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Combinator

theory
A function with no free variables. A term is either a constant, a variable or of the form A B denoting the application of term A (a function of one argument) to term B. Juxtaposition associates to the left in the absence of parentheses. All combinators can be defined from two basic combinators – S and K. These two and a third, I, are defined thus:
S f g x = f x (g x) K x y = x I x = x = S K K x
There is a simple translation between combinatory logic and lambda-calculus. The size of equivalent expressions in the two languages are of the same order.
Other combinators were added by David Turner in 1979 when he used combinators to implement SASL:
B f g x = f (g x) C f g x = f x g S’ c f g x = c (f x) (g x) B* c f g x = c (f (g x)) C’ c f g x = c (f x) g
See fixed point combinator, curried function, supercombinators.
(2002-11-03)

Tagged:

• Combinatorial

[kuh m-bahy-nuh-tawr-ee-uh l, -tohr-, kom-buh-] /kəmˌbaɪ nəˈtɔr i əl, -ˈtoʊr-, ˌkɒm bə-/ adjective 1. of, relating to, or involving the of elements, as in phonetics or music. 2. of or relating to the enumeration of the number of ways of doing some specific task or of arranging items in a specific configuration. 3. Mathematics. of […]

• Combinatorial-analysis

noun, Mathematics. 1. the branch of mathematics that deals with permutations and combinations, especially used in statistics and probability. noun 1. the branch of mathematics concerned with the theory of enumeration, or combinations and permutations, in order to solve problems about the possibility of constructing arrangements of objects which satisfy specified conditions Also called combinatorics […]

• Combinatorially

[kuh m-bahy-nuh-tawr-ee-uh l, -tohr-, kom-buh-] /kəmˌbaɪ nəˈtɔr i əl, -ˈtoʊr-, ˌkɒm bə-/ adjective 1. of, relating to, or involving the of elements, as in phonetics or music. 2. of or relating to the enumeration of the number of ways of doing some specific task or of arranging items in a specific configuration. 3. Mathematics. of […]

• Combinatorial-topology

noun, Mathematics. 1. the branch of topology that deals with the properties of geometric figures by considering the figures as being composed of elementary geometric figures, as points or lines.

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