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|
{-# LANGUAGE DerivingStrategies #-}
{-# LANGUAGE DerivingVia #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE InstanceSigs #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE MultiWayIf #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE UndecidableInstances #-}
module DerivingViaCompile where
import Data.Void
import Data.Complex
import Data.Functor.Const
import Data.Functor.Identity
import Data.Ratio
import Control.Monad.Reader
import Control.Monad.State
import Control.Monad.Writer
import Control.Applicative hiding (WrappedMonad(..))
import Data.Bifunctor
import Data.Monoid
import Data.Kind
type f ~> g = forall xx. f xx -> g xx
-----
-- Simple example
-----
data Foo a = MkFoo a a
deriving Show
via (Identity (Foo a))
-----
-- Eta reduction at work
-----
newtype Flip p a b = Flip { runFlip :: p b a }
instance Bifunctor p => Bifunctor (Flip p) where
bimap f g = Flip . bimap g f . runFlip
instance Bifunctor p => Functor (Flip p a) where
fmap f = Flip . first f . runFlip
newtype Bar a = MkBar (Either a Int)
deriving Functor
via (Flip Either Int)
-----
-- Monad transformers
-----
type MTrans = (Type -> Type) -> (Type -> Type)
-- From `constraints'
data Dict c where
Dict :: c => Dict c
newtype a :- b = Sub (a => Dict b)
infixl 1 \\
(\\) :: a => (b => r) -> (a :- b) -> r
r \\ Sub Dict = r
-- With `-XQuantifiedConstraints' this just becomes
--
-- type Lifting cls trans = forall mm. cls mm => cls (trans mm)
--
-- type LiftingMonad trans = Lifting Monad trans
--
class LiftingMonad (trans :: MTrans) where
proof :: Monad m :- Monad (trans m)
instance LiftingMonad (StateT s :: MTrans) where
proof :: Monad m :- Monad (StateT s m)
proof = Sub Dict
instance Monoid w => LiftingMonad (WriterT w :: MTrans) where
proof :: Monad m :- Monad (WriterT w m)
proof = Sub Dict
instance (LiftingMonad trans, LiftingMonad trans') => LiftingMonad (ComposeT trans trans' :: MTrans) where
proof :: forall m. Monad m :- Monad (ComposeT trans trans' m)
proof = Sub (Dict \\ proof @trans @(trans' m) \\ proof @trans' @m)
newtype Stack :: MTrans where
Stack :: ReaderT Int (StateT Bool (WriterT String m)) a -> Stack m a
deriving newtype
( Functor
, Applicative
, Monad
, MonadReader Int
, MonadState Bool
, MonadWriter String
)
deriving (MonadTrans, MFunctor)
via (ReaderT Int `ComposeT` StateT Bool `ComposeT` WriterT String)
class MFunctor (trans :: MTrans) where
hoist :: Monad m => (m ~> m') -> (trans m ~> trans m')
instance MFunctor (ReaderT r :: MTrans) where
hoist :: Monad m => (m ~> m') -> (ReaderT r m ~> ReaderT r m')
hoist nat = ReaderT . fmap nat . runReaderT
instance MFunctor (StateT s :: MTrans) where
hoist :: Monad m => (m ~> m') -> (StateT s m ~> StateT s m')
hoist nat = StateT . fmap nat . runStateT
instance MFunctor (WriterT w :: MTrans) where
hoist :: Monad m => (m ~> m') -> (WriterT w m ~> WriterT w m')
hoist nat = WriterT . nat . runWriterT
infixr 9 `ComposeT`
newtype ComposeT :: MTrans -> MTrans -> MTrans where
ComposeT :: { getComposeT :: f (g m) a } -> ComposeT f g m a
deriving newtype (Functor, Applicative, Monad)
instance (MonadTrans f, MonadTrans g, LiftingMonad g) => MonadTrans (ComposeT f g) where
lift :: forall m. Monad m => m ~> ComposeT f g m
lift = ComposeT . lift . lift
\\ proof @g @m
instance (MFunctor f, MFunctor g, LiftingMonad g) => MFunctor (ComposeT f g) where
hoist :: forall m m'. Monad m => (m ~> m') -> (ComposeT f g m ~> ComposeT f g m')
hoist f = ComposeT . hoist (hoist f) . getComposeT
\\ proof @g @m
-----
-- Using tuples in a `via` type
-----
newtype X a = X (a, a)
deriving (Semigroup, Monoid)
via (Product a, Sum a)
deriving (Show, Eq)
via (a, a)
-----
-- Abstract data types
-----
class C f where
c :: f a -> Int
