lean4-htt/library/init/data/option/basic.lean

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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
-/
prelude
import init.logic init.category
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 ααα
| (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
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
@[inline] def option_fmap {α : Type u} {β : Type v} (f : α → β) : option α → option β
| none := none
| (some a) := some (f a)
@[inline] def option_bind {α : Type u} {β : Type v} : option α → (α → option β) → option β
| none b := none
| (some a) b := b a
instance : monad option :=
{map := @option_fmap, ret := @some, bind := @option_bind}
def option_orelse {α : Type u} : option α → option α → option α
| (some a) o := some a
| none (some a) := some a
| none none := none
instance {α : Type u} : alternative option :=
alternative.mk @option_fmap @some (@fapp _ _) @none @option_orelse
def option_t (m : Type u → Type v) [monad m] (α : Type u) : Type v :=
m (option α)
@[inline] def option_t_fmap {m : Type u → Type v} [monad m] {α β : Type u} (f : α → β) (e : option_t m α) : option_t m β :=
show m (option β), from
do o ← e,
match o with
| none := return none
| (some a) := return (some (f a))
end
@[inline] def option_t_bind {m : Type u → Type v} [monad m] {α β : Type u} (a : option_t m α) (b : α → option_t m β)
: option_t m β :=
show m (option β), from
do o ← a,
match o with
| none := return none
| (some a) := b a
end
@[inline] def option_t_return {m : Type u → Type v} [monad m] {α : Type u} (a : α) : option_t m α :=
show m (option α), from
return (some a)
instance {m : Type u → Type v} [monad m] : monad (option_t m) :=
{map := @option_t_fmap m _, ret := @option_t_return m _, bind := @option_t_bind m _}
def option_t_orelse {m : Type u → Type v} [monad m] {α : Type u} (a : option_t m α) (b : option_t m α) : option_t m α :=
show m (option α), from
do o ← a,
match o with
| none := b
| (some v) := return (some v)
end
def option_t_fail {m : Type u → Type v} [monad m] {α : Type u} : option_t m α :=
show m (option α), from
return none
instance {m : Type u → Type v} [monad m] : alternative (option_t m) :=
{map := @option_t_fmap m _,
pure := @option_t_return m _,
seq := @fapp (option_t m) (@option_t.monad m _),
failure := @option_t_fail m _,
orelse := @option_t_orelse m _}