Simplified Gamma:
Gamma1 =: (d.0 1)(,`)(`:6)("0)
Viktor Cerovski wrote:
>
>
> Marshall Lochbaum wrote:
>>
>> Having taken an incredibly shallow look at the first few pages of SICM, I
>> will now highly recommend to you the conjunction
>>
>> T=: 2 : '] , u d. (i.<:n)'
>>
>> where (u T n) gives the first n components of the "local tuple" of the
>> function u. It may then be applied to a time t to obtain the actual value
>> of this vector. So:
>>
>> *: T 4
>> ] , (*: , +: , 2"0)"0
>>
>> For the record, I am not entirely sure how this works with vector outputs
>> (or inputs, but these seem less important).
>>
> It works fine for vector arguments.
> Let's rework it first to fit the sought gamma:
>
> Gamma =: (d.0 1)(]`,`)(`:6)("0)
>
> *: Gamma
> (] , (*: , +:)"0)"0
>
> *: Gamma i.10
> 0 0 0
> 1 1 2
> 2 4 4
> 3 9 6
> 4 16 8
> 5 25 10
> 6 36 12
> 7 49 14
> 8 64 16
> 9 81 18
>
> For vector q=.*:,+:,<:
>
> (*:,+:,<:) Gamma i.10
> 0 0 0 _1 0 2 1
> 1 1 2 0 2 2 1
> 2 4 4 1 4 2 1
> 3 9 6 2 6 2 1
> 4 16 8 3 8 2 1
> 5 25 10 4 10 2 1
> 6 36 12 5 12 2 1
> 7 49 14 6 14 2 1
> 8 64 16 7 16 2 1
> 9 81 18 8 18 2 1
>
>
>
>
>>
>> -----Original Message-----
>> From: [email protected]
>> [mailto:[email protected]] On Behalf Of Alex Gian
>> Sent: Thursday, December 09, 2010 7:53 PM
>> To: Programming forum
>> Subject: [Jprogramming] Verbs that take verbs as arguments (pt 2)
>>
>> Sorry to plague you with more newbie questions, but I'm a little pressed
>> for time here.
>>
>> OK, for anyone familiar with Scheme/Lisp/λ-calculus etc, here's what I'm
>> trying to do:
>>
>> (define (gamma q)
>> (lambda(t)
>> (list t (q t) ((d1 q) t)))
>>
>>
>> In other words, I want to pass a monadic verb (call it 'q') to the
>> 'gamma' verb/function and I want the result to be a monadic
>> verb/function that will accept a value ('t') and return a three elem
>> array of rank 1 t, q t, q D.1 t
>>
>> IOW, something like
>> testfunc =. gamma @ q
>> testfunc 1.1
>> 1.1 (q 1.1) ((q D.1) 1.1)
>>
>> (In case anyone wonders why the weird questions, I am working through
>> Sussman & Wisdom's SICM, and would like to try the code in parallel in J
>> to compare the two notations.)
>>
>> I suppose I am really trying to figure how J deals with anonymous
>> functions. Where I am getting stuck is the scoping of the values of y
>> (and x) in explicit definitions.
>>
>> I /could/ do it as a dyad, but
>> gamma=: dyad : 'y,(x y),x D.1 y'
>> doesn't seem to work for me either, and I really would prefer monadic,
>> kinda seeing how "currying" maps to J.
>>
>
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