{-# LANGUAGE PatternSynonyms, TypeApplications #-}
{-|
Module      : Parsley.Internal.Core.Defunc
Description : Combinator-level defunctionalisation
License     : BSD-3-Clause
Maintainer  : Jamie Willis
Stability   : experimental

This module contains the infrastructure and definitions of defunctionalised
terms that can be used by the user and the frontend.

@since 1.0.0.0
-}
module Parsley.Internal.Core.Defunc (
    Defunc(..),
    pattern COMPOSE_H, pattern FLIP_H, pattern FLIP_CONST, pattern UNIT,
    lamTerm, lamTermBool
  ) where

--import Data.Typeable                 (Typeable, (:~:)(Refl), eqT)
import Language.Haskell.TH.Syntax    (Lift(..))
import Parsley.Internal.Common.Utils (WQ(..), Code, Quapplicative(..))
import Parsley.Internal.Core.Lam     (normaliseGen, Lam(..))

{-
  TODO: We should support Typeable in LIFTED to be more general, but I don't want changes to
  Defunc to impact back-compat in parsley itself. We should consider not exposing the datatype
  anymore, but exposing smart-constructors in Parsley.Defunctionalized.
  This will come in parsley-2.0.0.0.
-}

{-|
This datatype is useful for providing an /inspectable/ representation of common Haskell functions.
These can be provided in place of `WQ` to any combinator that requires it. The only difference is
that the Parsley compiler is able to manipulate and match on the constructors, which might lead to
optimisations. They can also be more convenient than constructing the `WQ` object itself:

> ID ~= WQ id [||id||]
> APP_H f x ~= WQ (f x) [||f x||]

@since 0.1.0.0
-}
data Defunc a where
  -- | Corresponds to the standard @id@ function
  ID      :: Defunc (a -> a)
  -- | Corresponds to the standard @(.)@ function applied to no arguments.
  COMPOSE :: Defunc ((b -> c) -> (a -> b) -> (a -> c))
  -- | Corresponds to the standard @flip@ function applied to no arguments.
  FLIP    :: Defunc ((a -> b -> c) -> b -> a -> c)
  -- | Corresponds to function application of two other `Defunc` values.
  APP_H   :: Defunc (a -> b) -> Defunc a -> Defunc b
  -- | Corresponds to the partially applied @(== x)@ for some `Defunc` value @x@.
  EQ_H    :: Eq a => Defunc a -> Defunc (a -> Bool)
  -- | Represents a liftable, showable value.
  LIFTED  :: (Show a, Lift a{-, Typeable a-}) => a -> Defunc a
  -- | Represents the standard @(:)@ function applied to no arguments.
  CONS    :: Defunc (a -> [a] -> [a])
  -- | Represents the standard @const@ function applied to no arguments.
  CONST   :: Defunc (a -> b -> a)
  -- | Represents the empty list @[]@.
  EMPTY   :: Defunc [a]
  -- | Wraps up any value of type `WQ`.
  BLACK   :: WQ a -> Defunc a

  -- Syntax constructors
  {-|
  Represents the regular Haskell @if@ syntax.

  @since 0.1.1.0
  -}
  IF_S    :: Defunc Bool -> Defunc a -> Defunc a -> Defunc a
  {-|
  Represents a Haskell lambda abstraction.

  @since 0.1.1.0
  -}
  LAM_S   :: (Defunc a -> Defunc b) -> Defunc (a -> b)
  {-|
  Represents a Haskell let binding.

  @since 0.1.1.0
  -}
  LET_S   :: Defunc a -> (Defunc a -> Defunc b) -> Defunc b

{-|
This instance is used to manipulate values of `Defunc`.

