Linda, every time you try to use x u&.v y ↔ vi (v x) u (v y) to make a
substitution, you must remember to respect rank (I know that one sentence in
the definition of &. doesn't say so explicitly, so you must remember for
yourself).
Open (>) is rank 0, i.e. operates on individual atoms, so somewhere in your
replacement you must do likewise. The most straightforward way to say this is
just to say it:
sh =: 13 : '< (>x) ,~ (>y)' NB. vi (v x) u (v y)
h =: 13 : 'x sh"0/ y' NB. g with sh"0 substituted for ,~&.>
(B h A) -: (B g A)
1
sh
[: < ([: > [) ,~ [: > ]
h f.
([: < ([: > [) ,~ [: > ])"0/
Here, it's the isolation of vi (v x) u (v y) and the explicit application of it
at "0 (rank zero) that makes the substitution work. Try removing the "0 or
embedding sh into h directly (in its x and y form, as opposed to its tacit
from) and see what happens.
Finally I'll recommend, as I do every time we discuss this, that you step back,
try to shelve any preconceptions, and with new eyes, sincerely compare
([: < ([: > [) ,~ [: > ])"0/
with
,~ each/
and perhaps reconsider your position on eliminating conjunctions. If your goal
is simplicity, to make J easier to learn for kids, I just can't see how anyone
would look at those two expressions and say "whoa, the first one is simpler".
-Dan
PS: And not to pick nits, but the first sentence contains a conjunction as well
(") and not only is it necessary, it's fundamental to the solution. So if we're
going to accept ", why not also accept &. and stop worrying?
> On Apr 4, 2014, at 2:25 AM, "Linda Alvord" <[email protected]> wrote:
>
> Here’s the problem. Hopefully this looks better and fully defines the
> problem.
>
> f=: 13 :' (B=:;:''am pm''),~&.>/A=:<"1 ":":"0>:i.y'
> f 12
> ┌────┬────┬────┬────┬────┬────┬────┬──
> ──┬────┬────┬────┬────┐
> │1 am│2 am│3 am│4 am│5 am│6 am│7 am│8 am│9 am│10am│11am│12am│
> ├────┼────┼────┼────┼────┼────┼────┼──
> ──┼────┼────┼────┼────┤
> │1 pm│2 pm│3 pm│4 pm│5 pm│6 pm│7 pm│8 pm│9 pm│10pm│11pm│12pm│
> └────┴────┴────┴────┴────┴────┴────┴──
> ──┴────┴────┴────┴────┘
> A
> ┌──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┐
> │1 │2 │3 │4 │5 │6 │7 │8 │9 │10│11│12│
> └──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┘
> B
> ┌──┬──┐
> │am│pm│
> └──┴──┘
> g=: 13 :'x(,~&.>)/y'
> B g A
> ┌────┬────┬────┬────┬────┬────┬────┬──
> ──┬────┬────┬────┬────┐
> │1 am│2 am│3 am│4 am│5 am│6 am│7 am│8 am│9 am│10am│11am│12am│
> ├────┼────┼────┼────┼────┼────┼────┼──
> ──┼────┼────┼────┼────┤
> │1 pm│2 pm│3 pm│4 pm│5 pm│6 pm│7 pm│8 pm│9 pm│10pm│11pm│12pm│
> └────┴────┴────┴────┴────┴────┴────┴──
> ──┴────┴────┴────┴────┘
> g
> ,~&.>/
>
> NB. x u&.v y ↔ vi (v x) u (v y) Definition of Under
>
>
> I can’t seem to write a simple definition h=: but use the second
> definition of under.
>
> It should have the same result as B g A when you enter B h A
>
> Linda
>
>
>
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