourDigit)
+  | .extended n => `(Std.Time.Year.extended $(quote n))
+
+private def convertZoneName : ZoneName → MacroM (TSyntax `term)
+  | .short => `(Std.Time.ZoneName.short)
+  | .full => `(Std.Time.ZoneName.full)
+
+private def convertOffsetX : OffsetX → MacroM (TSyntax `term)
+  | .hour => `(Std.Time.OffsetX.hour)
+  | .hourMinute => `(Std.Time.OffsetX.hourMinute)
+  | .hourMinuteColon => `(Std.Time.OffsetX.hourMinuteColon)
+  | .hourMinuteSecond => `(Std.Time.OffsetX.hourMinuteSecond)
+  | .hourMinuteSecondColon => `(Std.Time.OffsetX.hourMinuteSecondColon)
+
+private def convertOffsetO : OffsetO → MacroM (TSyntax `term)
+  | .short => `(Std.Time.OffsetO.short)
+  | .full  => `(Std.Time.OffsetO.full)
+
+private def convertOffsetZ : OffsetZ → MacroM (TSyntax `term)
+  | .hourMinute => `(Std.Time.OffsetZ.hourMinute)
+  | .full => `(Std.Time.OffsetZ.full)
+  | .hourMinuteSecondColon => `(Std.Time.OffsetZ.hourMinuteSecondColon)
+
+private def convertModifier : Modifier → MacroM (TSyntax `term)
+  | .G p => do `(Std.Time.Modifier.G $(← convertText p))
+  | .y p => do `(Std.Time.Modifier.y $(← convertYear p))
+  | .u p => do `(Std.Time.Modifier.u $(← convertYear p))
+  | .D p => do `(Std.Time.Modifier.D $(← convertNumber p))
+  | .MorL p =>
+    match p with
+    | .inl num => do `(Std.Time.Modifier.MorL (.inl $(← convertNumber num)))
+    | .inr txt => do `(Std.Time.Modifier.MorL (.inr $(← convertText txt)))
+  | .d p => do `(Std.Time.Modifier.d $(← convertNumber p))
+  | .Qorq p =>
+    match p with
+    | .inl num => do `(Std.Time.Modifier.Qorq (.inl $(← convertNumber num)))
+    | .inr txt => do `(Std.Time.Modifier.Qorq (.inr $(← convertText txt)))
+  | .w p => do `(Std.Time.Modifier.w $(← convertNumber p))
+  | .W p => do `(Std.Time.Modifier.W $(← convertNumber p))
+  | .E p => do `(Std.Time.Modifier.E $(← convertText p))
+  | .eorc p =>
+    match p with
+    | .inl num => do `(Std.Time.Modifier.eorc (.inl $(← convertNumber num)))
+    | .inr txt => do `(Std.Time.Modifier.eorc (.inr $(← convertText txt)))
+  | .F p => do `(Std.Time.Modifier.F $(← convertNumber p))
+  | .a p => do `(Std.Time.Modifier.a $(← convertText p))
+  | .h p => do `(Std.Time.Modifier.h $(← convertNumber p))
+  | .K p => do `(Std.Time.Modifier.K $(← convertNumber p))
+  | .k p => do `(Std.Time.Modifier.k $(← convertNumber p))
+  | .H p => do `(Std.Time.Modifier.H $(← convertNumber p))
+  | .m p => do `(Std.Time.Modifier.m $(← convertNumber p))
+  | .s p => do `(Std.Time.Modifier.s $(← convertNumber p))
+  | .S p => do `(Std.Time.Modifier.S $(← convertFraction p))
+  | .A p => do `(Std.Time.Modifier.A $(← convertNumber p))
+  | .n p => do `(Std.Time.Modifier.n $(← convertNumber p))
+  | .N p => do `(Std.Time.Modifier.N $(← convertNumber p))
+  | .V => `(Std.Time.Modifier.V)
+  | .z p => do `(Std.Time.Modifier.z $(← convertZoneName p))
+  | .O p => do `(Std.Time.Modifier.O $(← convertOffsetO p))
+  | .X p => do `(Std.Time.Modifier.X $(← convertOffsetX p))
+  | .x p => do `(Std.Time.Modifier.x $(← convertOffsetX p))
+  | .Z p => do `(Std.Time.Modifier.Z $(← convertOffsetZ p))
+
+private def convertFormatPart : FormatPart → MacroM (TSyntax `term)
+  | .string s => `(.string $(Syntax.mkStrLit s))
+  | .modifier mod => do `(.modifier $(← convertModifier mod))
+
+private def syntaxNat (n : Nat) : MacroM (TSyntax `term) := do
+  let info ← MonadRef.mkInfoFromRefPos
+  pure { raw := Syntax.node1 info `num (Lean.Syntax.atom info (toString n)) }
+
+private def syntaxString (n : String) : MacroM (TSyntax `term) := do
+  let info ← MonadRef.mkInfoFromRefPos
+  pure { raw := Syntax.node1 info `str (Lean.Syntax.atom info (toString n)) }
+
+private def syntaxInt (n : Int) : MacroM (TSyntax `term) := do
+  match n with
+  | .ofNat n => `(Int.ofNat $(Syntax.mkNumLit <| toString n))
+  | .negSucc n => `(Int.negSucc $(Syntax.mkNumLit <| toString n))
+
+private def syntaxBounded (n : Int) : MacroM (TSyntax `term) := do
+ `(Std.Time.Internal.Bounded.LE.ofNatWrapping $(← syntaxInt n) (by decide))
+
+private def syntaxVal (n : Int) : MacroM (TSyntax `term) := do
+ `(Std.Time.Internal.UnitVal.ofInt $(← syntaxInt n))
+
+private def convertOffset (offset : Std.Time.TimeZone.Offset) : MacroM (TSyntax `term) := do
+ `(Std.Time.TimeZone.Offset.ofSeconds $(← syntaxVal offset.second.val))
+
+private def convertTimezone (tz : Std.Time.TimeZone) : MacroM (TSyntax `term) := do
+ `(Std.Time.TimeZone.mk $(← convertOffset tz.offset) $(Syntax.mkStrLit tz.name) $(Syntax.mkStrLit tz.abbreviation) false)
+
+private def convertPlainDate (d : Std.Time.PlainDate) : MacroM (TSyntax `term) := do
+ `(Std.Time.PlainDate.ofYearMonthDayClip $(← syntaxInt d.year) $(← syntaxBounded d.month.val) $(← syntaxBounded d.day.val))
+
+private def convertPlainTime (d : Std.Time.PlainTime) : MacroM (TSyntax `term) := do
+ `(Std.Time.PlainTime.mk $(← syntaxBounded d.hour.val) $(← syntaxBounded d.minute.val) ⟨true, $(← syntaxBounded d.second.snd.val)⟩ $(← syntaxBounded d.nanosecond.val))
+
+private def convertPlainDateTime (d : Std.Time.PlainDateTime) : MacroM (TSyntax `term) := do
+ `(Std.Time.PlainDateTime.mk $(← convertPlainDate d.date) $(← convertPlainTime d.time))
+
+private def convertZonedDateTime (d : Std.Time.ZonedDateTime) (identifier := false) : MacroM (TSyntax `term) := do
+  let plain ← convertPlainDateTime d.toPlainDateTime
+
+  if identifier then
+    `(Std.Time.ZonedDateTime.ofPlainDateTime $plain <$> Std.Time.Database.defaultGetZoneRules $(Syntax.mkStrLit d.timezone.name))
+  else
+    `(Std.Time.ZonedDateTime.ofPlainDateTime $plain (Std.Time.TimeZone.ZoneRules.ofTimeZone $(← convertTimezone d.timezone)))
+
+/--
+Defines a syntax for zoned datetime values. It expects a string representing a datetime with
+timezone information.
+
+Example:
+`zoned("2024-10-13T15:00:00-03:00")`
+-/
+syntax "zoned(" str ")" : term
+
+/--
+Defines a syntax for zoned datetime values. It expects a string representing a datetime and a
+timezone information as a term.
+
+Example:
+`zoned("2024-10-13T15:00:00", timezone)`
+-/
+syntax "zoned(" str "," term ")" : term
+
+
+/--
+Defines a syntax for datetime values without timezone. The input should be a string in an
+ISO8601-like format.
+
+Example:
+`datetime("2024-10-13T15:00:00")`
+-/
+syntax "datetime(" str ")" : term
+
+/--
+Defines a syntax for date-only values. The input string represents a date in formats like "YYYY-MM-DD".
+
+Example:
+`date("2024-10-13")`
+-/
+syntax "date(" str ")" : term
+
+/--
+Defines a syntax for time-only values. The string should represent a time, either in 24-hour or
+12-hour format.
+
+Example:
+`time("15:00:00")` or `time("03:00:00 PM")`
+-/
+syntax "time(" str ")" : term
+
+/--
+Defines a syntax for UTC offset values. The string should indicate the time difference from UTC
+(e.g., "-03:00").
+
+Example:
+`offset("-03:00")`
+-/
+syntax "offset(" str ")" : term
+
+/--
+Defines a syntax for timezone identifiers. The input string should be a valid timezone name or
+abbreviation.
+
+Example:
+`timezone("America/Sao_Paulo")`
+-/
+syntax "timezone(" str ")" : term
+
+
+macro_rules
+  | `(zoned( $date:str )) => do
+      match ZonedDateTime.fromLeanDateTimeWithZoneString date.getString with
+      | .ok res => do return ← convertZonedDateTime res
+      | .error _ =>
+        match ZonedDateTime.fromLeanDateTimeWithIdentifierString date.getString with
+        | .ok res => do return ← convertZonedDateTime res (identifier := true)
+        | .error res => Macro.throwErrorAt date s!"error: {res}"
+
+  | `(zoned( $date:str, $timezone )) => do
+      match PlainDateTime.fromLeanDateTimeString date.getString with
+      | .ok res => do
+        let plain ← convertPlainDateTime res
+        `(Std.Time.ZonedDateTime.ofPlainDateTime $plain $timezone)
+      | .error res => Macro.throwErrorAt date s!"error: {res}"
+
+  | `(datetime( $date:str )) => do
+      match PlainDateTime.fromLeanDateTimeString date.getString with
+      | .ok res => do
+        return ← convertPlainDateTime res
+      | .error res => Macro.throwErrorAt date s!"error: {res}"
+
+  | `(date( $date:str )) => do
+      match PlainDate.fromSQLDateString date.getString with
+      | .ok res => return ← convertPlainDate res
+      | .error res => Macro.throwErrorAt date s!"error: {res}"
+
+  | `(time( $time:str )) => do
+      match PlainTime.fromLeanTime24Hour time.getString with
+      | .ok res => return ← convertPlainTime res
+      | .error res => Macro.throwErrorAt time s!"error: {res}"
+
+  | `(offset( $offset:str )) => do
+      match TimeZone.Offset.fromOffset offset.getString with
+      | .ok res => return ← convertOffset res
+      | .error res => Macro.throwErrorAt offset s!"error: {res}"
+
+  | `(timezone( $tz:str )) => do
+      match TimeZone.fromTimeZone tz.getString with
+      | .ok res => return ← convertTimezone res
+      | .error res => Macro.throwErrorAt tz s!"error: {res}"

src/Std/Time/Notation/Spec.lean

@@ -0,0 +1,113 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Date
+import Std.Time.Time
+import Std.Time.Zoned
+import Std.Time.DateTime
+import Std.Time.Format.Basic
+
+namespace Std
+namespace Time
+open Lean Parser Command Std
+
+private def convertText : Text → MacroM (TSyntax `term)
+  | .short => `(Std.Time.Text.short)
+  | .full => `(Std.Time.Text.full)
+  | .narrow => `(Std.Time.Text.narrow)
+
+private def convertNumber : Number → MacroM (TSyntax `term)
+  | ⟨padding⟩ => `(Std.Time.Number.mk $(quote padding))
+
+private def convertFraction : Fraction → MacroM (TSyntax `term)
+  | .nano => `(Std.Time.Fraction.nano)
+  | .truncated digits => `(Std.Time.Fraction.truncated $(quote digits))
+
+private def convertYear : Year → MacroM (TSyntax `term)
+  | .twoDigit => `(Std.Time.Year.twoDigit)
+  | .fourDigit => `(Std.Time.Year.fourDigit)
+  | .extended n => `(Std.Time.Year.extended $(quote n))
+
+private def convertZoneName : ZoneName → MacroM (TSyntax `term)
+  | .short => `(Std.Time.ZoneName.short)
+  | .full => `(Std.Time.ZoneName.full)
+
+private def convertOffsetX : OffsetX → MacroM (TSyntax `term)
+  | .hour => `(Std.Time.OffsetX.hour)
+  | .hourMinute => `(Std.Time.OffsetX.hourMinute)
+  | .hourMinuteColon => `(Std.Time.OffsetX.hourMinuteColon)
+  | .hourMinuteSecond => `(Std.Time.OffsetX.hourMinuteSecond)
+  | .hourMinuteSecondColon => `(Std.Time.OffsetX.hourMinuteSecondColon)
+
+private def convertOffsetO : OffsetO → MacroM (TSyntax `term)
+  | .short => `(Std.Time.OffsetO.short)
+  | .full  => `(Std.Time.OffsetO.full)
+
+private def convertOffsetZ : OffsetZ → MacroM (TSyntax `term)
+  | .hourMinute => `(Std.Time.OffsetZ.hourMinute)
+  | .full => `(Std.Time.OffsetZ.full)
+  | .hourMinuteSecondColon => `(Std.Time.OffsetZ.hourMinuteSecondColon)
+
+private def convertModifier : Modifier → MacroM (TSyntax `term)
+  | .G p => do `(Std.Time.Modifier.G $(← convertText p))
+  | .y p => do `(Std.Time.Modifier.y $(← convertYear p))
+  | .u p => do `(Std.Time.Modifier.u $(← convertYear p))
+  | .D p => do `(Std.Time.Modifier.D $(← convertNumber p))
+  | .MorL p =>
+    match p with
+    | .inl num => do `(Std.Time.Modifier.MorL (.inl $(← convertNumber num)))
+    | .inr txt => do `(Std.Time.Modifier.MorL (.inr $(← convertText txt)))
+  | .d p => do `(Std.Time.Modifier.d $(← convertNumber p))
+  | .Qorq p =>
+    match p with
+    | .inl num => do `(Std.Time.Modifier.Qorq (.inl $(← convertNumber num)))
+    | .inr txt => do `(Std.Time.Modifier.Qorq (.inr $(← convertText txt)))
+  | .w p => do `(Std.Time.Modifier.w $(← convertNumber p))
+  | .W p => do `(Std.Time.Modifier.W $(← convertNumber p))
+  | .E p => do `(Std.Time.Modifier.E $(← convertText p))
+  | .eorc p =>
+    match p with
+    | .inl num => do `(Std.Time.Modifier.eorc (.inl $(← convertNumber num)))
+    | .inr txt => do `(Std.Time.Modifier.eorc (.inr $(← convertText txt)))
+  | .F p => do `(Std.Time.Modifier.F $(← convertNumber p))
+  | .a p => do `(Std.Time.Modifier.a $(← convertText p))
+  | .h p => do `(Std.Time.Modifier.h $(← convertNumber p))
+  | .K p => do `(Std.Time.Modifier.K $(← convertNumber p))
+  | .k p => do `(Std.Time.Modifier.k $(← convertNumber p))
+  | .H p => do `(Std.Time.Modifier.H $(← convertNumber p))
+  | .m p => do `(Std.Time.Modifier.m $(← convertNumber p))
+  | .s p => do `(Std.Time.Modifier.s $(← convertNumber p))
+  | .S p => do `(Std.Time.Modifier.S $(← convertFraction p))
+  | .A p => do `(Std.Time.Modifier.A $(← convertNumber p))
+  | .n p => do `(Std.Time.Modifier.n $(← convertNumber p))
+  | .N p => do `(Std.Time.Modifier.N $(← convertNumber p))
+  | .V => `(Std.Time.Modifier.V)
+  | .z p => do `(Std.Time.Modifier.z $(← convertZoneName p))
+  | .O p => do `(Std.Time.Modifier.O $(← convertOffsetO p))
+  | .X p => do `(Std.Time.Modifier.X $(← convertOffsetX p))
+  | .x p => do `(Std.Time.Modifier.x $(← convertOffsetX p))
+  | .Z p => do `(Std.Time.Modifier.Z $(← convertOffsetZ p))
+
+private def convertFormatPart : FormatPart → MacroM (TSyntax `term)
+  | .string s => `(.string $(Syntax.mkStrLit s))
+  | .modifier mod => do `(.modifier $(← convertModifier mod))
+
+/--
+Syntax for defining a date spec at compile time.
+-/
+syntax "datespec(" str ")" : term
+
+macro_rules
+  | `(datespec( $format_string:str )) => do
+    let input := format_string.getString
+    let format : Except String (GenericFormat .any) := GenericFormat.spec input
+    match format with
+    | .ok res =>
+      let alts ← res.string.mapM convertFormatPart
+      let alts := alts.foldl Syntax.TSepArray.push (Syntax.TSepArray.mk #[] (sep := ","))
+      `(⟨[$alts,*]⟩)
+    | .error err =>
+      Macro.throwErrorAt format_string s!"cannot compile spec: {err}"

src/Std/Time/Time.lean

@@ -0,0 +1,9 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Time.Basic
+import Std.Time.Time.HourMarker
+import Std.Time.Time.PlainTime

