Was (wer) ist combinatory logic - definition
LOGICAL FORMALISM USING COMBINATORS INSTEAD OF VARIABLES
Combinator; Combinatorial logic (mathematics); Combinatory Logic; Abstraction elimination; K combinator; S combinator; Combinators; Combinatory algebra; S-combinator; Lambda elimination; Combinator calculus
combinatory logic
<logic> A system for reducing the operational notation of
logic, mathematics or a functional language to a sequence
of modifications to the input data structure. First
introduced in the 1920's by Schoenfinkel. Re-introduced
independently by Haskell Curry in the late 1920's (who
quickly learned of Schoenfinkel's work after he had the idea).
Curry is really responsible for most of the development, at
least up until work with Feys in 1958.
See combinator.
(1995-01-05)
Combinatory logic
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel Translated by Stefan Bauer-Mengelberg as "On the building blocks of mathematical logic" in Jean van Heijenoort, 1967.
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)
Wikipedia
Combinatory logic
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages. It is based on combinators, which were introduced by Schönfinkel in 1920 with the idea of providing an analogous way to build up functions—and to remove any mention of variables—particularly in predicate logic. A combinator is a higher-order function that uses only function application and earlier defined combinators to define a result from its arguments.
