Author | Stenlund, Sรถren. author |
---|---|
Title | Combinators, ฮป-Terms and Proof Theory [electronic resource] / by Sรถren Stenlund |
Imprint | Dordrecht : Springer Netherlands, 1972 |
Connect to | http://dx.doi.org/10.1007/978-94-010-2913-1 |
Descript | X, 177 p. online resource |
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