Hybrid: reasoning with higher-order abstract syntax in coq and isabelle
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Abstract
We present recent work on the Hybrid system, a logical framework for specifying and reasoning about languages and deductive systems. One of the main areas of application of this system is developing formal proofs of properties of programming languages. It is well-known that those languages that are formally proven to be sound can better provide a solid basis for building software systems that are reliable and secure.
Hybrid is designed to exploit the advantages of higher-order abstract syntax within the well-understood setting of higher-order logic as implemented in a variety of general theorem proving systems. It is currently implemented in both Isabelle/HOL and Coq.
Hybrid is definitional and introduces no new axioms. In particular, a de Bruijn representation of lambda-terms provides a definitional layer that allows the user to represent object languages using higher-order abstract syntax, while offering tools for reasoning about them at the higher level.
We describe a variety of features of Hybrid, including two-level reasoning and inductive reasoning about open terms, and we present case studies to illustrate these features. We also discuss both classical and constructive versions of Hybrid.
References
[1]
}}Y. Bertot and P. Cast´eran. Interactive Theorem Proving and Program Development. Coq'Art: The Calculus of Inductive Constructions. Springer, 2004.
[2]
}}V. Capretta and A. P. Felty. Combining de Bruijn indices and higher-order abstract syntax in Coq. In Types for Proofs and Programs, International Workshop, TYPES 2006, Revised Selected Papers, pages 63--77. Springer-Verlag Lecture Notes in Computer Science, 2007.
[3]
}}A. Felty and A. Momigliano. Hybrid: A definitional two-level approach to reasoning with higher-order abstract syntax. Journal of Automated Reasoning. To appear (http://arxiv.org/abs/0811.4367).
[4]
}}A. P. Felty and A. Momigliano. Reasoning with hypothetical judgments and open terms in Hybrid. In 11th International ACM SIGPLAN Symposium on Principles and Practice of Declarative Programming, pages 83--92, 2009.
[5]
}}A. Momigliano, A. J. Martin, and A. P. Felty. Two-level Hybrid: A system for reasoning using higher-order abstract syntax. Electronic Notes in Theoretical Computer Science, 196:85--93, 2008. Proceedings of the 2007 International Workshop on Logical Frameworks and Metalanguages: Theory and Practice.
[6]
}}T. Nipkow, L. C. Paulson, and M. Wenzel. Isabelle/HOL: A Proof Assistant for Higher-Order Logic, volume 2283 of Lecture Notes in Computer Science. Springer, 2002.
Index Terms
- Hybrid: reasoning with higher-order abstract syntax in coq and isabelle
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Published In
September 2010
62 pages
Copyright © 2010 Copyright is held by the author/owner(s).
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Association for Computing Machinery
New York, NY, United States
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Published: 25 September 2010
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ICFP '10
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ICFP '10: ACM SIGPLAN International Conference on Functional Programming
September 25, 2010
Maryland, Baltimore, USA
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MSFP '10 Paper Acceptance Rate 4 of 8 submissions, 50%;
Overall Acceptance Rate 4 of 8 submissions, 50%
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