The page at
http://code.jsoftware.com/wiki/Vocabulary/Inverses#Obverses_Of_Primitives
has a good bit on what primitives have inverses, but it seems that you
have found some combinations not listed there. Would you be willing to
add what you have found to that page?
Henry Rich
On 3/2/2016 7:39 PM, Louis de Forcrand wrote:
The way J handles inverses to functions is quite unique and, while not
always very useful, can lead to compact but very descriptive code:
+/&.:*: NB. distance
+&.^. NB. multiplication
u&.(a.&i.) NB. u applied to y’s indices in a., then indexed out of a.
etc.
However, some less easily invertible functions, such as , (ravel), {: and
related,
A., m&{ , and others, don’t have a monadic inverse because they are “lossy”
functions,
in that there is no function u such that
y -: u@v y NB. where v is a lossy function
for an arbitrary y.
However, while there are other lossy functions which I have not cited, the ones
I
did are particular in that they are invertible with trains of related dyadic
functions:
u&., y <—> ($ $ u@,) y
u&.(m&{.) y <—> (m&}. , u@(m&{.)) y NB. extends to others like }.
etc.
NB.
although {. already has an inverse
u&.A. y <—> (A.~ u@A.) y
These are all simply “cosmetic”, in that you can obviously write them out
by hand, but then again, &. is basically cosmetic too. Nevertheless, it leads
to more elegant and concise code (and sometimes leads to new ways of
thinking about a problem). However, one inverse that could possibly
lead to (possibly big?) gains in speed with special code would be:
u&.(m&{) y <—> (m&}~ u@(m&{)) y
This might already be implemented for the fork case.
I’ve checked, and m&{ already has an inverse, although I don’t see what it’s
useful for.
On a side note, I’ve noticed that <;.1 has an inverse according to b._1, but
using it yields a nonce error (which means it hasn’t been implemented yet,
right?). <;._1@(m&,) could be recognised as a whole as well, so that
u&.(<;._1@(m&,)) y <—> ({. ;@, m ,&.> }.)@u@(<;._1@(m&,))
Or it could be added as an obverse to the cut standard library verb.
Again, this can all be done by hand, of course.
Louis
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