Right. For this reason (or similar ones, like when g is a train), I
usually say the identity is ([: 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 chance of logic.
First, we have the the definition of capped fork in §II.F, following the
definition of non-capped fork:
- "If f is a cap ([:) the capped branch simplifies the forks to g
h y and g x h y . "
- "The ranks of the hook and fork are infinite."
Then, we have the definition of @: in the vocabulary
- "@: is equivalent to @ except that ranks are infinite."
Atop u@v mv lv rv
u@v y ↔ u v y . For example, +:@- 7 is _14 (double the negation).
Moreover, the monadic uses of u@v and u&v are equivalent.
x u@v y ↔ u x v y . For example, 3 +:@- 7 is _8 (double
the difference).
-----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?
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