src/Std/Time/Time/Basic.lean

@@ -0,0 +1,7 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Time.Unit.Basic

src/Std/Time/Time/HourMarker.lean

@@ -0,0 +1,71 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Time.Basic
+
+namespace Std
+namespace Time
+open Internal
+
+set_option linter.all true
+
+/--
+`HourMarker` represents the two 12-hour periods of the day: `am` for hours between 12:00 AM and
+11:59 AM, and `pm` for hours between 12:00 PM and 11:59 PM.
+-/
+inductive HourMarker
+
+  /--
+  Ante meridiem.
+  -/
+  | am
+
+  /--
+  Post meridiem.
+  -/
+  | pm
+  deriving Repr, BEq
+
+namespace HourMarker
+
+/--
+`ofOrdinal` converts an `Hour.Ordinal` value to an `HourMarker`, indicating whether it is AM or PM.
+-/
+def ofOrdinal (time : Hour.Ordinal) : HourMarker :=
+  if time.val ≥ 12 then
+    .pm
+  else
+    .am
+
+/--
+Converts a 12-hour clock time to a 24-hour clock time based on the `HourMarker`.
+-/
+def toAbsolute (marker : HourMarker) (time : Bounded.LE 1 12) : Hour.Ordinal :=
+  match marker with
+  | .am => if time.val = 12 then 0 else time.expand (by decide) (by decide)
+  | .pm => if time.val = 12 then 12 else time.add 12 |>.emod 24 (by decide)
+
+/--
+Converts a 24-hour clock time to a 12-hour clock time with a `HourMarker`.
+-/
+def toRelative (hour : Hour.Ordinal) : Bounded.LE 1 12 × HourMarker :=
+  if h₀ : hour.val = 0 then
+    (⟨12, by decide⟩, .am)
+  else if h₁ : hour.val ≤ 12 then
+     if hour.val = 12 then
+      (⟨12, by decide⟩, .pm)
+    else
+      Int.ne_iff_lt_or_gt.mp h₀ |>.by_cases
+        (nomatch Int.not_le.mpr · <| hour.property.left)
+        (⟨hour.val, And.intro · h₁⟩, .am)
+  else
+    let h := Int.not_le.mp h₁
+    let t := hour |>.truncateBottom h |>.sub 12
+    (t.expandTop (by decide), .pm)
+
+end HourMarker
+end Time
+end Std

src/Std/Time/Time/PlainTime.lean

@@ -0,0 +1,297 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Time.Basic
+
+namespace Std
+namespace Time
+open Internal
+
+set_option linter.all true
+
+/--
+Represents a specific point in a day, including hours, minutes, seconds, and nanoseconds.
+-/
+structure PlainTime where
+
+  /--
+  `Hour` component of the `PlainTime`
+  -/
+  hour : Hour.Ordinal
+
+  /--
+  `Minute` component of the `PlainTime`
+  -/
+  minute : Minute.Ordinal
+
+  /--
+  `Second` component of the `PlainTime`
+  -/
+  second : Sigma Second.Ordinal
+
+  /--
+  `Nanoseconds` component of the `PlainTime`
+  -/
+  nanosecond : Nanosecond.Ordinal
+  deriving Repr
+
+instance : Inhabited PlainTime where
+  default := ⟨0, 0, Sigma.mk false 0, 0, by decide⟩
+
+instance : BEq PlainTime where
+  beq x y := x.hour.val == y.hour.val && x.minute == y.minute
+          && x.second.snd.val == y.second.snd.val && x.nanosecond == y.nanosecond
+
+namespace PlainTime
+
+/--
+Creates a `PlainTime` value representing midnight (00:00:00.000000000).
+-/
+def midnight : PlainTime :=
+  ⟨0, 0, ⟨true, 0⟩, 0⟩
+
+/--
+Creates a `PlainTime` value from the provided hours, minutes, seconds and nanoseconds components.
+-/
+@[inline]
+def ofHourMinuteSecondsNano (hour : Hour.Ordinal) (minute : Minute.Ordinal) (second : Second.Ordinal leap) (nano : Nanosecond.Ordinal) : PlainTime :=
+  ⟨hour, minute, Sigma.mk leap second, nano⟩
+
+/--
+Creates a `PlainTime` value from the provided hours, minutes, and seconds.
+-/
+@[inline]
+def ofHourMinuteSeconds (hour : Hour.Ordinal) (minute : Minute.Ordinal) (second : Second.Ordinal leap) : PlainTime :=
+  ofHourMinuteSecondsNano hour minute second 0
+
+/--
+Converts a `PlainTime` value to the total number of milliseconds.
+-/
+def toMilliseconds (time : PlainTime) : Millisecond.Offset :=
+  time.hour.toOffset.toMilliseconds +
+  time.minute.toOffset.toMilliseconds +
+  time.second.snd.toOffset.toMilliseconds +
+  time.nanosecond.toOffset.toMilliseconds
+
+/--
+Converts a `PlainTime` value to the total number of nanoseconds.
+-/
+def toNanoseconds (time : PlainTime) : Nanosecond.Offset :=
+  time.hour.toOffset.toNanoseconds +
+  time.minute.toOffset.toNanoseconds +
+  time.second.snd.toOffset.toNanoseconds +
+  time.nanosecond.toOffset
+
+/--
+Converts a `PlainTime` value to the total number of seconds.
+-/
+def toSeconds (time : PlainTime) : Second.Offset :=
+  time.hour.toOffset.toSeconds +
+  time.minute.toOffset.toSeconds +
+  time.second.snd.toOffset
+
+/--
+Converts a `PlainTime` value to the total number of minutes.
+-/
+def toMinutes (time : PlainTime) : Minute.Offset :=
+  time.hour.toOffset.toMinutes +
+  time.minute.toOffset +
+  time.second.snd.toOffset.toMinutes
+
+/--
+Converts a `PlainTime` value to the total number of hours.
+-/
+def toHours (time : PlainTime) : Hour.Offset :=
+  time.hour.toOffset
+
+/--
+Creates a `PlainTime` value from a total number of nanoseconds.
+-/
+def ofNanoseconds (nanos : Nanosecond.Offset) : PlainTime :=
+  have totalSeconds := nanos.ediv 1000000000
+  have remainingNanos := Bounded.LE.byEmod nanos.val 1000000000 (by decide)
+  have hours := Bounded.LE.byEmod (totalSeconds.val / 3600) 24 (by decide)
+  have minutes := (Bounded.LE.byEmod totalSeconds.val 3600 (by decide)).ediv 60 (by decide)
+  have seconds := Bounded.LE.byEmod totalSeconds.val 60 (by decide)
+  let nanos := Bounded.LE.byEmod nanos.val 1000000000 (by decide)
+  PlainTime.mk hours minutes (Sigma.mk false seconds) nanos
+
+/--
+Creates a `PlainTime` value from a total number of millisecond.
+-/
+@[inline]
+def ofMilliseconds (millis : Millisecond.Offset) : PlainTime :=
+  ofNanoseconds millis.toNanoseconds
+
+/--
+Creates a `PlainTime` value from a total number of seconds.
+-/
+@[inline]
+def ofSeconds (secs : Second.Offset) : PlainTime :=
+  ofNanoseconds secs.toNanoseconds
+
+/--
+Creates a `PlainTime` value from a total number of minutes.
+-/
+@[inline]
+def ofMinutes (secs : Minute.Offset) : PlainTime :=
+  ofNanoseconds secs.toNanoseconds
+
+/--
+Creates a `PlainTime` value from a total number of hours.
+-/
+@[inline]
+def ofHours (hour : Hour.Offset) : PlainTime :=
+  ofNanoseconds hour.toNanoseconds
+
+/--
+Adds seconds to a `PlainTime`.
+-/
+@[inline]
+def addSeconds (time : PlainTime) (secondsToAdd : Second.Offset) : PlainTime :=
+  let totalSeconds := time.toNanoseconds + secondsToAdd.toNanoseconds
+  ofNanoseconds totalSeconds
+
+/--
+Subtracts seconds from a `PlainTime`.
+-/
+@[inline]
+def subSeconds (time : PlainTime) (secondsToSub : Second.Offset) : PlainTime :=
+  addSeconds time (-secondsToSub)
+
+/--
+Adds minutes to a `PlainTime`.
+-/
+@[inline]
+def addMinutes (time : PlainTime) (minutesToAdd : Minute.Offset) : PlainTime :=
+  let total := time.toNanoseconds + minutesToAdd.toNanoseconds
+  ofNanoseconds total
+
+/--
+Subtracts minutes from a `PlainTime`.
+-/
+@[inline]
+def subMinutes (time : PlainTime) (minutesToSub : Minute.Offset) : PlainTime :=
+  addMinutes time (-minutesToSub)
+
+/--
+Adds hours to a `PlainTime`.
+-/
+@[inline]
+def addHours (time : PlainTime) (hoursToAdd : Hour.Offset) : PlainTime :=
+  let total := time.toNanoseconds + hoursToAdd.toNanoseconds
+  ofNanoseconds total
+
+/--
+Subtracts hours from a `PlainTime`.
+-/
+@[inline]
+def subHours (time : PlainTime) (hoursToSub : Hour.Offset) : PlainTime :=
+  addHours time (-hoursToSub)
+
+/--
+Adds nanoseconds to a `PlainTime`.
+-/
+def addNanoseconds (time : PlainTime) (nanosToAdd : Nanosecond.Offset) : PlainTime :=
+  let total := time.toNanoseconds + nanosToAdd
+  ofNanoseconds total
+
+/--
+Subtracts nanoseconds from a `PlainTime`.
+-/
+def subNanoseconds (time : PlainTime) (nanosToSub : Nanosecond.Offset) : PlainTime :=
+  addNanoseconds time (-nanosToSub)
+
+/--
+Adds milliseconds to a `PlainTime`.
+-/
+def addMilliseconds (time : PlainTime) (millisToAdd : Millisecond.Offset) : PlainTime :=
+  let total := time.toMilliseconds + millisToAdd
+  ofMilliseconds total
+
+/--
+Subtracts milliseconds from a `PlainTime`.
+-/
+def subMilliseconds (time : PlainTime) (millisToSub : Millisecond.Offset) : PlainTime :=
+  addMilliseconds time (-millisToSub)
+
+/--
+Creates a new `PlainTime` by adjusting the `second` component to the given value.
+-/
+@[inline]
+def withSeconds (pt : PlainTime) (second : Sigma Second.Ordinal) : PlainTime :=
+  { pt with second := second }
+
+/--
+Creates a new `PlainTime` by adjusting the `minute` component to the given value.
+-/
+@[inline]
+def withMinutes (pt : PlainTime) (minute : Minute.Ordinal) : PlainTime :=
+  { pt with minute := minute }
+
+/--
+Creates a new `PlainTime` by adjusting the milliseconds component inside the `nano` component of its `time` to the given value.
+-/
+@[inline]
+def withMilliseconds (pt : PlainTime) (millis : Millisecond.Ordinal) : PlainTime :=
+  let minorPart := pt.nanosecond.emod 1000 (by decide)
+  let majorPart := millis.mul_pos 1000000 (by decide) |>.addBounds minorPart
+  { pt with nanosecond := majorPart |>.expandTop (by decide) }
+
+/--
+Creates a new `PlainTime` by adjusting the `nano` component to the given value.
+-/
+@[inline]
+def withNanoseconds (pt : PlainTime) (nano : Nanosecond.Ordinal) : PlainTime :=
+  { pt with nanosecond := nano }
+
+/--
+Creates a new `PlainTime` by adjusting the `hour` component to the given value.
+-/
+@[inline]
+def withHours (pt : PlainTime) (hour : Hour.Ordinal) : PlainTime :=
+  { pt with hour := hour }
+
+/--
+`Millisecond` component of the `PlainTime`
+-/
+@[inline]
+def millisecond (pt : PlainTime) : Millisecond.Ordinal :=
+  pt.nanosecond.ediv 1000000 (by decide)
+
+instance : HAdd PlainTime Nanosecond.Offset PlainTime where
+  hAdd := addNanoseconds
+
+instance : HSub PlainTime Nanosecond.Offset PlainTime where
+  hSub := subNanoseconds
+
+instance : HAdd PlainTime Millisecond.Offset PlainTime where
+  hAdd := addMilliseconds
+
+instance : HSub PlainTime Millisecond.Offset PlainTime where
+  hSub := subMilliseconds
+
+instance : HAdd PlainTime Second.Offset PlainTime where
+  hAdd := addSeconds
+
+instance : HSub PlainTime Second.Offset PlainTime where
+  hSub := subSeconds
+
+instance : HAdd PlainTime Minute.Offset PlainTime where
+  hAdd := addMinutes
+
+instance : HSub PlainTime Minute.Offset PlainTime where
+  hSub := subMinutes
+
+instance : HAdd PlainTime Hour.Offset PlainTime where
+  hAdd := addHours
+
+instance : HSub PlainTime Hour.Offset PlainTime where
+  hSub := subHours
+
+end PlainTime
+end Time
+end Std

