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: [email protected] [mailto:programming-
[email protected]] On Behalf Of bob therriault
Sent: Thursday, November 29, 2012 12:00 PM
To: [email protected]
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?
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