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Adapting Proofs-as-Programs

The Curry--Howard Protocol

By Iman Poernomo , John N. Crossley , Martin Wirsing

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  • ISBN13: 978-0-3872-3759-6
  • 432 Pages
  • User Level: Science
  • Publication Date: April 27, 2007
  • Available eBook Formats: PDF
Full Description
This monograph details several important advances in the area known as the proofs-as-programs paradigm, a set of approaches to developing programs from proofs in constructive logic. It serves the dual purpose of providing a state-of-the-art overview of the field and detailing tools and techniques to stimulate further research. One of the book’s central themes is a general, abstract framework for developing new systems of program synthesis by adapting proofs-as-programs to new contexts, which the authors call the Curry--Howard Protocol. This protocol is used to provide two novel applications for industrial-scale, complex software engineering: contractual imperative program synthesis and structured software synthesis. These applications constitute an exemplary justification for the applicability of the protocol to different contexts. The book is intended for graduate students in computer science or mathematics who wish to extend their background in logic and type theory as well as gain experience working with logical frameworks and practical proof systems. In addition, the proofs-as-programs research community, and the wider computational logic, formal methods and software engineering communities will benefit. The applications given in the book should be of interest for researchers working in the target problem domains.
Table of Contents

Table of Contents

  1. Part I. Prologue.
  2. Introduction.
  3. Part II. Generalizing Proofs
  4. as
  5. Programs.
  6. Functional Program Synthesis.
  7. The Curry
  8. Howard protocol.
  9. Part III. Imperative Proofs
  10. as
  11. Programs.
  12. Intuitionistic Hoare Logic.
  13. Properties of Intuitionistic Hoare Logic.
  14. Proofs
  15. as
  16. Imperative
  17. Programs.
  18. Part IV. Structured Proofs
  19. as
  20. Programs.
  21. Reasoning about Structured Specifications.
  22. Proof
  23. theoretic Properties of SSL.
  24. Structured Proofs
  25. as
  26. Programs.
  27. Generic Specifications.
  28. Structured Program Synthesis.
  29. Part V. Epilogue.
  30. Conclusions: Toward Constructive Logic as a Practical 4GL.
  31. Part VI. Appendix.
  32. A: Constructive Logic.
  33. References.
  34. Index.

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