{-# LANGUAGE
    TypeFamilies
  , ConstraintKinds
  , MultiParamTypeClasses
  , FlexibleInstances
  , UndecidableInstances
  #-}
-----------------------------------------------------------------------------
-- |
-- Module      :  Data.Algebra.Internal
-- Copyright   :  (c) Sjoerd Visscher 2013
-- License     :  BSD-style (see the file LICENSE)
--
-- Maintainer  :  sjoerd@w3future.com
-- Stability   :  experimental
-- Portability :  non-portable
-----------------------------------------------------------------------------
module Data.Algebra.Internal where

import GHC.Exts (Constraint)
import Control.Applicative (Const)
import Data.Monoid (Ap)

import GHC.Conc (STM)
import Control.Arrow ((&&&))

-- | The signature datatype for the class @c@.
type family Signature (c :: * -> Constraint) :: * -> *

class Traversable f => AlgebraSignature f where
  -- | The class for which @f@ is the signature.
  type Class f :: * -> Constraint
  -- | Translate the operations of the signature to method calls of the class.
  evaluate :: Class f b => f b -> b

class Algebra f a where
  -- | An algebra @f a -> a@ corresponds to an instance of @a@ of the class @Class f@.
  --   In some cases, for example for tuple types, you can give an algebra generically for every signature:
  --
  -- > instance (Class f m, Class f n) => Algebra f (m, n) where
  -- >   algebra fmn = (evaluate (fmap fst fmn), evaluate (fmap snd fmn))
  algebra :: AlgebraSignature f => f a -> a

-- | If you just want to applicatively lift existing instances, you can use this default implementation of `algebra`.
algebraA :: (Applicative g, Class f b, AlgebraSignature f) => f (g b) -> g b
algebraA :: f (g b) -> g b
algebraA = (f b -> b) -> g (f b) -> g b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap f b -> b
forall (f :: * -> *) b. (AlgebraSignature f, Class f b) => f b -> b
evaluate (g (f b) -> g b) -> (f (g b) -> g (f b)) -> f (g b) -> g b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. f (g b) -> g (f b)
forall (t :: * -> *) (f :: * -> *) a.
(Traversable t, Applicative f) =>
t (f a) -> f (t a)
sequenceA

instance Algebra f () where
  algebra :: f () -> ()
algebra = () -> f () -> ()
forall a b. a -> b -> a
const ()
instance (Class f m, Class f n) => Algebra f (m, n) where
  algebra :: f (m, n) -> (m, n)
algebra = f m -> m
forall (f :: * -> *) b. (AlgebraSignature f, Class f b) => f b -> b
evaluate (f m -> m) -> (f (m, n) -> f m) -> f (m, n) -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. ((m, n) -> m) -> f (m, n) -> f m
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (m, n) -> m
forall a b. (a, b) -> a
fst (f (m, n) -> m) -> (f (m, n) -> n) -> f (m, n) -> (m, n)
forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
&&& f n -> n
forall (f :: * -> *) b. (AlgebraSignature f, Class f b) => f b -> b
evaluate (f n -> n) -> (f (m, n) -> f n) -> f (m, n) -> n
forall b c a. (b -> c) -> (a -> b) -> a -> c
. ((m, n) -> n) -> f (m, n) -> f n
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (m, n) -> n
forall a b. (a, b) -> b
snd

instance Class f b => Algebra f (a -> b) where algebra :: f (a -> b) -> a -> b
algebra = f (a -> b) -> a -> b
forall (g :: * -> *) (f :: * -> *) b.
(Applicative g, Class f b, AlgebraSignature f) =>
f (g b) -> g b
algebraA
instance Class f b => Algebra f (IO b) where algebra :: f (IO b) -> IO b
algebra = f (IO b) -> IO b
forall (g :: * -> *) (f :: * -> *) b.
(Applicative g, Class f b, AlgebraSignature f) =>
f (g b) -> g b
algebraA
instance Class f b => Algebra f (Maybe b) where algebra :: f (Maybe b) -> Maybe b
algebra = f (Maybe b) -> Maybe b
forall (g :: * -> *) (f :: * -> *) b.
(Applicative g, Class f b, AlgebraSignature f) =>
f (g b) -> g b
algebraA
instance Class f b => Algebra f (Either a b) where algebra :: f (Either a b) -> Either a b
algebra = f (Either a b) -> Either a b
forall (g :: * -> *) (f :: * -> *) b.
(Applicative g, Class f b, AlgebraSignature f) =>
f (g b) -> g b
algebraA
instance Class f b => Algebra f (STM b) where algebra :: f (STM b) -> STM b
algebra = f (STM b) -> STM b
forall (g :: * -> *) (f :: * -> *) b.
(Applicative g, Class f b, AlgebraSignature f) =>
f (g b) -> g b
algebraA
instance (Class f b, Applicative g) => Algebra f (Ap g b) where algebra :: f (Ap g b) -> Ap g b
algebra = f (Ap g b) -> Ap g b
forall (g :: * -> *) (f :: * -> *) b.
(Applicative g, Class f b, AlgebraSignature f) =>
f (g b) -> g b
algebraA
instance (Monoid m, Class f b) => Algebra f (Const m b) where algebra :: f (Const m b) -> Const m b
algebra = f (Const m b) -> Const m b
forall (g :: * -> *) (f :: * -> *) b.
(Applicative g, Class f b, AlgebraSignature f) =>
f (g b) -> g b
algebraA