>module Model.Category where

>class CategoryExpr cat where
>   data Ob cat 
>   data Mor cat 
>   mor_source :: Mor cat -> Ob cat
>   mor_target :: Mor cat -> Ob cat
>   identity :: Ob cat -> Mor cat
>   mor_compose :: Mor cat -> Mor cat -> Mor cat
>   obj_eq :: Ob cat -> Ob cat -> Bool
>   mor_reduce :: Mor cat -> Mor cat

>composable_morphisms :: (CategoryExpr cat) => Mor cat -> Mor cat -> Bool
>composable_morphisms m n = obj_eq (mor_target m) (mor_source n)

>data FunctorCat dom cod

>instance (CategoryExpr dom, CategoryExpr cod) => CategoryExpr (FunctorCat dom cod) where
>   data Ob (FunctorCat dom cod) = Functor (Ob dom -> Ob cod)
>                                          (Mor dom -> Mor cod)
>   data Mor (FunctorCat dom cod) = NaturalTransformation (Ob dom -> Mor cod)
>   mor_source (NaturalTransformation f) = Functor (\obj -> mor_source (f obj))
>                                                 (\g -> f (mor_source g))
>   mor_target (NaturalTransformation f) = Functor (\obj -> mor_target (f obj))
>                                                 (\g -> f (mor_target g))
>   identity (Functor f m) = NaturalTransformation (\obj -> identity (f obj))
>   mor_compose (NaturalTransformation f) (NaturalTransformation g) = NaturalTransfromation (\a -> mor_compose (f a) (g a))
>   obj_eq (Functor f m) (Functor f' m') = -- ????


>data Terminal

>instance CategoryExpr Terminal where
>   data Ob Terminal = TerminalObject
>   data Mor Terminal = TerminalArrow (Ob Terminal)
>   mor_source (TerminalArrow x) = x
>   mor_target (TerminalArrow _) = TerminalObject
>   identity TerminalObject = TerminalArrow TerminalObject
>   mor_compose (TerminalArrow _) (TerminalArrow y) = TerminalArrow y
>   obj_eq TerminalObject TerminalObject = True
>   mor_reduce z = z