Abstract
Isabelle, which is available from http://isabelle.in.tum.de , is a generic framework for interactive theorem proving. The Isabelle/Pure meta-logic allows the formalization of the syntax and inference rules of a broad range of object-logics following the general idea of natural deduction [32,33]. The logical core is implemented according to the well-known “LCF approach” of secure inferences as abstract datatype constructors in ML [16]; explicit proof terms are also available [8]. Isabelle/Isar provides sophisticated extra-logical infrastructure supporting structured proofs and specifications, including concepts for modular theory development. Isabelle/HOL is a large application within the generic framework, with plenty of logic-specific add-on tools and a large theory library. Other notable object-logics are Isabelle/ZF (Zermelo-Fraenkel set-theory, see [34,36] and Isabelle/HOLCF [26] (Scott’s domain theory within HOL). Users can build further formal-methods tools on top, e.g. see [53].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aehlig, K., Haftmann, F., Nipkow, T.: A compiled implementation of normalization by evaluation. In: Theorem Proving in Higher Order Logics (TPHOLs 2008). LNCS. Springer, Heidelberg (2008)
Alkassar, E., Schirmer, N., Starostin, A.: Formal pervasive verification of a paging mechanism. In: Ramakrishnan, C.R., Rehof, J. (eds.) Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2008). LNCS, vol. 4963, pp. 109–123. Springer, Heidelberg (2008)
Aspinall, D.: Proof General: A generic tool for proof development. In: European Joint Conferences on Theory and Practice of Software (ETAPS) (2000)
Avigad, J., Donnelly, K., Gray, D., Raff, P.: A formally verified proof of the prime number theorem. ACM Trans. Comput. Logic 9(1:2), 1–23 (2007)
Ballarin, C.: Locales and locale expressions in Isabelle/Isar. In: Berardi, S., Coppo, M., Damiani, F. (eds.) TYPES 2003. LNCS, vol. 3085. Springer, Heidelberg (2004)
Ballarin, C.: Interpretation of locales in Isabelle: Theories and proof contexts. In: Borwein, J.M., Farmer, W.M. (eds.) MKM 2006. LNCS (LNAI), vol. 4108. Springer, Heidelberg (2006)
Bauer, G., Wenzel, M.: Calculational reasoning revisited — an Isabelle/Isar experience. In: Boulton, R.J., Jackson, P.B. (eds.) TPHOLs 2001. LNCS, vol. 2152. Springer, Heidelberg (2001)
Berghofer, S., Nipkow, T.: Proof terms for simply typed higher order logic. In: Aagaard, M.D., Harrison, J. (eds.) TPHOLs 2000. LNCS, vol. 1869. Springer, Heidelberg (2000)
Berghofer, S., Nipkow, T.: Executing higher order logic. In: Callaghan, P., Luo, Z., McKinna, J., Pollack, R. (eds.) TYPES 2000. LNCS, vol. 2277, pp. 24–40. Springer, Heidelberg (2002)
Berghofer, S., Nipkow, T.: Random testing in Isabelle/HOL. In: Cuellar, J., Liu, Z. (eds.) Software Engineering and Formal Methods (SEFM 2004), pp. 230–239. IEEE Computer Society Press, Los Alamitos (2004)
Berghofer, S., Wenzel, M.: Inductive datatypes in HOL — lessons learned in Formal-Logic Engineering. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690. Springer, Heidelberg (1999)
Berghofer, S., Wenzel, M.: Logic-free reasoning in Isabelle/Isar. In: Mathematical Knowledge Management (MKM 2008), LNCS (LNAI). Springer, Heidelberg (2008)
Bortin, M., Broch Johnsen, E., Lüth, C.: Structured formal development in Isabelle. Nordic Journal of Computing 13 (2006)
Bulwahn, L., Krauss, A., Haftmann, F., Erkök, L., Matthews, J.: Imperative functional programming in Isabelle/HOL. In: Theorem Proving in Higher Order Logics (TPHOLs 2008). LNCS. Springer, Heidelberg (2008)
