There is a programming language-theoretic definition of equivalence (not
restricted to functions). It is quite clever, but can be boiled down to: is
there a way, within the language, to tell the difference between two values?
Because j has no hard abstractions, the question of equality is rather simple,
and is in fact pretty similar to u f.`'' -: v f.`''. Because--if you said u
and v were equivalent, but -. u f.`'' -: v f.`'', then that is a way of
distinguishing u and v, so they cannot be equivalent.
That this allows you to distinguish {{x+y}} from {{x +y}} seems not very
useful (though I can imagine cases where it would be important), but consider
u versus u ((2 :'u y') :(2 :'x u y')) 0. This also seems useless, but I
profited from a very similar distinction in the threading routines I posted
here last month.
I will add that, in a symbolic context, the name used to refer to something
may have significance, which is another case in which preservation of
input->output mapping is not exactly what you want to ensure; f. erases such
information.
f. also erases information about the target of $:, which may mean it considers
to be identical verbs which actually behave differently.
On Tue, 3 May 2022, Raul Miller wrote:
There isn't really a better way to do that test.
Conceptually, what you want is a test that determines whether two
verbs would always produce the same results for the same arguments,
but that's a problem involving infinities. It's proof territory.
That said, typically we solve this kind of problem by hand, rather
than using a test on the structure of the verb.
Good luck,
--
Raul
On Tue, May 3, 2022 at 5:20 AM Ric Sherlock <tikk...@gmail.com> wrote:
I want to test if a particular verb was provided to my adverb.
I came up with the solution below. Is there a better way?
myadverb = {{
res=. u {:y
if. theverb f.`'' -: u f.`'' do.
res=. ({.y) ,: res
end.
res
}}
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