u&.(w v) y NB. usage: u and v monadic, w dyadic
would then behave like
u&.(w&(v y)) y NB. (v y) evaluated to a constant and bound by &
(let W be the temporary monadic verb result of evaluating w&(v y)
then we get u&.W y)
e.g. (values made up for ease of understanding/calculation)
currently, this could equivalently be written like
ew =. exemption 8e3
+&ew interest 8e3 - ew NB. repetitive structure: +&ew interest -&ew 8e3
8060
read “apply interest under subtraction of its exemption”
with (eager) “evaluation parentheses” around (its exemption)
so “it” is evaluated exactly once and refers to the y
seen by the verb result of the &. expression
generalizations:
• u&.:(w v) y should work analogously then (obviously)
• there could even be pseudo inverses of non-invertible
verbs such as {. so u&.{. (head, tail) could get
evaluated to ({.^:_1 with tail)@u head which in turn
would yield ({.^:_1 with tail) uh for uh=.u head
and eventually uh, tail
that would make the “under hook” even more useful
• dyadic: x u&.(w v) y ←→ u&.(w&(v y)) x
so ⟨under hook⟩ y ←→ y ⟨under hook⟩ y
experience shows that oftentimes its passive is more useful
but that’s due to imo inconsistent choices of operand order in J
since that’s not going to change, it might be better to
swap x and y in the rhs of the above equivalence
and that equivalence seems to be a better idea than
x u&.(w v) y ←→ u&.(w&(x v y)) y
so ⟨under hook v⟩ y ←→ ⟨under hook v~⟩ y
background information and a word of caution
general use case: &. switches back and forth between spaces
Say, what exactly needs to be done in one direction is easily
expressed depending on the point to be mapped. The map is
bijective but the other direction’s calculation is harder
to express without knowing the target point. Now let that
calculation be inferred by the JE.
One still needs to take care that wherever one gets at using u,
the inverse is still an inverse. It’s very useful whenever this holds.
Use it at your own risk, though, just like anything else.
make under work with hooks, too.
u&.(w v) y NB. usage: u and v monadic, w dyadicwould then behave likeu&.(w&(v y)) y NB. (v y) evaluated to a constant and bound by &(letWbe the temporary monadic verb result of evaluatingw&(v y)then we getu&.W y)e.g. (values made up for ease of understanding/calculation)
currently, this could equivalently be written like
read “apply interest under subtraction of its exemption” with (eager) “evaluation parentheses” around (its exemption) so “it” is evaluated exactly once and refers to the
yseen by the verb result of the&.expressiongeneralizations:
•
u&.:(w v) yshould work analogously then (obviously)• there could even be pseudo inverses of non-invertible verbs such as
{.sou&.{. (head, tail)could get evaluated to({.^:_1 with tail)@u headwhich in turn would yield({.^:_1 with tail) uhforuh=.u headand eventuallyuh, tailthat would make the “under hook” even more useful• dyadic:
x u&.(w v) y←→u&.(w&(v y)) xso⟨under hook⟩ y←→y ⟨under hook⟩ yexperience shows that oftentimes its passive is more useful but that’s due to imo inconsistent choices of operand order in J since that’s not going to change, it might be better to swap x and y in the rhs of the above equivalence
and that equivalence seems to be a better idea than
x u&.(w v) y←→u&.(w&(x v y)) yso⟨under hook v⟩ y←→⟨under hook v~⟩ ybackground information and a word of caution
general use case:
&.switches back and forth between spaces Say, what exactly needs to be done in one direction is easily expressed depending on the point to be mapped. The map is bijective but the other direction’s calculation is harder to express without knowing the target point. Now let that calculation be inferred by the JE.One still needs to take care that wherever one gets at using
u, the inverse is still an inverse. It’s very useful whenever this holds. Use it at your own risk, though, just like anything else.