src/Std/Time/Time/Unit/Basic.lean

@@ -0,0 +1,329 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Internal
+import Std.Time.Time.Unit.Hour
+import Std.Time.Time.Unit.Minute
+import Std.Time.Time.Unit.Second
+import Std.Time.Time.Unit.Nanosecond
+import Std.Time.Time.Unit.Millisecond
+
+/-!
+This module defines various units used for measuring, counting, and converting between hours, minutes,
+second, nanosecond, millisecond and nanoseconds.
+
+The units are organized into types representing these time-related concepts, with operations provided
+to facilitate conversions and manipulations between them.
+-/
+
+namespace Std
+namespace Time
+open Internal
+
+set_option linter.all true
+
+namespace Nanosecond.Offset
+
+/--
+Converts a `Nanosecond.Offset` to a `Millisecond.Offset`.
+-/
+@[inline]
+def toMilliseconds (offset : Nanosecond.Offset) : Millisecond.Offset :=
+  offset.div 1000000
+
+/--
+Converts a `Millisecond.Offset` to a `Nanosecond.Offset`.
+-/
+@[inline]
+def ofMilliseconds (offset : Millisecond.Offset) : Nanosecond.Offset :=
+  offset.mul 1000000
+
+/--
+Converts a `Nanosecond.Offset` to a `Second.Offset`.
+-/
+@[inline]
+def toSeconds (offset : Nanosecond.Offset) : Second.Offset :=
+  offset.div 1000000000
+
+/--
+Converts a `Second.Offset` to a `Nanosecond.Offset`.
+-/
+@[inline]
+def ofSeconds (offset : Second.Offset) : Nanosecond.Offset :=
+  offset.mul 1000000000
+
+/--
+Converts a `Nanosecond.Offset` to a `Minute.Offset`.
+-/
+@[inline]
+def toMinutes (offset : Nanosecond.Offset) : Minute.Offset :=
+  offset.div 60000000000
+
+/--
+Converts a `Minute.Offset` to a `Nanosecond.Offset`.
+-/
+@[inline]
+def ofMinutes (offset : Minute.Offset) : Nanosecond.Offset :=
+  offset.mul 60000000000
+
+/--
+Converts a `Nanosecond.Offset` to an `Hour.Offset`.
+-/
+@[inline]
+def toHours (offset : Nanosecond.Offset) : Hour.Offset :=
+  offset.div 3600000000000
+
+/--
+Converts an `Hour.Offset` to a `Nanosecond.Offset`.
+-/
+@[inline]
+def ofHours (offset : Hour.Offset) : Nanosecond.Offset :=
+  offset.mul 3600000000000
+
+end Nanosecond.Offset
+
+namespace Millisecond.Offset
+
+/--
+Converts a `Millisecond.Offset` to a `Nanosecond.Offset`.
+-/
+@[inline]
+def toNanoseconds (offset : Millisecond.Offset) : Nanosecond.Offset :=
+  offset.mul 1000000
+
+/--
+Converts a `Nanosecond.Offset` to a `Millisecond.Offset`.
+-/
+@[inline]
+def ofNanoseconds (offset : Nanosecond.Offset) : Millisecond.Offset :=
+  offset.div 1000000
+
+/--
+Converts a `Millisecond.Offset` to a `Second.Offset`.
+-/
+@[inline]
+def toSeconds (offset : Millisecond.Offset) : Second.Offset :=
+  offset.div 1000
+
+/--
+Converts a `Second.Offset` to a `Millisecond.Offset`.
+-/
+@[inline]
+def ofSeconds (offset : Second.Offset) : Millisecond.Offset :=
+  offset.mul 1000
+
+/--
+Converts a `Millisecond.Offset` to a `Minute.Offset`.
+-/
+@[inline]
+def toMinutes (offset : Millisecond.Offset) : Minute.Offset :=
+  offset.div 60000
+
+/--
+Converts a `Minute.Offset` to a `Millisecond.Offset`.
+-/
+@[inline]
+def ofMinutes (offset : Minute.Offset) : Millisecond.Offset :=
+  offset.mul 60000
+
+/--
+Converts a `Millisecond.Offset` to an `Hour.Offset`.
+-/
+@[inline]
+def toHours (offset : Millisecond.Offset) : Hour.Offset :=
+  offset.div 3600000
+
+/--
+Converts an `Hour.Offset` to a `Millisecond.Offset`.
+-/
+@[inline]
+def ofHours (offset : Hour.Offset) : Millisecond.Offset :=
+  offset.mul 3600000
+
+end Millisecond.Offset
+
+namespace Second.Offset
+
+/--
+Converts a `Second.Offset` to a `Nanosecond.Offset`.
+-/
+@[inline]
+def toNanoseconds (offset : Second.Offset) : Nanosecond.Offset :=
+  offset.mul 1000000000
+
+/--
+Converts a `Nanosecond.Offset` to a `Second.Offset`.
+-/
+@[inline]
+def ofNanoseconds (offset : Nanosecond.Offset) : Second.Offset :=
+  offset.div 1000000000
+
+/--
+Converts a `Second.Offset` to a `Millisecond.Offset`.
+-/
+@[inline]
+def toMilliseconds (offset : Second.Offset) : Millisecond.Offset :=
+  offset.mul 1000
+
+/--
+Converts a `Millisecond.Offset` to a `Second.Offset`.
+-/
+@[inline]
+def ofMilliseconds (offset : Millisecond.Offset) : Second.Offset :=
+  offset.div 1000
+
+/--
+Converts a `Second.Offset` to a `Minute.Offset`.
+-/
+@[inline]
+def toMinutes (offset : Second.Offset) : Minute.Offset :=
+  offset.div 60
+
+/--
+Converts a `Minute.Offset` to a `Second.Offset`.
+-/
+@[inline]
+def ofMinutes (offset : Minute.Offset) : Second.Offset :=
+  offset.mul 60
+
+/--
+Converts a `Second.Offset` to an `Hour.Offset`.
+-/
+@[inline]
+def toHours (offset : Second.Offset) : Hour.Offset :=
+  offset.div 3600
+
+/--
+Converts an `Hour.Offset` to a `Second.Offset`.
+-/
+@[inline]
+def ofHours (offset : Hour.Offset) : Second.Offset :=
+  offset.mul 3600
+
+end Second.Offset
+
+namespace Minute.Offset
+
+/--
+Converts a `Minute.Offset` to a `Nanosecond.Offset`.
+-/
+@[inline]
+def toNanoseconds (offset : Minute.Offset) : Nanosecond.Offset :=
+  offset.mul 60000000000
+
+/--
+Converts a `Nanosecond.Offset` to a `Minute.Offset`.
+-/
+@[inline]
+def ofNanoseconds (offset : Nanosecond.Offset) : Minute.Offset :=
+  offset.div 60000000000
+
+/--
+Converts a `Minute.Offset` to a `Millisecond.Offset`.
+-/
+@[inline]
+def toMilliseconds (offset : Minute.Offset) : Millisecond.Offset :=
+  offset.mul 60000
+
+/--
+Converts a `Millisecond.Offset` to a `Minute.Offset`.
+-/
+@[inline]
+def ofMilliseconds (offset : Millisecond.Offset) : Minute.Offset :=
+  offset.div 60000
+
+/--
+Converts a `Minute.Offset` to a `Second.Offset`.
+-/
+@[inline]
+def toSeconds (offset : Minute.Offset) : Second.Offset :=
+  offset.mul 60
+
+/--
+Converts a `Second.Offset` to a `Minute.Offset`.
+-/
+@[inline]
+def ofSeconds (offset : Second.Offset) : Minute.Offset :=
+  offset.div 60
+
+/--
+Converts a `Minute.Offset` to an `Hour.Offset`.
+-/
+@[inline]
+def toHours (offset : Minute.Offset) : Hour.Offset :=
+  offset.div 60
+
+/--
+Converts an `Hour.Offset` to a `Minute.Offset`.
+-/
+@[inline]
+def ofHours (offset : Hour.Offset) : Minute.Offset :=
+  offset.mul 60
+
+end Minute.Offset
+
+namespace Hour.Offset
+
+/--
+Converts an `Hour.Offset` to a `Nanosecond.Offset`.
+-/
+@[inline]
+def toNanoseconds (offset : Hour.Offset) : Nanosecond.Offset :=
+  offset.mul 3600000000000
+
+/--
+Converts a `Nanosecond.Offset` to an `Hour.Offset`.
+-/
+@[inline]
+def ofNanoseconds (offset : Nanosecond.Offset) : Hour.Offset :=
+  offset.div 3600000000000
+
+/--
+Converts an `Hour.Offset` to a `Millisecond.Offset`.
+-/
+@[inline]
+def toMilliseconds (offset : Hour.Offset) : Millisecond.Offset :=
+  offset.mul 3600000
+
+/--
+Converts a `Millisecond.Offset` to an `Hour.Offset`.
+-/
+@[inline]
+def ofMilliseconds (offset : Millisecond.Offset) : Hour.Offset :=
+  offset.div 3600000
+
+/--
+Converts an `Hour.Offset` to a `Second.Offset`.
+-/
+@[inline]
+def toSeconds (offset : Hour.Offset) : Second.Offset :=
+  offset.mul 3600
+
+/--
+Converts a `Second.Offset` to an `Hour.Offset`.
+-/
+@[inline]
+def ofSeconds (offset : Second.Offset) : Hour.Offset :=
+  offset.div 3600
+
+/--
+Converts an `Hour.Offset` to a `Minute.Offset`.
+-/
+@[inline]
+def toMinutes (offset : Hour.Offset) : Minute.Offset :=
+  offset.mul 60
+
+/--
+Converts a `Minute.Offset` to an `Hour.Offset`.
+-/
+@[inline]
+def ofMinutes (offset : Minute.Offset) : Hour.Offset :=
+  offset.div 60
+
+end Hour.Offset
+
+end Time
+end Std

src/Std/Time/Time/Unit/Hour.lean

@@ -0,0 +1,111 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Internal.Rat
+import Std.Time.Internal
+import Std.Time.Time.Unit.Minute
+import Std.Time.Time.Unit.Second
+
+namespace Std
+namespace Time
+namespace Hour
+open Std.Internal
+open Internal
+
+set_option linter.all true
+
+/--
+`Ordinal` represents a bounded value for hours, ranging from 0 to 23.
+-/
+def Ordinal := Bounded.LE 0 23
+  deriving Repr, BEq, LE, LT
+
+instance : OfNat Ordinal n :=
+  inferInstanceAs (OfNat (Bounded.LE 0 (0 + (23 : Nat))) n)
+
+instance : Inhabited Ordinal where
+  default := 0
+
+instance {x y : Ordinal} : Decidable (x ≤ y) :=
+  inferInstanceAs (Decidable (x.val ≤ y.val))
+
+instance {x y : Ordinal} : Decidable (x < y) :=
+  inferInstanceAs (Decidable (x.val < y.val))
+
+/--
+`Offset` represents an offset in hours, defined as an `Int`. This can be used to express durations
+or differences in hours.
+-/
+def Offset : Type := UnitVal 3600
+  deriving Repr, BEq, Inhabited, Add, Sub, Neg, ToString
+
+instance : OfNat Offset n :=
+  ⟨UnitVal.ofNat n⟩
+
+namespace Ordinal
+
+/--
+Creates an `Ordinal` from an integer, ensuring the value is within bounds.
+-/
+@[inline]
+def ofInt (data : Int) (h : 0 ≤ data ∧ data ≤ 23) : Ordinal :=
+  Bounded.LE.mk data h
+
+/--
+Converts an `Ordinal` into a relative hour in the range of 1 to 12.
+-/
+def toRelative (ordinal : Ordinal) : Bounded.LE 1 12 :=
+  (ordinal.add 11).emod 12 (by decide) |>.add 1
+
+/--
+Converts an Ordinal into a 1-based hour representation within the range of 1 to 24.
+-/
+def shiftTo1BasedHour (ordinal : Ordinal) : Bounded.LE 1 24 :=
+  if h : ordinal.val < 1
+    then Internal.Bounded.LE.ofNatWrapping 24 (by decide)
+    else ordinal.truncateBottom (Int.not_lt.mp h) |>.expandTop (by decide)
+/--
+Creates an `Ordinal` from a natural number, ensuring the value is within the valid bounds for hours.
+-/
+@[inline]
+def ofNat (data : Nat) (h : data ≤ 23) : Ordinal :=
+  Bounded.LE.ofNat data h
+
+/--
+Creates an `Ordinal` from a `Fin` value.
+-/
+@[inline]
+def ofFin (data : Fin 24) : Ordinal :=
+  Bounded.LE.ofFin data
+
+/--
+Converts an `Ordinal` to an `Offset`, which represents the duration in hours as an integer value.
+-/
+@[inline]
+def toOffset (ordinal : Ordinal) : Offset :=
+  UnitVal.ofInt ordinal.val
+
+end Ordinal
+namespace Offset
+
+/--
+Creates an `Offset` from a natural number.
+-/
+@[inline]
+def ofNat (data : Nat) : Offset :=
+  UnitVal.ofInt data
+
+/--
+Creates an `Offset` from an integer.
+-/
+@[inline]
+def ofInt (data : Int) : Offset :=
+  UnitVal.ofInt data
+
+end Offset
+end Hour
+end Time
+end Std

src/Std/Time/Time/Unit/Millisecond.lean

@@ -0,0 +1,96 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Internal.Rat
+import Std.Time.Internal
+import Std.Time.Time.Unit.Nanosecond
+
+namespace Std
+namespace Time
+namespace Millisecond
+open Std.Internal
+open Internal
+
+set_option linter.all true
+
+/--
+`Ordinal` represents a bounded value for milliseconds, ranging from 0 to 999 milliseconds.
+-/
+def Ordinal := Bounded.LE 0 999
+  deriving Repr, BEq, LE, LT
+
+instance : OfNat Ordinal n :=
+  inferInstanceAs (OfNat (Bounded.LE 0 (0 + (999 : Nat))) n)
+
+instance : Inhabited Ordinal where
+  default := 0
+
+instance {x y : Ordinal} : Decidable (x ≤ y) :=
+  inferInstanceAs (Decidable (x.val ≤ y.val))
+
+instance {x y : Ordinal} : Decidable (x < y) :=
+  inferInstanceAs (Decidable (x.val < y.val))
+
+/--
+`Offset` represents a duration offset in milliseconds.
+-/
+def Offset : Type := UnitVal (1 / 1000)
+  deriving Repr, BEq, Inhabited, Add, Sub, Neg, LE, LT, ToString
+
+instance : OfNat Offset n :=
+  ⟨UnitVal.ofNat n⟩
+
+namespace Offset
+
+/--
+Creates an `Offset` from a natural number.
+-/
+@[inline]
+def ofNat (data : Nat) : Offset :=
+  UnitVal.ofInt data
+
+/--
+Creates an `Offset` from an integer.
+-/
+@[inline]
+def ofInt (data : Int) : Offset :=
+  UnitVal.ofInt data
+
+end Offset
+namespace Ordinal
+
+/--
+Creates an `Ordinal` from an integer, ensuring the value is within bounds.
+-/
+@[inline]
+def ofInt (data : Int) (h : 0 ≤ data ∧ data ≤ 999) : Ordinal :=
+  Bounded.LE.mk data h
+
+/--
+Creates an `Ordinal` from a natural number, ensuring the value is within bounds.
+-/
+@[inline]
+def ofNat (data : Nat) (h : data ≤ 999) : Ordinal :=
+  Bounded.LE.ofNat data h
+
+/--
+Creates an `Ordinal` from a `Fin`, ensuring the value is within bounds.
+-/
+@[inline]
+def ofFin (data : Fin 1000) : Ordinal :=
+  Bounded.LE.ofFin data
+
+/--
+Converts an `Ordinal` to an `Offset`.
+-/
+@[inline]
+def toOffset (ordinal : Ordinal) : Offset :=
+  UnitVal.ofInt ordinal.val
+
+end Ordinal
+end Millisecond
+end Time
+end Std

src/Std/Time/Time/Unit/Minute.lean

@@ -0,0 +1,96 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Internal.Rat
+import Std.Time.Internal
+import Std.Time.Time.Unit.Second
+
+namespace Std
+namespace Time
+namespace Minute
+open Std.Internal
+open Internal
+
+set_option linter.all true
+
+/--
+`Ordinal` represents a bounded value for minutes, ranging from 0 to 59. This is useful for representing the minute component of a time.
+-/
+def Ordinal := Bounded.LE 0 59
+  deriving Repr, BEq, LE, LT
+
+instance : OfNat Ordinal n :=
+  inferInstanceAs (OfNat (Bounded.LE 0 (0 + (59 : Nat))) n)
+
+instance : Inhabited Ordinal where
+  default := 0
+
+instance {x y : Ordinal} : Decidable (x ≤ y) :=
+  inferInstanceAs (Decidable (x.val ≤ y.val))
+
+instance {x y : Ordinal} : Decidable (x < y) :=
+  inferInstanceAs (Decidable (x.val < y.val))
+
+/--
+`Offset` represents a duration offset in minutes.
+-/
+def Offset : Type := UnitVal 60
+  deriving Repr, BEq, Inhabited, Add, Sub, Neg, ToString
+
+instance : OfNat Offset n :=
+  ⟨UnitVal.ofInt <| Int.ofNat n⟩
+
+namespace Ordinal
+
+/--
+Creates an `Ordinal` from an integer, ensuring the value is within bounds.
+-/
+@[inline]
+def ofInt (data : Int) (h : 0 ≤ data ∧ data ≤ 59) : Ordinal :=
+  Bounded.LE.mk data h
+
+/--
+Creates an `Ordinal` from a natural number, ensuring the value is within bounds.
+-/
+@[inline]
+def ofNat (data : Nat) (h : data ≤ 59) : Ordinal :=
+  Bounded.LE.ofNat data h
+
+/--
+Creates an `Ordinal` from a `Fin`, ensuring the value is within bounds.
+-/
+@[inline]
+def ofFin (data : Fin 60) : Ordinal :=
+  Bounded.LE.ofFin data
+
+/--
+Converts an `Ordinal` to an `Offset`.
+-/
+@[inline]
+def toOffset (ordinal : Ordinal) : Offset :=
+  UnitVal.ofInt ordinal.val
+
+end Ordinal
+namespace Offset
+
+/--
+Creates an `Offset` from a natural number.
+-/
+@[inline]
+def ofNat (data : Nat) : Offset :=
+  UnitVal.ofInt data
+
+/--
+Creates an `Offset` from an integer.
+-/
+@[inline]
+def ofInt (data : Int) : Offset :=
+  UnitVal.ofInt data
+
+end Offset
+end Minute
+end Time
+end Std

src/Std/Time/Time/Unit/Nanosecond.lean

@@ -0,0 +1,124 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Internal.Rat
+import Std.Time.Internal
+
+namespace Std
+namespace Time
+namespace Nanosecond
+open Std.Internal
+open Internal
+
+set_option linter.all true
+
+/--
+`Ordinal` represents a nanosecond value that is bounded between 0 and 999,999,999 nanoseconds.
+-/
+def Ordinal := Bounded.LE 0 999999999
+  deriving Repr, BEq, LE, LT
+
+instance : OfNat Ordinal n where
+  ofNat := Bounded.LE.ofFin (Fin.ofNat n)
+
+instance : Inhabited Ordinal where
+  default := 0
+
+instance {x y : Ordinal} : Decidable (x ≤ y) :=
+  inferInstanceAs (Decidable (x.val ≤ y.val))
+
+instance {x y : Ordinal} : Decidable (x < y) :=
+  inferInstanceAs (Decidable (x.val < y.val))
+
+/--
+`Offset` represents a time offset in nanoseconds.
+-/
+def Offset : Type := UnitVal (1 / 1000000000)
+  deriving Repr, BEq, Inhabited, Add, Sub, Neg, LE, LT, ToString
+
+instance { x y : Offset } : Decidable (x ≤ y) :=
+  inferInstanceAs (Decidable (x.val ≤ y.val))
+
+instance : OfNat Offset n :=
+  ⟨UnitVal.ofNat n⟩
+
+namespace Offset
+
+/--
+Creates an `Offset` from a natural number.
+-/
+@[inline]
+def ofNat (data : Nat) : Offset :=
+  UnitVal.ofInt data
+
+/--
+Creates an `Offset` from an integer.
+-/
+@[inline]
+def ofInt (data : Int) : Offset :=
+  UnitVal.ofInt data
+
+end Offset
+
+/--
+`Span` represents a bounded value for nanoseconds, ranging between -999999999 and 999999999.
+This can be used for operations that involve differences or adjustments within this range.
+-/
+def Span := Bounded.LE (-999999999) 999999999
+  deriving Repr, BEq, LE, LT
+
+instance : Inhabited Span where default := Bounded.LE.mk 0 (by decide)
+
+namespace Span
+
+/--
+Creates a new `Offset` out of a `Span`.
+-/
+def toOffset (span : Span) : Offset :=
+  UnitVal.ofInt span.val
+
+end Span
+
+namespace Ordinal
+
+/--
+`Ordinal` represents a bounded value for nanoseconds in a day, which ranges between 0 and 86400000000000.
+-/
+def OfDay := Bounded.LE 0 86400000000000
+  deriving Repr, BEq, LE, LT
+
+/--
+Creates an `Ordinal` from an integer, ensuring the value is within bounds.
+-/
+@[inline]
+def ofInt (data : Int) (h : 0 ≤ data ∧ data ≤ 999999999) : Ordinal :=
+  Bounded.LE.mk data h
+
+/--
+Creates an `Ordinal` from a natural number, ensuring the value is within bounds.
+-/
+@[inline]
+def ofNat (data : Nat) (h : data ≤ 999999999) : Ordinal :=
+  Bounded.LE.ofNat data h
+
+/--
+Creates an `Ordinal` from a `Fin`, ensuring the value is within bounds.
+-/
+@[inline]
+def ofFin (data : Fin 1000000000) : Ordinal :=
+  Bounded.LE.ofFin data
+
+/--
+Converts an `Ordinal` to an `Offset`.
+-/
+@[inline]
+def toOffset (ordinal : Ordinal) : Offset :=
+  UnitVal.ofInt ordinal.val
+
+end Ordinal
+end Nanosecond
+end Time
+end Std

