A comparison of Mizar and Isar

Journal of Automated Reasoning

Volumn 29, Issue 3-4, 2002, Pages 389-411

  Wenzel, Markus ^a   Wiedijk, Freek ^b  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

Formalized mathematics; Proof sketches; Structured proof languages

Indexed keywords

FORMAL LOGIC; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; NUMERICAL METHODS; THEOREM PROVING;

FORMALIZED MATHEMATICS; PROOF SKETCHES;

FORMAL LANGUAGES;

EID: 0036992197     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021935419355     Document Type: Article

References (28)

1. Abel, A., Chang, B.-Y. E. and Pfenning, F.: Human-readable machine-verifiable proofs for teaching constructive logic, IJCAR Workshop on Proof Transformations, Proof Presentations and Complexity of Proofs (PTP-01), 2001, http://www.tcs.informatik.uni-moenchen.de/~abel/pup01,ps.gz.
2. Aspinall, D.: Proof general: A generic tool for proof development, in European Joint Conferences on Theory and Practice of Software (ETAPS), 2000.
3. Bauer, G. and Wenzel, M.: Computer-assisted mathematics at work - The Hahn-Banach theorem in Isabelle/Isar, in T. Coquand. P. Dybjer, B. Nordström and J. Smith (eds), Types for Proofs and Programs: TYPES'99, LNCS 1956, 2000.
4. Bauer, G. and Wenzel, M.: Calculational reasoning revisited - An Isabelle/Isar experience, in R. J. Boulton and P. B. Jackson (eds), Theorem Proving in Higher Order Logics: TPHOLs 2001, LNCS 2152 2001.
5. Berghofer, S. and Nipkow, T.: Proof terms for simply typed higher order logic, in J. Harrison and M. Aagaard (eds) Theorem Proving in Higher Order Logics: TPHOLs 2000, LNCS 1869 2000.
6. Burstall, R.: Teaching people to write proofs: A tool, in CafeOBJ Symposium, Numazu, Japan, 1998.
7. de Bruijn, N.: The mathematical vernacular, a language for mathematics with typed sets, in P. Dybjer et. al. (eds), Proceedings of the Workshop on Programming Languages, Marstrand, Sweden, 1987.
8. Harrison, J.: A Mizar mode for HOL, in Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics, TPHOLs '96, LNCS 1125, Springer, 1996.
9. Muzaleski, M.; An Outline of PC Mizar, Fondation Philippe le Hodey, Brussels, 1993, http://www.cs.kun.n1/~freek/nizar/mizarmanual.ps.gz.
10. Nipkow, T., Paulson, L. and Wenzel, M.: Isabelle/HOL-A Proof Assistant for Higher-Order Logic, LNCS 2283, Springer, 2002.
11. Paulson, L. C.: The foundation of a generic theorem prover, J. Automated Reasoning 5(3) (1989).
12. Paulson, L.: Isabelle: A Generic Theorem Prover, LNCS 828, Springer, 1994.
13. Paulson, L.: The Isabelle reference manual, 2002a. http://isabelle.in.tum.de/doc/ref.pdf.
14. Paulson, L. C.: Isabelle's logics: FOL and ZF, 2002b. http://isabelle/in.tum.de/doc/logics-ZF.pdf.
15. Rudnicki, P.: An overview of the MIZAR project, in 1992 Workshop on Types for Proofs and Programs, Bastad, 1992.
16. Syme, D.: DECLARE: A prototype declarative proof system for higher order logic, Technical Report 416, University of Cambridge Computer Laboratory, 1997.
17. Syme, D.: Declarative theorem proving for operational semantics, Ph.D. thesis, University of Cambridge, 1998.
18. Syme, D.: Three tactic theorem proving, in Theorem Proving in Higher Order Logics, TPHOLs '99, Nice, France, LNCS 1690, Springer, 1999.
19. Trybulec, A.: Some features of the Mizar language, Presented at a workshop in Turin, Italy, 1993.
20. Wenzel, M: Isar - A generic interpretative approach to readable formal proof documents, in Y. Bertot, G. Dowek, A. Hirschowitz, C. Paulin and L. Thery (eds.). Theorem Proving in Higher Order Logics: TPHOLs '99, LNCS 1690, 1999.
21. Wenzel, M.: Isabelle/Isar - A versatile environment for human-readable formal proof documents, Ph.D. thesis, Institut für Informatik. Technische Universität Minchen, 2002a. http://tumbl.biblio.tu-menchen.de/pub1/diss/in/2002/wenzel.html.
22. Wenzel, M.: The Isabelle/Isar Reference Manual, TU München, 2002b. http://isabelle,in.tum.de/doc/isar-ref.pdf.
23. Wiedijk, F., Mizar: An impression, 1993, http://www.cs.kun.n1/~freek/mizar/mizarintro.ps.gz.
24. Wiedijk, F.: The mathematical vernacular, 2000 http://www.cs.kun.n1/~free/notes/mv.ps.gz.
25. Wiedijk, F.: Mizar light for HOL light, in R. J. Boulton and P. B. Jackson (eds), Theorem Proving in Higher Order Logics: TPHOLs 2001, LNCS 2152 2001.
26. Wiedijk, F.; Formal proof sketches, 2002, http://www.cs.kun.n1/~freek/notes/sketches.ps.gz.
27. Zammit, V. On the implementation of an extensible declarative proof language, in Theorem Proving in Higher Order Logics, TPHOLs '99, Nice, France, LNCS 1690, Springer, 1999a.
28. Zammit, V.: On the readability of machine checkable formal proofs, Ph.D. thesis, University of Kent, 1999b.