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|
{-# LANGUAGE GeneralizedNewtypeDeriving, DeriveFunctor #-}
module Clothes
where
import Prelude hiding ((.), id)
import Control.Category
import Data.Functor.Classes (Eq1(..), Show1(..), liftShowsPrec2, showsUnaryWith)
import Data.Functor.Identity
import qualified Data.List.NonEmpty as NE
import Data.Typeable
import Test.Tasty.QuickCheck
data UnitF a = UnitF deriving(Eq, Show, Typeable)
data F a = F [a]
deriving(Eq, Show, Typeable, Functor)
instance Eq1 F where
liftEq eq (F as) (F bs) = liftEq eq as bs
instance Show1 F where
liftShowsPrec sp sl d (F as)
= showsUnaryWith (liftShowsPrec sp sl) "F" d as
data G a = NoG | G1 a | Gn [a]
deriving(Eq, Show, Typeable, Functor)
instance Eq1 G where
liftEq _ NoG NoG = True
liftEq _ NoG _ = False
liftEq eq (G1 a) (G1 b) = a `eq` b
liftEq _ (G1 _) _ = False
liftEq eq (Gn as) (Gn bs) = liftEq eq as bs
liftEq _ (Gn _ ) _ = False
instance Show1 G where
liftShowsPrec sp sl d = \case
NoG -> showString "NoG"
G1 a -> showsUnaryWith sp "G1" d a
Gn as -> showsUnaryWith (liftShowsPrec sp sl) "Gn" d as
data H a = NoH1 | NoH2 | H1 [a] | H2 [a] | H3 [a]
deriving(Eq, Show, Typeable, Functor)
instance Show1 H where
liftShowsPrec sp sl d = \case
NoH1 -> showString "NoH1"
NoH2 -> showString "NoH2"
H1 as -> showsUnaryWith (liftShowsPrec sp sl) "H1" d as
H2 as -> showsUnaryWith (liftShowsPrec sp sl) "H2" d as
H3 as -> showsUnaryWith (liftShowsPrec sp sl) "H3" d as
instance Eq1 H where
liftEq _ NoH1 NoH1 = True
liftEq _ NoH1 _ = False
liftEq _ NoH2 NoH2 = True
liftEq _ NoH2 _ = False
liftEq eq (H1 as) (H1 bs) = liftEq eq as bs
liftEq _ (H1 _ ) _ = False
liftEq eq (H2 as) (H2 bs) = liftEq eq as bs
liftEq _ (H2 _ ) _ = False
liftEq eq (H3 as) (H3 bs) = liftEq eq as bs
liftEq _ (H3 _ ) _ = False
data I a = NoI1 | NoI2 | NoI3 | I1 a | I2 (a,a)
deriving(Eq, Show, Typeable)
instance Show1 I where
liftShowsPrec sp sl d = \case
NoI1 -> showString "NoI1"
NoI2 -> showString "NoI2"
NoI3 -> showString "NoI3"
I1 a -> showsUnaryWith sp "I1" d a
I2 aa -> showsUnaryWith (liftShowsPrec2 sp sl sp sl) "I2" d aa
instance Eq1 I where
liftEq _ NoI1 NoI1 = True
liftEq _ NoI1 _ = False
liftEq _ NoI2 NoI2 = True
liftEq _ NoI2 _ = False
liftEq _ NoI3 NoI3 = True
liftEq _ NoI3 _ = False
liftEq eq (I1 a) (I1 b) = a `eq` b
liftEq _ (I1 _ ) _ = False
liftEq eq (I2 (a,b)) (I2 (c,d)) = (a `eq` c) && (b `eq` d)
liftEq _ (I2 _ ) _ = False
instance Arbitrary a => Arbitrary (F a) where
arbitrary
= scale (`div` 2) $
F <$> arbitrary
instance Arbitrary a => Arbitrary (G a) where
arbitrary
= scale (`div` 2) $
oneof
[ pure NoG
, G1 <$> arbitrary
, Gn <$> arbitrary
]
instance Arbitrary a => Arbitrary (H a) where
arbitrary
