The Lambda Calculus: Its Syntax and Semantics
North-Holland, 1984 - 621 strani
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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application assume assumption axioms Böhm trees BT(M calculus called chapter Church-Rosser Clearly closed compact complete computable Consider consistent constant Construct continuous contracted contradiction corollary corresponding defined DEFINITION denotes directed element equality equations equivalent example exercise exists extended extensional fact finite fixed point follows functions given head Hence holds induction induction hypothesis infinite introduced labelled lambda lattice lemma logic Moreover normal notation Note notion of reduction numerals object obtained occurrence operation partial path PROOF proposition proved recursive recursive functions redex relation REMARK represent respectively result rule satisfies Scott sequence Show shown Similarly solvable standard step strategy structure substitution subterm Suppose theorem theory topology trivial unsolvable variable Write X-terms