src/Std/Time/Time/Unit/Second.lean

@@ -0,0 +1,110 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Internal.Rat
+import Std.Time.Time.Unit.Nanosecond
+
+namespace Std
+namespace Time
+namespace Second
+open Std.Internal
+open Internal
+
+set_option linter.all true
+
+/--
+`Ordinal` represents a bounded value for second, which ranges between 0 and 59 or 60. This accounts
+for potential leap second.
+-/
+def Ordinal (leap : Bool) := Bounded.LE 0 (.ofNat (if leap then 60 else 59))
+
+instance : BEq (Ordinal leap) where
+  beq x y := BEq.beq x.val y.val
+
+instance : LE (Ordinal leap) where
+  le x y := LE.le x.val y.val
+
+instance : LT (Ordinal leap) where
+  lt x y := LT.lt x.val y.val
+
+instance : Repr (Ordinal l) where
+  reprPrec r := reprPrec r.val
+
+instance : OfNat (Ordinal leap) n := by
+  have inst := inferInstanceAs (OfNat (Bounded.LE 0 (0 + (59 : Nat))) n)
+  cases leap
+  · exact inst
+  · exact ⟨inst.ofNat.expandTop (by decide)⟩
+
+instance {x y : Ordinal l} : Decidable (x ≤ y) :=
+  inferInstanceAs (Decidable (x.val ≤ y.val))
+
+instance {x y : Ordinal l} : Decidable (x < y) :=
+  inferInstanceAs (Decidable (x.val < y.val))
+
+/--
+`Offset` represents an offset in seconds. It is defined as an `Int`.
+-/
+def Offset : Type := UnitVal 1
+  deriving Repr, BEq, Inhabited, Add, Sub, Neg, LE, LT, ToString
+
+instance : OfNat Offset n :=
+  ⟨UnitVal.ofNat n⟩
+
+namespace Offset
+
+/--
+Creates an `Second.Offset` from a natural number.
+-/
+@[inline]
+def ofNat (data : Nat) : Second.Offset :=
+  UnitVal.ofInt data
+
+/--
+Creates an `Second.Offset` from an integer.
+-/
+@[inline]
+def ofInt (data : Int) : Second.Offset :=
+  UnitVal.ofInt data
+
+end Offset
+
+namespace Ordinal
+
+/--
+Creates an `Ordinal` from an integer, ensuring the value is within bounds.
+-/
+@[inline]
+def ofInt (data : Int) (h : 0 ≤ data ∧ data ≤ Int.ofNat (if leap then 60 else 59)) : Ordinal leap :=
+  Bounded.LE.mk data h
+
+/--
+Creates an `Ordinal` from a natural number, ensuring the value is within bounds.
+-/
+@[inline]
+def ofNat (data : Nat) (h : data ≤ (if leap then 60 else 59)) : Ordinal leap :=
+  Bounded.LE.ofNat data h
+
+/--
+Creates an `Ordinal` from a `Fin`, ensuring the value is within bounds.
+-/
+@[inline]
+def ofFin (data : Fin (if leap then 61 else 60)) : Ordinal leap :=
+  match leap with
+  | true => Bounded.LE.ofFin data
+  | false => Bounded.LE.ofFin data
+
+/--
+Converts an `Ordinal` to an `Second.Offset`.
+-/
+@[inline]
+def toOffset (ordinal : Ordinal leap) : Second.Offset :=
+  UnitVal.ofInt ordinal.val
+
+end Ordinal
+end Second
+end Time
+end Std

src/Std/Time/Zoned.lean

@@ -0,0 +1,180 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Zoned.DateTime
+import Std.Time.Zoned.ZoneRules
+import Std.Time.Zoned.ZonedDateTime
+import Std.Time.Zoned.Database
+
+namespace Std
+namespace Time
+
+set_option linter.all true
+
+namespace PlainDateTime
+
+/--
+Get the current time.
+-/
+@[inline]
+def now : IO PlainDateTime := do
+  let tm ← Timestamp.now
+  let rules ← Database.defaultGetLocalZoneRules
+  let ltt := rules.findLocalTimeTypeForTimestamp tm
+
+  return PlainDateTime.ofTimestampAssumingUTC tm |>.addSeconds ltt.getTimeZone.toSeconds
+
+end PlainDateTime
+
+namespace PlainDate
+
+/--
+Get the current date.
+-/
+@[inline]
+def now : IO PlainDate :=
+  PlainDateTime.date <$> PlainDateTime.now
+
+end PlainDate
+namespace PlainTime
+
+/--
+Get the current time.
+-/
+@[inline]
+def now : IO PlainTime :=
+  PlainDateTime.time <$> PlainDateTime.now
+
+end PlainTime
+
+namespace DateTime
+
+/--
+Converts a `PlainDate` with a `TimeZone` to a `DateTime`
+-/
+@[inline]
+def ofPlainDate (pd : PlainDate) (tz : TimeZone) : DateTime tz :=
+  DateTime.ofTimestamp (Timestamp.ofPlainDateAssumingUTC pd) tz
+
+/--
+Converts a `DateTime` to a `PlainDate`
+-/
+@[inline]
+def toPlainDate (dt : DateTime tz) : PlainDate :=
+  Timestamp.toPlainDateAssumingUTC dt.toTimestamp
+
+/--
+Converts a `DateTime` to a `PlainTime`
+-/
+@[inline]
+def toPlainTime (dt : DateTime tz) : PlainTime :=
+  dt.date.get.time
+
+end DateTime
+namespace DateTime
+
+/--
+Gets the current `ZonedDateTime`.
+-/
+@[inline]
+def now : IO (DateTime tz) := do
+  let tm ← Timestamp.now
+  return DateTime.ofTimestamp tm tz
+
+end DateTime
+namespace ZonedDateTime
+
+/--
+Gets the current `ZonedDateTime`.
+-/
+@[inline]
+def now : IO ZonedDateTime := do
+  let tm ← Timestamp.now
+  let rules ← Database.defaultGetLocalZoneRules
+  return ZonedDateTime.ofTimestamp tm rules
+
+/--
+Gets the current `ZonedDateTime` using the identifier of a time zone.
+-/
+@[inline]
+def nowAt (id : String) : IO ZonedDateTime := do
+  let tm ← Timestamp.now
+  let rules ← Database.defaultGetZoneRules id
+  return ZonedDateTime.ofTimestamp tm rules
+
+/--
+Converts a `PlainDate` to a `ZonedDateTime`.
+-/
+@[inline]
+def ofPlainDate (pd : PlainDate) (zr : TimeZone.ZoneRules) : ZonedDateTime :=
+  ZonedDateTime.ofPlainDateTime (pd.atTime PlainTime.midnight) zr
+
+/--
+Converts a `PlainDate` to a `ZonedDateTime` using `TimeZone`.
+-/
+@[inline]
+def ofPlainDateWithZone (pd : PlainDate) (zr : TimeZone) : ZonedDateTime :=
+  ZonedDateTime.ofPlainDateTime (pd.atTime PlainTime.midnight) (TimeZone.ZoneRules.ofTimeZone zr)
+
+/--
+Converts a `ZonedDateTime` to a `PlainDate`
+-/
+@[inline]
+def toPlainDate (dt : ZonedDateTime) : PlainDate :=
+  dt.toPlainDateTime.date
+
+/--
+Converts a `ZonedDateTime` to a `PlainTime`
+-/
+@[inline]
+def toPlainTime (dt : ZonedDateTime) : PlainTime :=
+  dt.toPlainDateTime.time
+
+/--
+Creates a new `ZonedDateTime` out of a `PlainDateTime` and a time zone identifier.
+-/
+@[inline]
+def of (pdt : PlainDateTime) (id : String) : IO ZonedDateTime := do
+  let zr ← Database.defaultGetZoneRules id
+  return ZonedDateTime.ofPlainDateTime pdt zr
+
+end ZonedDateTime
+
+namespace PlainDateTime
+
+/--
+Converts a `PlainDateTime` to a `Timestamp` using the `ZoneRules`.
+-/
+@[inline]
+def toTimestamp (pdt : PlainDateTime) (zr : TimeZone.ZoneRules) : Timestamp :=
+  ZonedDateTime.ofPlainDateTime pdt zr |>.toTimestamp
+
+/--
+Converts a `PlainDateTime` to a `Timestamp` using the `TimeZone`.
+-/
+@[inline]
+def toTimestampWithZone (pdt : PlainDateTime) (tz : TimeZone) : Timestamp :=
+  ZonedDateTime.ofPlainDateTimeWithZone pdt tz |>.toTimestamp
+
+end PlainDateTime
+
+namespace PlainDate
+
+/--
+Converts a `PlainDate` to a `Timestamp` using the `ZoneRules`.
+-/
+@[inline]
+def toTimestamp (dt : PlainDate) (zr : TimeZone.ZoneRules) : Timestamp :=
+  ZonedDateTime.ofPlainDate dt zr |>.toTimestamp
+
+/--
+Converts a `PlainDate` to a `Timestamp` using the `TimeZone`.
+-/
+@[inline]
+def toTimestampWithZone (dt : PlainDate) (tz : TimeZone) : Timestamp :=
+  ZonedDateTime.ofPlainDateWithZone dt tz |>.toTimestamp
+
+end PlainDate

src/Std/Time/Zoned/Database.lean

@@ -0,0 +1,38 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Zoned.ZonedDateTime
+import Std.Time.Zoned.Database.Basic
+import Std.Time.Zoned.Database.TZdb
+import Std.Time.Zoned.Database.Windows
+import Init.System.Platform
+
+namespace Std
+namespace Time
+namespace Database
+open TimeZone.ZoneRules
+
+set_option linter.all true
+
+/--
+Gets the zone rules for a specific time zone identifier, handling Windows and non-Windows platforms.
+In windows it uses the current `icu.h` in Windows SDK. If it's linux or macos then it will use the `tzdata`
+files.
+-/
+def defaultGetZoneRules : String → IO TimeZone.ZoneRules :=
+  if System.Platform.isWindows
+    then getZoneRules WindowsDb.default
+    else getZoneRules TZdb.default
+
+/--
+Gets the local zone rules, accounting for platform differences.
+In windows it uses the current `icu.h` in Windows SDK. If it's linux or macos then it will use the `tzdata`
+files.
+-/
+def defaultGetLocalZoneRules : IO TimeZone.ZoneRules :=
+  if System.Platform.isWindows
+    then getLocalZoneRules WindowsDb.default
+    else getLocalZoneRules TZdb.default

src/Std/Time/Zoned/Database/Basic.lean

@@ -0,0 +1,114 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Zoned.ZoneRules
+import Std.Time.Zoned.Database.TzIf
+
+namespace Std
+namespace Time
+
+set_option linter.all true
+
+/--
+A timezone database from which we can read the `ZoneRules` of some area by it's id.
+-/
+protected class Database (α : Type) where
+
+  /--
+  Retrieves the zone rules information (`ZoneRules`) for a given area at a specific point in time.
+  -/
+  getZoneRules : α → String → IO TimeZone.ZoneRules
+
+  /--
+  Retrieves the local zone rules information (`ZoneRules`) at a given timestamp.
+  -/
+  getLocalZoneRules : α → IO TimeZone.ZoneRules
+
+namespace TimeZone
+
+/--
+Converts a Boolean value to a corresponding `StdWall` type.
+-/
+def convertWall : Bool → StdWall
+  | true => .standard
+  | false => .wall
+
+/--
+Converts a Boolean value to a corresponding `UTLocal` type.
+-/
+def convertUt : Bool → UTLocal
+  | true => .ut
+  | false => .local
+
+/--
+Converts a given time index into a `LocalTimeType` by using a time zone (`tz`) and its identifier.
+-/
+def convertLocalTimeType (index : Nat) (tz : TZif.TZifV1) (identifier : String) : Option LocalTimeType := do
+  let localType ← tz.localTimeTypes.get? index
+  let offset := Offset.ofSeconds <| .ofInt localType.gmtOffset
+  let abbreviation ← tz.abbreviations.getD index (offset.toIsoString true)
+  let wallflag := convertWall (tz.stdWallIndicators.getD index true)
+  let utLocal := convertUt (tz.utLocalIndicators.getD index true)
+
+  return {
+    gmtOffset := offset
+    isDst := localType.isDst
+    abbreviation
+    wall := wallflag
+    utLocal
+    identifier
+  }
+
+/--
+Converts a transition.
+-/
+def convertTransition (times: Array LocalTimeType) (index : Nat) (tz : TZif.TZifV1) : Option Transition := do
+  let time := tz.transitionTimes.get! index
+  let time := Second.Offset.ofInt time
+  let indice := tz.transitionIndices.get! index
+  return { time, localTimeType := times.get! indice.toNat }
+
+/--
+Converts a `TZif.TZifV1` structure to a `ZoneRules` structure.
+-/
+def convertTZifV1 (tz : TZif.TZifV1) (id : String) : Except String ZoneRules := do
+  let mut times : Array LocalTimeType := #[]
+
+  for i in [0:tz.header.typecnt.toNat] do
+    if let some result := convertLocalTimeType i tz id
+      then times := times.push result
+      else .error s!"cannot convert local time {i} of the file"
+
+  let mut transitions := #[]
+
+  for i in [0:tz.transitionTimes.size] do
+    if let some result := convertTransition times i tz
+      then transitions := transitions.push result
+      else .error s!"cannot convert transition {i} of the file"
+
+  -- Local time for timestamps before the first transition is specified by the first time
+  -- type (time type 0).
+
+  let initialLocalTimeType ←
+    if let some res := convertLocalTimeType 0 tz id
+      then .ok res
+      else .error s!"empty transitions for {id}"
+
+  .ok { transitions, initialLocalTimeType }
+
+/--
+Converts a `TZif.TZifV2` structure to a `ZoneRules` structure.
+-/
+def convertTZifV2 (tz : TZif.TZifV2) (id : String) : Except String ZoneRules := do
+   convertTZifV1 tz.toTZifV1 id
+
+/--
+Converts a `TZif.TZif` structure to a `ZoneRules` structure.
+-/
+def convertTZif (tz : TZif.TZif) (id : String) : Except String ZoneRules := do
+  if let some v2 := tz.v2
+    then convertTZifV2 v2 id
+    else convertTZifV1 tz.v1 id

src/Std/Time/Zoned/Database/TZdb.lean

@@ -0,0 +1,92 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.DateTime
+import Std.Time.Zoned.TimeZone
+import Std.Time.Zoned.ZoneRules
+import Std.Time.Zoned.Database.Basic
+
+namespace Std
+namespace Time
+namespace Database
+
+set_option linter.all true
+
+/--
+Represents a Time Zone Database (TZdb) configuration with paths to local and general timezone data.
+-/
+structure TZdb where
+
+  /--
+  The path to the local timezone file. This is typically a symlink to a file within the timezone
+  database that corresponds to the current local time zone.
+  -/
+  localPath : System.FilePath := "/etc/localtime"
+
+  /--
+  The path to the directory containing all available time zone files. These files define various
+  time zones and their rules.
+  -/
+  zonesPath : System.FilePath := "/usr/share/zoneinfo/"
+
+namespace TZdb
+open TimeZone
+
+/--
+Returns a default `TZdb` instance with common timezone data paths for most Linux distributions and macOS.
+-/
+@[inline]
+def default : TZdb := {}
+
+/--
+Parses binary timezone data into zone rules based on a given timezone ID.
+-/
+def parseTZif (bin : ByteArray) (id : String) : Except String ZoneRules := do
+  let database ← TZif.parse.run bin
+  convertTZif database id
+
+/--
+Reads a TZif file from disk and retrieves the zone rules for the specified timezone ID.
+-/
+def parseTZIfFromDisk (path : System.FilePath) (id : String) : IO ZoneRules := do
+  let binary ← try IO.FS.readBinFile path catch _ => throw <| IO.userError s!"cannot find {id} in the local timezone database"
+  IO.ofExcept (parseTZif binary id)
+
+/--
+Extracts a timezone ID from a file path.
+-/
+def idFromPath (path : System.FilePath) : Option String := do
+  let res := path.components.toArray
+  let last ← res.get? (res.size - 1)
+  let last₁ ← res.get? (res.size - 2)
+
+  if last₁ = some "zoneinfo"
+    then last
+    else last₁ ++ "/" ++ last
+
+/--
+Retrieves the timezone rules from the local timezone data file.
+-/
+def localRules (path : System.FilePath) : IO ZoneRules := do
+  let localTimePath ←
+    try
+      IO.Process.run { cmd := "readlink", args := #["-f", path.toString] }
+    catch _ =>
+      throw <| IO.userError "cannot find the local timezone database"
+
+  if let some id := idFromPath localTimePath
+    then parseTZIfFromDisk path id
+    else throw (IO.userError "cannot read the id of the path.")
+
+/--
+Reads timezone rules from disk based on the provided file path and timezone ID.
+-/
+def readRulesFromDisk (path : System.FilePath) (id : String) : IO ZoneRules := do
+  parseTZIfFromDisk (System.FilePath.join path id) id
+
+instance : Std.Time.Database TZdb where
+  getLocalZoneRules db := localRules db.localPath
+  getZoneRules db id := readRulesFromDisk db.zonesPath id

