Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- 1 Determinacy in a synchronous π-calculus
- 2 Classical coordination mechanisms in the chemical model
- 3 Sequential algorithms as bistable maps
- 4 The semantics of dataflow with firing
- 5 Kahn networks at the dawn of functional programming
- 6 A simple type-theoretic language: Mini-TT
- 7 Program semantics and infinite regular terms
- 8 Algorithms for equivalence and reduction to minimal form for a class of simple recursive equations
- 9 Generalized finite developments
- 10 Semantics of program representation graphs
- 11 From Centaur to the Meta-Environment: a tribute to a great meta-technologist
- 12 Towards a theory of document structure
- 13 Grammars as software libraries
- 14 The Leordo computation system
- 15 Theorem-proving support in programming language semantics
- 16 Nominal verification of algorithm W
- 17 A constructive denotational semantics for Kahn networks in Coq
- 18 Asclepios: a research project team at INRIA for the analysis and simulation of biomedical images
- 19 Proxy caching in split TCP: dynamics, stability and tail asymptotics
- 20 Two-by-two static, evolutionary, and dynamic games
- 21 Reversal strategies for adjoint algorithms
- 22 Reflections on INRIA and the role of Gilles Kahn
- 23 Can a systems biologist fix a Tamagotchi?
- 24 Computational science: a new frontier for computing
- 25 The descendants of Centaur: a personal view on Gilles Kahn's work
- 26 The tower of informatic models
- References
15 - Theorem-proving support in programming language semantics
Published online by Cambridge University Press: 06 August 2010
By
Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- 1 Determinacy in a synchronous π-calculus
- 2 Classical coordination mechanisms in the chemical model
- 3 Sequential algorithms as bistable maps
- 4 The semantics of dataflow with firing
- 5 Kahn networks at the dawn of functional programming
- 6 A simple type-theoretic language: Mini-TT
- 7 Program semantics and infinite regular terms
- 8 Algorithms for equivalence and reduction to minimal form for a class of simple recursive equations
- 9 Generalized finite developments
- 10 Semantics of program representation graphs
- 11 From Centaur to the Meta-Environment: a tribute to a great meta-technologist
- 12 Towards a theory of document structure
- 13 Grammars as software libraries
- 14 The Leordo computation system
- 15 Theorem-proving support in programming language semantics
- 16 Nominal verification of algorithm W
- 17 A constructive denotational semantics for Kahn networks in Coq
- 18 Asclepios: a research project team at INRIA for the analysis and simulation of biomedical images
- 19 Proxy caching in split TCP: dynamics, stability and tail asymptotics
- 20 Two-by-two static, evolutionary, and dynamic games
- 21 Reversal strategies for adjoint algorithms
- 22 Reflections on INRIA and the role of Gilles Kahn
- 23 Can a systems biologist fix a Tamagotchi?
- 24 Computational science: a new frontier for computing
- 25 The descendants of Centaur: a personal view on Gilles Kahn's work
- 26 The tower of informatic models
- References
Summary
Abstract
We describe how the formal description of a programming language can be encoded in the Coq theorem prover. Four aspects are covered: Natural semantics (as advocated by Gilles Kahn), axiomatic semantics, denotational semantics, and abstract interpretation. We show that most of these aspects have an executable counterpart and describe how this can be used to support proofs about programs.
Introduction
Nipkow demonstrated in that theorem provers could be used to formalize many aspects of programming language semantics. In this paper, we want to push the experiment further to show that this formalization effort also has a practical outcome, in that it makes it possible to integrate programming tools inside theorem provers in an uniform way. We re-visit the study of operational, denotational semantics, axiomatic semantics, and weakest pre-condiction calculus as already studied by Nipkow and we add a small example of a static analysis tool based on abstract interpretation.
To integrate the programming tools inside the theorem prover we rely on the possibility to execute the algorithms after they have been formally described and proved correct, a technique known as reflection. We also implemented a parser, so that the theorem prover can be used as a playground to experiment on sample programs. We performed this experiment using the Coq system. The tools that are formally described can also be “extracted” outside the proof environment, so that they become stand alone programs.
- Type
- Chapter
- Information
- From Semantics to Computer ScienceEssays in Honour of Gilles Kahn, pp. 337 - 362Publisher: Cambridge University PressPrint publication year: 2009
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