Power and Rank with negative-one right operand
⍣¯1 ⋄ ⍤¯1
- Inverse and major-cell - are special cases that certainly deserve a mention and the ability to become first-class objects.
Unfortunately right at this moment I can't think of any others.
Are you also considering left operand currying of conjunctions?
This topic relates to a recent thread in comp.lang.apl where the arguments of residue are under discussion. Aaron Hsu refers to the
auxiliary and
substantive arguments which in APL are often left and right. He argues that this permits the monadic form of a primitive to be directly related to the dyad with its auxiliary argument edilded.
From both Rank and Power we see that the roles are often reversed for conjunctions, the substantive operand being on the left - the auxiliary on the right.
Currying the right operand can then be seen as effectively eliding the left or substantive. More generally useful would be the ability to curry the substantive leaving the auxiliary to be the only missing link in forming an entire family of related functions.
This of course means that in order to call the derived adverb the auxiliary is now placed on the left, giving the effect of two left operands. An oddity with a ready precedent, albeit reversed, in the derivation function-compose-array, e.g. decrement
dec←-∘1 ⋄ dec 3
2
that gives the effect of two right arguments.