100 lines
3.2 KiB
Text
100 lines
3.2 KiB
Text
/-
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Copyright (c) 2014 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Leonardo de Moura
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-/
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prelude
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import init.logic init.monad init.alternative
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open decidable
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universe variables u v
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attribute [instance]
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definition option_is_inhabited (A : Type u) : inhabited (option A) :=
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⟨none⟩
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attribute [instance]
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definition option_has_decidable_eq {A : Type u} [H : decidable_eq A] : ∀ o₁ o₂ : option A, decidable (o₁ = o₂)
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| none none := is_true rfl
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| none (some v₂) := is_false (λ H, option.no_confusion H)
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| (some v₁) none := is_false (λ H, option.no_confusion H)
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| (some v₁) (some v₂) :=
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match (H v₁ v₂) with
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| (is_true e) := is_true (congr_arg (@some A) e)
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| (is_false n) := is_false (λ H, option.no_confusion H (λ e, absurd e n))
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end
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attribute [inline]
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definition option_fmap {A : Type u} {B : Type v} (f : A → B) : option A → option B
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| none := none
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| (some a) := some (f a)
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attribute [inline]
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definition option_bind {A : Type u} {B : Type v} : option A → (A → option B) → option B
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| none b := none
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| (some a) b := b a
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attribute [instance]
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definition option_is_monad : monad option :=
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monad.mk @option_fmap @some @option_bind
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definition option_orelse {A : Type u} : option A → option A → option A
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| (some a) o := some a
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| none (some a) := some a
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| none none := none
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attribute [instance]
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definition option_is_alternative {A : Type u} : alternative option :=
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alternative.mk @option_fmap @some (@fapp _ _) @none @option_orelse
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definition optionT (M : Type (max 1 u) → Type v) [monad M] (A : Type u) : Type v :=
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M (option A)
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attribute [inline]
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definition optionT_fmap {M : Type (max 1 u) → Type v} [monad M] {A B : Type u} (f : A → B) (e : optionT M A) : optionT M B :=
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show M (option B), from
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do o ← e,
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match o with
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| none := return none
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| (some a) := return (some (f a))
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end
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attribute [inline]
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definition optionT_bind {M : Type (max 1 u) → Type v} [monad M] {A B : Type u} (a : optionT M A) (b : A → optionT M B)
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: optionT M B :=
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show M (option B), from
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do o ← a,
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match o with
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| none := return none
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| (some a) := b a
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end
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attribute [inline]
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definition optionT_return {M : Type (max 1 u) → Type v} [monad M] {A : Type u} (a : A) : optionT M A :=
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show M (option A), from
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return (some a)
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attribute [instance]
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definition optionT_is_monad {M : Type (max 1 u) → Type v} [monad M] {A : Type u} : monad (optionT M) :=
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monad.mk (@optionT_fmap M _) (@optionT_return M _) (@optionT_bind M _)
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definition optionT_orelse {M : Type (max 1 u) → Type v} [monad M] {A : Type u} (a : optionT M A) (b : optionT M A) : optionT M A :=
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show M (option A), from
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do o ← a,
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match o with
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| none := b
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| (some v) := return (some v)
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end
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definition optionT_fail {M : Type (max 1 u) → Type v} [monad M] {A : Type u} : optionT M A :=
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show M (option A), from
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return none
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attribute [instance]
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definition optionT_is_alternative {M : Type (max 1 u) → Type v} [monad M] {A : Type u} : alternative (optionT M) :=
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alternative.mk
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(@optionT_fmap M _)
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(@optionT_return M _)
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(@fapp (optionT M) (@optionT_is_monad M _ A))
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(@optionT_fail M _)
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(@optionT_orelse M _)
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