@since 0.1.0.0
-}
instance Quapplicative Defunc where
  makeQ :: a -> Code a -> Defunc a
makeQ a
x Code a
qx        = WQ a -> Defunc a
forall a. WQ a -> Defunc a
BLACK (a -> Code a -> WQ a
forall (q :: Type -> Type) a. Quapplicative q => a -> Code a -> q a
makeQ a
x Code a
qx)
  _val :: Defunc a -> a
_val Defunc a
ID           = a
forall a. a -> a
id
  _val Defunc a
COMPOSE      = a
forall b c a. (b -> c) -> (a -> b) -> a -> c
(.)
  _val Defunc a
FLIP         = a
forall a b c. (a -> b -> c) -> b -> a -> c
flip
  _val (APP_H Defunc (a -> a)
f Defunc a
x)  = Defunc (a -> a) -> a -> a
forall (q :: Type -> Type) a. Quapplicative q => q a -> a
_val Defunc (a -> a)
f (Defunc a -> a
forall (q :: Type -> Type) a. Quapplicative q => q a -> a
_val Defunc a
x)
  _val (LIFTED a
x)   = a
x
  _val (EQ_H Defunc a
x)     = (Defunc a -> a
forall (q :: Type -> Type) a. Quapplicative q => q a -> a
_val Defunc a
x a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==)
  _val Defunc a
CONS         = (:)
  _val Defunc a
CONST        = a
forall a b. a -> b -> a
const
  _val Defunc a
EMPTY        = []
  _val (BLACK WQ a
f)    = WQ a -> a
forall (q :: Type -> Type) a. Quapplicative q => q a -> a
_val WQ a
f
  -- Syntax
  _val (IF_S Defunc Bool
c Defunc a
t Defunc a
e) = if Defunc Bool -> Bool
forall (q :: Type -> Type) a. Quapplicative q => q a -> a
_val Defunc Bool
c then Defunc a -> a
forall (q :: Type -> Type) a. Quapplicative q => q a -> a
_val Defunc a
t else Defunc a -> a
forall (q :: Type -> Type) a. Quapplicative q => q a -> a
_val Defunc a
e
  _val (LAM_S Defunc a -> Defunc b
f)    = \a
x -> Defunc b -> b
forall (q :: Type -> Type) a. Quapplicative q => q a -> a
_val (Defunc a -> Defunc b
f (a -> Code a -> Defunc a
forall (q :: Type -> Type) a. Quapplicative q => a -> Code a -> q a
makeQ a
x Code a
forall a. HasCallStack => a
undefined))
  _val (LET_S Defunc a
x Defunc a -> Defunc a
f)  = let y :: a
y = Defunc a -> a
forall (q :: Type -> Type) a. Quapplicative q => q a -> a
_val Defunc a
x in Defunc a -> a
forall (q :: Type -> Type) a. Quapplicative q => q a -> a
_val (Defunc a -> Defunc a
f (a -> Code a -> Defunc a
forall (q :: Type -> Type) a. Quapplicative q => a -> Code a -> q a
makeQ a
y Code a
forall a. HasCallStack => a
undefined))
  _code :: Defunc a -> Code a
_code = Lam a -> Code a
forall a. Lam a -> Code a
normaliseGen (Lam a -> Code a) -> (Defunc a -> Lam a) -> Defunc a -> Code a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Defunc a -> Lam a
forall a. Defunc a -> Lam a
lamTerm
  >*< :: Defunc (a -> b) -> Defunc a -> Defunc b
(>*<) = Defunc (a -> b) -> Defunc a -> Defunc b
forall a b. Defunc (a -> b) -> Defunc a -> Defunc b
APP_H

{-|
This pattern represents fully applied composition of two `Defunc` values.

@since 0.1.0.0
-}
pattern COMPOSE_H     :: () => ((x -> y -> z) ~ ((b -> c) -> (a -> b) -> a -> c)) => Defunc x -> Defunc y -> Defunc z
pattern $bCOMPOSE_H :: Defunc x -> Defunc y -> Defunc z
$mCOMPOSE_H :: forall r z.
Defunc z
-> (forall x y b c a.
    ((x -> y -> z) ~ ((b -> c) -> (a -> b) -> a -> c)) =>
    Defunc x -> Defunc y -> r)
-> (Void# -> r)
-> r
COMPOSE_H f g = APP_H (APP_H COMPOSE f) g
{-|
This pattern corresponds to the standard @flip@ function applied to a single argument.

