in reply to Re: RFC: A Perlesque Introduction to Haskell, Part One (draft)
in thread RFC: A Perlesque Introduction to Haskell, Part One (DRAFT)

What you call extensionality is what I've known as currying.

Then I should do a better job.

Extensionality says that the following two definitions are equivalent:

foo = foldl1 f bar xs = foldl1 f xs -- note: xs is free on both sides
The reason this works is that xs is free on both sides of bar: it's basically a placeholder that says "a list should go here". Both of these functions have type (a -> a) -> [a] -> a (modulo monomorphism-restriction annoyances).

On the other hand, the function application

foldl f -- note: not a definition (type is [a] -> a)
is a curried expression: while foldl f xs returns a scalar, foldl f returns a function from lists to scalars. To me, currying means partial function application, and it's useful for producing ad-hoc functions where lambda is overkill.

I like your point that currying is easier to understand when you know about type signatures, and thanks for the link to MJD's talk.

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