refactor: module-ize Std.Classes (#9079)
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Sebastian Ullrich
GitHub
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9 changed files with 62 additions and 30 deletions
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@ -303,7 +303,7 @@ In particular, if `x < y` then the result is `Ordering.lt`. If `x = y` then the
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`compareOfLessAndBEq` uses `BEq` instead of `DecidableEq`.
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-/
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@[inline] def compareOfLessAndEq {α} (x y : α) [LT α] [Decidable (x < y)] [DecidableEq α] : Ordering :=
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@[inline, expose] def compareOfLessAndEq {α} (x y : α) [LT α] [Decidable (x < y)] [DecidableEq α] : Ordering :=
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if x < y then Ordering.lt
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else if x = y then Ordering.eq
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else Ordering.gt
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@ -329,7 +329,7 @@ by `cmp₂` to break the tie.
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To lexicographically combine two `Ordering`s, use `Ordering.then`.
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-/
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@[inline] def compareLex (cmp₁ cmp₂ : α → β → Ordering) (a : α) (b : β) : Ordering :=
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@[inline, expose] def compareLex (cmp₁ cmp₂ : α → β → Ordering) (a : α) (b : β) : Ordering :=
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(cmp₁ a b).then (cmp₂ a b)
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section Lemmas
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@ -457,7 +457,7 @@ Examples:
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* `compareOn (· % 3) 5 6 = .gt`
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* `compareOn (·.foldl max 0) [1, 2, 3] [3, 2, 1] = .eq`
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-/
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@[inline] def compareOn [ord : Ord β] (f : α → β) (x y : α) : Ordering :=
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@[inline, expose] def compareOn [ord : Ord β] (f : α → β) (x y : α) : Ordering :=
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compare (f x) (f y)
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instance : Ord Nat where
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@ -724,7 +724,7 @@ protected theorem compare_eq_compare_toList {α n} [Ord α] {a b : Vector α n}
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end Vector
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/-- The lexicographic order on pairs. -/
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def lexOrd [Ord α] [Ord β] : Ord (α × β) where
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@[expose] def lexOrd [Ord α] [Ord β] : Ord (α × β) where
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compare := compareLex (compareOn (·.1)) (compareOn (·.2))
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/--
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@ -781,7 +781,7 @@ Inverts the order of an `Ord` instance.
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The result is an `Ord α` instance that returns `Ordering.lt` when `ord` would return `Ordering.gt`
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and that returns `Ordering.gt` when `ord` would return `Ordering.lt`.
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-/
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protected def opposite (ord : Ord α) : Ord α where
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@[expose] protected def opposite (ord : Ord α) : Ord α where
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compare x y := ord.compare y x
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/--
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@ -792,13 +792,13 @@ In particular, `ord.on f` compares `x` and `y` by comparing `f x` and `f y` acco
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The function `compareOn` can be used to perform this comparison without constructing an intermediate
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`Ord` instance.
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-/
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protected def on (_ : Ord β) (f : α → β) : Ord α where
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@[expose] protected def on (_ : Ord β) (f : α → β) : Ord α where
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compare := compareOn f
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/--
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Constructs the lexicographic order on products `α × β` from orders for `α` and `β`.
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-/
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protected abbrev lex (_ : Ord α) (_ : Ord β) : Ord (α × β) :=
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@[expose] protected abbrev lex (_ : Ord α) (_ : Ord β) : Ord (α × β) :=
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lexOrd
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/--
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@ -811,7 +811,7 @@ The function `compareLex` can be used to perform this comparison without constru
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intermediate `Ord` instance. `Ordering.then` can be used to lexicographically combine the results of
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comparisons.
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-/
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protected def lex' (ord₁ ord₂ : Ord α) : Ord α where
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@[expose] protected def lex' (ord₁ ord₂ : Ord α) : Ord α where
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compare := compareLex ord₁.compare ord₂.compare
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end Ord
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@ -3,5 +3,9 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Paul Reichert
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-/
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module
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prelude
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import Std.Classes.Ord
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public import Std.Classes.Ord
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public section
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@ -3,10 +3,14 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Kim Morrison
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-/
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module
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prelude
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import Std.Classes.Ord.Basic
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import Std.Classes.Ord.SInt
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import Std.Classes.Ord.UInt
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import Std.Classes.Ord.String
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import Std.Classes.Ord.BitVec
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import Std.Classes.Ord.Vector
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public import Std.Classes.Ord.Basic
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public import Std.Classes.Ord.SInt
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public import Std.Classes.Ord.UInt
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public import Std.Classes.Ord.String
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public import Std.Classes.Ord.BitVec
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public import Std.Classes.Ord.Vector
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public section
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@ -3,8 +3,12 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Markus Himmel, Paul Reichert, Robin Arnez
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-/
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module
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prelude
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import Init.Data.Ord
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public import Init.Data.Ord
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public section
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/-!
