The Parametric Lambda Calculus: A Metamodel for Computation (Texts in Theoretical Computer Science. An EATCS Series) - Softcover

Ronchi Della Rocca, Simona; Paolini, Luca

Softcover

ISBN 10: 3642057462 ISBN 13: 9783642057465

Publisher: Springer, 2010

Synopsis

The A-calculus was invented by Church in the 1930s with the purpose of sup- plying a logical foundation for logic and mathematics [25]. Its use by Kleene as a coding for computable functions makes it the first programming lan- guage, in an abstract sense, exactly as the Thring machine can be considered the first computer machine [57]. The A-calculus has quite a simple syntax (with just three formation rules for terms) and a simple operational seman- tics (with just one operation, substitution), and so it is a very basic setting for studying computation properties. The first contact between A-calculus and real programming languages was in the years 1956-1960, when McCarthy developed the LISP programming language, inspired from A-calculus, which is the first "functional" program- ming language, Le., where functions are first-dass citizens [66]. But the use of A-calculus as an abstract paradigm for programming languages started later as the work of three important scientists: Strachey, Landin and B6hm.

About this title

From the Back Cover

The parametric lambda calculus is a metamodel for reasoning about various kinds of computations. Its syntactic definition is based on the notion of "sets of input values", and different lambda calculi can be obtained from it by instantiating such sets in suitable ways.

The parametric lambda calculus is used as a tool for presenting in a uniform way basic notions of programming languages, and for studying with a uniform approach some lambda calculi modeling different kinds of computations, such as call-by-name, both in its lazy and non-lazy versions, and call-by-value. The parametric presentation allows us both to prove in one step all the fundamental properties of different calculi, and to compare them with each other.

The book includes some classical results in the field of lambda calculi, but completely rephrased using the parametric approach, together with some new results. The lambda calculi are presented from a computer science viewpoint, with particular emphasis on their semantics, both operational and denotational.

This book is dedicated to researchers, and can be used as a textbook for masters or Ph.D. courses on the foundations of computer science.

About the Author

Simona Ronchi Della Rocca: Full Professor of Foundations of Computer Science since 1987, Member of the Editorial Board of TOCL (ACM Transactions on Computational Logic), Member of the Organizing Committee of LICS (Logic in Computer Science), Member of the Accademy of Sciences of Torino

Luca Paolini: PhD student in Computer Science and Discrete Mathematics, Università di Genova and Université de la Mediterranée.

 

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Edition details

• Publisher: Springer
• Publication date: 2010
• ISBN 10: 3642057462
• ISBN 13: 9783642057465
• Binding: Paperback
• Language: English
• Number of pages: 262