@since 0.1.0.0
-}
pattern FLIP_H        :: () => ((x -> y) ~ ((a -> b -> c) -> b -> a -> c)) => Defunc x -> Defunc y
pattern $bFLIP_H :: Defunc x -> Defunc y
$mFLIP_H :: forall r y.
Defunc y
-> (forall x a b c.
    ((x -> y) ~ ((a -> b -> c) -> b -> a -> c)) =>
    Defunc x -> r)
-> (Void# -> r)
-> r
FLIP_H f      = APP_H FLIP f
{-|
Represents the flipped standard @const@ function applied to no arguments.

@since 0.1.0.0
-}
pattern FLIP_CONST    :: () => (x ~ (a -> b -> b)) => Defunc x
pattern $bFLIP_CONST :: Defunc x
$mFLIP_CONST :: forall r x.
Defunc x
-> (forall a b. (x ~ (a -> b -> b)) => r) -> (Void# -> r) -> r
FLIP_CONST    = FLIP_H CONST
{-|
This pattern represents the unit value @()@.

@since 0.1.0.0
-}
pattern UNIT          :: Defunc ()
pattern $bUNIT :: Defunc ()
$mUNIT :: forall r. Defunc () -> (Void# -> r) -> (Void# -> r) -> r
UNIT          = LIFTED ()

-- TODO: This is deprecated in favour of Typeable as of parsley 2.0.0.0
{-|
Specialised conversion for functions returning `Bool`. This will go
as soon as `Defunc` has a `Typeable` constraint in parsley 2.

@since 1.0.1.0
-}
lamTermBool :: Defunc (a -> Bool) -> Lam (a -> Bool)
lamTermBool :: Defunc (a -> Bool) -> Lam (a -> Bool)
lamTermBool (APP_H Defunc (a -> a -> Bool)
CONST (LIFTED a
True)) = (Lam a -> Lam Bool) -> Lam (a -> Bool)
forall a a. (Lam a -> Lam a) -> Lam (a -> a)
Abs (Lam Bool -> Lam a -> Lam Bool
forall a b. a -> b -> a
const Lam Bool
T)
lamTermBool (APP_H Defunc (a -> a -> Bool)
CONST (LIFTED a
False)) = (Lam a -> Lam Bool) -> Lam (a -> Bool)
forall a a. (Lam a -> Lam a) -> Lam (a -> a)
Abs (Lam Bool -> Lam a -> Lam Bool
forall a b. a -> b -> a
const Lam Bool
F)
lamTermBool Defunc (a -> Bool)
f = Defunc (a -> Bool) -> Lam (a -> Bool)
forall a. Defunc a -> Lam a
lamTerm Defunc (a -> Bool)
f

{-|
Converts a `Defunc` value into an equivalent `Lam` value, discarding
the inspectivity of functions.

