Technically, you cannot curry (which should probably be called
"schönfinkeln"; see
https://en.wikipedia.org/wiki/Currying#cite_note-4) in Haskell because
all Haskell functions take only a single element. (This is true at
least unless product types are involved.) So I agree with Panicz that
the two Haskell forms are equivalent an no currying is going on.

For a programming language like Scheme, the notion makes sense, though.

Mathematically, it is just the adjunction going from Hom(X x Y, Z) to
Hom(X, Z^Y).

Marc

Am Mi., 1. Juli 2020 um 11:21 Uhr schrieb Panicz Maciej Godek
<xxxxxx@gmail.com>:
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>
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> śr., 1.07.2020, 00:16 użytkownik John Cowan <xxxxxx@ccil.org> napisał:
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>> What you call currying define is not genuine currying, though it is extremely useful.
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> To be fair, all instances of the word 'curried' are in question marks, and the document does contain the following explanation:
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> This feature, sometimes incorrectly called "currying" [...]
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> On the other hand, a lot of things here depend on a point of view. If we consider Lisp functions to receive multiple arguments, then indeed this is not currying. However, if we consider them to receive a single argument that is a list, then I think that saying that it is explicitly parenthesized currying is non-controversial.
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> I believe that e.g. Haskell's
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> f x y = v
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> is equivalent to
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> ((f x) y) = v
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> That is, both forms are equuvalent. (And both are curried)
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>>   There is, however, a proposal for an adaptation of genuine currying: in this case, lambda invocation with too few arguments returns a procedure representing partial evaluation, whereas lambda invocation with too many arguments invokes the lambda with just enough arguments and then invokes the result (which must be a procedure) with the remaining arguments.
>>
>> See <https://github.com/johnwcowan/r7rs-work/blob/master/BeyondCurryingHemann.md>, which also links to Hemann's paper.
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> I have been doing similar experiments
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> https://bitbucket.org/panicz/slayer/src/26a8b3ff05ad9d34a98a636d771e3875496f2d69/guile-modules/extra/common.scm#lines-514
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> But in my experience, rather than increasing language's expressivity, it mostly adds confusion to the code base.
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>