[Jprogramming] Revisisting the Y combinator

Tue Nov 13 17:46:01 UTC 2018

Mike, that was great!!
I managed to deal with odds and evens.
However, because of [: which I can't seem to remove, it won't turn tacit.
It is almost "high school ready"
flla=: 13 :'1{"1([:+/\|.)^:(<:i.y)1 1'
 flla 10
1 1 2 3 5 8 13 21 34 55
 flla 11
1 1 2 3 5 8 13 21 34 55 89
 flla
┌─┬─┬─────────────────────────┐
│3│:│1{"1([:+/\|.)^:(<:i.y)1 1│
└─┴─┴─────────────────────────┘
 
Linda
-----Original Message-----
From: Programming <programming-bounces at forums.jsoftware.com> On Behalf Of 'Mike Day' via Programming
Sent: Monday, November 12, 2018 1:59 PM
To: programming at jsoftware.com
Subject: Re: [Jprogramming] Revisisting the Y combinator
NB. I've omitted Jose's rather lengthy original posting to save space.
Re Linda's quoted Fibonacci verb,
13 :',(([:+/\|.)^:2)^:(<`(1,1:))y'
I couldn't understand it until I checked the vocabulary entry for ^:
a) u ^: (<n) does the same as u ^: (i.n)
b) u ^: (v1`v2) y does u^:(v1 y) (v2 y)
The engine of this fibonacci sequence generator is
  ([:+/\|.)
as in
  ([:+/\|.) 1 1   NB. f2 f3 given f1 f2 = 1 1
1 2
The rest is controlling the repetition of the engine's application.
So, developing the sequence,
  ([:+/\|.)^:(0 1 2 3 4) 1 1  NB. generate pairs f2 f3, f3 f4, ... ,f5 f6
1 1
1 2
2 3
3 5
5 8
  ([:+/\|.)^:2^:(0 1 2) 1 1  NB. only generate "even" pairs
1 1
2 3
5 8
  ([:+/\|.)^:2^:(<3) 1 1   NB. using ^: property (a), as above,
1 1
2 3
5 8
  ([:+/\|.)^:2^:(<`(1,1:)) 3   NB. gerund form of power, see (b) above
1 1
2 3
5 8
  ,([:+/\|.)^:2^:(<`(1,1:)) 3 NB. ravel result
1 1 2 3 5 8
I can't get my head round the Y combinator, but this isn't an example!
Linda wondered why it stopped at 34 or 89 but not 55.
By its construction , this Fibonacci only does even numbers, yielding elements 1 to 2*y
We could start from f0 f1, ie 0 1:
  ,([:+/\|.)^:2^:(<`(0,1:)) 3  NB. odd-number version
0 1 1 2 3 5
Cheers,
Mike
On 12/11/2018 08:20, Linda Alvord wrote:
> Sorry about the post in the wrong thread.
>> There should be some "Y combinator" at work in here.
>> f=: 13 :',([:+/\|.)^:2^:(<`(0,1:))y'
>>> f 5
> 0 1 1 2 3 5 8 13 21 34
> f 6
> 0 1 1 2 3 5 8 13 21 34 55 89
>> I can't seem to stop at 55. Any ideas?
>> Linda
>> -----Original Message-----
> From: Programming <programming-bounces at forums.jsoftware.com> On Behalf 
> Of Linda Alvord
> Sent: Friday, November 9, 2018 12:56 AM
> To: programming at jsoftware.com
> Subject: Re: [Jprogramming] Revisisting the Y combinator
>> Jose, I'm not sure I'll be able to follow your ideas.
>> !i.11x
> 1 1 2 6 24 120 720 5040 40320 362880 3628800
>>> However, Fibohacci would be a nice primitive.
>> Linda
>> -----Original Message-----
> From: Programming <programming-bounces at forums.jsoftware.com> On Behalf 
> Of 'Pascal Jasmin' via Programming
> Sent: Thursday, November 8, 2018 10:41 PM
> To: programming at jsoftware.com
> Subject: Re: [Jprogramming] Revisisting the Y combinator
>>>>> Interesting, thank you Jose.
>> I'll note that if the argument to Y is not an ar of an adverb then J (806 and 807) will crash when the result verb is called.
>>> ________________________________
> From: Jose Mario Quintana <jose.mario.quintana at gmail.com>
>
---
This email has been checked for viruses by Avast antivirus software.
https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.avast.com%2Fantivirus&data=02%7C01%7C%7C70903383dc2f4151efd808d648d0decc%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C636776459254645130&sdata=mP7rC7yN%2BuJS4qiMVFghLinRoT3ekbmvO7oRI4xHtqc%3D&reserved=0
----------------------------------------------------------------------
For information about J forums see https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.jsoftware.com%2Fforums.htm&data=02%7C01%7C%7C70903383dc2f4151efd808d648d0decc%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C636776459254645130&sdata=6k9%2FprHwUzkgNvyoCY0efJMeeQb4x3EJogOrQXXXCJk%3D&reserved=0