= scale (`div` 2) $
oneof
[ pure NoH1
, pure NoH2
, H1 <$> arbitrary
, H2 <$> arbitrary
, H3 <$> arbitrary
]
instance Arbitrary a => Arbitrary (I a) where
arbitrary
= scale (`div` 2) $
oneof
[ pure NoI1
, pure NoI2
, pure NoI3
, I1 <$> arbitrary
, I2 <$> arbitrary
]
newtype NatTransf f g
= NatTransf {applyNat :: (forall a . f a -> g a)}
instance Category NatTransf where
id = NatTransf id
f . g = NatTransf (applyNat f . applyNat g)
point :: (forall a . a -> f a) -> NatTransf Identity f
point mkPoint
= NatTransf (\(Identity a) -> mkPoint a)
unit :: (forall a . f a) -> NatTransf UnitF f
unit u
= NatTransf (\UnitF -> u)
headF :: NatTransf NE.NonEmpty Identity
headF
= NatTransf (\(a NE.:| _) -> Identity a)
terminal :: NatTransf f UnitF
terminal
= NatTransf (const UnitF)
instance (ArbitraryF f, ArbitraryF g) => Arbitrary (NatTransf f g) where
arbitrary
= scale (`div` 2) $
do fromList <- arbitraryf
pure (fromList . flattenf)
class ArbitraryF f where
arbitraryf :: Gen (NatTransf [] f)
flattenf :: NatTransf f []
instance ArbitraryF F where
arbitraryf
= pure $ NatTransf F
flattenf
= NatTransf (\(F as) -> as)
instance ArbitraryF G where
arbitraryf
= mkArbitraryf
[unit NoG]
[point G1 , point (Gn . pure)]
[NatTransf (Gn . NE.toList)]
flattenf
= NatTransf $ \case
NoG -> []
G1 a -> [a]
Gn as -> as
instance ArbitraryF H where
arbitraryf
= mkArbitraryf
[unit NoH1, unit NoH2]
[point (H1 . pure), point (H2 . pure)]
[ NatTransf (H1 . NE.toList)
, NatTransf (H2 . NE.toList)
, NatTransf (H2 . NE.toList)
]
flattenf
= NatTransf $ \case
NoH1 -> []
NoH2 -> []
H1 as -> as
H2 as -> as
H3 as -> as
instance ArbitraryF I where
arbitraryf
= mkArbitraryf
[unit NoI1, unit NoI2, unit NoI3]
[point I1, NatTransf (\(Identity a) -> I2 (a, a))]
[ NatTransf mkI2 ]
where
mkI2 = \case
a NE.:| [] -> I2 (a, a)
a NE.:| (b:_) -> I2 (a, b)
flattenf
= NatTransf $ \case
NoI1 -> []
NoI2 -> []
NoI3 -> []
I1 a -> [a]
I2 (a,b) -> [a,b]
mkArbitraryf
:: [NatTransf UnitF f]
-> [NatTransf Identity f]
-> [NatTransf NE.NonEmpty f]
-> Gen (NatTransf [] f)
mkArbitraryf us is ls
= do let nullary = us
unary = is ++ map (. terminal) nullary
nary = ls ++ map (. headF) unary
build <$> elements nullary <*> elements unary <*> elements nary
where
build u i l
= NatTransf $ \case
[] -> applyNat u UnitF
[a] -> applyNat i (Identity a)
a:as -> applyNat l (a NE.:| as)
newtype FG
= FG (NatTransf F G)
deriving (Arbitrary)
newtype GH
= GH (NatTransf G H)
deriving (Arbitrary)
newtype HI
= HI (NatTransf H I)
deriving (Arbitrary)
instance Show FG
where show _ = "<natural-transformation :: F -> G>"
instance Show GH
where show _ = "<natural-transformation :: G -> H>"
instance Show HI
where show _ = "<natural-transformation :: H -> I>"
|
