I think what you are looking for is the definition of the & conjunction. You need to understand what it means to be a verb defined that way.
And, for this, you need to read the reference documentation: http://www.jsoftware.com/help/dictionary/d630n.htm states: x m&v y <---> m&v^:x y Here, x, m and y are nouns and v is the base verb. Let's call this "Rule A" It also states: x u&n y <---> u&n^:x y Here, x, n and y are nouns and u is the base verb. Let's call this "Rule B" (I say "base" verb, because u&n is a composite verb, derived from the dyadic definition of u with n as its right argument.) ------------------- But it also states: m&v y is defined as m v y and u&n y is defined as y u n Let's call these "Rule C" and "Rule D". ------------------- In other words, ((2x&*) &1) 3 Rule D works with u: (2x&*), n: 1, y: 3, and gives us 3 (2x&*) 1 Rule B works with x: 3, u: (2x&*), y: 1 ((2x&*)^:3) 1 By the way, I should probably note that we need the outer parenthesis there to prevent the 3 and 1 from being interpreted as a single token. But there are a couple other ways we could have done that: (2x&*)^:(3) 1 or (2x&*)^:3 (1) We could also have used an expression to generate the value 1. For example: (2x&*)^:3 ]1 or (2x&*)^:3 >:0 ------------------- Does that make sense? Thanks, -- Raul On Thu, Feb 19, 2015 at 9:08 AM, Fausto Saporito <[email protected]> wrote: > Hello Raul, > > thanks for the explanation. I'm still trying to understand it, but I > thini I got it. > > Sorry my mistake about missing parenthesis. > > So, I'm missing the rule to understand this passage: > > ((2x&*) &1) 3 <---> ((2x&*)^:3) 1 > > But maybe this subject is too much advance for my J actual knowledge. > > thanks, > Fausto > > > 2015-02-19 14:48 GMT+01:00 Raul Miller <[email protected]>: >> Please be careful here: >> >> 3 ((2x&*) &1) 3 >> >> is equivalent to each of these: >> ((2x&*) &1) ((2x&*) &1) ((2x&*) &1) 3 >> (((3(2x&*)1) (2x&*)1) (2x&*)1) >> ((((2x&*)(2x&*)(2x&*)1) (2x&*)1) (2x&*)1) >> ((8 (2x&*)1) (2x&*)1) >> (((2x&*)(2x&*)(2x&*)(2x&*)(2x&*)(2x&*)(2x&*)(2x&*)1) (2x&*)1) >> (256 (2x&*)1) >> >> and I'm not going to carry out the final step, which involves 256 >> copies of the verb 2x&* >> >> Hopefully you can see why each of these expressions is equivalent. But >> if something doesn't make sense, it's probably worth talking through >> the issue (or at least showing a more gradual sequence of equivalences >> for that step). >> >> On the other hand, >> ((2x&*) &1^:3 3 >> >> is not a valid expression because of the unbalanced parenthesis. >> >> If you got rid of one of those left parenthesis, you'd get >> (2x&*) &1^:3 3 >> which is equivalent to >> (2x&*) &1^:(3 3) >> but that is a verb which you probably did not intend. >> >> If you instead insert a right parenthesis between the pair of threes, >> you would get >> ((2x&*) &1^:3) 3 >> >> which indeed is equivalent to your first expression. >> >> But note that you are not repeating three times 2x&* but instead are >> repeating three times ((2x&*)1) in much the same manner as the >> original expression. >> >> Thanks, >> >> -- >> Raul >> >> >> On Thu, Feb 19, 2015 at 8:11 AM, Fausto Saporito >> <[email protected]> wrote: >>> Hello Jose, >>> >>> I understand you are applying this identity : x u&n y <--> u&n^:x y >>> >>> But I cannot see the correct mapping in your expressions. >>> I suppose this is an hook, so >>> >>> (u v) y --> y u v y >>> >>> 3 ((2x&*) &1) 3 >>> >>> ((2x&*) &1^:3 3 >>> >>> means repeat three times 2*1, i.e. 2*1*2*1*2*1 = 8 >>> >>> correct ? >>> >>> thanks, >>> Fausto >>> >>> >>> 2015-02-19 1:19 GMT+01:00 Henry Rich <[email protected]>: >>>> If you're going to use dissect, get 3.6.42 (released today). Previous >>>> versions had a confusing title for the verbs. >>>> >>>> Even with the picture it's amazing what this little phrase does. Two >>>> nested >>>> powers, with the result of one power feeding back into the exponent of the >>>> next iteration of the same verb. >>>> >>>> Henry Rich >>>> >>>> >>>> On 2/18/2015 7:12 PM, Jose Mario Quintana wrote: >>>>> >>>>> ((2x&*) &1) 3 >>>>> 8 >>>>> ((2x&*)^:3) 1 >>>>> 8 >>>>> ((3x&*) &1) 2 >>>>> 9 >>>>> ((3x&*)^:2) 1 >>>>> 9 >>>>> >>>>> >>>>> Does dissect >>>>> >>>>> >>>>> http://www.jsoftware.com/jwiki/action/show/Vocabulary/Dissect?action=show&redirect=Addons%2Fdebug%2Fdissect >>>>> >>>>> help to follow the execution of the sentences? >>>>> >>>>> >>>>> >>>>> >>>>> >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
