Combinatory logic Volume 1

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. A combinator is a higher-order function that uses only function application and earlier defined combinators to define a result from its arguments.

Preface Explanation of Notations Introduction Chapter 1 Formal Systems Chapter 2 Epitheory Chapter 3 Lambda-Conversion Chapter 4 The Church-Rosser Theorem Chapter 5 Intuitive Theory of Combinators Chapter 6 Synthetic Theory of Combinators Chapter 7 Logistic Foundations Chapter 8 Introduction to Illative Combinatory Logic Chapter 9 The Basic Theory of Functionality Chapter 10 The Stronger Theories of Functionality Appendix A: List of Basic Constants Appendix B: List of Properties of Relations Bibliography Index

Haskell Brooks Curry (/ˈhæskəl ˈkɜːri/; September 12, 1900 – September 1, 1982) was an American mathematician and logician. Curry is best known for his work in combinatory logic; while the initial concept of combinatory logic was based on a single paper by Moses Schönfinkel,[1] much of the development was done by Curry. Curry is also known for Curry's paradox and the Curry–Howard correspondence. There are three programming languages named after him, Haskell, Brook and Curry, as well as the concept of currying, a technique used for transforming functions in mathematics and computer science.

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