@since 1.0.1.0
-}
lamTerm :: {-forall a.-} Defunc a -> Lam a
lamTerm :: Defunc a -> Lam a
lamTerm Defunc a
ID = (Lam a -> Lam a) -> Lam (a -> a)
forall a a. (Lam a -> Lam a) -> Lam (a -> a)
Abs Lam a -> Lam a
forall a. a -> a
id
lamTerm Defunc a
COMPOSE = (Lam (b -> c) -> Lam ((a -> b) -> a -> c))
-> Lam ((b -> c) -> (a -> b) -> a -> c)
forall a a. (Lam a -> Lam a) -> Lam (a -> a)
Abs (\Lam (b -> c)
f -> (Lam (a -> b) -> Lam (a -> c)) -> Lam ((a -> b) -> a -> c)
forall a a. (Lam a -> Lam a) -> Lam (a -> a)
Abs (\Lam (a -> b)
g -> (Lam a -> Lam c) -> Lam (a -> c)
forall a a. (Lam a -> Lam a) -> Lam (a -> a)
Abs (Lam (b -> c) -> Lam b -> Lam c
forall a b. Lam (a -> b) -> Lam a -> Lam b
App Lam (b -> c)
f (Lam b -> Lam c) -> (Lam a -> Lam b) -> Lam a -> Lam c
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Lam (a -> b) -> Lam a -> Lam b
forall a b. Lam (a -> b) -> Lam a -> Lam b
App Lam (a -> b)
g)))
lamTerm Defunc a
FLIP = (Lam (a -> b -> c) -> Lam (b -> a -> c))
-> Lam ((a -> b -> c) -> b -> a -> c)
forall a a. (Lam a -> Lam a) -> Lam (a -> a)
Abs (\Lam (a -> b -> c)
f -> (Lam b -> Lam (a -> c)) -> Lam (b -> a -> c)
forall a a. (Lam a -> Lam a) -> Lam (a -> a)
Abs (\Lam b
x -> (Lam a -> Lam c) -> Lam (a -> c)
forall a a. (Lam a -> Lam a) -> Lam (a -> a)
Abs (\Lam a
y -> Lam (b -> c) -> Lam b -> Lam c
forall a b. Lam (a -> b) -> Lam a -> Lam b
App (Lam (a -> b -> c) -> Lam a -> Lam (b -> c)
forall a b. Lam (a -> b) -> Lam a -> Lam b
App Lam (a -> b -> c)
f Lam a
y) Lam b
x)))
lamTerm (APP_H Defunc (a -> a)
f Defunc a
x) = Lam (a -> a) -> Lam a -> Lam a
forall a b. Lam (a -> b) -> Lam a -> Lam b
App (Defunc (a -> a) -> Lam (a -> a)
forall a. Defunc a -> Lam a
lamTerm Defunc (a -> a)
f) (Defunc a -> Lam a
forall a. Defunc a -> Lam a
lamTerm Defunc a
x)
{-lamTerm (LIFTED b) | Just Refl <- eqT @a @Bool = case b of
  False -> F
  True -> T-}
lamTerm (LIFTED a
x) = Bool -> Code a -> Lam a
forall a. Bool -> Code a -> Lam a
Var Bool
True [||x||]
lamTerm (EQ_H Defunc a
x) = (Lam a -> Lam Bool) -> Lam (a -> Bool)
forall a a. (Lam a -> Lam a) -> Lam (a -> a)
Abs (Lam (a -> Bool) -> Lam a -> Lam Bool
forall a b. Lam (a -> b) -> Lam a -> Lam b
App (Lam (a -> a -> Bool) -> Lam a -> Lam (a -> Bool)
forall a b. Lam (a -> b) -> Lam a -> Lam b
App (Bool -> Code (a -> a -> Bool) -> Lam (a -> a -> Bool)
forall a. Bool -> Code a -> Lam a
Var Bool
True [||(==)||]) (Defunc a -> Lam a
forall a. Defunc a -> Lam a
lamTerm Defunc a
x)))
lamTerm Defunc a
CONS = Bool -> Code (a -> [a] -> [a]) -> Lam (a -> [a] -> [a])
forall a. Bool -> Code a -> Lam a
Var Bool
True [||(:)||]
lamTerm Defunc a
EMPTY = Bool -> Code [a] -> Lam [a]
forall a. Bool -> Code a -> Lam a
Var Bool
True [||[]||]
lamTerm Defunc a
CONST = (Lam a -> Lam (b -> a)) -> Lam (a -> b -> a)
forall a a. (Lam a -> Lam a) -> Lam (a -> a)
Abs ((Lam b -> Lam a) -> Lam (b -> a)
forall a a. (Lam a -> Lam a) -> Lam (a -> a)
Abs ((Lam b -> Lam a) -> Lam (b -> a))
-> (Lam a -> Lam b -> Lam a) -> Lam a -> Lam (b -> a)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Lam a -> Lam b -> Lam a
forall a b. a -> b -> a
const)
lamTerm (BLACK WQ a
x) = Bool -> Code a -> Lam a
forall a. Bool -> Code a -> Lam a
Var Bool
False (WQ a -> Code a
forall (q :: Type -> Type) a. Quapplicative q => q a -> Code a
_code WQ a
x)
lamTerm (LAM_S Defunc a -> Defunc b
f) = (Lam a -> Lam b) -> Lam (a -> b)
forall a a. (Lam a -> Lam a) -> Lam (a -> a)
Abs ((Defunc a -> Defunc b) -> Lam a -> Lam b
forall a b. (Defunc a -> Defunc b) -> Lam a -> Lam b
adaptLam Defunc a -> Defunc b
f)
lamTerm (IF_S Defunc Bool
c Defunc a
t Defunc a
e) = Lam Bool -> Lam a -> Lam a -> Lam a
forall a. Lam Bool -> Lam a -> Lam a -> Lam a
If (Defunc Bool -> Lam Bool
forall a. Defunc a -> Lam a
lamTerm Defunc Bool
c) (Defunc a -> Lam a
forall a. Defunc a -> Lam a
lamTerm Defunc a
t) (Defunc a -> Lam a
forall a. Defunc a -> Lam a
lamTerm Defunc a
e)
lamTerm (LET_S Defunc a
x Defunc a -> Defunc a
f) = Lam a -> (Lam a -> Lam a) -> Lam a
forall a b. Lam a -> (Lam a -> Lam b) -> Lam b
Let (Defunc a -> Lam a
forall a. Defunc a -> Lam a
lamTerm Defunc a
x) ((Defunc a -> Defunc a) -> Lam a -> Lam a
forall a b. (Defunc a -> Defunc b) -> Lam a -> Lam b
adaptLam Defunc a -> Defunc a
f)

