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" Combinators, [lambda]-Terms and Proof Theory "
by Sören Stenlund.
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BL
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| Record Number
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728934
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b548688
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| Main Entry
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by Sören Stenlund.
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| Title & Author
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Combinators, [lambda]-Terms and Proof Theory\ by Sören Stenlund.
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| Publication Statement
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Dordrecht: Springer Netherlands, 1972
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| Series Statement
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Synthese library, v. 42.
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(192 pages)
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| ISBN
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940102913X
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: 9789401029131
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| Contents
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1. The Theory of Combinators and the?-Calculus --;1. Introduction --;2. Informal theory of combinators --;3. Equality and reduction --;4. The?-calculus --;5. Equivalence of the?-calculus and the theory of combinators --;6. Set-theoretical interpretations of combinators --;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.
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| Abstract
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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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Logic.
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Philosophy (General)
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Sören Stenlund
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