Suppose I would like to normalise a vector. Easy: %+/&.:*:. Nice and
pretty, gotta love under.
What if I've got an array of vectors, and I want to normalise all of them?
There are two ways, corresponding to two different representations:
%+/&.:*:"1 and %"_1 _ +/&.:*:. The former corresponds to an array where
the last axis is the axis axis, and the latter to an array where the
leading axis is the axis axis (which may seem odd, but I've found it
useful).
There are two operations involved: a division and a reduction. Neither of
these _needs_ to be applied at rank, but we cannot avoid ranking _both_ of
them. Now suppose the axis axis is neither leading nor trailing. Then we
need: (%"_1 _ +/&.:*:)"n.
" is inherently eachy. That is not a bad thing--sometimes there are
eaches to be eached--but it does mean it is somewhat heavy-handed. |: is
an interesting alternative. %"_1 1 can be written as %&.(0&|:`a:). And
the sum can be performed moving the axis in question to the front rather
than to the back.
I therefore propose a 'transpose-ish' family of conjunctions. Say: t. t:
t.. t:: (RIP Taylor series). u t. n brings axis n to the front (brings it
near) before applying u; u t.. n brings axis n to the rear (brings it far,
hence the longer suffix); u t: n brings axis n to the front before
applying u, but returns it afterwards (hence two dots); t:: should be
obvious.
Advantages: encourages holistic, array-oriented thinking over eachy
thinking. Distinguishes rank's role as a vehicle for repetition from its
role as a general alternative to the axis operator. A single application
under transpose can replace nested applications at rank.
Disadvantages: harder to teach. Maybe harder to understand (though
operations on high-dimensional arrays may be difficult to understand
regardless). Probably harder to implement performantly. I propose too
many primitives, and if The Powers That Be are not wise enough to reject
them all, they will turn the language into C++.
Thoughts?
-E
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