6841e47aa4
In Lean 4, we will support the more general `a + ·` ==> `fun x, a + x` `· + b` ==> `fun x, x + b` `· + ·` ==> `fun x y, x + y` `f · y` ==> `fun x, f a y` `g · · b` ==> `fun x y, g x y b`
59 lines
1.6 KiB
Text
59 lines
1.6 KiB
Text
/-
|
||
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
|
||
Released under Apache 2.0 license as described in the file LICENSE.
|
||
Authors: Leonardo de Moura
|
||
-/
|
||
prelude
|
||
import init.data.repr
|
||
|
||
universes u v
|
||
|
||
inductive Ordering
|
||
| lt | Eq | gt
|
||
|
||
instance : HasRepr Ordering :=
|
||
⟨(λ s, match s with | Ordering.lt := "lt" | Ordering.Eq := "Eq" | Ordering.gt := "gt")⟩
|
||
|
||
namespace Ordering
|
||
def swap : Ordering → Ordering
|
||
| lt := gt
|
||
| Eq := Eq
|
||
| gt := lt
|
||
|
||
@[inline] def orElse : Ordering → Ordering → Ordering
|
||
| lt _ := lt
|
||
| Eq o := o
|
||
| gt _ := gt
|
||
|
||
theorem swapSwap : ∀ (o : Ordering), o.swap.swap = o
|
||
| lt := rfl
|
||
| Eq := rfl
|
||
| gt := rfl
|
||
end Ordering
|
||
|
||
@[inline] def cmpUsing {α : Type u} (lt : α → α → Prop) [DecidableRel lt] (a b : α) : Ordering :=
|
||
if lt a b then Ordering.lt
|
||
else if lt b a then Ordering.gt
|
||
else Ordering.Eq
|
||
|
||
def cmp {α : Type u} [HasLess α] [DecidableRel (HasLess.Less : α → α → Prop)] (a b : α) : Ordering :=
|
||
cmpUsing HasLess.Less a b
|
||
|
||
instance : DecidableEq Ordering :=
|
||
{decEq := λ a b,
|
||
match a with
|
||
| Ordering.lt :=
|
||
match b with
|
||
| Ordering.lt := isTrue rfl
|
||
| Ordering.Eq := isFalse (λ h, Ordering.noConfusion h)
|
||
| Ordering.gt := isFalse (λ h, Ordering.noConfusion h)
|
||
| Ordering.Eq :=
|
||
match b with
|
||
| Ordering.lt := isFalse (λ h, Ordering.noConfusion h)
|
||
| Ordering.Eq := isTrue rfl
|
||
| Ordering.gt := isFalse (λ h, Ordering.noConfusion h)
|
||
| Ordering.gt :=
|
||
match b with
|
||
| Ordering.lt := isFalse (λ h, Ordering.noConfusion h)
|
||
| Ordering.Eq := isFalse (λ h, Ordering.noConfusion h)
|
||
| Ordering.gt := isTrue rfl}
|