Re: [stack] recursive combinators in other languages

----- Original Message ----- 
From: "rahul" <[email protected]>
To: <[email protected]>
Sent: Sunday, March 16, 2008 3:15 AM
Subject: Re: [stack] recursive combinators in other languages


> Christopher Diggins:
> 
>>> Are there other languages that use the same form?
>>
>> Well this isn't so much a language property, as a feature of the
>> standard library. Some languages make it easy to define combinators of
>> that form, but they aren't idiomatic (Haskell for example).
> 
> Well, it is certainly possible to achieve the same in any language that
> support lambdas, but none are as elegent as in Joy (AFAIK). I was
> surprised by the very consise definition and pervasive use of these
> in Nial. (Is it done the same way in K and J ?)

at one point i thought it might be useful to have a set of joy-style
recursive combinators in k.  we have six iterators which cover most
of the iteration cases encountered (e.g. */ for product, -': for 
pairwise difference, &c.), so the usefulness of a parallel set of 
"recursors" depends on how often nothing but recursion will do.  in 
many instances, an algorithm you'd normally define recursively has 
an iterative solution which can then be expressed with iterators, e.g.:

    fibonacci:(|+\)\1 1

but it isn't difficult to define the recursors:

    rec:{[c;h;f;g;x]$[c x;h x;f[x;rec[c;h;f;g]g x]]}

    fac:rec[0=;{1};*/;-1+]
    fac 5
  120

rec takes four arguments, each of which is a function, and a fifth
argument, which is the data over which to recur.

> 
> see also Q5 in
> http://www.latrobe.edu.au/philosophy/phimvt/joy/faq1.html
> 
> 
> 
> 
> ...
>>> The definition of factorial in Nial is given by
>>>
>>> factorial is recur [ 0 =, 1 first, pass, product, -1 +]
> 
> ------------------------------------
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> 
> 
> 

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