Yes, it is cheating. :) The problem is that the only names allowed
should refer to arguments (a la λ-calculus) and once you replace AAr the
assignment is visible.
I think I figured out a way but I have tested it only a little bit,
M=. 'if. * y do. y * u <: y else. 1 end.' (1 :)
M=. (5!:1)<'M'
Y=. (1 : '<(<,'':''),<(<(,''0'');1),<(,''0'');, (''u
u`:6('',(5!:5<''u''),'')`:6 y'')')(1 : 'u (u`:6)')
M Y("0) i.11
1 1 2 6 24 120 720 5040 40320 362880 3628800
It looks ugly but I guess that is the price one has to pay to be orthodox
and fully functional.
On Fri, Nov 16, 2018 at 12:22 AM 'Pascal Jasmin' via Programming <
[email protected]> wrote:
> I can cheat, by hiding the assignment in another function.
>
> AAr =: 1 : '(5!:1 < ''a'') a =. 1 : m'
>
> 'u u`:6('',(5!:5<''u''),'')`:6 y' AAr
> <(<,':'),<(<(,'0');1),<(,'0');,:'u u`:6('',(5!:5<''u''),'')`:6 y' (1 : 'u
> u`:6('',(5!:5<''u''),'')`:6 y')
>
> this is not the same as Y though.
>
> but this is,
>
> YAr =: 1 : '1 : (''(5!:1 < ''''a'''') a =. 1 : '' , ''('' , m , '')'' )'
> Y1 =. '''u u`:6('',(5!:5<''u''),'')`:6 y''' YAr
>
>
>
>
> ________________________________
> From: Jose Mario Quintana <[email protected]>
> To: [email protected]
> Sent: Thursday, November 15, 2018 6:01 PM
> Subject: Re: [Jprogramming] Revisisting the Y combinator
>
>
>
> Some authors regard functional programming as programming without any
> assignments.
>
> The wicked tacit fixed version of Y has no assignments whatsoever but it is
> produced and it works by means of non-standard J code. I could alter
> slightly the non-tacit version,
>
> Y=. '(5!:1<''v'')v=. 1 : (''u u`:6('',(5!:5<''u''),'')`:6 y'')'(1 :)
>
> and get rid of its single assignment using a bit of wicked code but that
> defeats my purpose.
>
> I cannot figure out how to produce an orthodox version of Y with no
> assignments; then again, Y, actually, XY was the most complicated non-tacit
> entity I have produced in a couple of decades and my failure probably means
> little.
>
> I would be very interested to see an orthodox version of Y with no
> assignments if anyone can produce one.
>
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