curried function
A {function} of N {arguments} can
be 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, e.g. (average 4), is 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 formalist {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 {Christopher
Strachey} 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 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]
(1994-12-14)