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{-#LANGUAGE PolyKinds, TypeFamilies, TypeOperators, ConstraintKinds, UndecidableInstances, FlexibleInstances, FunctionalDependencies, MultiParamTypeClasses, TypeOperators, KindSignatures #-} | |
import qualified Prelude ((.), id, String) | |
import Data.Proxy | |
import GHC.Exts | |
import GHC.TypeLits | |
class SmallCategory cat where | |
name :: Proxy cat -> Prelude.String | |
id ::(Objects cat a, CategoryMorphism cat morph) => morph a a | |
type Objects cat :: a -> Constraint | |
-- type Morph cat :: a -> a -> b | |
class CategoryMorphism cat morph | cat -> morph, morph -> cat where | |
(.) :: (Objects cat a, Objects cat b, Objects cat c) => b `morph` c -> a `morph` b -> a `morph` c | |
instance SmallCategory "Hask" where | |
id = Prelude.id | |
name Proxy = "Hask" | |
type Objects "Hask" = Vacuous "Hask" | |
-- type Morph "Hask" = (->) | |
instance CategoryMorphism "Hask" (->) where | |
(.) = (Prelude..) | |
--what I wish, using monoids and vector spaces as examples: | |
-- data Monoid = forall a. Monoid {identity :: a, op :: a -> a -> a} | |
-- instance SmallCategory "Monoids" FOR SOME MONOID m where | |
-- id = ((op m) (identity m)) | |
-- (.) = op m | |
-- type Objects "Monoids" a = (a ~ Monoid) | |
-- type Vector = [Double] | |
-- type Matrix = [[Double]] | |
-- instance SmallCategory "FinVect_k" where | |
-- id = fgsfds -- k-dimensional identity matrix | |
-- (.) = matrixMultiply | |
-- type Objects "FinVect_k" a = (a ~ forall m. [m]) | |
-- let m = Monoid 0 (+) using "Monoids" in 1 . 2 . 3 | |
-- let k = 3 using "FinVect_k" in a . b . c . d . id . e . a --rotation matrices for example |
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