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# Type classes related to `Ord`
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@ -82,7 +86,7 @@ instance [OrientedCmp cmp] : ReflCmp cmp where
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instance OrientedCmp.opposite [OrientedCmp cmp] : OrientedCmp fun a b => cmp b a where
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eq_swap := OrientedCmp.eq_swap (cmp := cmp)
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instance OrientedOrd.opposite [Ord α] [OrientedOrd α] : letI := Ord.opposite ‹_›; OrientedOrd α :=
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instance OrientedOrd.opposite [Ord α] [OrientedOrd α] : letI := Ord.opposite (α := α) ‹_›; OrientedOrd α :=
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OrientedCmp.opposite (cmp := compare)
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theorem OrientedCmp.gt_iff_lt [OrientedCmp cmp] {a b : α} : cmp a b = .gt ↔ cmp b a = .lt := by
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@ -197,7 +201,7 @@ theorem TransOrd.isGE_trans [Ord α] [TransOrd α] {a b c : α} :
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instance TransCmp.opposite [TransCmp cmp] : TransCmp fun a b => cmp b a where
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isLE_trans := flip TransCmp.isLE_trans
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instance TransOrd.opposite [Ord α] [TransOrd α] : letI := Ord.opposite ‹_›; TransOrd α :=
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instance TransOrd.opposite [Ord α] [TransOrd α] : letI := Ord.opposite (α := α) ‹_›; TransOrd α :=
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TransCmp.opposite (cmp := compare)
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theorem TransCmp.lt_of_lt_of_eq [TransCmp cmp] {a b c : α} (hab : cmp a b = .lt)
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@ -330,7 +334,7 @@ instance LawfulEqCmp.opposite [OrientedCmp cmp] [LawfulEqCmp cmp] :
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exact LawfulEqCmp.eq_of_compare
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instance LawfulEqOrd.opposite [Ord α] [OrientedOrd α] [LawfulEqOrd α] :
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letI := Ord.opposite ‹_›; LawfulEqOrd α :=
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letI := Ord.opposite (α := α) ‹_›; LawfulEqOrd α :=
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LawfulEqCmp.opposite (cmp := compare)
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theorem LawfulEqCmp.compare_eq_iff_eq {a b : α} : cmp a b = .eq ↔ a = b :=
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@ -449,7 +453,7 @@ instance LawfulBEqCmp.opposite [OrientedCmp cmp] [LawfulBEqCmp cmp] :
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simp [OrientedCmp.eq_comm (cmp := cmp), LawfulBEqCmp.compare_eq_iff_beq]
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instance LawfulBEqOrd.opposite [Ord α] [OrientedOrd α] [LawfulBEqOrd α] :
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letI := Ord.opposite ‹_›; LawfulBEqOrd α :=
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letI := Ord.opposite (α := α) ‹_›; LawfulBEqOrd α :=
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LawfulBEqCmp.opposite (cmp := compare)
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end LawfulBEq
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@ -3,9 +3,13 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Markus Himmel, Paul Reichert, Robin Arnez
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-/
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module
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prelude
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import Std.Classes.Ord.Basic
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import Init.Data.BitVec.Lemmas
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public import Std.Classes.Ord.Basic
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public import Init.Data.BitVec.Lemmas
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public section
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/-!
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# Instances for strings.
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@ -3,9 +3,13 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Markus Himmel, Paul Reichert, Robin Arnez
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-/
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module
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prelude
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import Std.Classes.Ord.Basic
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import Init.Data.SInt.Lemmas
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public import Std.Classes.Ord.Basic
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public import Init.Data.SInt.Lemmas
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public section
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/-!
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# Instances for fixed width signed integer types.
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@ -3,9 +3,13 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Markus Himmel, Paul Reichert, Robin Arnez
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-/
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module
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prelude
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import Std.Classes.Ord.Basic
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import Init.Data.String.Lemmas
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public import Std.Classes.Ord.Basic
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public import Init.Data.String.Lemmas
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public section
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/-!
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# Instances for strings.
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@ -3,9 +3,13 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Markus Himmel, Paul Reichert, Robin Arnez
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-/
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module
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prelude
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import Std.Classes.Ord.Basic
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import Init.Data.UInt.Lemmas
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public import Std.Classes.Ord.Basic
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public import Init.Data.UInt.Lemmas
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public section
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/-!
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# Instances for fixed width unsigned integer types.
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@ -3,9 +3,13 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Markus Himmel, Paul Reichert, Robin Arnez
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-/
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module
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prelude
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import Std.Classes.Ord.Basic
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import Init.Data.Vector.Lemmas
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public import Std.Classes.Ord.Basic
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public import Init.Data.Vector.Lemmas
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public section
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/-!
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# Instances for `Vector`
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