/-
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 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

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