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The lambda calculus. Its syntax and semantics. Rev. ed. (English) Zbl 0551.03007
Studies in Logic and the Foundations of Mathematics, 103. Amsterdam-New York-Oxford: North-Holland. XV, 621 p. hbk: $ 70.00; Dfl. 250.00; pbk: $ 35.00; Dfl. 125.00 (1984).
This revised version of the lambda calculus book by H. Barendregt can be considered as a fundamental work in the subject (for a review of the first edition (1981) see [Zbl 0467.03010]). The various aspects of that calculus have been explored and explained: conversion, reduction, theories and models. After the classical books by H. B. Curry and R. Feys [Combinatory logic. Vol. I (1958; Zbl 0081.241)] and H. B. Curry, J. R. Hindley, J. P. Seldin [Combinatory logic. Vol. II (1972; Zbl 0242.02029)], the lambda calculus community finds in Barendregt’s book a very interesting and comprehensive account of what has been done in the area, especially during the 70’s and the early 80’s. The revised edition of that book gives a closer look at the models of lambda calculus and includes recent results.
Another reference for persons interested in the subject is J. W. Klop’s work: [Combinatory reduction systems (1980; Zbl 0466.03006)].
Reviewer: A.Pettorossi

03B40 Combinatory logic and lambda calculus
03-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
68Q65 Abstract data types; algebraic specification
68Q55 Semantics in the theory of computing