adaptLam :: (Defunc a -> Defunc b) -> (Lam a -> Lam b)
adaptLam :: (Defunc a -> Defunc b) -> Lam a -> Lam b
adaptLam Defunc a -> Defunc b
f = Defunc b -> Lam b
forall a. Defunc a -> Lam a
lamTerm (Defunc b -> Lam b) -> (Lam a -> Defunc b) -> Lam a -> Lam b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Defunc a -> Defunc b
f (Defunc a -> Defunc b) -> (Lam a -> Defunc a) -> Lam a -> Defunc b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Lam a -> Defunc a
forall a. Lam a -> Defunc a
defuncTerm
  where
    defuncTerm :: Lam a -> Defunc a
    defuncTerm :: Lam a -> Defunc a
defuncTerm (Abs Lam a -> Lam b
f)    = (Defunc a -> Defunc b) -> Defunc (a -> b)
forall a a. (Defunc a -> Defunc a) -> Defunc (a -> a)
LAM_S (Lam b -> Defunc b
forall a. Lam a -> Defunc a
defuncTerm (Lam b -> Defunc b) -> (Defunc a -> Lam b) -> Defunc a -> Defunc b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Lam a -> Lam b
f (Lam a -> Lam b) -> (Defunc a -> Lam a) -> Defunc a -> Lam b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Defunc a -> Lam a
forall a. Defunc a -> Lam a
lamTerm)
    defuncTerm (App Lam (a -> a)
f Lam a
x)  = Defunc (a -> a) -> Defunc a -> Defunc a
forall a b. Defunc (a -> b) -> Defunc a -> Defunc b
APP_H (Lam (a -> a) -> Defunc (a -> a)
forall a. Lam a -> Defunc a
defuncTerm Lam (a -> a)
f) (Lam a -> Defunc a
forall a. Lam a -> Defunc a
defuncTerm Lam a
x)
    defuncTerm (Var Bool
_ Code a
x)  = Code a -> Defunc a
forall a. Code a -> Defunc a
unsafeBLACK Code a
x
    defuncTerm (If Lam Bool
c Lam a
t Lam a
e) = Defunc Bool -> Defunc a -> Defunc a -> Defunc a
forall a. Defunc Bool -> Defunc a -> Defunc a -> Defunc a
IF_S (Lam Bool -> Defunc Bool
forall a. Lam a -> Defunc a
defuncTerm Lam Bool
c) (Lam a -> Defunc a
forall a. Lam a -> Defunc a
defuncTerm Lam a
t) (Lam a -> Defunc a
forall a. Lam a -> Defunc a
defuncTerm Lam a
e)
    defuncTerm (Let Lam a
x Lam a -> Lam a
f)  = Defunc a -> (Defunc a -> Defunc a) -> Defunc a
forall a b. Defunc a -> (Defunc a -> Defunc b) -> Defunc b
LET_S (Lam a -> Defunc a
forall a. Lam a -> Defunc a
defuncTerm Lam a
x) (Lam a -> Defunc a
forall a. Lam a -> Defunc a
defuncTerm (Lam a -> Defunc a) -> (Defunc a -> Lam a) -> Defunc a -> Defunc a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Lam a -> Lam a
f (Lam a -> Lam a) -> (Defunc a -> Lam a) -> Defunc a -> Lam a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Defunc a -> Lam a
forall a. Defunc a -> Lam a
lamTerm)
    defuncTerm Lam a
T          = Bool -> Defunc Bool
forall a. (Show a, Lift a) => a -> Defunc a
LIFTED Bool
True
    defuncTerm Lam a
F          = Bool -> Defunc Bool
forall a. (Show a, Lift a) => a -> Defunc a
LIFTED Bool
False