src/Std/Time/Zoned/Database/TzIf.lean

@@ -0,0 +1,328 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Init.Data.Range
+import Std.Internal.Parsec
+import Std.Internal.Parsec.ByteArray
+
+-- Based on: https://www.rfc-editor.org/rfc/rfc8536.html
+
+namespace Std
+namespace Time
+namespace TimeZone
+namespace TZif
+open Std.Internal.Parsec Std.Internal.Parsec.ByteArray
+
+set_option linter.all true
+
+private abbrev Int32 := Int
+
+private abbrev Int64 := Int
+
+/--
+Represents the header of a TZif file, containing metadata about the file's structure.
+-/
+structure Header where
+
+  /--
+  The version of the TZif file format.
+  -/
+  version : UInt8
+
+  /--
+  The count of UT local indicators in the file.
+  -/
+  isutcnt : UInt32
+
+  /--
+  The count of standard/wall indicators in the file.
+  -/
+  isstdcnt : UInt32
+
+  /--
+  The number of leap second records.
+  -/
+  leapcnt : UInt32
+
+  /--
+  The number of transition times in the file.
+  -/
+  timecnt : UInt32
+
+  /--
+  The number of local time types in the file.
+  -/
+  typecnt : UInt32
+
+  /--
+  The total number of characters used in abbreviations.
+  -/
+  charcnt : UInt32
+  deriving Repr, Inhabited
+
+/--
+Represents the local time type information, including offset and daylight saving details.
+-/
+structure LocalTimeType where
+
+  /--
+  The GMT offset in seconds for this local time type.
+  -/
+  gmtOffset : Int32
+
+  /--
+  Indicates if this local time type observes daylight saving time.
+  -/
+  isDst : Bool
+
+  /--
+  The index into the abbreviation string table for this time type.
+  -/
+  abbreviationIndex : UInt8
+  deriving Repr, Inhabited
+
+/--
+Represents a leap second record, including the transition time and the correction applied.
+-/
+structure LeapSecond where
+
+  /--
+  The transition time of the leap second event.
+  -/
+  transitionTime : Int64
+
+  /--
+  The correction applied during the leap second event in seconds.
+  -/
+  correction : Int64
+  deriving Repr, Inhabited
+
+/--
+Represents version 1 of the TZif format.
+-/
+structure TZifV1 where
+
+  /--
+  The header information of the TZif file.
+  -/
+  header : Header
+
+  /--
+  The array of transition times in seconds since the epoch.
+  -/
+  transitionTimes : Array Int32
+
+  /--
+  The array of local time type indices corresponding to each transition time.
+  -/
+  transitionIndices : Array UInt8
+
+  /--
+  The array of local time type structures.
+  -/
+  localTimeTypes : Array LocalTimeType
+
+  /--
+  The array of abbreviation strings used by local time types.
+  -/
+  abbreviations : Array String
+
+  /--
+  The array of leap second records.
+  -/
+  leapSeconds : Array LeapSecond
+
+  /--
+  The array indicating whether each transition time uses wall clock time or standard time.
+  -/
+  stdWallIndicators : Array Bool
+
+  /--
+  The array indicating whether each transition time uses universal time or local time.
+  -/
+  utLocalIndicators : Array Bool
+  deriving Repr, Inhabited
+
+/--
+Represents version 2 of the TZif format, extending TZifV1 with an optional footer.
+-/
+structure TZifV2 extends TZifV1 where
+
+  /--
+  An optional footer for additional metadata in version 2.
+  -/
+  footer : Option String
+  deriving Repr, Inhabited
+
+/--
+Represents a TZif file, which can be either version 1 or version 2.
+-/
+structure TZif where
+
+  /--
+  The data for version 1 of the TZif file.
+  -/
+  v1 : TZifV1
+
+  /--
+  Optionally, the data for version 2 of the TZif file.
+  -/
+  v2 : Option TZifV2
+  deriving Repr, Inhabited
+
+private def toUInt32 (bs : ByteArray) : UInt32 :=
+  assert! bs.size == 4
+  (bs.get! 0).toUInt32 <<< 0x18 |||
+  (bs.get! 1).toUInt32 <<< 0x10 |||
+  (bs.get! 2).toUInt32 <<< 0x8  |||
+  (bs.get! 3).toUInt32
+
+private def toInt32 (bs : ByteArray) : Int32 :=
+  let n := toUInt32 bs |>.toNat
+  if n < (1 <<< 31)
+    then Int.ofNat n
+    else Int.negOfNat (UInt32.size - n)
+
+private def toInt64 (bs : ByteArray) : Int64 :=
+  let n := ByteArray.toUInt64BE! bs |>.toNat
+  if n < (1 <<< 63)
+    then Int.ofNat n
+    else Int.negOfNat (UInt64.size - n)
+
+private def manyN (n : Nat) (p : Parser α) : Parser (Array α) := do
+  let mut result := #[]
+  for _ in [0:n] do
+    let x ← p
+    result := result.push x
+  return result
+
+private def pu64 : Parser UInt64 := ByteArray.toUInt64LE! <$> take 8
+private def pi64 : Parser Int64 := toInt64 <$> take 8
+private def pu32 : Parser UInt32 := toUInt32 <$> take 4
+private def pi32 : Parser Int32 := toInt32 <$> take 4
+private def pu8 : Parser UInt8 := any
+private def pbool : Parser Bool := (· != 0) <$> pu8
+
+private def parseHeader : Parser Header :=
+  Header.mk
+    <$> (pstring "TZif" *> pu8)
+    <*> (take 15 *> pu32)
+    <*> pu32
+    <*> pu32
+    <*> pu32
+    <*> pu32
+    <*> pu32
+
+private def parseLocalTimeType : Parser LocalTimeType :=
+  LocalTimeType.mk
+    <$> pi32
+    <*> pbool
+    <*> pu8
+
+private def parseLeapSecond (p : Parser Int) : Parser LeapSecond :=
+  LeapSecond.mk
+    <$> p
+    <*> pi32
+
+private def parseTransitionTimes (size : Parser Int32) (n : UInt32) : Parser (Array Int32) :=
+  manyN (n.toNat) size
+
+private def parseTransitionIndices (n : UInt32) : Parser (Array UInt8) :=
+  manyN (n.toNat) pu8
+
+private def parseLocalTimeTypes (n : UInt32) : Parser (Array LocalTimeType) :=
+  manyN (n.toNat) parseLocalTimeType
+
+private def parseAbbreviations (times : Array LocalTimeType) (n : UInt32) : Parser (Array String) := do
+  let mut strings := #[]
+  let mut current := ""
+  let mut chars ← manyN n.toNat pu8
+
+  for time in times do
+    for indx in [time.abbreviationIndex.toNat:n.toNat] do
+      let char := chars.get! indx
+      if char = 0 then
+        strings := strings.push current
+        current := ""
+        break
+      else
+        current := current.push (Char.ofUInt8 char)
+
+  return strings
+
+private def parseLeapSeconds (size : Parser Int) (n : UInt32) : Parser (Array LeapSecond) :=
+  manyN (n.toNat) (parseLeapSecond size)
+
+private def parseIndicators (n : UInt32) : Parser (Array Bool) :=
+  manyN (n.toNat) pbool
+
+private def parseTZifV1 : Parser TZifV1 := do
+  let header ← parseHeader
+
+  let transitionTimes ← parseTransitionTimes pi32 header.timecnt
+  let transitionIndices ← parseTransitionIndices header.timecnt
+  let localTimeTypes ← parseLocalTimeTypes header.typecnt
+  let abbreviations ← parseAbbreviations localTimeTypes header.charcnt
+  let leapSeconds ← parseLeapSeconds pi32 header.leapcnt
+  let stdWallIndicators ← parseIndicators header.isstdcnt
+  let utLocalIndicators ← parseIndicators header.isutcnt
+
+  return {
+      header
+      transitionTimes
+      transitionIndices
+      localTimeTypes
+      abbreviations
+      leapSeconds
+      stdWallIndicators
+      utLocalIndicators
+  }
+
+private def parseFooter : Parser (Option String) := do
+  let char ← pu8
+
+  if char = 0x0A then pure () else return none
+
+  let tzString ← many (satisfy (· ≠ 0x0A))
+  let mut str := ""
+
+  for byte in tzString do
+    str := str.push (Char.ofUInt8 byte)
+
+  return str
+
+private def parseTZifV2 : Parser (Option TZifV2) := optional do
+  let header ← parseHeader
+
+  let transitionTimes ← parseTransitionTimes pi64 header.timecnt
+  let transitionIndices ← parseTransitionIndices header.timecnt
+  let localTimeTypes ← parseLocalTimeTypes header.typecnt
+  let abbreviations ← parseAbbreviations localTimeTypes header.charcnt
+  let leapSeconds ← parseLeapSeconds pi64 header.leapcnt
+  let stdWallIndicators ← parseIndicators header.isstdcnt
+  let utLocalIndicators ← parseIndicators header.isutcnt
+
+  return {
+      header
+      transitionTimes
+      transitionIndices
+      localTimeTypes
+      abbreviations
+      leapSeconds
+      stdWallIndicators
+      utLocalIndicators
+      footer := ← parseFooter
+  }
+
+/--
+Parses a TZif file, which may be in either version 1 or version 2 format.
+-/
+def parse : Parser TZif := do
+  let v1 ← parseTZifV1
+  let v2 ← parseTZifV2
+  return { v1, v2 }
+
+end TZif

src/Std/Time/Zoned/Database/Windows.lean

@@ -0,0 +1,89 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.DateTime
+import Std.Time.Zoned.TimeZone
+import Std.Time.Zoned.ZoneRules
+import Std.Time.Zoned.Database.Basic
+
+namespace Std
+namespace Time
+namespace Database
+
+set_option linter.all true
+
+namespace Windows
+
+/--
+Fetches the next timezone transition for a given timezone identifier and timestamp.
+-/
+@[extern "lean_windows_get_next_transition"]
+opaque getNextTransition : @&String → Int64 → Bool → IO (Option (Int64 × TimeZone))
+
+/--
+Fetches the timezone at a timestamp.
+-/
+@[extern "lean_get_windows_local_timezone_id_at"]
+opaque getLocalTimeZoneIdentifierAt : Int64 → IO String
+
+/--
+Retrieves the timezone rules, including all transitions, for a given timezone identifier.
+-/
+def getZoneRules (id : String) : IO TimeZone.ZoneRules := do
+  let mut start := -2147483648
+  let mut transitions : Array TimeZone.Transition := #[]
+
+  let mut initialLocalTimeType ←
+    if let some res := ← Windows.getNextTransition id start true
+      then pure (toLocalTime res.snd)
+      else throw (IO.userError "cannot find first transition in zone rules")
+
+  while true do
+    let result ← Windows.getNextTransition id start false
+
+    if let some res := result then
+      transitions := transitions.push { time := Second.Offset.ofInt start.toInt, localTimeType := toLocalTime res.snd }
+
+      -- Avoid zone rules for more than year 3000
+      if res.fst ≤ start ∨ res.fst >= 32503690800 then
+        break
+
+      start := res.fst
+    else
+      break
+
+  return { transitions, initialLocalTimeType }
+
+  where
+    toLocalTime (res : TimeZone) : TimeZone.LocalTimeType :=
+      {
+        gmtOffset := res.offset,
+        abbreviation := res.abbreviation,
+        identifier := res.name,
+        isDst := res.isDST,
+        wall := .wall,
+        utLocal := .local
+      }
+
+end Windows
+
+/--
+Represents a Time Zone Database that we get from ICU available on Windows SDK.
+-/
+structure WindowsDb where
+
+namespace WindowsDb
+open TimeZone
+
+/--
+Returns a default `WindowsDb` instance.
+-/
+@[inline]
+def default : WindowsDb := {}
+
+instance : Std.Time.Database WindowsDb where
+  getZoneRules _ id := Windows.getZoneRules id
+  getLocalZoneRules _ := Windows.getZoneRules =<< Windows.getLocalTimeZoneIdentifierAt (-2147483648)

