Re: [stack] sweetening concatenative syntax

On Mar 6, 2008, at 6:12 PM, Stevan Apter wrote:

> forget about the partial application case.  what i want in my toolkit
> is a single combinator 'map' which takes an n-ary function and applies
> it to each of a list of length-n lists.

Ah, I think maybe there's some confusion here over what we mean by  
"list". (Yes, really!) In Joy, lists, stacks, and functions are all  
magically the same thing. I assume it's similar in XY as well. In  
Fifth, lists, stacks, and functions are all different things. This is  
just one more example of the endless complication that types introduce.

The 'mapx' function I gave before took a list of lists and a function  
of type 'a b -> b'. In other words, the function is restricted to  
taking only two arguments as is standard for the 'fold' combinator.

It sounds to me like what you're describing is a function that takes a  
list of *stacks* and applies an n-ary function to each stack in the  
list. This is doable, where 'map' below is the "normal" map you'd find  
in a language like ML, Haskell, or Fifth:

    mapx :: {(Stack A)} [A -> B] -> {(Stack B)}
    mapx = quote [infra] compose map

There are some limitations. In particular, all stacks in the list need  
to be of the same type. Due to how row variables in stack types must  
get instantiated (the row variables are stripped out), all stacks must  
have the same number of elements and elements in corresponding  
positions in each stack must be of the same type.

This limitation probably isn't too onerous in practice as I can't  
imagine the use case for mapping over a list of elements of various  
types. Note that when I say all elements must be the same type, I  
don't mean that they must all be ints or that they must all be  
strings. You can always introduce sum types for handling any  
combination of types you want. The only requirement is that you  
explicitly wrap up all types into the sum type with the appropriate  
constructors. A sum type deconstructor ensures that you handle all  
possible cases when you translate back to the "raw" types.

- John