Combinatory Logic

Combinatory logic is a notation to eliminate the need for 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. A combinator is a higher-order function that uses only function application and earlier defined combinators to define a result from its arguments.

Read more about Combinatory Logic:  Combinatory Logic in Mathematics, Combinatory Logic in Computing, Summary of The Lambda Calculus, Combinatory Calculi, Undecidability of Combinatorial Calculus

Other articles related to "combinatory logic, logic, logics":

Applicative Computing Systems
... In combinatory logic the only metaoperator is application in a sense of applying one object to other ... In lambda calculus two metaoperators are used application – the same as in combinatory logic, and functional abstraction which binds the only variable ...
Predicate Functor Logic - Motivation
... Quine proposed PFL as a way of algebraizing first-order logic in a manner analogous to how Boolean algebra algebraizes propositional logic ... PFL to have exactly the expressive power of first-order logic with identity ... Hence the metamathematics of PFL are exactly those of first-order logic with no interpreted predicate letters both logics are sound, complete, and undecidable ...
Haskell Curry - Life
... Curry's interest in mathematical logic started during this period when he was introduced to the Principia Mathematica, the attempt by Alfred North Whitehead and ... equations, his interests continued to shift to logic ... he discovered the work of Moses Schönfinkel in combinatory logic ...
Combinatory Logic - Applications - Logic
... The Curry–Howard isomorphism implies a connection between logic and programming every proof of a theorem of intuitionistic logic corresponds to a reduction of a typed lambda term, and conversely ... Specifically, a typed combinatory logic corresponds to a Hilbert system in proof theory ... fragment of the intuitionistic logic, which can be seen as follows ...
Computability - Formal Models of Computation
... Combinatory logic is a concept which has many similarities to -calculus, but also important differences exist (e.g ... fixed point combinator Y has normal form in combinatory logic but not in -calculus) ... Combinatory logic was developed with great ambitions understanding the nature of paradoxes, making foundations of mathematics more economic (conceptually ...

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