88 lines
2.8 KiB
Text
88 lines
2.8 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.core init.control.monad init.control.alternative init.coe
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open Decidable
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universes u v
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namespace Option
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def toMonad {m : Type → Type} [Monad m] [Alternative m] {A} : Option A → m A
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| none := failure
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| (some a) := pure a
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@[macroInline] def getOrElse {α : Type u} : Option α → α → α
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| (some x) _ := x
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| none e := e
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@[inline] def get {α : Type u} [Inhabited α] : Option α → α
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| (some x) := x
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| none := default α
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@[inline] def toBool {α : Type u} : Option α → Bool
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| (some _) := true
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| none := false
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@[inline] def isSome {α : Type u} : Option α → Bool
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| (some _) := true
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| none := false
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@[inline] def isNone {α : Type u} : Option α → Bool
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| (some _) := false
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| none := true
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@[inline] protected def bind {α : Type u} {β : Type v} : Option α → (α → Option β) → Option β
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| none b := none
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| (some a) b := b a
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@[inline] protected def map {α β} (f : α → β) (o : Option α) : Option β :=
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Option.bind o (some ∘ f)
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theorem mapId {α} : (Option.map id : Option α → Option α) = id :=
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funext (fun o => match o with | none := rfl | some x := rfl)
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instance : Monad Option :=
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{pure := @some, bind := @Option.bind, map := @Option.map}
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@[macroInline] protected def orelse {α : Type u} : Option α → Option α → Option α
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| (some a) _ := some a
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| none b := b
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/- Remark: when using the polymorphic notation `a <|> b` is not a `[macroInline]`.
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Thus, `a <|> b` will make `Option.orelse` to behave like it was marked as `[inline]`. -/
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instance : Alternative Option :=
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{ failure := @none,
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orelse := @Option.orelse,
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..Option.Monad }
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@[inline] protected def lt {α : Type u} (r : α → α → Prop) : Option α → Option α → Prop
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| none (some x) := True
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| (some x) (some y) := r x y
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| _ _ := False
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instance decidableRelLt {α : Type u} (r : α → α → Prop) [s : DecidableRel r] : DecidableRel (Option.lt r)
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| none (some y) := isTrue trivial
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| (some x) (some y) := s x y
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| (some x) none := isFalse notFalse
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| none none := isFalse notFalse
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end Option
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instance (α : Type u) : Inhabited (Option α) :=
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⟨none⟩
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instance {α : Type u} [DecidableEq α] : DecidableEq (Option α) :=
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{decEq := fun a b => match a, b with
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| none, none := isTrue rfl
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| none, (some v₂) := isFalse (fun h => Option.noConfusion h)
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| (some v₁), none := isFalse (fun h => Option.noConfusion h)
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| (some v₁), (some v₂) :=
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match decEq v₁ v₂ with
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| (isTrue e) := isTrue (congrArg (@some α) e)
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| (isFalse n) := isFalse (fun h => Option.noConfusion h (fun e => absurd e n))}
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instance {α : Type u} [HasLess α] : HasLess (Option α) := ⟨Option.lt HasLess.Less⟩
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