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2016 | OriginalPaper | Buchkapitel

ML Pattern-Matching, Recursion, and Rewriting: From FoCaLiZe to Dedukti

verfasst von : Raphaël Cauderlier, Catherine Dubois

Erschienen in: Theoretical Aspects of Computing – ICTAC 2016

Verlag: Springer International Publishing

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Abstract

The programming environment FoCaLiZe allows the user to specify, implement, and prove programs with the help of the theorem prover Zenon. In the actual version, those proofs are verified by Coq. In this paper we propose to extend the FoCaLiZe compiler by a backend to the Dedukti language in order to benefit from Zenon Modulo, an extension of Zenon for Deduction modulo. By doing so, FoCaLiZe can benefit from a technique for finding and verifying proofs more quickly. The paper focuses mainly on the process that overcomes the lack of local pattern-matching and recursive definitions in Dedukti.

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Fußnoten
Literatur
1.
Zurück zum Zitat Assaf, A.: A framework for defining computational higher-order logics. Ph.D. thesis, École Polytechnique (2015) Assaf, A.: A framework for defining computational higher-order logics. Ph.D. thesis, École Polytechnique (2015)
2.
Zurück zum Zitat Assaf, A., Burel, G.: Translating HOL to Dedukti. In: Kaliszyk, C., Paskevich, A. (eds.) Proceedings Fourth Workshop on Proof eXchange for Theorem Proving. EPTCS, vol. 186, Berlin, Germany, pp. 74–88 (2015) Assaf, A., Burel, G.: Translating HOL to Dedukti. In: Kaliszyk, C., Paskevich, A. (eds.) Proceedings Fourth Workshop on Proof eXchange for Theorem Proving. EPTCS, vol. 186, Berlin, Germany, pp. 74–88 (2015)
3.
Zurück zum Zitat Bonichon, R., Delahaye, D., Doligez, D.: Zenon: an extensible automated theorem prover producing checkable proofs. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS (LNAI), vol. 4790, pp. 151–165. Springer, Heidelberg (2007). doi:10.1007/978-3-540-75560-9_13 CrossRef Bonichon, R., Delahaye, D., Doligez, D.: Zenon: an extensible automated theorem prover producing checkable proofs. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS (LNAI), vol. 4790, pp. 151–165. Springer, Heidelberg (2007). doi:10.​1007/​978-3-540-75560-9_​13 CrossRef
4.
Zurück zum Zitat Burel, G.: A shallow embedding of resolution and superposition proofs into the \(\lambda {\varPi }\)-calculus modulo. In: Blanchette, J.C., Urban, J. (eds.) PxTP 2013. 3rd International Workshop on Proof Exchange for Theorem Proving. EasyChair Proceedings in Computing, vol. 14, Lake Placid, USA, pp. 43–57 (2013) Burel, G.: A shallow embedding of resolution and superposition proofs into the \(\lambda {\varPi }\)-calculus modulo. In: Blanchette, J.C., Urban, J. (eds.) PxTP 2013. 3rd International Workshop on Proof Exchange for Theorem Proving. EasyChair Proceedings in Computing, vol. 14, Lake Placid, USA, pp. 43–57 (2013)
5.
Zurück zum Zitat Cauderlier, R.: Object-oriented mechanisms for interoperability between proof systems. Ph.D. thesis, Conservatoire National des Arts et Métiers, Paris (draft) Cauderlier, R.: Object-oriented mechanisms for interoperability between proof systems. Ph.D. thesis, Conservatoire National des Arts et Métiers, Paris (draft)
6.
Zurück zum Zitat Cauderlier, R., Dubois, C.: Objects and subtyping in the \(\lambda \varPi \)-calculus modulo. In: Post-proceedings of the 20th International Conference on Types for Proofs and Programs (TYPES 2014). Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl, Paris (2014) Cauderlier, R., Dubois, C.: Objects and subtyping in the \(\lambda \varPi \)-calculus modulo. In: Post-proceedings of the 20th International Conference on Types for Proofs and Programs (TYPES 2014). Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl, Paris (2014)
7.