newtype X2 f a = X2 (f a)
instance C (X2 f) where
c = const 0
deriving via (X2 IO) instance C IO
----
-- Testing parser
----
newtype P0 a = P0 a deriving Show via a
newtype P1 a = P1 [a] deriving Show via [a]
newtype P2 a = P2 (a, a) deriving Show via (a, a)
newtype P3 a = P3 (Maybe a) deriving Show via (First a)
newtype P4 a = P4 (Maybe a) deriving Show via (First $ a)
newtype P5 a = P5 a deriving Show via (Identity $ a)
newtype P6 a = P6 [a] deriving Show via ([] $ a)
newtype P7 a = P7 (a, a) deriving Show via (Identity $ (a, a))
newtype P8 a = P8 (Either () a) deriving Functor via (($) (Either ()))
newtype f $ a = APP (f a) deriving newtype Show deriving newtype Functor
----
-- From Baldur's notes
----
----
-- 1
----
newtype WrapApplicative f a = WrappedApplicative (f a)
deriving (Functor, Applicative)
instance (Applicative f, Num a) => Num (WrapApplicative f a) where
(+) = liftA2 (+)
(*) = liftA2 (*)
negate = fmap negate
fromInteger = pure . fromInteger
abs = fmap abs
signum = fmap signum
instance (Applicative f, Fractional a) => Fractional (WrapApplicative f a) where
recip = fmap recip
fromRational = pure . fromRational
instance (Applicative f, Floating a) => Floating (WrapApplicative f a) where
pi = pure pi
sqrt = fmap sqrt
exp = fmap exp
log = fmap log
sin = fmap sin
cos = fmap cos
asin = fmap asin
atan = fmap atan
acos = fmap acos
sinh = fmap sinh
cosh = fmap cosh
asinh = fmap asinh
atanh = fmap atanh
acosh = fmap acosh
instance (Applicative f, Semigroup s) => Semigroup (WrapApplicative f s) where
(<>) = liftA2 (<>)
instance (Applicative f, Monoid m) => Monoid (WrapApplicative f m) where
mempty = pure mempty
----
-- 2
----
class Pointed p where
pointed :: a -> p a
newtype WrapMonad f a = WrappedMonad (f a)
deriving newtype (Pointed, Monad)
instance (Monad m, Pointed m) => Functor (WrapMonad m) where
fmap = liftM
instance (Monad m, Pointed m) => Applicative (WrapMonad m) where
pure = pointed
(<*>) = ap
-- data
data Sorted a = Sorted a a a
deriving (Functor, Applicative)
via (WrapMonad Sorted)
deriving (Num, Fractional, Floating, Semigroup, Monoid)
via (WrapApplicative Sorted a)
instance Monad Sorted where
(>>=) :: Sorted a -> (a -> Sorted b) -> Sorted b
Sorted a b c >>= f = Sorted a' b' c' where
Sorted a' _ _ = f a
Sorted _ b' _ = f b
Sorted _ _ c' = f c
instance Pointed Sorted where
pointed :: a -> Sorted a
pointed a = Sorted a a a
----
-- 3
----
class IsZero a where
isZero :: a -> Bool
newtype WrappedNumEq a = WrappedNumEq a
newtype WrappedShow a = WrappedShow a
newtype WrappedNumEq2 a = WrappedNumEq2 a
instance (Num a, Eq a) => IsZero (WrappedNumEq a) where
isZero :: WrappedNumEq a -> Bool
isZero (WrappedNumEq a) = 0 == a
instance Show a => IsZero (WrappedShow a) where
isZero :: WrappedShow a -> Bool
isZero (WrappedShow a) = "0" == show a
instance (Num a, Eq a) => IsZero (WrappedNumEq2 a) where
isZero :: WrappedNumEq2 a -> Bool
isZero (WrappedNumEq2 a) = a + a == a
newtype INT = INT Int
deriving newtype Show
deriving IsZero via (WrappedNumEq Int)
newtype VOID = VOID Void deriving IsZero via (WrappedShow Void)
----
-- 4
----
class Bifunctor p => Biapplicative p where
bipure :: a -> b -> p a b
biliftA2
:: (a -> b -> c)
-> (a' -> b' -> c')
-> p a a'
-> p b b'
-> p c c'
instance Biapplicative (,) where
bipure = (,)
biliftA2 f f' (a, a') (b, b') =
(f a b, f' a' b')
newtype WrapBiapp p a b = WrapBiap (p a b)
deriving newtype (Bifunctor, Biapplicative, Eq)
instance (Biapplicative p, Num a, Num b) => Num (WrapBiapp p a b) where
(+) = biliftA2 (+) (+)
(-) = biliftA2 (*) (*)
(*) = biliftA2 (*) (*)
negate = bimap negate negate
abs = bimap abs abs
signum = bimap signum signum
fromInteger n = fromInteger n `bipure` fromInteger n
newtype INT2 = INT2 (Int, Int)
deriving IsZero via (WrappedNumEq2 (WrapBiapp (,) Int Int))
