Combinatory logic

Combinatory logic is a formal system of function application in which combinators express computation without variables or quantifiers. Its rules permit the elimination of bound variables from expressions.

S combinator: The combinator defined by S f g x = f x (g x), which distributes an argument to two functions. Together with K, it is enough to express every computable function.
Function application: The operation of applying a function to an argument to produce a result. Combinatory expressions compute by repeated application.
Moses Schönfinkel: A Russian logician who introduced combinatory logic in a 1924 paper on eliminating bound variables. His variable-free system established the subject's original form.
SKI combinator calculus: A formulation of combinatory logic using the S, K, and I combinators. It is a compact basis for writing and reducing combinatory expressions.
SK calculus: A combinator calculus based on S and K, without a primitive identity combinator. It shows that I is definable rather than essential to a complete basis.
K combinator: The combinator defined by K x y = x, which returns its first argument and ignores the second. It supplies constant functions and forms the basic pair S K.
Lambda calculus: A formal system of function abstraction and application that uses bound variables. It provides the variable-based notation that combinatory logic can eliminate.
Haskell Curry: An American mathematician and logician who developed combinatory logic and its connections to functional abstraction. Curry expanded Schönfinkel's ideas into a systematic theory.
Turner’s supercombinators: A compilation technique that groups function definitions into closed units to support efficient lazy evaluation. It applies combinator-based compilation to functional programs.
BCKW logic: A family of combinatory systems whose primitives encode restrictions on variable use in logic. Its combinators track structural rules that ordinary combinatory logic leaves unrestricted.

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