[Haskell-cafe] Curry and uncurry

[Derek Elkins]

On Wed, 2007-10-03 at 22:31 +1000, Stuart Cook wrote:
> On 10/3/07, PR Stanley <prstanley at ntlworld.com> wrote:
> >         Without looking at the standard prelude, define the
> >         higher-order library function curry that converts a function
> >         on pairs into a curried
> >         function, and conversely, the function uncurry
> >         that converts a curried
> >         function with two arguments into a function on pairs.
> 
> In other words, take a function like[1]
> 
>   add a b = a + b
> 
> and make the following possible:
> 
>   (uncurry add) (2, 3)
> 
> Conversely, take a function like
> 
>   sub' (a, b) = a - b
> 
> and make the following possible:
> 
>   (curry sub') 4 1
> 
> 
> >         Hint: first write down the types of the two functions.
> 
> This, I think, is the key part, and it's a useful technique for
> Haskell in general.
> 
> First, write down the (general) type of a curried function, and the
> type of the corresponding uncurried function. Use those types to
> figure out what types curry and uncurry should have. Once you've done
> that, the implementation (which is pretty straightforward) should
> reveal itself.

Indeed, modulo bottom, the implementation of these functions is
-completely- determined by the types.  Djinn, for example, can
automatically generate the implementations from the types.