lean4-htt/library/init/option.lean
2016-07-07 00:52:52 -07:00

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
Basic datatypes
-/
prelude
import init.logic init.monad init.alternative
open decidable
definition option_is_inhabited [instance] (A : Type) : inhabited (option A) :=
inhabited.mk none
definition option_has_decidable_eq [instance] {A : Type} [H : decidable_eq A] : ∀ o₁ o₂ : option A, decidable (o₁ = o₂)
| none none := tt rfl
| none (some v₂) := ff (λ H, option.no_confusion H)
| (some v₁) none := ff (λ H, option.no_confusion H)
| (some v₁) (some v₂) :=
match H v₁ v₂ with
| tt e := tt (congr_arg (@some A) e)
| ff n := ff (λ H, option.no_confusion H (λ e, absurd e n))
end
inline definition option_fmap {A B : Type} (f : A → B) (e : option A) : option B :=
option.cases_on e
none
(λ a, some (f a))
inline definition option_bind {A B : Type} (a : option A) (b : A → option B) : option B :=
option.cases_on a
none
(λ a, b a)
definition option_is_monad [instance] : monad option :=
monad.mk @option_fmap @some @option_bind
definition option_orelse {A : Type} : option A → option A → option A
| (some a) _ := some a
| none (some a) := some a
| none none := none
definition option_is_alternative [instance] {A : Type} : alternative option :=
alternative.mk @option_fmap @some (@fapp _ _) @none @option_orelse