Categorical Combinators, Sequential Algorithms, and Functional Programming (Progress in Theoretical Computer Science) 1993rd Edition by P.-L. Curien (PDF)

Description

This book is a revised edition of the monograph which appeared under the same title in the series Research Notes in Theoretical Computer Science, Pit­ man, in 1986. In addition to a general effort to improve typography, English, and presentation, the main novelty of this second edition is the integration of some new material. Part of it is mine (mostly jointly with coauthors). Here is brief guide to these additions. I have augmented the account of categorical combinatory logic with a description of the confluence properties of rewriting systems of categor­ ical combinators (Hardin, Yokouchi), and of the newly developed cal­ culi of explicit substitutions (Abadi, Cardelli, Curien, Hardin, Levy, and Rios), which are similar in spirit to the categorical combinatory logic, but are closer to the syntax of A-calculus (Section 1.2). The study of the full abstraction problem for PCF and extensions of it has been enriched with a new full abstraction result: the model of sequential algorithms is fully abstract with respect to an extension of PCF with a control operator (Cartwright, Felleisen, Curien). An order­ extensional model of error-sensitive sequential algorithms is also fully abstract for a corresponding extension of PCF with a control operator and errors (Sections 2.6 and 4.1). I suggest that sequential algorithms lend themselves to a decomposition of the function spaces that leads to models of linear logic (Lamarche, Curien), and that connects sequentiality with games (Joyal, Blass, Abramsky) (Sections 2.1 and 2.6).

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book requires serious familiarity with calculus to get through. If equations filled with Greek symbols makes your head spin then stay away.As for the Functional programming part:”The language described is called CDS0, and should be the ‘machine language’ of a higher level programming lannguage CDS taking some features of ML (mostly data abstraction facilities); hence CDS should be compiled into CDS0 before execution. Only the material of sections 2 and 3 (i.e. the calculus of the expressions of CDS0, without type control), is already implemented.”This book Looks like it has a lot of good content but it’s by no means an introductory text to the topics in the title. Being anything but comfortable in calculus and not even remotely interested in learning functional programming at such a low level I can’t really comment on the quality of the content.

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