Chaieb, A., Wenzel, M.: Context aware calculation and deduction — ring equalities via Gröbner Bases in Isabelle. In: Kauers, M., et al. (eds.) MKM/CALCULEMUS 2007. LNCS (LNAI), vol. 4573. Springer, Heidelberg (2007)
Gordon, M.J.C., Milner, R., Wadsworth, C.P.: Edinburgh LCF. LNCS, vol. 78. Springer, Heidelberg (1979)
Haftmann, F., Nipkow, T.: A code generator framework for Isabelle/HOL. In: K. Schneider, J. Brandt (eds.) Theorem Proving in Higher Order Logics: Emerging Trends Proceedings. Dept. Comp. Sci., U. Kaiserslautern (2007)
Haftmann, F., Wenzel, M.: Constructive type classes in Isabelle. In: Altenkirch, T., McBride, C. (eds.) TYPES 2006. LNCS, vol. 4502. Springer, Heidelberg (2007)
Haftmann, F., Wenzel, M.: Local theory specifications in Isabelle/Isar (2008), http://www.in.tum.de/~wenzelm/papers/local-theory.pdf
Heiser, G., Elphinstone, K., Kuz, I., Klein, G., Petters, S.M.: Towards trustworthy computing systems: taking microkernels to the next level. SIGOPS Operating Systems Review 41(4), 3–11 (2007)
Kammüller, F., Wenzel, M., Paulson, L.C.: Locales: A sectioning concept for Isabelle. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690. Springer, Heidelberg (1999)
Klein, G., Nipkow, T.: A machine-checked model for a Java-like language, virtual machine and compiler. ACM Trans. Progr. Lang. Syst. 28(4), 619–695 (2006), http://doi.acm.org/10.1145/1146809.1146811
Krauss, A.: Partial recursive functions in Higher-Order Logic. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130. Springer, Heidelberg (2006)
Leinenbach, D., Petrova, E.: Pervasive compiler verification — from verified programs to verified systems. In: Workshop on Systems Software Verification (SSV 2008). Elsevier, Amsterdam (2008)
Lochbihler, A.: Type safe nondeterminism — a formal semantics of Java threads. In: Foundations of Object-Oriented Languages (FOOL 2008) (2008)
Müller, O., Nipkow, T., von Oheimb, D., Slotosch, O.: HOLCF = HOL + LCF. Journal of Functional Programming 9, 191–223 (1999)
Nipkow, T.: Order-sorted polymorphism in Isabelle. In: Huet, G., Plotkin, G. (eds.) Logical Environments. Cambridge University Press, Cambridge (1993)
Nipkow, T.: Structured proofs in Isar/HOL. In: Geuvers, H., Wiedijk, F. (eds.) TYPES 2002. LNCS, vol. 2646. Springer, Heidelberg (2003)
Nipkow, T., Bauer, G., Schultz, P.: Flyspeck I: Tame graphs. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 21–35. Springer, Heidelberg (2006)
Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
Obua, S.: Flyspeck II: The basic linear programs. Ph.D. thesis, Technische Universität München (2008)
Paulson, L.C.: Natural deduction as higher-order resolution. Journal of Logic Programming 3 (1986)
Paulson, L.C.: Isabelle: the next 700 theorem provers. In: Odifreddi, P. (ed.) Logic and Computer Science. Academic Press, London (1990)
Paulson, L.C.: Set theory for verification: I. From foundations to functions. Journal of Automated Reasoning 11(3) (1993)
Paulson, L.C.: A fixedpoint approach to implementing (co)inductive definitions. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814. Springer, Heidelberg (1994)
Paulson, L.C.: Set theory for verification: II. Induction and recursion. Journal of Automated Reasoning 15(2) (1995)
Paulson, L.C.: Generic automatic proof tools. In: Veroff, R. (ed.) Automated Reasoning and its Applications: Essays in Honor of Larry Wos. MIT Press, Cambridge (1997)
