Re: [stack] sweetening concatenative syntax

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.  not map1, map2, ... for each
case.  is that what's going on here?  or does typing rule out having
such a combinator?


----- Original Message ----- 
From: "John Nowak" <[email protected]>
To: <[email protected]>
Sent: Thursday, March 06, 2008 5:40 PM
Subject: Re: [stack] sweetening concatenative syntax


> 
> On Mar 6, 2008, at 5:00 PM, Stevan Apter wrote:
> 
>> ack.  it's been so long since i looked at this stuff that i'd
>> forgotten that 'map' in f/g and XY is an extension of the standard
>> definition:  given a list of k-length lists, it applies a n-ary
>> function n>=k to each element of the list.  so e.g.
>>
>>    [[1 2][3 4][5 6]][+]map -> [3 7 11]
>>
>> if n>k, then e.g. f "projects":
>>
>>    [[1][3 4][5 6 7]][+ *][map] -> [[1 + *][7 *] 18]
>>
>> i knew it looked more complex than it had to be!  anyway, i'd
>> be curious how you would write this combinator (call it 'mapx').
> 
> (I'm only going to handle the first case of 'map' above. There's no  
> way for the type system to handle the second.)
> 
> Here's one way, writing other highly useful combinators as we go:
> 
> f map     = [ ] [x xs -> x f i xs f map cons] unlist
> z f foldl = [z] [x xs -> xs z x f i f foldl] unlist
> foldl1    = [uncons swap] dip fold
> mapx      = [foldl1] compose map
> 
> Here's another, this time pointfree. I stole the definition of 'foldl'  
> from Cat; there may be a better one. The 'pa' function is partial  
> application (a [B a -> C] -> [B -> C]). Note that this version of map  
> is tail recursive, unlike the above version:
> 
> foldl  = swapd [dip] pa [uncons swap] swap compose [null? not] while
> foldl1 = [uncons swap] dip fold
> rmap   = null swap [cons] compose fold
> map    = rmap reverse
> mapx   = [foldl1] compose map
> 
> - John
>