curried function

mathematics, programming A function of N arguments that

is considered as a function of one argument which returns

another function of N-1 arguments. E.g. in Haskell we can

define:

average :: Int -@# (Int -@# Int)

(The parentheses are optional). A partial application of

average, to one Int, e.g. (average 4), returns a function of

type (Int -@# Int) which averages its argument with 4. In

uncurried languages a function must always be applied to all

its arguments but a partial application can be represented

using a lambda abstraction:

x -@# average(4,x)

Currying is necessary if full laziness is to be applied to

functional sub-expressions.

It was named after the logician Haskell Curry but the

19th-century logician, Gottlob Frege was the first to

propose it and it was first referred to in ["Uber die

Bausteine der mathematischen Logik", M. Schoenfinkel,

Mathematische Annalen. Vol 92 (1924)].

David Turner said he got the term from ChristopherStrachey who invented the term "currying" and used it in his

lecture notes on programming languages written circa 1967.

Strachey also remarked that it ought really to be called

"Schoenfinkeling".

Stefan Kahrs [e-mail] reported hearing somebody in

Germany trying to introduce "scho"nen" for currying and

"finkeln" for "uncurrying". The verb "scho"nen" means "to

beautify"; "finkeln" isn't a German word, but it suggests "to

fiddle".

["Some philosophical aspects of combinatory logic",

H. B. Curry, The Kleene Symposium, Eds. J. Barwise,

J. Keisler, K. Kunen, North Holland, 1980, pp. 85-101]

(2002-07-24)