Paulson, L.C.: A generic tableau prover and its integration with Isabelle. Journal of Universal Computer Science 5(3) (1999)
Paulson, L.C.: The relative consistency of the axiom of choice — mechanized using Isabelle/ZF. LMS Journal of Computation and Mathematics 6, 198–248 (2003)
Paulson, L.C.: Organizing numerical theories using axiomatic type classes. Journal of Automated Reasoning 33(1) (2004)
Paulson, L.C., Susanto, K.W.: Source-level proof reconstruction for interactive theorem proving. In: Schneider, K., Brandt, J. (eds.) TPHOLs 2007. LNCS, vol. 4732. Springer, Heidelberg (2007)
Slind, K.: Function definition in higher order logic. In: von Wright, J., Harrison, J., Grundy, J. (eds.) TPHOLs 1996. LNCS, vol. 1125. Springer, Heidelberg (1996)
Tuch, H., Klein, G., Norrish, M.: Types, bytes, and separation logic. In: Principles of Programming Languages (POPL 2007), pp. 97–108. ACM Press, New York (2007)
Urban, C.: Nominal techniques in Isabelle/HOL. Journal of Automated Reasoning 40, 327–356 (2008)
Urban, C., Cheney, J., Berghofer, S.: Mechanizing the metatheory of LF. In: 23rd IEEE Symp. Logic in Computer Science (LICS) (2008)
Wasserrab, D., Nipkow, T., Snelting, G., Tip, F.: An operational semantics and type safety proof for multiple inheritance in C++. In: Object Oriented Programming, Systems, Languages, and Applications (OOPSLA 2006), pp. 345–362. ACM Press, New York (2006)
Weber, T.: Bounded model generation for Isabelle/HOL. In: Ahrendt, W., Baumgartner, P., de Nivelle, H., Ranise, S., Tinelli, C. (eds.) Workshops Disproving and Pragmatics of Decision Procedures (PDPAR 2004), vol. 125, pp. 103–116. Elsevier, Amsterdam (2005)
Wenzel, M.: Type classes and overloading in higher-order logic. In: Gunter, E.L., Felty, A.P. (eds.) TPHOLs 1997. LNCS, vol. 1275. Springer, Heidelberg (1997)
Wenzel, M.: Isar — a generic interpretative approach to readable formal proof documents. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690. Springer, Heidelberg (1999)
Wenzel, M.: Structured induction proofs in Isabelle/Isar. In: Borwein, J.M., Farmer, W.M. (eds.) MKM 2006. LNCS (LNAI), vol. 4108. Springer, Heidelberg (2006)
Wenzel, M.: Isabelle/Isar — a generic framework for human-readable proof documents. In: R. Matuszewski, A. Zalewska (eds.) From Insight to Proof — Festschrift in Honour of Andrzej Trybulec, Studies in Logic, Grammar, and Rhetoric, vol. 10(23). University of Białystok (2007), http://www.in.tum.de/~wenzelm/papers/isar-framework.pdf
Wenzel, M., Paulson, L.C.: Isabelle/Isar. In: Wiedijk, F. (ed.) The Seventeen Provers of the World. LNCS (LNAI), vol. 3600. Springer, Heidelberg (2006)
Wenzel, M., Wolff, B.: Building formal method tools in the Isabelle/Isar framework. In: Schneider, K., Brandt, J. (eds.) TPHOLs 2007. LNCS, vol. 4732. Springer, Heidelberg (2007)
Wiedijk, F., Wenzel, M.: A comparison of the mathematical proof languages Mizar and Isar. Journal of Automated Reasoning 29(3-4) (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wenzel, M., Paulson, L.C., Nipkow, T. (2008). The Isabelle Framework. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2008. Lecture Notes in Computer Science, vol 5170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71067-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-71067-7_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71065-3
Online ISBN: 978-3-540-71067-7
eBook Packages: Computer ScienceComputer Science (R0)