6887a99f08
The new definitions are not fully general since they force data and state to be in the same universe.
96 lines
2.8 KiB
Text
96 lines
2.8 KiB
Text
/-
|
||
Copyright (c) 2016 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.monad init.category.alternative
|
||
universes u v
|
||
|
||
def state (σ α : Type u) : Type u :=
|
||
σ → α × σ
|
||
|
||
section
|
||
variables {σ α β : Type u}
|
||
|
||
@[inline] def state_return (a : α) : state σ α :=
|
||
λ s, (a, s)
|
||
|
||
@[inline] def state_bind (a : state σ α) (b : α → state σ β) : state σ β :=
|
||
λ s, match (a s) with (a', s') := b a' s' end
|
||
|
||
instance (σ : Type u) : monad (state σ) :=
|
||
{pure := @state_return σ, bind := @state_bind σ}
|
||
end
|
||
|
||
namespace state
|
||
@[inline] def read {σ : Type u} : state σ σ :=
|
||
λ s, (s, s)
|
||
|
||
@[inline] def write {σ : Type} : σ → state σ unit :=
|
||
λ s' s, ((), s')
|
||
|
||
@[inline] def write' {σ : Type u} : σ → state σ punit :=
|
||
λ s' s, (punit.star, s')
|
||
end state
|
||
|
||
def state_t (σ : Type u) (m : Type u → Type v) [monad m] (α : Type u) : Type (max u v) :=
|
||
σ → m (α × σ)
|
||
|
||
section
|
||
variable {σ : Type u}
|
||
variable {m : Type u → Type v}
|
||
variable [monad m]
|
||
variables {α β : Type u}
|
||
|
||
def state_t_return (a : α) : state_t σ m α :=
|
||
λ s, show m (α × σ), from
|
||
return (a, s)
|
||
|
||
def state_t_bind (act₁ : state_t σ m α) (act₂ : α → state_t σ m β) : state_t σ m β :=
|
||
λ s, show m (β × σ), from
|
||
do (a, new_s) ← act₁ s,
|
||
act₂ a new_s
|
||
end
|
||
|
||
instance (σ : Type u) (m : Type u → Type v) [monad m] : monad (state_t σ m) :=
|
||
{pure := @state_t_return σ m _, bind := @state_t_bind σ m _}
|
||
|
||
section
|
||
variable {σ : Type u}
|
||
variable {m : Type u → Type v}
|
||
variable [monad m]
|
||
variable [alternative m]
|
||
variable {α : Type u}
|
||
|
||
def state_t_orelse (act₁ act₂ : state_t σ m α) : state_t σ m α :=
|
||
λ s, act₁ s <|> act₂ s
|
||
|
||
def state_t_failure : state_t σ m α :=
|
||
λ s, failure
|
||
end
|
||
|
||
instance (σ : Type u) (m : Type u → Type v) [alternative m] [monad m] : alternative (state_t σ m) :=
|
||
{ state_t.monad σ m with
|
||
failure := @state_t_failure σ m _ _,
|
||
orelse := @state_t_orelse σ m _ _ }
|
||
|
||
namespace state_t
|
||
def read {σ : Type u} {m : Type u → Type v} [monad m] : state_t σ m σ :=
|
||
λ s, return (s, s)
|
||
|
||
def write {σ : Type} {m : Type → Type v} [monad m] : σ → state_t σ m unit :=
|
||
λ s' s, return ((), s')
|
||
|
||
def write' {σ : Type u} {m : Type u → Type v} [monad m] : σ → state_t σ m punit :=
|
||
λ s' s, return (punit.star, s')
|
||
|
||
def modify {σ : Type} {m : Type → Type v} [monad m] (f : σ → σ) : state_t σ m unit :=
|
||
do s ← read, write (f s)
|
||
|
||
def modify' {σ : Type u} {m : Type u → Type v} [monad m] (f : σ → σ) : state_t σ m punit :=
|
||
do s ← read, write' (f s)
|
||
|
||
def lift {α σ : Type u} {m : Type u → Type v} [monad m] (t : m α) : state_t σ m α :=
|
||
λ s, do a ← t, return (a, s)
|
||
end state_t
|