[Haskell-cafe] CCC MyType

[Lafras Uys]

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On 01/10/2010 04:54, Brent Yorgey wrote:
> On Wed, Sep 22, 2010 at 04:57:42PM +0200, Lafras Uys wrote:
>>
>>> 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
> 
> This doesn't seem right to me.  I would expect
> 
>   type Exp MyType = MyType
> 
> and 
> 
>   type Product MyType = SomeType
> 
> since the exponential objects corresponding to functions are
> precisely function types.

Thanks to everyone who have responded so far, on and off the list.

As one person noted, I had to dispense with the class assumptions first.
 This I've done and everything type checks. It was also suggested that I
choose more suggestive names for my data types.

Brent, you're right it is not correct. The following seems to work---at
least it type checks.

> newtype Fun a b = Fun {unFun :: a -> b }
> newtype Prod a b = Prod {unProd :: (a,b) } deriving (Show)

... class assumptions handled here.

> instance (Associative Fun Prod,
>           Disassociative Fun Prod,
>           Symmetric Fun Prod) => PreCartesian Fun where
>   type Product Fun = Prod
>   fst = Fun pFst
>   snd = Fun pSnd
>   diag = Fun pDiag

> pApply :: Prod (Fun a b) a -> b
> pApply (Prod (Fun f, x)) = f x

> pCurry :: ((Prod a b) -> c) -> a -> Fun b c
> pCurry p x = Fun (p . Prod . (,) x)

> instance (Symmetric Fun Prod,
>           Monoidal Fun Prod,
>           PreCartesian Fun) => CCC Fun where
>  type Exp Fun = Fun
>  apply = Fun pApply
>  curry (Fun f) = Fun (pCurry f)

I can now find explicit bindings for apply and curry, however not for
uncurry. The type signature for uncurry introduces a new type
constructor (<=>),

> uncurry :: <= a (Exp <= b c) -> <= (Product <=> a b) c

I'm not sure what the meaning of (<=>) is? If someone could provide some
pointers, I would be much obliged.

Thanks again for all the responses,

Lafras
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