src/Std/Time/Zoned/DateTime.lean

@@ -0,0 +1,516 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.DateTime
+import Std.Time.Zoned.TimeZone
+import Std.Internal
+
+namespace Std
+namespace Time
+open Internal
+
+set_option linter.all true
+
+/--
+Represents a specific point in time associated with a `TimeZone`.
+-/
+structure DateTime (tz : TimeZone) where
+  private mk ::
+
+  /--
+  `Timestamp` represents the exact moment in time. It's a UTC related `Timestamp`.
+  -/
+  timestamp : Timestamp
+
+  /--
+  `Date` is a `Thunk` containing the `PlainDateTime` that represents the local date and time, it's
+  used for accessing data like `day` and `month` without having to recompute the data everytime.
+  -/
+  date : Thunk PlainDateTime
+
+instance : BEq (DateTime tz) where
+  beq x y := x.timestamp == y.timestamp
+
+instance : Inhabited (DateTime tz) where
+  default := ⟨Inhabited.default, Thunk.mk fun _ => Inhabited.default⟩
+
+namespace DateTime
+
+/--
+Creates a new `DateTime` out of a `Timestamp` that is in a `TimeZone`.
+-/
+@[inline]
+def ofTimestamp (tm : Timestamp) (tz : TimeZone) : DateTime tz :=
+  DateTime.mk tm (Thunk.mk fun _ => tm.toPlainDateTimeAssumingUTC |>.addSeconds tz.toSeconds)
+
+/--
+Converts a `DateTime` to the number of days since the UNIX epoch.
+-/
+def toDaysSinceUNIXEpoch (date : DateTime tz) : Day.Offset :=
+  date.date.get.toDaysSinceUNIXEpoch
+
+/--
+Creates a `Timestamp` out of a `DateTime`.
+-/
+@[inline]
+def toTimestamp (date : DateTime tz) : Timestamp :=
+  date.timestamp
+
+/--
+Changes the `TimeZone` to a new one.
+-/
+@[inline]
+def convertTimeZone (date : DateTime tz) (tz₁ : TimeZone) : DateTime tz₁ :=
+  ofTimestamp date.timestamp tz₁
+
+/--
+Creates a new `DateTime` out of a `PlainDateTime`. It assumes that the `PlainDateTime` is relative
+to UTC.
+-/
+@[inline]
+def ofPlainDateTimeAssumingUTC (date : PlainDateTime) (tz : TimeZone) : DateTime tz :=
+  let tm := Timestamp.ofPlainDateTimeAssumingUTC date
+  DateTime.mk tm (Thunk.mk fun _ => date.addSeconds tz.toSeconds)
+
+/--
+Creates a new `DateTime` from a `PlainDateTime`, assuming that the `PlainDateTime`
+is relative to the given `TimeZone`.
+-/
+@[inline]
+def ofPlainDateTime (date : PlainDateTime) (tz : TimeZone) : DateTime tz :=
+  let tm := date.subSeconds tz.toSeconds
+  DateTime.mk (Timestamp.ofPlainDateTimeAssumingUTC tm) (Thunk.mk fun _ => date)
+
+/--
+Add `Hour.Offset` to a `DateTime`.
+-/
+@[inline]
+def addHours (dt : DateTime tz) (hours : Hour.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.addHours hours) tz
+
+/--
+Subtract `Hour.Offset` from a `DateTime`.
+-/
+@[inline]
+def subHours (dt : DateTime tz) (hours : Hour.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.subHours hours) tz
+
+/--
+Add `Minute.Offset` to a `DateTime`.
+-/
+@[inline]
+def addMinutes (dt : DateTime tz) (minutes : Minute.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.addMinutes minutes) tz
+
+/--
+Subtract `Minute.Offset` from a `DateTime`.
+-/
+@[inline]
+def subMinutes (dt : DateTime tz) (minutes : Minute.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.subMinutes minutes) tz
+
+/--
+Add `Second.Offset` to a `DateTime`.
+-/
+@[inline]
+def addSeconds (dt : DateTime tz) (seconds : Second.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.addSeconds seconds) tz
+
+/--
+Subtract `Second.Offset` from a `DateTime`.
+-/
+@[inline]
+def subSeconds (dt : DateTime tz) (seconds : Second.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.subSeconds seconds) tz
+
+/--
+Add `Millisecond.Offset` to a `DateTime`.
+-/
+@[inline]
+def addMilliseconds (dt : DateTime tz) (milliseconds : Millisecond.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.addMilliseconds milliseconds) tz
+
+/--
+Subtract `Millisecond.Offset` from a `DateTime`.
+-/
+@[inline]
+def subMilliseconds (dt : DateTime tz) (milliseconds : Millisecond.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.subMilliseconds milliseconds) tz
+
+/--
+Add `Nanosecond.Offset` to a `DateTime`.
+-/
+@[inline]
+def addNanoseconds (dt : DateTime tz) (nanoseconds : Nanosecond.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.addNanoseconds nanoseconds) tz
+
+/--
+Subtract `Nanosecond.Offset` from a `DateTime`.
+-/
+@[inline]
+def subNanoseconds (dt : DateTime tz) (nanoseconds : Nanosecond.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.subNanoseconds nanoseconds) tz
+
+/--
+Add `Day.Offset` to a `DateTime`.
+-/
+@[inline]
+def addDays (dt : DateTime tz) (days : Day.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.addDays days) tz
+
+/--
+Subtracts `Day.Offset` to a `DateTime`.
+-/
+@[inline]
+def subDays (dt : DateTime tz) (days : Day.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.subDays days) tz
+
+/--
+Add `Week.Offset` to a `DateTime`.
+-/
+@[inline]
+def addWeeks (dt : DateTime tz) (weeks : Week.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.addWeeks weeks) tz
+
+/--
+Subtracts `Week.Offset` to a `DateTime`.
+-/
+@[inline]
+def subWeeks (dt : DateTime tz) (weeks : Week.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.subWeeks weeks) tz
+
+/--
+Add `Month.Offset` to a `DateTime`, it clips the day to the last valid day of that month.
+-/
+def addMonthsClip (dt : DateTime tz) (months : Month.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.addMonthsClip months) tz
+
+/--
+Subtracts `Month.Offset` from a `DateTime`, it clips the day to the last valid day of that month.
+-/
+@[inline]
+def subMonthsClip (dt : DateTime tz) (months : Month.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.subMonthsClip months) tz
+
+/--
+Add `Month.Offset` from a `DateTime`, this function rolls over any excess days into the following
+month.
+-/
+def addMonthsRollOver (dt : DateTime tz) (months : Month.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.addMonthsRollOver months) tz
+
+/--
+Subtract `Month.Offset` from a `DateTime`, this function rolls over any excess days into the following
+month.
+-/
+@[inline]
+def subMonthsRollOver (dt : DateTime tz) (months : Month.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.subMonthsRollOver months) tz
+
+/--
+Add `Year.Offset` to a `DateTime`, this function rolls over any excess days into the following
+month.
+-/
+@[inline]
+def addYearsRollOver (dt : DateTime tz) (years : Year.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.addYearsRollOver years) tz
+
+/--
+Add `Year.Offset` to a `DateTime`, it clips the day to the last valid day of that month.
+-/
+@[inline]
+def addYearsClip (dt : DateTime tz) (years : Year.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.addYearsClip years) tz
+
+/--
+Subtract `Year.Offset` from a `DateTime`, this function rolls over any excess days into the following
+month.
+-/
+@[inline]
+def subYearsRollOver (dt : DateTime tz) (years : Year.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.subYearsRollOver years) tz
+
+/--
+Subtract `Year.Offset` from to a `DateTime`, it clips the day to the last valid day of that month.
+-/
+@[inline]
+def subYearsClip (dt : DateTime tz) (years : Year.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.subYearsClip years) tz
+
+/--
+Creates a new `DateTime tz` by adjusting the day of the month to the given `days` value, with any
+out-of-range days clipped to the nearest valid date.
+-/
+@[inline]
+def withDaysClip (dt : DateTime tz) (days : Day.Ordinal) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.withDaysClip days) tz
+
+/--
+Creates a new `DateTime tz` by adjusting the day of the month to the given `days` value, with any
+out-of-range days rolled over to the next month or year as needed.
+-/
+@[inline]
+def withDaysRollOver (dt : DateTime tz) (days : Day.Ordinal) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.withDaysRollOver days) tz
+
+/--
+Creates a new `DateTime tz` by adjusting the month to the given `month` value.
+The day remains unchanged, and any invalid days for the new month will be handled according to the `clip` behavior.
+-/
+@[inline]
+def withMonthClip (dt : DateTime tz) (month : Month.Ordinal) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.withMonthClip month) tz
+
+/--
+Creates a new `DateTime tz` by adjusting the month to the given `month` value.
+The day is rolled over to the next valid month if necessary.
+-/
+@[inline]
+def withMonthRollOver (dt : DateTime tz) (month : Month.Ordinal) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.withMonthRollOver month) tz
+
+/--
+Creates a new `DateTime tz` by adjusting the year to the given `year` value. The month and day remain unchanged,
+and any invalid days for the new year will be handled according to the `clip` behavior.
+-/
+@[inline]
+def withYearClip (dt : DateTime tz) (year : Year.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.withYearClip year) tz
+
+/--
+Creates a new `DateTime tz` by adjusting the year to the given `year` value. The month and day are rolled
+over to the next valid month and day if necessary.
+-/
+@[inline]
+def withYearRollOver (dt : DateTime tz) (year : Year.Offset) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.withYearRollOver year) tz
+
+/--
+Creates a new `DateTime tz` by adjusting the `hour` component.
+-/
+@[inline]
+def withHours (dt : DateTime tz) (hour : Hour.Ordinal) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.withHours hour) tz
+
+/--
+Creates a new `DateTime tz` by adjusting the `minute` component.
+-/
+@[inline]
+def withMinutes (dt : DateTime tz) (minute : Minute.Ordinal) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.withMinutes minute) tz
+
+/--
+Creates a new `DateTime tz` by adjusting the `second` component.
+-/
+@[inline]
+def withSeconds (dt : DateTime tz) (second : Sigma Second.Ordinal) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.withSeconds second) tz
+
+/--
+Creates a new `DateTime tz` by adjusting the `nano` component.
+-/
+@[inline]
+def withNanoseconds (dt : DateTime tz) (nano : Nanosecond.Ordinal) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.withNanoseconds nano) tz
+
+/--
+Creates a new `DateTime tz` by adjusting the `millisecond` component.
+-/
+@[inline]
+def withMilliseconds (dt : DateTime tz) (milli : Millisecond.Ordinal) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.withMilliseconds milli) tz
+
+/--
+Converts a `Timestamp` to a `PlainDateTime`
+-/
+@[inline]
+def toPlainDateTime (dt : DateTime tz) : PlainDateTime :=
+  dt.date.get
+
+/--
+Getter for the `Year` inside of a `DateTime`
+-/
+@[inline]
+def year (dt : DateTime tz) : Year.Offset :=
+  dt.date.get.year
+
+/--
+Getter for the `Month` inside of a `DateTime`
+-/
+@[inline]
+def month (dt : DateTime tz) : Month.Ordinal :=
+  dt.date.get.month
+
+/--
+Getter for the `Day` inside of a `DateTime`
+-/
+@[inline]
+def day (dt : DateTime tz) : Day.Ordinal :=
+  dt.date.get.day
+
+/--
+Getter for the `Hour` inside of a `DateTime`
+-/
+@[inline]
+def hour (dt : DateTime tz) : Hour.Ordinal :=
+  dt.date.get.hour
+
+/--
+Getter for the `Minute` inside of a `DateTime`
+-/
+@[inline]
+def minute (dt : DateTime tz) : Minute.Ordinal :=
+  dt.date.get.minute
+
+/--
+Getter for the `Second` inside of a `DateTime`
+-/
+@[inline]
+def second (dt : DateTime tz) : Second.Ordinal dt.date.get.time.second.fst :=
+  dt.date.get.second
+
+/--
+Getter for the `Milliseconds` inside of a `DateTime`
+-/
+@[inline]
+def millisecond (dt : DateTime tz) : Millisecond.Ordinal :=
+  dt.date.get.time.nanosecond.emod 1000 (by decide)
+
+/--
+Getter for the `Nanosecond` inside of a `DateTime`
+-/
+@[inline]
+def nanosecond (dt : DateTime tz) : Nanosecond.Ordinal :=
+  dt.date.get.time.nanosecond
+
+/--
+Gets the `Weekday` of a DateTime.
+-/
+@[inline]
+def weekday (dt : DateTime tz) : Weekday :=
+  dt.date.get.date.weekday
+
+/--
+Determines the era of the given `DateTime` based on its year.
+-/
+def era (date : DateTime tz) : Year.Era :=
+  date.year.era
+
+/--
+Sets the `DateTime` to the specified `desiredWeekday`.
+-/
+def withWeekday (dt : DateTime tz) (desiredWeekday : Weekday) : DateTime tz :=
+  ofPlainDateTime (dt.date.get.withWeekday desiredWeekday) tz
+
+/--
+Checks if the `DateTime` is in a leap year.
+-/
+def inLeapYear (date : DateTime tz) : Bool :=
+  date.year.isLeap
+
+/--
+Determines the ordinal day of the year for the given `DateTime`.
+-/
+def dayOfYear (date : DateTime tz) : Day.Ordinal.OfYear date.year.isLeap :=
+  ValidDate.dayOfYear ⟨⟨date.month, date.day⟩, date.date.get.date.valid⟩
+
+/--
+Determines the week of the year for the given `DateTime`.
+-/
+@[inline]
+def weekOfYear (date : DateTime tz) : Week.Ordinal :=
+  date.date.get.weekOfYear
+
+/--
+Returns the unaligned week of the month for a `DateTime` (day divided by 7, plus 1).
+-/
+def weekOfMonth (date : DateTime tz) : Bounded.LE 1 5 :=
+  date.date.get.weekOfMonth
+
+/--
+Determines the week of the month for the given `DateTime`. The week of the month is calculated based
+on the day of the month and the weekday. Each week starts on Monday because the entire library is
+based on the Gregorian Calendar.
+-/
+@[inline]
+def alignedWeekOfMonth (date : DateTime tz) : Week.Ordinal.OfMonth :=
+  date.date.get.alignedWeekOfMonth
+
+/--
+Determines the quarter of the year for the given `DateTime`.
+-/
+@[inline]
+def quarter (date : DateTime tz) : Bounded.LE 1 4 :=
+  date.date.get.quarter
+
+/--
+Getter for the `PlainTime` inside of a `DateTime`
+-/
+@[inline]
+def time (zdt : DateTime tz) : PlainTime :=
+  zdt.date.get.time
+
+/--
+Converts a `DateTime` to the number of days since the UNIX epoch.
+-/
+@[inline]
+def ofDaysSinceUNIXEpoch (days : Day.Offset) (time : PlainTime) (tz : TimeZone) : DateTime tz :=
+  DateTime.ofPlainDateTime (PlainDateTime.ofDaysSinceUNIXEpoch days time) tz
+
+instance : HAdd (DateTime tz) (Day.Offset) (DateTime tz) where
+  hAdd := addDays
+
+instance : HSub (DateTime tz) (Day.Offset) (DateTime tz) where
+  hSub := subDays
+
+instance : HAdd (DateTime tz) (Week.Offset) (DateTime tz) where
+  hAdd := addWeeks
+
+instance : HSub (DateTime tz) (Week.Offset) (DateTime tz) where
+  hSub := subWeeks
+
+instance : HAdd (DateTime tz) (Hour.Offset) (DateTime tz) where
+  hAdd := addHours
+
+instance : HSub (DateTime tz) (Hour.Offset) (DateTime tz) where
+  hSub := subHours
+
+instance : HAdd (DateTime tz) (Minute.Offset) (DateTime tz) where
+  hAdd := addMinutes
+
+instance : HSub (DateTime tz) (Minute.Offset) (DateTime tz) where
+  hSub := subMinutes
+
+instance : HAdd (DateTime tz) (Second.Offset) (DateTime tz) where
+  hAdd := addSeconds
+
+instance : HSub (DateTime tz) (Second.Offset) (DateTime tz) where
+  hSub := subSeconds
+
+instance : HAdd (DateTime tz) (Millisecond.Offset) (DateTime tz) where
+  hAdd := addMilliseconds
+
+instance : HSub (DateTime tz) (Millisecond.Offset) (DateTime tz) where
+  hSub := subMilliseconds
+
+instance : HAdd (DateTime tz) (Nanosecond.Offset) (DateTime tz) where
+  hAdd := addNanoseconds
+
+instance : HSub (DateTime tz) (Nanosecond.Offset) (DateTime tz) where
+  hSub := subNanoseconds
+
+instance : HSub (DateTime tz) (DateTime tz₁) Duration where
+  hSub x y := x.toTimestamp - y.toTimestamp
+
+instance : HAdd (DateTime tz) Duration (DateTime tz) where
+  hAdd x y := x.addNanoseconds y.toNanoseconds
+
+instance : HSub (DateTime tz) Duration (DateTime tz) where
+  hSub x y := x.subNanoseconds y.toNanoseconds
+
+end DateTime
+end Time
+end Std

src/Std/Time/Zoned/Offset.lean

@@ -0,0 +1,74 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Time
+
+namespace Std
+namespace Time
+namespace TimeZone
+open Internal
+
+set_option linter.all true
+
+/--
+Represents a timezone offset with an hour and second component.
+-/
+structure Offset where
+
+  /--
+  Creates an `Offset` from a given number of seconds.
+  -/
+  ofSeconds ::
+
+  /--
+  The same timezone offset in seconds.
+  -/
+  second : Second.Offset
+  deriving Repr
+
+instance : Inhabited Offset where
+  default := ⟨0⟩
+
+instance : BEq Offset where
+  beq x y := BEq.beq x.second y.second
+
+namespace Offset
+
+/--
+Converts an `Offset` to a string in ISO 8601 format. The `colon` parameter determines if the hour
+and minute components are separated by a colon (e.g., "+01:00" or "+0100").
+-/
+def toIsoString (offset : Offset) (colon : Bool) : String :=
+  let (sign, time) := if offset.second.val ≥ 0 then ("+", offset.second) else ("-", -offset.second)
+  let hour : Hour.Offset := time.ediv 3600
+  let minute := Int.ediv (Int.tmod time.val 3600) 60
+  let hourStr := if hour.val < 10 then s!"0{hour.val}" else toString hour.val
+  let minuteStr := if minute < 10 then s!"0{minute}" else toString minute
+    if colon then s!"{sign}{hourStr}:{minuteStr}"
+    else s!"{sign}{hourStr}{minuteStr}"
+
+/--
+A zero `Offset` representing UTC (no offset).
+-/
+def zero : Offset :=
+  { second := 0 }
+
+/--
+Creates an `Offset` from a given number of hour.
+-/
+def ofHours (n : Hour.Offset) : Offset :=
+  ofSeconds n.toSeconds
+
+/--
+Creates an `Offset` from a given number of hours and minutes.
+-/
+def ofHoursAndMinutes (n : Hour.Offset) (m : Minute.Offset) : Offset :=
+  ofSeconds (n.toSeconds + m.toSeconds)
+
+end Offset
+end TimeZone
+end Time
+end Std

src/Std/Time/Zoned/TimeZone.lean

@@ -0,0 +1,71 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Zoned.Offset
+
+namespace Std
+namespace Time
+
+set_option linter.all true
+
+/--
+A TimeZone structure that stores the timezone offset, the name, abbreviation and if it's in daylight
+saving time.
+-/
+structure TimeZone where
+
+  /--
+  The `Offset` of the date time.
+  -/
+  offset : TimeZone.Offset
+
+  /--
+  The name of the time zone.
+  -/
+  name : String
+
+  /--
+  The abbreviation of the time zone.
+  -/
+  abbreviation : String
+
+  /--
+  Day light saving flag.
+  -/
+  isDST : Bool
+  deriving Inhabited, Repr, BEq
+
+namespace TimeZone
+
+/--
+A zeroed `Timezone` representing UTC (no offset).
+-/
+def UTC : TimeZone :=
+  TimeZone.mk (Offset.zero) "UTC" "UTC" false
+
+/--
+A zeroed `Timezone` representing GMT (no offset).
+-/
+def GMT : TimeZone :=
+  TimeZone.mk (Offset.zero) "Greenwich Mean Time" "GMT" false
+
+/--
+Creates a `Timestamp` from a given number of hour.
+-/
+def ofHours (name : String) (abbreviation : String) (n : Hour.Offset) (isDST : Bool := false) : TimeZone :=
+  TimeZone.mk (Offset.ofHours n) name abbreviation isDST
+
+/--
+Creates a `Timestamp` from a given number of second.
+-/
+def ofSeconds (name : String) (abbreviation : String) (n : Second.Offset) (isDST : Bool := false) : TimeZone :=
+  TimeZone.mk (Offset.ofSeconds n) name abbreviation isDST
+
+/--
+Gets the number of seconds in a timezone offset.
+-/
+def toSeconds (tz : TimeZone) : Second.Offset :=
+  tz.offset.second

