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Proof presentation for Isabelle

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Theorem Proving in Higher Order Logics (TPHOLs 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1275))

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Abstract

We present an approach to the intelligible communication of formal proofs. Observing a close correspondence between the activities of formal-proof development and program development, and using this as a guideline, we apply well-known principles from program design to proof design and presentation, resulting in formal proofs presented in a literate style, that are hierarchically structured and emphasize calculation. We illustrate the practicability of this approach by describing its instantiation to the case of the interactive theorem prover Isabelle and by presenting a proof of the Church-Rosser theorem.

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References

  • Back, R., Grundy Grundy, J. & von WWright, J. (1996), Structured calculational proof, Technical Report TR-CS-96-09, Department of Computer Science, The Australian National University.

    Google Scholar 

  • Backhouse, R. C. (1989), ‘Making formality work for us’ Bulletin of the EATCS (38). 219–249.

    Google Scholar 

  • Backhouse.R.C. (1995), ‘The calculational method', Information Processing Letters 53.

    Google Scholar 

  • Barendregt, H. P. (1984), The Lambda Calculus: Its Syntax and Semantics, W. 103 of Studies in Logic and the Foundations of Mathematics.revised edn, North Holland.

    Google Scholar 

  • Carrington, D., Hayes. l.,Nickson.R., Watson.G. & Welsh, J. (1996), Structured presentation of refinements and proofs, in K. Ramamohanarao,ed., ‘Nineteenth Australian Computer Science Conference (AC3C'96)'.pp. 87–96.

    Google Scholar 

  • Coscoy, Y., Kahn, G.& Théry.L.(l995).Extracting text from proof, in M.Dezani & G. Plotkin, eds, ‘International Conference on Typed Lambda Calculi and Applications (TLCA'95)', LNCS 902.Springer.

    Google Scholar 

  • de Bruijn,N. G. (1972), ‘Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem', Indigationes Mathematics 34(5), 381–392.

    Google Scholar 

  • Dijkstra, E.W. & Scholten, C. (1990), Predicate Calculus and Predicate Transformers, Springer.

    Google Scholar 

  • Gasteren.A. J. M. v. (1987), On the Shape of Mathematical Arguments, LNCS 445, Springer.

    Google Scholar 

  • Gries, D. & Schneider F, B. (1993), A Logical Approach to Discrete Math, Springer.

    Google Scholar 

  • Grundy, J. (1996), ‘Transformational hierarchical reasoning'. The Comp. Jour 39(4).291–902.

    Google Scholar 

  • Huet, G. (1980), ‘Confluent reductions: Abstract properties and applications to term rewriting systems', Journal of the ACM 27(4), 797–821.

    Google Scholar 

  • Jones, C. B. ()990), Systematic Software Development Using VDM, Prentice Hall International.

    Google Scholar 

  • Kalvala, S. (1994), ‘Annotations in formal specifications and proofs', Formal Methods in Systems Design 5, 119–144.

    Google Scholar 

  • Kalvala, S. (1995), Proof annotation issues in Isabelle, in L. C. Paulson, ed., ‘First Isabelle Users Workshop', Technical Report number 379, Cambridge University Computer Laboratory.

    Google Scholar 

  • Knuth, D. (1984).'Literate programming'. The Computer Journal 17(2).97–111.

    Google Scholar 

  • Lamport, L. (1994). ‘How to write a proof', American Mathematical Monthly 102(7), 600–608.

    Google Scholar 

  • Nipkow T. (1996). More Church-Rosser proofs (in Isabelle/HOL). in M. McRobhn & J, K. Slaney, eds.'Automated Deduction — CADE-13', LNCS 1104.Springer, pp. 733–747.

    Google Scholar 

  • Paulson, L C. (1994), Isabelle, LNCS 828, Springer.

    Google Scholar 

  • Ramsey, N. (1994), ‘Literate programming simplified', IEEE Software 11(5), 97–105.

    Google Scholar 

  • Robinson, P.J. & Staples, J. (1993), ‘Formalizing a hierarchical structure gf practical mathematical reasoning', Journal of Logic and Computation 3(1), 47–61.

    Google Scholar 

  • Simons, M. (1996), The Presentation of Formal Proofs, PhD thesis, TU Berlin.

    Google Scholar 

  • Simons, M &. Sintzoff, M. (1997), Algebraic composition and refinement of proofs. In prep.

    Google Scholar 

  • Takahashi, M. (1995), ‘Parallel reductions in λ-calculus', Inf. and Comp. 118(1), 120–127.

    Google Scholar 

  • Wong, W. (1994).mweb: proof script management utilities. Manual for the HOL contrib package.

    Google Scholar 

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Elsa L. Gunter Amy Felty

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© 1997 Springer-Verlag Berlin Heidelberg

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Simons, M. (1997). Proof presentation for Isabelle. In: Gunter, E.L., Felty, A. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1997. Lecture Notes in Computer Science, vol 1275. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028399

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  • DOI: https://doi.org/10.1007/BFb0028399

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63379-2

  • Online ISBN: 978-3-540-69526-4

  • eBook Packages: Springer Book Archive

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