Zurück zum Zitat Cauderlier, R., Halmagrand, P.: Checking Zenon Modulo proofs in Dedukti. In: Kaliszyk, C., Paskevich, A. (eds.) Proceedings 4th Workshop on Proof eXchange for Theorem Proving. EPTCS, vol. 186, Berlin, Germany, pp. 57–73 (2015) Cauderlier, R., Halmagrand, P.: Checking Zenon Modulo proofs in Dedukti. In: Kaliszyk, C., Paskevich, A. (eds.) Proceedings 4th Workshop on Proof eXchange for Theorem Proving. EPTCS, vol. 186, Berlin, Germany, pp. 57–73 (2015)
8.
Zurück zum Zitat Cousineau, D., Dowek, G.: Embedding pure type systems in the \(\lambda {\varPi }\)-calculus modulo. In: Rocca, S.R.D. (ed.) TLCA 2007. LNCS, vol. 4583, pp. 102–117. Springer, Heidelberg (2007). doi:10.1007/978-3-540-73228-0_9 CrossRef Cousineau, D., Dowek, G.: Embedding pure type systems in the \(\lambda {\varPi }\)-calculus modulo. In: Rocca, S.R.D. (ed.) TLCA 2007. LNCS, vol. 4583, pp. 102–117. Springer, Heidelberg (2007). doi:10.​1007/​978-3-540-73228-0_​9 CrossRef
9.
Zurück zum Zitat Delahaye, D., Doligez, D., Gilbert, F., Halmagrand, P., Hermant, O.: Zenon Modulo: when Achilles outruns the tortoise using deduction modulo. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19. LNCS, vol. 8312, pp. 274–290. Springer, Heidelberg (2013). doi:10.1007/978-3-642-45221-5_20 CrossRef Delahaye, D., Doligez, D., Gilbert, F., Halmagrand, P., Hermant, O.: Zenon Modulo: when Achilles outruns the tortoise using deduction modulo. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19. LNCS, vol. 8312, pp. 274–290. Springer, Heidelberg (2013). doi:10.​1007/​978-3-642-45221-5_​20 CrossRef
10.
11.
Zurück zum Zitat Giesl, J., Raffelsieper, M., Schneider-Kamp, P., Swiderski, S., Thiemann, R.: Automated termination proofs for Haskell by term rewriting. ACM Trans. Program. Lang. Syst. 33(2), 7:1–7:39 (2011)CrossRef Giesl, J., Raffelsieper, M., Schneider-Kamp, P., Swiderski, S., Thiemann, R.: Automated termination proofs for Haskell by term rewriting. ACM Trans. Program. Lang. Syst. 33(2), 7:1–7:39 (2011)CrossRef
12.
13.
Zurück zum Zitat Klop, J.W., van Oostrom, V., de Vrijer, R.: Lambda calculus with patterns. Theoret. Comput. Sci. 398(1–3), 16–31 (2008). Calculi, Types and Applications: Essays in honour of M. Coppo, M. Dezani-Ciancaglini and S. Ronchi Della RoccaMathSciNetCrossRefMATH Klop, J.W., van Oostrom, V., de Vrijer, R.: Lambda calculus with patterns. Theoret. Comput. Sci. 398(1–3), 16–31 (2008). Calculi, Types and Applications: Essays in honour of M. Coppo, M. Dezani-Ciancaglini and S. Ronchi Della RoccaMathSciNetCrossRefMATH
14.
Zurück zum Zitat Lucas, S., Peña, R.: Rewriting techniques for analysing termination and complexity bounds of Safe programs. In: LOPSTR 2008, pp. 43–57 (2008) Lucas, S., Peña, R.: Rewriting techniques for analysing termination and complexity bounds of Safe programs. In: LOPSTR 2008, pp. 43–57 (2008)
15.
Zurück zum Zitat Pessaux, F.: FoCaLiZe: inside an F-IDE. In: Dubois, C., Giannakopoulou, D., Méry, D. (eds.) Proceedings 1st Workshop on Formal Integrated Development Environment, F-IDE 2014. EPTCS, vol. 149, Grenoble, France, pp. 64–78 (2014) Pessaux, F.: FoCaLiZe: inside an F-IDE. In: Dubois, C., Giannakopoulou, D., Méry, D. (eds.) Proceedings 1st Workshop on Formal Integrated Development Environment, F-IDE 2014. EPTCS, vol. 149, Grenoble, France, pp. 64–78 (2014)
16.
Zurück zum Zitat Peyton Jones, S.L.: The Implementation of Functional Programming Languages. Prentice-Hall International Series in Computer Science. Prentice-Hall, Inc., Upper Saddle River (1987)MATH Peyton Jones, S.L.: The Implementation of Functional Programming Languages. Prentice-Hall International Series in Computer Science. Prentice-Hall, Inc., Upper Saddle River (1987)MATH
17.
Zurück zum Zitat Saillard, R.: Type checking in the \(\lambda {\varPi }\)-calculus modulo: theory and practice. Ph.D. thesis, MINES Paritech (2015) Saillard, R.: Type checking in the \(\lambda {\varPi }\)-calculus modulo: theory and practice. Ph.D. thesis, MINES Paritech (2015)
Metadaten
Titel
ML Pattern-Matching, Recursion, and Rewriting: From FoCaLiZe to Dedukti
verfasst von
Raphaël Cauderlier
Catherine Dubois
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-46750-4_26

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