e9b4b811de
@kha, `eqn_compiler.lemmas` is false by default. I will keep them disabled until I remove the inductive compiler. I'm building the new inductive datatype module (to replace the inductive compiler), and the lemmas will fail to be proved in the next commits until the transition is complete.
85 lines
2.6 KiB
Text
85 lines
2.6 KiB
Text
/-
|
||
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.core init.control.monad init.control.alternative init.coe
|
||
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 α → α → α
|
||
| (some x) _ := x
|
||
| none e := e
|
||
|
||
def to_bool {α : Type u} : option α → bool
|
||
| (some _) := tt
|
||
| none := ff
|
||
|
||
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
|
||
|
||
def get {α : Type u} : Π {o : option α}, is_some o → α
|
||
| (some x) h := x
|
||
| none h := false.rec _ $ bool.ff_ne_tt h
|
||
|
||
@[inline] protected def bind {α : Type u} {β : Type v} : option α → (α → option β) → option β
|
||
| none b := none
|
||
| (some a) b := b a
|
||
|
||
protected def map {α β} (f : α → β) (o : option α) : option β :=
|
||
option.bind o (some ∘ f)
|
||
|
||
theorem map_id {α} : (option.map id : option α → option α) = id :=
|
||
funext (λo, match o with | none := rfl | some x := rfl)
|
||
|
||
instance : monad option :=
|
||
{pure := @some, bind := @option.bind, map := @option.map}
|
||
|
||
protected def 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 :=
|
||
{ failure := @none,
|
||
orelse := @option.orelse }
|
||
|
||
protected def lt {α : Type u} (r : α → α → Prop) : option α → option α → Prop
|
||
| none (some x) := true
|
||
| (some x) (some y) := r x y
|
||
| _ _ := false
|
||
|
||
instance decidable_rel_lt {α : Type u} (r : α → α → Prop) [s : decidable_rel r] : decidable_rel (option.lt r)
|
||
| none (some y) := is_true trivial
|
||
| (some x) (some y) := s x y
|
||
| (some x) none := is_false not_false
|
||
| none none := is_false not_false
|
||
|
||
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))
|
||
|
||
instance {α : Type u} [has_lt α] : has_lt (option α) := ⟨option.lt (<)⟩
|