Abstract
Window inference is a proof paradigm where a theorem is proved by stepwise transformation, including transformations that change subterms while taking the context of these subterms into account. Originally developed for mathematical equivalence reasoning, window inference has proved powerful in other fields as well, and in particular for reasoning about refinement of programs. Although window inference is powerful and flexible, it has many limitations. The paper shows how some restrictions can be relaxed without compromising the elegance and simplicity of the window inference paradigm. We suggest a number of extensions, discuss their possible implementations and give examples of their use.
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R. J. Back. Refinement diagrams. In J.M. Morris and R.C.F. Shaw, editors, Proc. 4th Refinement Workshop, Workshops in Computer Science, pages 125–137, Cambridge, England, 9–11 January 1991. Springer-Verlag.
R. J. Back, J. Grundy, and J. von Wright. Structured calculational proof. Tech. Rpt. 65, Turku Centre for Computer Science, November 1996. to appear in Formal Aspects of Computing.
R. J. Back and J. von Wright. Refinement Calculus: A Systematic Introduction. Springer-Verlag, 1998.
H. Becht, A. Bloesch, R. Nickson and I. Hayes. Ergo 4.1 Reference Manual. Tech.Rpt. 96-31, Dept. Computer Science, Queensland University, November 1996.
M. J. Butler, J. Grundy, T. Långbacka, R. Ruksenas, and J. von Wright. The refinement calculator: Proof support for program refinement. In Proc. FMP'97 — Formal Methods Pacific, Discrete Mathematics and Theoretical Computer Science, Wellington, New Zealand, July 1997. Springer-Verlag.
M. J. C. Gordon and T. F. Melham. Introduction to HOL. Cambridge University Press, New York, 1993.
J. Grundy. A window inference tool for refinement. In Jones et al, editor, Proc. 5th Refinement Workshop, London, Jan. 1992. Springer-Verlag.
J. Grundy. A Method of Program Refinement. PhD thesis, University of Cambridge Computer Laboratory, Cambridge, England, 1993. Tech. Rpt. 318.
J. Grundy. Transformational Hierarchical Reasoning. The Computer Journal, 39(4):291–302, 1996.
P. Heuberger. The minimal user-interface of a simple refinement tool. In Proc. 3rd Workshop on User Interfaces for Theorem Provers, INRIA Sophia-Antipolis, September 1997.
R. Nickson. Window inference for data refinement. In Proc. 5th Australasian Refinement Workshop, University of Queensland, 1996.
R. Nickson and I. Hayes. Supporting contexts in program refinement. Tech.Rpt. 96-29, Dept. Computer Science, Queensland University, 1996.
P. J. Robinson and J. Staples. Formalising a hierarchical structure of practical mathematical reasoning. Journal of Logic and Computation, 3(1):47–61, 1993.
M. Staples. Window inference in Isabelle. In Proc. Isabelle Users Workshop, University of Cambridge Computer Laboratory, September 1995.
M. Utting. The Ergo 5 Generic Proof Engine. Tech.Rpt. 97-44, Dept. Computer Science, Queensland University, 1997.
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© 1998 Springer-Verlag Berlin Heidelberg
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von Wright, J. (1998). Extending window inference. In: Grundy, J., Newey, M. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1998. Lecture Notes in Computer Science, vol 1479. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055127
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DOI: https://doi.org/10.1007/BFb0055127
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