<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)

In computer programming, a parser combinator is a higher-order function that accepts several parsers as input and returns a new parser as its output. In this context, a parser is a function accepting strings as input and returning some structure as output, typically a parse tree or a set of indices representing locations in the string where parsing stopped successfully.

A combinator library is a software library which implements combinators for a functional programming language; "the key idea is this: a combinator library offers functions (the combinators) that combine functions together to make bigger functions".pg 35 of "History of Haskell" These kinds of libraries are particularly useful for allowing domain-specific programming languages to be easily embedded into a general purpose language by defining a few primitive functions for the given domain and turning over the task of expanding higher-level constructs to the general language.