Defunc.hs

{-# 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, charPred
  ) where

import Data.Typeable                    (Typeable, (:~:)(Refl), eqT)
import Language.Haskell.TH.Syntax       (Lift(..))
import Data.RangeSet                    (fromRanges, empty, complement)
import Parsley.Internal.Common.Utils    (WQ(..), Code, Quapplicative(..))
import Parsley.Internal.Core.CharPred   (CharPred(..), pattern Item, pattern Specific)
import Parsley.Internal.Core.Lam        (normaliseGen, Lam(..))

import qualified Parsley.Internal.Core.CharPred as CharPred (lamTerm)

{-|
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, typable 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

  {-|
  Designed to be a specialised form of character predicate: is a character within some given ranges
  (which are inclusive at both ends).

  @since 2.0.0.0
  -}
  RANGES  :: Bool                  -- ^ Does the range test for membership (@True@) or /no/ membership (@False@).
          -> [(Char, Char)]        -- ^ List of ranges of the form @(l, u)@: @l@ and @u@ are inclusive to the range.
          -> Defunc (Char -> Bool)

  -- 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 x qx               = BLACK (makeQ x qx)
  _val ID                  = id
  _val COMPOSE             = (.)
  _val FLIP                = flip
  _val (APP_H f x)         = _val f (_val x)
  _val (LIFTED x)          = x
  _val (EQ_H x)            = (_val x ==)
  _val CONS                = (:)
  _val CONST               = const
  _val EMPTY               = []
  _val (BLACK f)           = _val f
  -- Syntax
  _val (IF_S c t e)        = if _val c then _val t else _val e
  _val (LAM_S f)           = \x -> _val (f (makeQ x undefined))
  _val (LET_S x f)         = let y = _val x in _val (f (makeQ y undefined))
  _val (RANGES True rngs)  = \c -> any (\(l, u) -> l <= c || c <= u) rngs
  _val (RANGES False rngs) = \c -> all (\(l, u) -> l >= c || c >= u) rngs
  _code = normaliseGen . lamTerm
  (>*<) = 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 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 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 FLIP_CONST    = FLIP_H CONST
{-|
This pattern represents the unit value @()@.

@since 0.1.0.0
-}
pattern UNIT          :: Defunc ()
pattern UNIT          = LIFTED ()

{-|
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 ID = Abs id
lamTerm COMPOSE = Abs (\f -> Abs (\g -> Abs (App f . App g)))
lamTerm FLIP = Abs (\f -> Abs (\x -> Abs (\y -> App (App f y) x)))
lamTerm (APP_H f x) = App (lamTerm f) (lamTerm x)
lamTerm (LIFTED b) | Just Refl <- eqT @a @Bool = if b then T else F
lamTerm (LIFTED x) = Var True [||x||]
lamTerm (EQ_H x) = Abs (App (App (Var True [||(==)||]) (lamTerm x)))
lamTerm CONS = Var True [||(:)||]
lamTerm EMPTY = Var True [||[]||]
lamTerm CONST = Abs (Abs . const)
lamTerm (BLACK x) = Var False (_code x)
lamTerm rngs@(RANGES _ _) = CharPred.lamTerm (charPred rngs)
lamTerm (LAM_S f) = Abs (adaptLam f)
lamTerm (IF_S c t e) = If (lamTerm c) (lamTerm t) (lamTerm e)
lamTerm (LET_S x f) = Let (lamTerm x) (adaptLam f)

{-|
Converts a `Defunc` value into an equivalent `CharPred` value.

@since 2.1.0.0
-}
charPred :: Defunc (Char -> Bool) -> CharPred
charPred (EQ_H (LIFTED c)) = Specific c
charPred (RANGES False []) = Item
charPred (RANGES True [(l, u)]) | l == minBound, u == maxBound = Item
charPred (RANGES True cs) = Ranges (fromRanges cs)
charPred (RANGES False cs) = Ranges (complement (fromRanges cs))
charPred (APP_H CONST (LIFTED True)) = Item
charPred (APP_H CONST (LIFTED False)) = Ranges empty
charPred p = UserPred (_val p) (lamTerm p)

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

unsafeBLACK :: Code a -> Defunc a
unsafeBLACK = BLACK . WQ undefined

instance Show (Defunc a) where
  show COMPOSE = "(.)"
  show FLIP = "flip"
  show (FLIP_H f) = concat ["(flip ", show f, ")"]
  show (COMPOSE_H f g) = concat ["(", show f, " . ", show g, ")"]
  show (APP_H f x) = concat ["(", show f, " ", show x, ")"]
  show (LIFTED x) = show x
  show (EQ_H x) = concat ["(== ", show x, ")"]
  show ID  = "id"
  show EMPTY = "[]"
  show CONS = "(:)"
  show CONST = "const"
  show (IF_S c b e) = concat ["(if ", show c, " then ", show b, " else ", show e, ")"]
  show (LAM_S _) = "f"
  show p@RANGES{} = show (charPred p)
  show _ = "x"