[Haskell-cafe] CCC MyType

[Lafras Uys]

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List,

I'm trying to wrap my head around Haskell and Category Theory---very new
to both and in keeping with character, I've jumped into the deep-end.
The categories and category-extras packages have helped to illustrate
some concepts. However, I remain confused and hope someone can point me
in the right direction.

The ultimate goal is to construct my own instance of a CCC. Here is the
class definition for CCC from the categories package:

> class ( Cartesian (<=)
>       , Symmetric (<=) (Product (<=))
>       , Monoidal (<=) (Product (<=))
>       ) => CCC (<=) where
>    type Exp (<=) :: * -> * -> *
>    apply :: (Product (<=) (Exp (<=) a b) a) <= b
>    curry :: ((Product (<=) a b) <= c) -> a <= Exp (<=) b c
>    uncurry :: (a <= (Exp (<=) b c)) -> (Product (<=>) a b <= c)

I have the following:

> {-# LANGUAGE  TypeFamilies,
>               MultiParamTypeClasses,
>               UndecidableInstances #-}

> import Control.Category.Braided
> import Control.Category.Associative
> import Control.Category.Cartesian
> import Control.Category.Monoidal
> import Control.Category.Cartesian.Closed

> data MyType a b = MyType {f::(a -> b)}
> data SomeType a b = SomeType {g::(a,b)}

> instance (Symmetric MyType (Product MyType),
>           Monoidal MyType (Product MyType),
>           PreCartesian MyType) => CCC MyType where

>   type Exp MyType = SomeType

It type checks in ghci and gives the appropriate warnings that apply,
curry and uncurry have not been defined---I can't see how to define
these. Is it actually possible with the two data types I have?

I would really appreciate some help.

Lafras
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