**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":

... 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 ...

... 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 ...

... 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 ...

...

**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 ...

### Famous quotes containing the word logic:

“There is no morality by instinct.... There is no social salvation—in the end—without taking thought; without mastery of *logic* and application of *logic* to human experience.”

—Katharine Fullerton Gerould (1879–1944)