Right. For this reason (or similar ones, like when g is a train), I phrase the identity as ([: f g) ↔ f@:(g) .
As to where this is stated: well, it's recorded informally in innumerable documents and J learning materials. If you're looking for formal guarantees in canonical material (the DoJ), you'll have to arrive at the equivalence through a chain of logic. First, we have the the definition of capped fork in §II.F, following the definition of non-capped fork [1]: (A) "If f is a cap ([:) the capped branch simplifies the forks to i. g h y and ii. g x h y" (B) "The ranks of the hook and fork are infinite." Then, we have the definition of @: in the vocabulary [2]: (C) "@: is equivalent to @ except that ranks are infinite." Which refers back to the definition of @, which is given in the Vocabulary as [3]: (D) " u@v y ↔ u v y" (E) "x u@v y ↔ u x v y . So, after adjusting for the different names given to the verbs, we the following correspondences: (Ai) "([: f g) y ↔ g h y" vs (D) "f@g y ↔ f g y" (Aii) "x ([: f g) y ↔ g x h y" vs (E) "x f@g y ↔ u f g y" (B) "The ranks of the hook and fork are infinite" vs (C) "@: is equivalent to @ except that ranks are infinite." Which, as far as I can tell, establishes the identity ([: f g) ↔ f@:g (provided we heed the advice given in latter's definition, i.e. "because a conjunction applies to the entity immediately to its right, expressions to the right of conjunctions commonly require parenthesization.") What provoked your doubt? -Dan [1] §II.F, definition of trains http://www.jsoftware.com/help/dictionary/dictf.htm [2] Vocabulary entry for @: http://www.jsoftware.com/help/dictionary/d622.htm [3] Vocabulary entry for @ http://www.jsoftware.com/help/dictionary/d620.htm -----Original Message----- From: programming-boun...@forums.jsoftware.com [mailto:programming- boun...@forums.jsoftware.com] On Behalf Of bob therriault Sent: Thursday, November 29, 2012 12:00 PM To: programm...@jsoftware.com Subject: Re: [Jprogramming] @: and capped fork HI Ian, If your v includes an adverb such as / the long left reach of conjunctions could get you into trouble. That would be part of the parsing rules for verbs vs conjunctions. (+:@:+/) 3 4 5 42 ([:+:+/) 3 4 5 24 Cheers, bob On 2012-11-29, at 8:49 AM, Ian Clark wrote: > Department of Sudden Doubts... > > If u and v are verbs, do (u@:v) and ([: u v) really behave the same > under all circumstances? > > If so, where would I go to find this fact written up? > ---------------------------------------------------------------------- > 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