Abstract
The Focal language (formerly FoC) allows one to incrementally build modules and to formally prove their correctness. In this paper, we present two formal semantics for encoding Focal constructions in the Coq proof assistant. The first one is implemented in the Focal compiler to have the correctness of Focal libraries verified with the Coq proof-checker. The second one formalizes the Focal structures and their main properties as Coq terms (called mixDrecs). The relations between the two embeddings are examined in the last part of the paper.
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References
Ancona, D., Zucca, E.: An algebra of mixin modules. In: Parisi-Presicce, F. (ed.) WADT 1997. LNCS, vol. 1376, pp. 92–106. Springer, Heidelberg (1998)
Betarte, G.: Dependent Record Types and Formal Abstract Reasoning: Theory and Practice. PhD thesis, University of Göteborg (1998)
Bognar, M., de Vrijer, R.: A calculus of lambda calculus contexts. Journal of Automated Reasoning 27(1) (2001)
Boulmé, S.: Spécification d’un environnement dédié à la programmation certifiée de bibliothèques de Calcul Formel. Thèse de doctorat, Université Paris 6 (2000), http://www-lsr.imag.fr/Les.Personnes/Sylvain.Boulme/pub/sbthese.ps.gz
Boulmé, S., Hardin, T., Rioboo, R.: Some hints for polynomials in the Foc project. In: Proc. Calculemus (2001)
Coquand, T., Pollack, R., Takeyama, M.: A logical framework with dependently typed records. In: Hofmann, M.O. (ed.) TLCA 2003. LNCS, vol. 2701, pp. 105–119. Springer, Heidelberg (2003)
de Bruijn, N.G.: Telescopic mappings in typed λ-calculus. Information and Computation 91(2) (1991)
Hirschowitz, T., Leroy, X.: Mixin modules in a call-by-value setting. In: Le Métayer, D. (ed.) ESOP 2002. LNCS, vol. 2305, pp. 6–20. Springer, Heidelberg (2002)
Hofmann, M., et al.: Inheritance of proofs. TAPOS 4(1), 51–69 (1998)
Kopylov, A.: Dependent intersection: A new way of defining records in type theory. In: LICS (2003)
Lee, S., Friedman, D.P.: Enriching the lambda calculus with contexts: Toward a theory of incremental program construction. In: Proceedings of ICFP, ACM SIGPLAN notices, New York (1996)
Mason, I.A.: Computing with contexts. Higher-Order and Symbolic Computation 12 (1999)
Odersky, M., Cremet, V., Röckl, C., Zenger, M.: A nominal theory of objects with dependent types. In: FOOL 10 (2003)
Poll, E., Thompson, S.: Integrating Computer Algebra and Reasoning through the Type System of Aldor. In: Kirchner, H. (ed.) FroCos 2000. LNCS(LNAI), vol. 1794, pp. 136–150. Springer, Heidelberg (2000)
Pollack, R.: Dependently typed records for representing mathematical structures. In: Aagaard, M.D., Harrison, J. (eds.) TPHOLs 2000. LNCS, vol. 1869, pp. 462–479. Springer, Heidelberg (2000)
Prevosto, V.: Conception et Implantation du langage FoC pour le développement de logiciels certifiés. Thèse de doctorat, Université Paris 6 (2003), http://www.mpi-sb.mpg.de/~prevosto/papiers/these.ps.gz
Prevosto, V., Doligez, D.: Inheritance of algorithms and proofs in the computer algebra library foc. Journal of Automated Reasoning 29(3-4) (2002)
Rioboo, R.: Programmer le calcul formel, des algorithmes à la sémantique. Habilitation, Université Paris 6 (2002)
Sands, D.: Computing with contexts: A simple approach. In: Second Workshop on Higher-Order Operational Techniques in Semantics, ENTCS, vol. 10 (1997)
Sato, M., Sakurai, T., Kameyama, Y.: A simply typed context calculus with first-class environments. J. of Functional and Logic Programming 4 (2002)
The Coq Development Team. The Coq Proof Assistant Reference Manual Version 8.0. INRIA-Rocquencourt (2004)
The Focal development team. Focal, version 0.2 Tutorial and reference manual. LIP6 – INRIA – CNAM (2004), http://modulogic.inria.fr/focal/download/
Thompson, S.: Logic and Dependent Types in the Aldor Computer Algebra System. In: Proc. Calculemus (2000)
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Prevosto, V., Boulmé, S. (2005). Proof Contexts with Late Binding. In: Urzyczyn, P. (eds) Typed Lambda Calculi and Applications. TLCA 2005. Lecture Notes in Computer Science, vol 3461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11417170_24
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DOI: https://doi.org/10.1007/11417170_24
Publisher Name: Springer, Berlin, Heidelberg
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