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

65 lines
1.9 KiB
Text
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

/-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import .basic
universes u v
@[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 :=
{pure := @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 : alternative option :=
{ option.monad with
failure := @none,
orelse := @option_orelse }
def option_t (m : Type u → Type v) [monad m] (α : Type u) : Type v :=
m (option α)
@[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) :=
{pure := @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) :=
{ option_t.monad with
failure := @option_t_fail m _,
orelse := @option_t_orelse m _ }
def option_t.lift {m : Type u → Type v} [monad m] {α : Type u} (a : m α) : option_t m α :=
(some <$> a : m (option α))