----
-- 5
----
class Monoid a => MonoidNull a where
null :: a -> Bool
newtype WrpMonNull a = WRM a deriving (Eq, Semigroup, Monoid)
instance (Eq a, Monoid a) => MonoidNull (WrpMonNull a) where
null :: WrpMonNull a -> Bool
null = (== mempty)
deriving via (WrpMonNull Any) instance MonoidNull Any
deriving via () instance MonoidNull ()
deriving via Ordering instance MonoidNull Ordering
----
-- 6
----
-- https://github.com/mikeizbicki/subhask/blob/f53fd8f465747681c88276c7dabe3646fbdf7d50/src/SubHask/Algebra.hs#L635
class Lattice a where
sup :: a -> a -> a
(.>=) :: a -> a -> Bool
(.>) :: a -> a -> Bool
newtype WrapOrd a = WrappedOrd a
deriving newtype (Eq, Ord)
instance Ord a => Lattice (WrapOrd a) where
sup = max
(.>=) = (>=)
(.>) = (>)
deriving via [a] instance Ord a => Lattice [a]
deriving via (a, b) instance (Ord a, Ord b) => Lattice (a, b)
--mkLattice_(Bool)
deriving via Bool instance Lattice Bool
--mkLattice_(Char)
deriving via Char instance Lattice Char
--mkLattice_(Int)
deriving via Int instance Lattice Int
--mkLattice_(Integer)
deriving via Integer instance Lattice Integer
--mkLattice_(Float)
deriving via Float instance Lattice Float
--mkLattice_(Double)
deriving via Double instance Lattice Double
--mkLattice_(Rational)
deriving via Rational instance Lattice Rational
----
-- 7
----
-- https://hackage.haskell.org/package/linear-1.20.7/docs/src/Linear-Affine.html
class Functor f => Additive f where
zero :: Num a => f a
(^+^) :: Num a => f a -> f a -> f a
(^+^) = liftU2 (+)
(^-^) :: Num a => f a -> f a -> f a
x ^-^ y = x ^+^ fmap negate y
liftU2 :: (a -> a -> a) -> f a -> f a -> f a
instance Additive [] where
zero = []
liftU2 f = go where
go (x:xs) (y:ys) = f x y : go xs ys
go [] ys = ys
go xs [] = xs
instance Additive Maybe where
zero = Nothing
liftU2 f (Just a) (Just b) = Just (f a b)
liftU2 _ Nothing ys = ys
liftU2 _ xs Nothing = xs
instance Applicative f => Additive (WrapApplicative f) where
zero = pure 0
liftU2 = liftA2
deriving via (WrapApplicative ((->) a)) instance Additive ((->) a)
deriving via (WrapApplicative Complex) instance Additive Complex
deriving via (WrapApplicative Identity) instance Additive Identity
instance Additive ZipList where
zero = ZipList []
liftU2 f (ZipList xs) (ZipList ys) = ZipList (liftU2 f xs ys)
class Additive (Diff p) => Affine p where
type Diff p :: Type -> Type
(.-.) :: Num a => p a -> p a -> Diff p a
(.+^) :: Num a => p a -> Diff p a -> p a
(.-^) :: Num a => p a -> Diff p a -> p a
p .-^ v = p .+^ fmap negate v
-- #define ADDITIVEC(CTX,T) instance CTX => Affine T where type Diff T = T ; \
-- (.-.) = (^-^) ; {-# INLINE (.-.) #-} ; (.+^) = (^+^) ; {-# INLINE (.+^) #-} ; \
-- (.-^) = (^-^) ; {-# INLINE (.-^) #-}
-- #define ADDITIVE(T) ADDITIVEC((), T)
newtype WrapAdditive f a = WrappedAdditive (f a)
instance Additive f => Affine (WrapAdditive f) where
type Diff (WrapAdditive f) = f
WrappedAdditive a .-. WrappedAdditive b = a ^-^ b
WrappedAdditive a .+^ b = WrappedAdditive (a ^+^ b)
WrappedAdditive a .-^ b = WrappedAdditive (a ^-^ b)
-- ADDITIVE(((->) a))
deriving via (WrapAdditive ((->) a)) instance Affine ((->) a)
-- ADDITIVE([])
deriving via (WrapAdditive []) instance Affine []
-- ADDITIVE(Complex)
deriving via (WrapAdditive Complex) instance Affine Complex
-- ADDITIVE(Maybe)
deriving via (WrapAdditive Maybe) instance Affine Maybe
-- ADDITIVE(ZipList)
deriving via (WrapAdditive ZipList) instance Affine ZipList
-- ADDITIVE(Identity)
deriving via (WrapAdditive Identity) instance Affine Identity
----
-- 8
----
class C2 a b c where
c2 :: a -> b -> c
instance C2 a b (Const a b) where
c2 x _ = Const x
newtype Fweemp a = Fweemp a
deriving (C2 a b)
via (Const a (b :: Type))
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