Towards the Theory. Introduction. Conversion. Reduction. Theories. Models. Conversion. Classical Lambda Calculus. The Theory of Combinators. Classical Lambda Calculus (Continued). The Lambda-Calculus. Böhm Trees. Reduction. Fundamental Theorems. Strongly Equivalent Reductions. Reduction Strategies. Labelled Reduction. Other Notions of Reduction. Theories. Sensible Theories. Other Lambda Theories. Models. Construction of Models. Local Structure of Models. Global Structure of Models. Combinatory Groups. Appendices: Typed Lambda Calculus. Illative Combinatory Logic. Variables. References.
The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given and then the general theory (of categorical models) is developed. Indications are given of those parts of the book which can be used to form a coherent course.
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- © North Holland 1984
- 11th September 2014
- North Holland
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@qu:This book is (almost) an encyclopedia of type-free lambda calculus... The reviewer is surprised by the author's success in getting in such an amount of material with motivations and complete proofs... @source:Zentralblatt für Mathematik @qu:It brings together virtually all of the current knowledge on the subject and will be indispensable for serious students of the lambda calculus... @source:Journal of Symbolic Logic @qu:There must have been an exceptional amount of effort to ensure the high quality of text and printing... @source:Journal of Symbolic Logic