an:03877147
Zbl 0551.03007
Barendregt, H. P.
The lambda calculus. Its syntax and semantics. Rev. ed
EN
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).
00426464
1984
b
03B40 03-01 03-02 68Q65 68Q55
syntax; semantics; reduction systems; type-free lambda calculus; models
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 \textit{H. B. Curry} and \textit{R. Feys} [Combinatory logic. Vol. I (1958; Zbl 0081.241)] and \textit{H. B. Curry}, \textit{J. R. Hindley}, \textit{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 \textit{J. W. Klop's} work: [Combinatory reduction systems (1980; Zbl 0466.03006)].
A.Pettorossi
Zbl 0467.03010; Zbl 0081.241; Zbl 0242.02029; Zbl 0466.03006