src/Std/Time/Zoned/ZoneRules.lean

@@ -0,0 +1,225 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.DateTime
+import Std.Time.Zoned.TimeZone
+
+namespace Std
+namespace Time
+namespace TimeZone
+open Internal
+
+set_option linter.all true
+
+/--
+Represents the type of local time in relation to UTC.
+-/
+inductive UTLocal
+  /--
+  Universal Time (UT), often referred to as UTC.
+  -/
+  | ut
+
+  /--
+  Local time that is not necessarily UTC.
+  -/
+  | local
+  deriving Repr, Inhabited
+
+/--
+Represents types of wall clocks or standard times.
+-/
+inductive StdWall
+  /--
+  Time based on a wall clock, which can include daylight saving adjustments.
+  -/
+  | wall
+
+  /--
+  Standard time without adjustments for daylight saving.
+  -/
+  | standard
+  deriving Repr, Inhabited
+
+/--
+Represents a type of local time, including offset and daylight saving information.
+-/
+structure LocalTimeType where
+
+  /--
+  The offset from GMT for this local time.
+  -/
+  gmtOffset : TimeZone.Offset
+
+  /--
+  Indicates if daylight saving time is observed.
+  -/
+  isDst : Bool
+
+  /--
+  The abbreviation for this local time type (e.g., "EST", "PDT").
+  -/
+  abbreviation : String
+
+  /--
+  Indicates if the time is wall clock or standard time.
+  -/
+  wall : StdWall
+
+  /--
+  Distinguishes between universal time and local time.
+  -/
+  utLocal : UTLocal
+
+  /--
+  ID of the timezone
+  -/
+  identifier : String
+  deriving Repr, Inhabited
+
+namespace LocalTimeType
+
+/--
+Gets the `TimeZone` offset from a `LocalTimeType`.
+-/
+def getTimeZone (time : LocalTimeType) : TimeZone :=
+  ⟨time.gmtOffset, time.identifier, time.abbreviation, time.isDst⟩
+
+end LocalTimeType
+
+/--
+Represents a time zone transition, mapping a time to a local time type.
+-/
+structure Transition where
+
+  /--
+  The specific time of the transition event.
+  -/
+  time : Second.Offset
+
+  /--
+  The local time type associated with this transition.
+  -/
+  localTimeType : LocalTimeType
+  deriving Repr, Inhabited
+
+/--
+Represents the rules for a time zone.
+-/
+structure ZoneRules where
+
+  /--
+  The first `LocalTimeType` used as a fallback when no matching transition is found.
+  -/
+  initialLocalTimeType : LocalTimeType
+
+  /--
+  The array of transitions for the time zone.
+  -/
+  transitions : Array Transition
+
+  deriving Repr, Inhabited
+
+namespace Transition
+
+/--
+Create a TimeZone from a Transition.
+-/
+def createTimeZoneFromTransition (transition : Transition) : TimeZone :=
+  let name := transition.localTimeType.identifier
+  let offset := transition.localTimeType.gmtOffset
+  let abbreviation := transition.localTimeType.abbreviation
+  TimeZone.mk offset name abbreviation transition.localTimeType.isDst
+
+/--
+Applies the transition to a Timestamp.
+-/
+def apply (timestamp : Timestamp) (transition : Transition) : Timestamp :=
+  let offsetInSeconds := transition.localTimeType.gmtOffset.second |>.add transition.localTimeType.gmtOffset.second
+  timestamp.addSeconds offsetInSeconds
+
+/--
+Finds the transition corresponding to a given timestamp in `Array Transition`.
+If the timestamp falls between two transitions, it returns the most recent transition before the timestamp.
+-/
+def findTransitionIndexForTimestamp (transitions : Array Transition) (timestamp : Timestamp) : Option Nat :=
+  let value := timestamp.toSecondsSinceUnixEpoch
+  if let some idx := transitions.findIdx? (fun t => t.time.val > value.val)
+    then some idx
+    else none
+
+/--
+Finds the transition corresponding to a given timestamp in `Array Transition`.
+If the timestamp falls between two transitions, it returns the most recent transition before the timestamp.
+-/
+def findTransitionForTimestamp (transitions : Array Transition) (timestamp : Timestamp) : Option Transition :=
+  if let some idx := findTransitionIndexForTimestamp transitions timestamp
+    then transitions.get? (idx - 1)
+    else transitions.back?
+
+/--
+Find the current `TimeZone` out of a `Transition` in a `Array Transition`
+-/
+def timezoneAt (transitions : Array Transition) (tm : Timestamp) : Except String TimeZone :=
+  if let some transition := findTransitionForTimestamp transitions tm
+    then .ok transition.createTimeZoneFromTransition
+    else .error "cannot find local timezone."
+
+end Transition
+namespace ZoneRules
+
+/--
+Creates ZoneRules with a fixed GMT offset.
+-/
+def fixedOffsetZone (second : Second.Offset) (identifier : Option String := none) (abbreviation : Option String := none) : ZoneRules :=
+  let offset : Offset := { second }
+  {
+    transitions := #[],
+    initialLocalTimeType := {
+      gmtOffset := offset,
+      isDst := false, abbreviation := abbreviation.getD (offset.toIsoString true),
+      wall := .standard,
+      utLocal := .ut,
+      identifier := identifier.getD (offset.toIsoString true)
+    }
+  }
+
+/--
+Creates ZoneRules with a fixed offset of UTC (GMT+0).
+-/
+@[inline]
+def UTC : ZoneRules :=
+  fixedOffsetZone 0 "UTC" "UTC"
+
+/--
+Finds the `LocalTimeType` corresponding to a given `Timestamp` in `ZoneRules`.
+If the timestamp falls between two transitions, it returns the most recent transition before the timestamp.
+If no transition is found, it falls back to `initialLocalTimeType`.
+-/
+@[inline]
+def findLocalTimeTypeForTimestamp (zr : ZoneRules) (timestamp : Timestamp) : LocalTimeType :=
+  Transition.findTransitionForTimestamp zr.transitions timestamp
+  |>.map (·.localTimeType)
+  |>.getD zr.initialLocalTimeType
+
+/--
+Find the current `TimeZone` out of a `Transition` in a `ZoneRules`
+-/
+@[inline]
+def timezoneAt (zr : ZoneRules) (tm : Timestamp) : TimeZone :=
+  Transition.timezoneAt zr.transitions tm
+  |>.toOption
+  |>.getD (zr.initialLocalTimeType |>.getTimeZone)
+
+/--
+Creates `ZoneRules` for the given `TimeZone`.
+-/
+@[inline]
+def ofTimeZone (tz : TimeZone) : ZoneRules :=
+  let ltt :=  LocalTimeType.mk tz.offset tz.isDST tz.abbreviation .wall .local tz.name
+  ZoneRules.mk ltt #[]
+
+end ZoneRules

src/Std/Time/Zoned/ZonedDateTime.lean

@@ -0,0 +1,587 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+prelude
+import Std.Time.Zoned.DateTime
+import Std.Time.Zoned.ZoneRules
+
+namespace Std
+namespace Time
+
+set_option linter.all true
+
+/--
+Represents a date and time with timezone information.
+-/
+structure ZonedDateTime where
+  private mk::
+
+  /--
+  The plain datetime component, evaluated lazily.
+  -/
+  date : Thunk PlainDateTime
+
+  /--
+  The corresponding timestamp for the datetime.
+  -/
+  timestamp : Timestamp
+
+  /--
+  The timezone rules applied to this datetime.
+  -/
+  rules : TimeZone.ZoneRules
+
+  /--
+  The timezone associated with this datetime.
+  -/
+  timezone : TimeZone
+
+instance : Inhabited ZonedDateTime where
+  default := ⟨Thunk.mk Inhabited.default, Inhabited.default, Inhabited.default, Inhabited.default⟩
+
+namespace ZonedDateTime
+open DateTime
+
+/--
+Creates a new `ZonedDateTime` out of a `Timestamp` and a `ZoneRules`.
+-/
+@[inline]
+def ofTimestamp (tm : Timestamp) (rules : TimeZone.ZoneRules) : ZonedDateTime :=
+  let tz := rules.timezoneAt tm
+  ZonedDateTime.mk (Thunk.mk fun _ => tm.toPlainDateTimeAssumingUTC.addSeconds tz.toSeconds) tm rules tz
+
+/--
+Creates a new `ZonedDateTime` out of a `PlainDateTime` and a `ZoneRules`.
+-/
+@[inline]
+def ofPlainDateTime (pdt : PlainDateTime) (zr : TimeZone.ZoneRules) : ZonedDateTime :=
+  let tm := pdt.toTimestampAssumingUTC
+
+  let transition :=
+    let value := tm.toSecondsSinceUnixEpoch
+    if let some idx := zr.transitions.findIdx? (fun t => t.time.val ≥ value.val)
+      then do
+        let last ← zr.transitions.get? (idx - 1)
+        let next ← zr.transitions.get? idx <|> zr.transitions.back?
+
+        let utcNext := next.time.sub last.localTimeType.gmtOffset.second.abs
+
+        if utcNext.val > tm.toSecondsSinceUnixEpoch.val
+          then pure last
+          else pure next
+
+      else zr.transitions.back?
+
+  let tz :=
+    transition
+    |>.map (·.localTimeType)
+    |>.getD zr.initialLocalTimeType
+    |>.getTimeZone
+
+  let tm := tm.subSeconds tz.toSeconds
+  ZonedDateTime.mk (Thunk.mk fun _ => tm.toPlainDateTimeAssumingUTC.addSeconds tz.toSeconds) tm zr tz
+
+/--
+Creates a new `ZonedDateTime` out of a `Timestamp` and a `TimeZone`.
+-/
+@[inline]
+def ofTimestampWithZone (tm : Timestamp) (tz : TimeZone) : ZonedDateTime :=
+  ofTimestamp tm (TimeZone.ZoneRules.ofTimeZone tz)
+
+/--
+Creates a new `ZonedDateTime` out of a `PlainDateTime` and a `TimeZone`.
+-/
+@[inline]
+def ofPlainDateTimeWithZone (tm : PlainDateTime) (tz : TimeZone) : ZonedDateTime :=
+  ofPlainDateTime tm (TimeZone.ZoneRules.ofTimeZone tz)
+
+/--
+Creates a new `Timestamp` out of a `ZonedDateTime`.
+-/
+@[inline]
+def toTimestamp (date : ZonedDateTime) : Timestamp :=
+  date.timestamp
+
+/--
+Changes the `ZoleRules` to a new one.
+-/
+@[inline]
+def convertZoneRules (date : ZonedDateTime) (tz₁ : TimeZone.ZoneRules) : ZonedDateTime :=
+  ofTimestamp date.toTimestamp tz₁
+
+/--
+Creates a new `ZonedDateTime` out of a `PlainDateTime`. It assumes that the `PlainDateTime` is relative
+to UTC.
+-/
+@[inline]
+def ofPlainDateTimeAssumingUTC (date : PlainDateTime) (tz : TimeZone.ZoneRules) : ZonedDateTime :=
+  ofTimestamp date.toTimestampAssumingUTC tz
+
+/--
+Converts a `ZonedDateTime` to a `PlainDateTime`
+-/
+@[inline]
+def toPlainDateTime (dt : ZonedDateTime) : PlainDateTime :=
+  dt.date.get
+
+/--
+Converts a `ZonedDateTime` to a `PlainDateTime`
+-/
+@[inline]
+def toDateTime (dt : ZonedDateTime) : DateTime dt.timezone :=
+  DateTime.ofTimestamp dt.timestamp dt.timezone
+
+/--
+Getter for the `PlainTime` inside of a `ZonedDateTime`
+-/
+@[inline]
+def time (zdt : ZonedDateTime) : PlainTime :=
+  zdt.date.get.time
+
+/--
+Getter for the `Year` inside of a `ZonedDateTime`
+-/
+@[inline]
+def year (zdt : ZonedDateTime) : Year.Offset :=
+  zdt.date.get.year
+
+/--
+Getter for the `Month` inside of a `ZonedDateTime`
+-/
+@[inline]
+def month (zdt : ZonedDateTime) : Month.Ordinal :=
+  zdt.date.get.month
+
+/--
+Getter for the `Day` inside of a `ZonedDateTime`
+-/
+@[inline]
+def day (zdt : ZonedDateTime) : Day.Ordinal :=
+  zdt.date.get.day
+
+/--
+Getter for the `Hour` inside of a `ZonedDateTime`
+-/
+@[inline]
+def hour (zdt : ZonedDateTime) : Hour.Ordinal :=
+  zdt.date.get.time.hour
+
+/--
+Getter for the `Minute` inside of a `ZonedDateTime`
+-/
+@[inline]
+def minute (zdt : ZonedDateTime) : Minute.Ordinal :=
+  zdt.date.get.minute
+
+/--
+Getter for the `Second` inside of a `ZonedDateTime`
+-/
+@[inline]
+def second (zdt : ZonedDateTime) : Second.Ordinal zdt.date.get.time.second.fst :=
+  zdt.date.get.time.second.snd
+
+/--
+Getter for the `Millisecond` inside of a `ZonedDateTime`.
+-/
+@[inline]
+def millisecond (dt : ZonedDateTime) : Millisecond.Ordinal :=
+  dt.date.get.time.millisecond
+
+/--
+Getter for the `Nanosecond` inside of a `ZonedDateTime`
+-/
+@[inline]
+def nanosecond (zdt : ZonedDateTime) : Nanosecond.Ordinal :=
+  zdt.date.get.time.nanosecond
+
+/--
+Getter for the `TimeZone.Offset` inside of a `ZonedDateTime`
+-/
+@[inline]
+def offset (zdt : ZonedDateTime) : TimeZone.Offset :=
+  zdt.timezone.offset
+
+/--
+Returns the weekday.
+-/
+@[inline]
+def weekday (zdt : ZonedDateTime) : Weekday :=
+  zdt.date.get.weekday
+
+/--
+Transforms a tuple of a `ZonedDateTime` into a `Day.Ordinal.OfYear`.
+-/
+@[inline]
+def dayOfYear (date : ZonedDateTime) : Day.Ordinal.OfYear date.year.isLeap :=
+  ValidDate.dayOfYear ⟨(date.month, date.day), date.date.get.date.valid⟩
+
+/--
+Determines the week of the year for the given `ZonedDateTime`.
+-/
+@[inline]
+def weekOfYear (date : ZonedDateTime) : Week.Ordinal :=
+  date.date.get.weekOfYear
+
+/--
+Returns the unaligned week of the month for a `ZonedDateTime` (day divided by 7, plus 1).
+-/
+def weekOfMonth (date : ZonedDateTime) : Internal.Bounded.LE 1 5 :=
+  date.date.get.weekOfMonth
+
+/--
+Determines the week of the month for the given `ZonedDateTime`. The week of the month is calculated based
+on the day of the month and the weekday. Each week starts on Monday because the entire library is
+based on the Gregorian Calendar.
+-/
+@[inline]
+def alignedWeekOfMonth (date : ZonedDateTime) : Week.Ordinal.OfMonth :=
+  date.date.get.alignedWeekOfMonth
+
+/--
+Determines the quarter of the year for the given `ZonedDateTime`.
+-/
+@[inline]
+def quarter (date : ZonedDateTime) : Internal.Bounded.LE 1 4 :=
+  date.date.get.quarter
+
+/--
+Add `Day.Offset` to a `ZonedDateTime`.
+-/
+def addDays (dt : ZonedDateTime) (days : Day.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.addDays days).toTimestampAssumingUTC dt.rules
+
+/--
+Subtract `Day.Offset` from a `ZonedDateTime`.
+-/
+def subDays (dt : ZonedDateTime) (days : Day.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.subDays days).toTimestampAssumingUTC dt.rules
+
+/--
+Add `Week.Offset` to a `ZonedDateTime`.
+-/
+def addWeeks (dt : ZonedDateTime) (weeks : Week.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.addWeeks weeks).toTimestampAssumingUTC dt.rules
+
+/--
+Subtract `Week.Offset` from a `ZonedDateTime`.
+-/
+def subWeeks (dt : ZonedDateTime) (weeks : Week.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.subWeeks weeks).toTimestampAssumingUTC dt.rules
+
+/--
+Add `Month.Offset` to a `ZonedDateTime`, clipping to the last valid day.
+-/
+def addMonthsClip (dt : ZonedDateTime) (months : Month.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.addMonthsClip months).toTimestampAssumingUTC dt.rules
+
+/--
+Subtract `Month.Offset` from a `ZonedDateTime`, clipping to the last valid day.
+-/
+def subMonthsClip (dt : ZonedDateTime) (months : Month.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.subMonthsClip months).toTimestampAssumingUTC dt.rules
+
+/--
+Add `Month.Offset` to a `ZonedDateTime`, rolling over excess days.
+-/
+def addMonthsRollOver (dt : ZonedDateTime) (months : Month.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.addMonthsRollOver months).toTimestampAssumingUTC dt.rules
+
+/--
+Subtract `Month.Offset` from a `ZonedDateTime`, rolling over excess days.
+-/
+def subMonthsRollOver (dt : ZonedDateTime) (months : Month.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.subMonthsRollOver months).toTimestampAssumingUTC dt.rules
+
+/--
+Add `Year.Offset` to a `ZonedDateTime`, rolling over excess days.
+-/
+def addYearsRollOver (dt : ZonedDateTime) (years : Year.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.addYearsRollOver years).toTimestampAssumingUTC dt.rules
+
+/--
+Add `Year.Offset` to a `ZonedDateTime`, clipping to the last valid day.
+-/
+def addYearsClip (dt : ZonedDateTime) (years : Year.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.addYearsClip years).toTimestampAssumingUTC dt.rules
+
+/--
+Subtract `Year.Offset` from a `ZonedDateTime`, clipping to the last valid day.
+-/
+def subYearsClip (dt : ZonedDateTime) (years : Year.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.subYearsClip years).toTimestampAssumingUTC dt.rules
+
+/--
+Subtract `Year.Offset` from a `ZonedDateTime`, rolling over excess days.
+-/
+def subYearsRollOver (dt : ZonedDateTime) (years : Year.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.subYearsRollOver years).toTimestampAssumingUTC dt.rules
+
+/--
+Add `Hour.Offset` to a `ZonedDateTime`.
+-/
+def addHours (dt : ZonedDateTime) (hours : Hour.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.addHours hours).toTimestampAssumingUTC dt.rules
+
+/--
+Subtract `Hour.Offset` from a `ZonedDateTime`.
+-/
+def subHours (dt : ZonedDateTime) (hours : Hour.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.subHours hours).toTimestampAssumingUTC dt.rules
+
+/--
+Add `Minute.Offset` to a `ZonedDateTime`.
+-/
+def addMinutes (dt : ZonedDateTime) (minutes : Minute.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.addMinutes minutes).toTimestampAssumingUTC dt.rules
+
+/--
+Subtract `Minute.Offset` from a `ZonedDateTime`.
+-/
+def subMinutes (dt : ZonedDateTime) (minutes : Minute.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.subMinutes minutes).toTimestampAssumingUTC dt.rules
+
+/--
+Add `Millisecond.Offset` to a `DateTime`.
+-/
+@[inline]
+def addMilliseconds (dt : ZonedDateTime) (milliseconds : Millisecond.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.addMilliseconds milliseconds).toTimestampAssumingUTC dt.rules
+
+/--
+Subtract `Millisecond.Offset` from a `DateTime`.
+-/
+@[inline]
+def subMilliseconds (dt : ZonedDateTime) (milliseconds : Millisecond.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.subMilliseconds milliseconds).toTimestampAssumingUTC dt.rules
+
+/--
+Add `Second.Offset` to a `ZonedDateTime`.
+-/
+def addSeconds (dt : ZonedDateTime) (seconds : Second.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.addSeconds seconds).toTimestampAssumingUTC dt.rules
+
+/--
+Subtract `Second.Offset` from a `ZonedDateTime`.
+-/
+def subSeconds (dt : ZonedDateTime) (seconds : Second.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.subSeconds seconds).toTimestampAssumingUTC dt.rules
+
+/--
+Add `Nanosecond.Offset` to a `ZonedDateTime`.
+-/
+def addNanoseconds (dt : ZonedDateTime) (nanoseconds : Nanosecond.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.addNanoseconds nanoseconds).toTimestampAssumingUTC dt.rules
+
+/--
+Subtract `Nanosecond.Offset` from a `ZonedDateTime`.
+-/
+def subNanoseconds (dt : ZonedDateTime) (nanoseconds : Nanosecond.Offset) : ZonedDateTime :=
+  let date := dt.timestamp.toPlainDateTimeAssumingUTC
+  ZonedDateTime.ofTimestamp (date.subNanoseconds nanoseconds).toTimestampAssumingUTC dt.rules
+
+/--
+Determines the era of the given `ZonedDateTime` based on its year.
+-/
+@[inline]
+def era (date : ZonedDateTime) : Year.Era :=
+  date.date.get.era
+
+/--
+Sets the `ZonedDateTime` to the specified `desiredWeekday`.
+-/
+def withWeekday (dt : ZonedDateTime) (desiredWeekday : Weekday) : ZonedDateTime :=
+  let date := dt.date.get
+  ZonedDateTime.ofPlainDateTime (date.withWeekday desiredWeekday) dt.rules
+
+/--
+Creates a new `ZonedDateTime` by adjusting the day of the month to the given `days` value, with any
+out-of-range days clipped to the nearest valid date.
+-/
+@[inline]
+def withDaysClip (dt : ZonedDateTime) (days : Day.Ordinal) : ZonedDateTime :=
+  let date := dt.date.get
+  ZonedDateTime.ofPlainDateTime (date.withDaysClip days) dt.rules
+
+/--
+Creates a new `ZonedDateTime` by adjusting the day of the month to the given `days` value, with any
+out-of-range days rolled over to the next month or year as needed.
+-/
+@[inline]
+def withDaysRollOver (dt : ZonedDateTime) (days : Day.Ordinal) : ZonedDateTime :=
+  let date := dt.date.get
+  ZonedDateTime.ofPlainDateTime (date.withDaysRollOver days) dt.rules
+
+/--
+Creates a new `ZonedDateTime` by adjusting the month to the given `month` value.
+The day remains unchanged, and any invalid days for the new month will be handled according to the `clip` behavior.
+-/
+@[inline]
+def withMonthClip (dt : ZonedDateTime) (month : Month.Ordinal) : ZonedDateTime :=
+  let date := dt.date.get
+  ZonedDateTime.ofPlainDateTime (date.withMonthClip month) dt.rules
+
+/--
+Creates a new `ZonedDateTime` by adjusting the month to the given `month` value.
+The day is rolled over to the next valid month if necessary.
+-/
+@[inline]
+def withMonthRollOver (dt : ZonedDateTime) (month : Month.Ordinal) : ZonedDateTime :=
+  let date := dt.date.get
+  ZonedDateTime.ofPlainDateTime (date.withMonthRollOver month) dt.rules
+
+/--
+Creates a new `ZonedDateTime` by adjusting the year to the given `year` value. The month and day remain unchanged,
+and any invalid days for the new year will be handled according to the `clip` behavior.
+-/
+@[inline]
+def withYearClip (dt : ZonedDateTime) (year : Year.Offset) : ZonedDateTime :=
+  let date := dt.date.get
+
+  ZonedDateTime.ofPlainDateTime (date.withYearClip year) dt.rules
+
+/--
+Creates a new `ZonedDateTime` by adjusting the year to the given `year` value. The month and day are rolled
+over to the next valid month and day if necessary.
+-/
+@[inline]
+def withYearRollOver (dt : ZonedDateTime) (year : Year.Offset) : ZonedDateTime :=
+  let date := dt.date.get
+  ZonedDateTime.ofPlainDateTime (date.withYearRollOver year) dt.rules
+
+/--
+Creates a new `ZonedDateTime` by adjusting the `hour` component.
+-/
+@[inline]
+def withHours (dt : ZonedDateTime) (hour : Hour.Ordinal) : ZonedDateTime :=
+  let date := dt.date.get
+  ZonedDateTime.ofPlainDateTime (date.withHours hour) dt.rules
+
+/--
+Creates a new `ZonedDateTime` by adjusting the `minute` component.
+-/
+@[inline]
+def withMinutes (dt : ZonedDateTime) (minute : Minute.Ordinal) : ZonedDateTime :=
+  let date := dt.date.get
+  ZonedDateTime.ofPlainDateTime (date.withMinutes minute) dt.rules
+
+/--
+Creates a new `ZonedDateTime` by adjusting the `second` component.
+-/
+@[inline]
+def withSeconds (dt : ZonedDateTime) (second : Sigma Second.Ordinal) : ZonedDateTime :=
+  let date := dt.date.get
+  ZonedDateTime.ofPlainDateTime (date.withSeconds second) dt.rules
+
+/--
+Creates a new `ZonedDateTime` by adjusting the `nano` component with a new `millis` that will set
+in the millisecond scale.
+-/
+@[inline]
+def withMilliseconds (dt : ZonedDateTime) (millis : Millisecond.Ordinal) : ZonedDateTime :=
+  let date := dt.date.get
+  ZonedDateTime.ofPlainDateTime (date.withMilliseconds millis) dt.rules
+
+/--
+Creates a new `ZonedDateTime` by adjusting the `nano` component.
+-/
+@[inline]
+def withNanoseconds (dt : ZonedDateTime) (nano : Nanosecond.Ordinal) : ZonedDateTime :=
+  let date := dt.date.get
+  ZonedDateTime.ofPlainDateTime (date.withNanoseconds nano) dt.rules
+
+/--
+Checks if the `ZonedDateTime` is in a leap year.
+-/
+def inLeapYear (date : ZonedDateTime) : Bool :=
+  date.year.isLeap
+
+/--
+Converts a `ZonedDateTime` to the number of days since the UNIX epoch.
+-/
+def toDaysSinceUNIXEpoch (date : ZonedDateTime) : Day.Offset :=
+  date.date.get.toDaysSinceUNIXEpoch
+
+/--
+Converts a `ZonedDateTime` to the number of days since the UNIX epoch.
+-/
+@[inline]
+def ofDaysSinceUNIXEpoch (days : Day.Offset) (time : PlainTime) (zt : TimeZone.ZoneRules) : ZonedDateTime :=
+  ZonedDateTime.ofPlainDateTime (PlainDateTime.ofDaysSinceUNIXEpoch days time) zt
+
+instance : HAdd ZonedDateTime Day.Offset ZonedDateTime where
+  hAdd := addDays
+
+instance : HSub ZonedDateTime Day.Offset ZonedDateTime where
+  hSub := subDays
+
+instance : HAdd ZonedDateTime Week.Offset ZonedDateTime where
+  hAdd := addWeeks
+
+instance : HSub ZonedDateTime Week.Offset ZonedDateTime where
+  hSub := subWeeks
+
+instance : HAdd ZonedDateTime Hour.Offset ZonedDateTime where
+  hAdd := addHours
+
+instance : HSub ZonedDateTime Hour.Offset ZonedDateTime where
+  hSub := subHours
+
+instance : HAdd ZonedDateTime Minute.Offset ZonedDateTime where
+  hAdd := addMinutes
+
+instance : HSub ZonedDateTime Minute.Offset ZonedDateTime where
+  hSub := subMinutes
+
+instance : HAdd ZonedDateTime Second.Offset ZonedDateTime where
+  hAdd := addSeconds
+
+instance : HSub ZonedDateTime Second.Offset ZonedDateTime where
+  hSub := subSeconds
+
+instance : HAdd ZonedDateTime Millisecond.Offset ZonedDateTime where
+  hAdd := addMilliseconds
+
+instance : HSub ZonedDateTime Millisecond.Offset ZonedDateTime where
+  hSub := subMilliseconds
+
+instance : HAdd ZonedDateTime Nanosecond.Offset ZonedDateTime where
+  hAdd := addNanoseconds
+
+instance : HSub ZonedDateTime Nanosecond.Offset ZonedDateTime where
+  hSub := subNanoseconds
+
+instance : HSub ZonedDateTime ZonedDateTime Duration where
+  hSub x y := x.toTimestamp - y.toTimestamp
+
+instance : HAdd ZonedDateTime Duration ZonedDateTime where
+  hAdd x y := x.addNanoseconds y.toNanoseconds
+
+instance : HSub ZonedDateTime Duration ZonedDateTime where
+  hSub x y := x.subNanoseconds y.toNanoseconds
+
+end ZonedDateTime
+end Time
+end Std