unsafeBLACK :: Code a -> Defunc a
unsafeBLACK :: Code a -> Defunc a
unsafeBLACK = WQ a -> Defunc a
forall a. WQ a -> Defunc a
BLACK (WQ a -> Defunc a) -> (Code a -> WQ a) -> Code a -> Defunc a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Code a -> WQ a
forall a. a -> Code a -> WQ a
WQ a
forall a. HasCallStack => a
undefined

instance Show (Defunc a) where
  show :: Defunc a -> String
show Defunc a
COMPOSE = String
"(.)"
  show Defunc a
FLIP = String
"flip"
  show (FLIP_H Defunc x
f) = [String] -> String
forall (t :: Type -> Type) a. Foldable t => t [a] -> [a]
concat [String
"(flip ", Defunc x -> String
forall a. Show a => a -> String
show Defunc x
f, String
")"]
  show (COMPOSE_H Defunc x
f Defunc y
g) = [String] -> String
forall (t :: Type -> Type) a. Foldable t => t [a] -> [a]
concat [String
"(", Defunc x -> String
forall a. Show a => a -> String
show Defunc x
f, String
" . ", Defunc y -> String
forall a. Show a => a -> String
show Defunc y
g, String
")"]
  show (APP_H Defunc (a -> a)
f Defunc a
x) = [String] -> String
forall (t :: Type -> Type) a. Foldable t => t [a] -> [a]
concat [String
"(", Defunc (a -> a) -> String
forall a. Show a => a -> String
show Defunc (a -> a)
f, String
" ", Defunc a -> String
forall a. Show a => a -> String
show Defunc a
x, String
")"]
  show (LIFTED a
x) = a -> String
forall a. Show a => a -> String
show a
x
  show (EQ_H Defunc a
x) = [String] -> String
forall (t :: Type -> Type) a. Foldable t => t [a] -> [a]
concat [String
"(== ", Defunc a -> String
forall a. Show a => a -> String
show Defunc a
x, String
")"]
  show Defunc a
ID  = String
"id"
  show Defunc a
EMPTY = String
"[]"
  show Defunc a
CONS = String
"(:)"
  show Defunc a
CONST = String
"const"
  show (IF_S Defunc Bool
c Defunc a
b Defunc a
e) = [String] -> String
forall (t :: Type -> Type) a. Foldable t => t [a] -> [a]
concat [String
"(if ", Defunc Bool -> String
forall a. Show a => a -> String
show Defunc Bool
c, String
" then ", Defunc a -> String
forall a. Show a => a -> String
show Defunc a
b, String
" else ", Defunc a -> String
forall a. Show a => a -> String
show Defunc a
e, String
")"]
  show (LAM_S Defunc a -> Defunc b
_) = String
"f"
  show Defunc a
_ = String
"x"