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Y combinator

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  Y combinator Lars Brinkhoff <lars.spam@nocrew.org> - 2013-10-03 09:57 +0200
    Re: Y combinator anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2013-10-03 13:09 +0000
      Re: Y combinator Lars Brinkhoff <lars.spam@nocrew.org> - 2013-10-07 15:06 +0200

#26102 — Y combinator

> Defining Y in ANS Forth (no RECURSIVE) is left as an exercise to the
> reader:-)

I read, I exercised, I posted.

: y ( xt1 -- xt2 )   here tuck 2>r  1 cells allot
   :noname r> postpone literal postpone @ r> compile, postpone ;
   dup rot ! ;

\ Sample usage, factorial function:
:noname ( u1 xt -- u2 )   over ?dup if 1- swap execute * else 2drop 1 then ;
y 6 swap execute .

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#26105

Lars Brinkhoff <lars.spam@nocrew.org> writes:
[Anton Ertl in 2002:-)]
>> Defining Y in ANS Forth (no RECURSIVE) is left as an exercise to the
>> reader:-)
>
>I read, I exercised, I posted.
>
>: y ( xt1 -- xt2 )   here tuck 2>r  1 cells allot
>   :noname r> postpone literal postpone @ r> compile, postpone ;
>   dup rot ! ;

Nice.

Now Curry's definition of Y is

Y = lambda f.(lambda x.f (x x))(lambda x.f (x x))

I am wondering what capabilities of Forth we have to remove until we
have to go to these lengths.

- anton
-- 
M. Anton Ertl  http://www.complang.tuwien.ac.at/anton/home.html
comp.lang.forth FAQs: http://www.complang.tuwien.ac.at/forth/faq/toc.html
     New standard: http://www.forth200x.org/forth200x.html
   EuroForth 2013: http://www.euroforth.org/ef13/

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#26344

anton@mips.complang.tuwien.ac.at (Anton Ertl) writes:
> Lars Brinkhoff <lars.spam@nocrew.org> writes:
>>: y ( xt1 -- xt2 )   here tuck 2>r  1 cells allot
>>   :noname r> postpone literal postpone @ r> compile, postpone ;
>>   dup rot ! ;
>
> Nice.
>
> Now Curry's definition of Y is
>
> Y = lambda f.(lambda x.f (x x))(lambda x.f (x x))
>
> I am wondering what capabilities of Forth we have to remove until we
> have to go to these lengths.

"Why" indeed.

I was tempted to submit this smaller version, but felt that the named
definition was not quite in the spirit of the original Y.

: y ( xt "name" -- )   >in @ create >in ! , ' ,  does> 2@ execute ;

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