80 lines
2.2 KiB
Text
80 lines
2.2 KiB
Text
/-
|
||
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
|
||
Released under Apache 2.0 license as described in the file LICENSE.
|
||
Authors: Leonardo de Moura
|
||
-/
|
||
prelude
|
||
import init.logic init.category.monad init.category.alternative
|
||
open decidable
|
||
|
||
universes u v
|
||
|
||
namespace option
|
||
|
||
def to_monad {m : Type → Type} [monad m] [alternative m] {A} : option A → m A
|
||
| none := failure
|
||
| (some a) := return a
|
||
|
||
def get_or_else {α : Type u} : option α → α → α
|
||
| (some x) _ := x
|
||
| none e := e
|
||
|
||
def is_some {α : Type u} : option α → bool
|
||
| (some _) := tt
|
||
| none := ff
|
||
|
||
def is_none {α : Type u} : option α → bool
|
||
| (some _) := ff
|
||
| none := tt
|
||
|
||
def get {α : Type u} : Π {o : option α}, is_some o → α
|
||
| (some x) h := x
|
||
| none h := false.rec _ $ bool.ff_ne_tt h
|
||
|
||
def rhoare {α : Type u} : bool → α → option α
|
||
| tt a := none
|
||
| ff a := some a
|
||
|
||
def lhoare {α : Type u} : α → option α → α
|
||
| a none := a
|
||
| _ (some b) := b
|
||
|
||
infixr `|>`:1 := rhoare
|
||
infixr `<|`:1 := lhoare
|
||
|
||
@[inline] protected def bind {α : Type u} {β : Type v} : option α → (α → option β) → option β
|
||
| none b := none
|
||
| (some a) b := b a
|
||
|
||
protected def map {α β} (f : α → β) (o : option α) : option β :=
|
||
option.bind o (some ∘ f)
|
||
|
||
theorem map_id {α} : (option.map id : option α → option α) = id :=
|
||
funext (λo, match o with | none := rfl | some x := rfl end)
|
||
|
||
instance : monad option :=
|
||
{pure := @some, bind := @option.bind, map := @option.map}
|
||
|
||
protected def orelse {α : Type u} : option α → option α → option α
|
||
| (some a) o := some a
|
||
| none (some a) := some a
|
||
| none none := none
|
||
|
||
instance : alternative option :=
|
||
{ failure := @none,
|
||
orelse := @option.orelse }
|
||
|
||
end option
|
||
|
||
instance (α : Type u) : inhabited (option α) :=
|
||
⟨none⟩
|
||
|
||
instance {α : Type u} [d : decidable_eq α] : decidable_eq (option α)
|
||
| none none := is_true rfl
|
||
| none (some v₂) := is_false (λ h, option.no_confusion h)
|
||
| (some v₁) none := is_false (λ h, option.no_confusion h)
|
||
| (some v₁) (some v₂) :=
|
||
match (d v₁ v₂) with
|
||
| (is_true e) := is_true (congr_arg (@some α) e)
|
||
| (is_false n) := is_false (λ h, option.no_confusion h (λ e, absurd e n))
|
||
end
|