Combinators : terms and proof theory. (Book, 1972) [WorldCat.org]
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Combinators : terms and proof theory.

Author: Soren Stenlund
Publisher: Dordrecht, Holl : D. Reidel Pub., 1972.
Series: Synthese library, 42.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

The aim of this monograph is to present some of the basic ideas and results in pure combinatory logic and their applications to some topics in proof theory, and also to present some work of my own.

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Document Type: Book
All Authors / Contributors: Soren Stenlund
ISBN: 9027703051 9789027703057
OCLC Number: 299359073
Notes: Akademisk avhandling--uppsala. Extra T.P. with thesis statement inserted. Bibliography P. 177-180.
Description: 184 pages
Contents: 1. The Theory of Combinators and the ?-Calculus.- 1. Introduction.- 2. Informal theory of combinators.- 2.1. Combinators and combinations.- 2.2. The combinators I, B, W, C, ?, ?.- 2.3. Extensionality.- 2.4. Alternative primitive combinators.- 2.5. Composite products, powers and deferred combinators.- 2.6. Truth-functions.- 3. Equality and reduction.- 3.2. Combinatory terms.- 3.3. ?-equality.- 3.4. Functional abstraction.- 3.5. Substitution.- 3.6. Weak reduction.- 3.7. Equality.- 3.8. Strong reduction.- 4. The ?-calculus.- 4.1. ?-terms.- 4.2. Substitution.- 4.3. Equality.- 4.4. Reduction.- 4.5. ?-reduction.- 4.6. Historical remarks.- 5. Equivalence of the ?-calculus and the theory of combinators.- 6. Set-theoretical interpretations of combinators.- 6.1. Introduction.- 6.2. Scott's models.- 6.3. Combinatorial completeness.- 6.4. A representation result.- 6.5. Limit spaces.- 7. Illative combinatory logic and the paradoxes.- 2. The Church-Rosser Property.- 1. Introduction.- 2. R-reductions.- 3. One-step reduction.- 4. Proof of main result.- 5. Generalization.- 6. Generalized weak reduction.- 3. Combinatory Arithmetic.- 1. Introduction.- 2. Combinatory definability.- 3. Fixed-points and numeral sequences.- 4. Undecidability results.- 4. Computable Functionals of Finite Type.- 1. Introduction.- 2. Finite types and terms of finite types.- 3. The equation calculus.- 4. The role of the induction rule.- 5. Soundness of the axioms.- 6. Defining axioms and uniqueness rules.- 7. Reduction rules.- 8. Computability and normal form.- 9. Interpretation of types and terms.- 5. Proofs in the Theory of Species.- 1. Introduction.- 2. Formulas, terms and types.- 3. A-terms and deductions.- 4. The equation calculus.- 5. Reduction and normal form.- 6. The strong normalization theorem.- 7. Interpretation of types and terms.- Index of Names.- Index of Subjects.
Series Title: Synthese library, 42.
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