Abstract
We address here the problem of automatically translating the Natural Semantics of programming languages to Coq, in order to prove formally general properties of languages. Natural Semantics [18] is a formalism for specifying semantics of programming languages inspired by Plotkin's Structural Operational Semantics [22]. The Coq proof development system [12], based on the Calculus of Constructions extended with inductive types (CCind), provides mechanized support including tactics for building goal-directed proofs. Our representation of a language in Coq is influenced by the encoding of logics used by Church [6] and in the Edinburgh Logical Framework (ELF) [15, 3].
Preview
Unable to display preview. Download preview PDF.
References
P. Aczel: An Introduction to Inductive Definitions. The Handbook of Mathematical Logic, J. Barwise ed., North-Holland, (1992) 739–782
Y. Bertot, R. Fraer: Reasoning with Executable Specifications. I. Joint Conference of Theory and Practice of Software Development, LNCS, Aarhus (1995)
Avion, Honsell, Mason: An Overview of the Edinburgh Logical Framework. Current Trends in Hardware Verification and Automated Theorem Proving (1988)
Y. Bertot, G. Kahn, L. Théry: Proof by Pointing. Proceedings of Theoretical Aspects Computer Science (TACS '94), Tohoku University, Sendai, Japan, LNCS (1994) 789
R. Burstall, J. Goguen: Algebras, theories and freeness: an introduction for computer scientists. Theoretical Foundations of Programming Methodology, (1982) 329–350
A. Church: A formulation of the simple theory of types. J. of Symbolic Logic, 5 (1940) 56–68
O. Dahl: Verifiable Programming. Prentice Hall International series in computer science (1992)
J. Despeyroux, A. Hirschowitz: Higher-Order Syntax and Induction in Coq. Pr. of the fifth Int. Conf. on Logic Programming and Automated Reasoning Kiev, (1994) 16–21
J. Despeyroux: Theo: an Interactive Proof Development System. Scandinavian J. on Computer Science and Numerical Analysis (BIT), 32 (1992) 15–29
T. Despeyroux: Typol and Natural Semantics. Notes de cours pour l'Ecole Jeunes Chercheurs du GRECO de Programmation (1991)
T. Despeyroux: Typol: a formalism to implement Natural Semantics. Technical Report 94, Inria, Sophia-Antipolis, France (1988)
G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Murthy, C. Parent, C. Paulin, B. Werner: The Coq Proof Assistant User's guide, Version 5.8. Technical Report 1154, Inria, Rocquencourt, France (1991)
P. Gardner: Representing Logics in Type Theory. Phd Thesis, Department of Computer Science, The University of Edinburgh (1992)
J. Hannan: Extended Natural Semantics. J. of Functional Programming, Cambridge University Press, 2 (1993) 123–152
R. Harper, F. Honsell, G. Plotkin: A Framework for Defining Logics. J. of the ACM, 40(1) (1993) 143–184
G. Huet: A Uniform Approach to Type Theory. Research Report 795, Inria, Rocquencourt, France (1988)
I. Jacobs. The Centaur 1.2 Manual. Technical report, Inria, Sophia-Antipolis, France (1992)
G. Kahn: Natural Semantics. Proceedings of the Symp. on Theorical Aspects of Computer Science, TACS, Passau, Germany (1987)
J.W. Lloyd: Foundations of Logic Programming. Ed. by L.Bolc, A.Bundy, P.Hayes and J.Siekmann, Germany (1987)
C. Paulin-Mohring: Inductive Definitions in the System Coq. Rules and Properties. Pr. of the Int. Conf. on Typed Lambda Calculi and Applications, LNCS 664 (1993) 328–345
J.C. Mitchell: Type Inference with Simple Subtypes. J. of Functional Programming, 1(3) (1991) 245–286
G.D. Plotkin: A Structural Approach to Operational Semantics. Technical Report, Aarhus, (1981) DAIMI FN-19
M. VanInwegen, E. Gunter: HOL-ML. Pr. of the Tech. Work. BRA ‘Types’ on ‘Proving Properties of Programming Languages', Ed. J. Despeyroux, INRIA, Sophia-Antipolis, France (1993)
D. Terrasse: Translation From Typol to Coq. Pr. of the Tech. Work. BRA on ‘Proving Properties of Programming Languages', Ed. J. Despeyroux, (1993)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Terrasse, D. (1995). Encoding natural semantics in Coq. In: Alagar, V.S., Nivat, M. (eds) Algebraic Methodology and Software Technology. AMAST 1995. Lecture Notes in Computer Science, vol 936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60043-4_56
Download citation
DOI: https://doi.org/10.1007/3-540-60043-4_56
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60043-5
Online ISBN: 978-3-540-49410-2
eBook Packages: Springer Book Archive