src/runtime/io.cpp

@@ -5,6 +5,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura, Sebastian Ullrich
 */
 #if defined(LEAN_WINDOWS)
+#include <icu.h>
 #include <windows.h>
 #include <io.h>
 #define NOMINMAX // prevent ntdef.h from defining min/max macros
@@ -630,6 +631,176 @@ extern "C" LEAN_EXPORT obj_res lean_io_prim_handle_put_str(b_obj_arg h, b_obj_ar
     }
 }
 
+/* Std.Time.Timestamp.now : IO Timestamp */
+extern "C" LEAN_EXPORT obj_res lean_get_current_time(obj_arg /* w */) {
+    using namespace std::chrono;
+
+    std::chrono::system_clock::time_point now = std::chrono::system_clock::now();
+    long long timestamp = std::chrono::duration_cast<std::chrono::nanoseconds>(now.time_since_epoch()).count();
+
+    long long secs = timestamp / 1000000000;
+    long long nano = timestamp % 1000000000;
+
+    lean_object *lean_ts = lean_alloc_ctor(0, 2, 0);
+    lean_ctor_set(lean_ts, 0, lean_int64_to_int(secs));
+    lean_ctor_set(lean_ts, 1, lean_int64_to_int(nano));
+
+    return lean_io_result_mk_ok(lean_ts);
+}
+
+/* Std.Time.Database.Windows.getNextTransition : @&String -> Int64 -> Bool -> IO (Option (Int64 × TimeZone)) */
+extern "C" LEAN_EXPORT obj_res lean_windows_get_next_transition(b_obj_arg timezone_str, uint64_t tm_obj, uint8 default_time, obj_arg /* w */) {
+#if defined(LEAN_WINDOWS)
+    UErrorCode status = U_ZERO_ERROR;
+    const char* dst_name_id = lean_string_cstr(timezone_str);
+
+    UChar tzID[256];
+    u_strFromUTF8(tzID, sizeof(tzID) / sizeof(tzID[0]), NULL, dst_name_id, strlen(dst_name_id), &status);
+
+    if (U_FAILURE(status)) {
+        return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to read identifier")));
+    }
+
+    UCalendar *cal = ucal_open(tzID, -1, NULL, UCAL_GREGORIAN, &status);
+
+    if (U_FAILURE(status)) {
+        ucal_close(cal);
+        return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to open calendar")));
+    }
+
+    int64_t tm = 0;
+
+    if (!default_time) {
+        int64_t timestamp_secs = (int64_t)tm_obj;
+
+        ucal_setMillis(cal, timestamp_secs * 1000, &status);
+        if (U_FAILURE(status)) {
+            ucal_close(cal);
+            return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to set calendar time")));
+        }
+
+        UDate nextTransition;
+        if (!ucal_getTimeZoneTransitionDate(cal, UCAL_TZ_TRANSITION_NEXT, &nextTransition, &status)) {
+            ucal_close(cal);
+            return io_result_mk_ok(mk_option_none());
+        }
+
+        if (U_FAILURE(status)) {
+            ucal_close(cal);
+            return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to get next transation")));
+        }
+
+        tm = (int64_t)(nextTransition / 1000.0);
+    }
+    
+    int32_t dst_offset = ucal_get(cal, UCAL_DST_OFFSET, &status);
+
+    if (U_FAILURE(status)) {
+        ucal_close(cal);
+        return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to get dst_offset")));
+    }
+
+    int is_dst = dst_offset != 0;
+
+    int32_t tzIDLength = ucal_getTimeZoneDisplayName(cal, is_dst ? UCAL_DST : UCAL_STANDARD, "en_US", tzID, 32, &status);
+
+    if (U_FAILURE(status)) {
+        ucal_close(cal);
+        return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to timezone identifier")));
+    }
+
+    char dst_name[256];
+    int32_t dst_name_len;
+    u_strToUTF8(dst_name, sizeof(dst_name), &dst_name_len, tzID, tzIDLength, &status);
+
+    if (U_FAILURE(status)) {
+        return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to convert DST name to UTF-8")));
+    }
+
+    UChar display_name[32];
+    int32_t display_name_len = ucal_getTimeZoneDisplayName(cal, is_dst ? UCAL_SHORT_DST : UCAL_SHORT_STANDARD, "en_US", display_name, 32, &status);
+
+    if (U_FAILURE(status)) {
+        ucal_close(cal);
+        return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to read abbreaviation")));
+    }
+
+    char display_name_str[256];
+    int32_t display_name_str_len;
+    u_strToUTF8(display_name_str, sizeof(display_name_str), &display_name_str_len, display_name, display_name_len, &status);
+
+    if (U_FAILURE(status)) {
+        ucal_close(cal);
+        return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to get abbreviation to cstr")));
+    }
+
+    int32_t zone_offset = ucal_get(cal, UCAL_ZONE_OFFSET, &status);
+    zone_offset += dst_offset;
+
+    if (U_FAILURE(status)) {
+        ucal_close(cal);
+        return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to get zone_offset")));
+    }
+
+    ucal_close(cal);
+
+    int offset_seconds = zone_offset / 1000;
+
+    lean_object *lean_tz = lean_alloc_ctor(0, 3, 1);
+    lean_ctor_set(lean_tz, 0, lean_int_to_int(offset_seconds));
+    lean_ctor_set(lean_tz, 1, lean_mk_string_from_bytes_unchecked(dst_name, dst_name_len));
+    lean_ctor_set(lean_tz, 2, lean_mk_string_from_bytes_unchecked(display_name_str, display_name_str_len));
+    lean_ctor_set_uint8(lean_tz, sizeof(void*)*3, is_dst);
+
+    lean_object *lean_pair = lean_alloc_ctor(0, 2, 0);
+    lean_ctor_set(lean_pair, 0, lean_box_uint64((uint64_t)tm));
+    lean_ctor_set(lean_pair, 1, lean_tz);
+
+    return lean_io_result_mk_ok(mk_option_some(lean_pair));
+#else
+    return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to get timezone, its windows only.")));
+#endif
+}
+
+/* Std.Time.Database.Windows.getLocalTimeZoneIdentifierAt : Int64 → IO String */
+extern "C" LEAN_EXPORT obj_res lean_get_windows_local_timezone_id_at(uint64_t tm_obj, obj_arg /* w */) {
+#if defined(LEAN_WINDOWS)
+    UErrorCode status = U_ZERO_ERROR;
+    UCalendar* cal = ucal_open(NULL, -1, NULL, UCAL_GREGORIAN, &status);
+
+    if (U_FAILURE(status)) {
+        return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to open calendar")));
+    }
+
+    int64_t timestamp_secs = (int64_t)tm_obj;
+    ucal_setMillis(cal, timestamp_secs * 1000, &status);
+
+    if (U_FAILURE(status)) {
+        ucal_close(cal);
+        return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to set calendar time")));
+    }
+
+    UChar tzId[256];
+    int32_t tzIdLength = ucal_getTimeZoneID(cal, tzId, sizeof(tzId) / sizeof(tzId[0]), &status);
+    ucal_close(cal);
+
+    if (U_FAILURE(status)) {
+        return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to get timezone ID")));
+    }
+
+    char tzIdStr[256];
+    u_strToUTF8(tzIdStr, sizeof(tzIdStr), NULL, tzId, tzIdLength, &status);
+
+    if (U_FAILURE(status)) {
+        return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("failed to convert timezone ID to UTF-8")));
+    }
+
+    return lean_io_result_mk_ok(lean_mk_ascii_string_unchecked(tzIdStr));
+#else
+    return lean_io_result_mk_error(lean_decode_io_error(EINVAL, mk_string("timezone retrieval is Windows-only")));
+#endif
+}
+
 /* monoMsNow : BaseIO Nat */
 extern "C" LEAN_EXPORT obj_res lean_io_mono_ms_now(obj_arg /* w */) {
     static_assert(sizeof(std::chrono::milliseconds::rep) <= sizeof(uint64), "size of std::chrono::nanoseconds::rep may not exceed 64");