define primrec in joy

icpdesign — 2005-08-20 21:24:49

The paper 'An Informal Tutorial on Joy', by Manfred von Thun, introduces the combinator 

primrec to compute the factorial of any integer. I am wondering if it is possible to define 

primrec using joy:



DEFINE

   primrec == ... 



Thanks

Taoufik

icpdesign — 2005-08-20 21:33:07

sorry but I am afraid that my previous message may not be clear.



The paper 'An Informal Tutorial on Joy', by Manfred von Thun, introduces the

combinator primrec that may be used to compute the factorial of any integer as follows:



factorial == [1] [*] primrec 



5 fatorial -> 120



I am wondering if it is possible to define primrec using joy language:



DEFINE

   primrec == ...



Thanks

Taoufik

Ivan Tomac — 2005-08-21 04:04:09

--- In concatenative@yahoogroups.com, "icpdesign"

<taoufik.dachraoui@w...> wrote:

 > The paper 'An Informal Tutorial on Joy', by Manfred von Thun,

 
introduces the combinator 

 > primrec to compute the factorial of any integer. I am wondering if

 
it is possible to define 

 > primrec using joy:

> 

> DEFINE

>    primrec == ... 

>



 
I don't have time to look into it right now but yes, it is possible.

Have a look at Brent Kirby's paper on Joy, "The Theory of

Concatenative Combinators" (http://tunes.org/~iepos/joy.html). It has

a lot of examples of how to construct combinators using other

combinators. It also mentions a few minimal bases of just two

combinators that can be used to create all other combinators.

 

 > Thanks

> Taoufik



 
Ivan

phimvt@lurac.latrobe.edu.au — 2005-08-22 07:40:53

On Sat, 20 Aug 2005, icpdesign wrote:



[..]



> I am wondering if it is possible to define primrec using joy

language:

> 

> DEFINE

>    primrec == ...



Here is a recursive solution:



DEFINE

  pr ==

    [ pop pop small ]

    [ pop pop ]

    [ [dup pred] dipd

      dup

      [pr] dip                   # recursion here

      i ]

    ifte;

  primrec ==

    [first] dip pr.

 

Note that pr could be used like this:

  5 1 [*] pr    ==>  120



Indeed, one might argue that pr is "better" than primrec.



If you did not want the recursion, there is likely to be another,

nonrecursive solution using the repeat combinator. But, as they say, "this

is left as an exercise". 



  - Manfred