The Parametric Lambda Calculus - A Meta-Model for Calculation

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.

List of contents

I. Syntax.- 1. The Parametric ?-Calculus.- 2. The Call-by-Name ?-Calculus.- 3. The Call-by-Value ?-Calculus.- 4. Further Reading.- II. Operational Semantics.- 5. Parametric Operational Semantics.- 6. Call-by-Name Operational Semantics.- 7. Call-by-Value Operational Semantics.- 8. Operational Extensionality.- 9. Further Reading.- III. Denotational Semantics.- 10. ??-Models.- 11. Call-by-Name Denotational Semantics.- 12. Call-by-Value Denotational Semantics.- 13. Filter ??-Models and Domains.- 14. Further Reading.- IV. Computational Power.- 15. Preliminaries.- 16. Representing Functions.

Product details

• Authors: Luca Paolini, Simona Ronchi Della Rocca
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 05.07.2004
• EAN: 9783540200321
• ISBN: 978-3-540-20032-1
• No. of pages: 248
• Weight: 580 g
• Illustrations: XIV, 248 p.
• Series: Texts in Theoretical Computer Science. An EATCS Series
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Basic principles; B, Künstliche Intelligenz, Artificial Intelligence, Compiler und Übersetzer, computer science, Theory of Computation, Logics and Meanings of Programs, Programming Languages, Compilers, Interpreters, Computers, Mathematical theory of computation, Computer programming / software engineering, Mathematical logic, Mathematical Logic and Foundations, Mathematical Logic and Formal Languages, Computer architecture & logic design, Programming & scripting languages: general, Compilers & interpreters, Programming languages (Electronic computers), Computer logic, Computation by Abstract Devices