Covariant, contravariant, and invariant functor explosion
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module Main
( main
) where
import Data.Foldable (traverse_)
import Data.List (intercalate)
data Variance =
Co | Contra | In
deriving (Bounded, Enum)
showVariance :: Variance -> String
showVariance Co = "O"
showVariance Contra = "I"
showVariance In = "X"
showParameter :: Int -> Variance -> String
showParameter n Co = "(a" ++ show n ++ " -> b" ++ show n ++ ")"
showParameter n Contra = "(b" ++ show n ++ " -> a" ++ show n ++ ")"
showParameter n In = "(a" ++ show n ++ " -> b" ++ show n ++ ") -> " ++
"(b" ++ show n ++ " -> a" ++ show n ++ ")"
showType :: [Variance] -> String
showType variances =
let
parameters :: String
parameters = intercalate " -> " . fmap (uncurry showParameter) $
[1 ..] `zip` variances
arguments :: String -> String
arguments t = intercalate " " . fmap ((t ++) . show) $
[1 .. length variances]
in
parameters ++ " -> f " ++ arguments "a"
++ " -> f " ++ arguments "b"
functors :: [String]
functors =
[ "class Functor" ++ foldMap showVariance variances ++ " f where\n" ++
" map" ++ foldMap showVariance variances ++ " :: " ++ showType variances
| count <- [1 .. 4]
, variances <- traverse (const [minBound .. maxBound])
[1 .. count] ]
main :: IO ()
main = traverse_ putStrLn functors
Haskell
INFO