Abstract
We introduce and study a tactic language, Hitac, for constructing hierarchical proofs, known as hiproofs. The idea of hiproofs is to superimpose a labelled hierarchical nesting on an ordinary proof tree. The labels and nesting are used to describe the organisation of the proof, typically relating to its construction process. This can be useful for understanding and navigating the proof. Tactics in our language construct hiproof structure together with an underlying proof tree. We provide both a big-step and a small-step operational semantics for evaluating tactic expressions. The big-step semantics captures the intended meaning, whereas the small-step semantics hints at possible implementations and provides a unified notion of proof state. We prove that these notions are equivalent and construct valid proofs.
This is a preview of subscription content, log in via an institution to check access.
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
Denney, E., Power, J., Tourlas, K.: Hiproofs: A hierarchical notion of proof tree. In: Proceedings of Mathematical Foundations of Programing Semantics (MFPS). Electronic Notes in Theoretical Computer Science (ENTCS). Elsevier, Amsterdam (2005)
Oliveira, M.V.M., Cavalcanti, A.L.C., Woodcock, J.C.P.: ArcAngel: a tactic language for refinement. Formal Aspects of Computing 15(1), 28–47 (2003)
Coen, C.S., Tassi, E., Zacchiroli, S.: Tinycals: Step by step tacticals. Electr. Notes Theor. Comput. Sci. 174(2), 125–142 (2007)
Pollack, R.: On extensibility of proof checkers. In: Smith, J., Dybjer, P., Nordström, B. (eds.) TYPES 1994. LNCS, vol. 996, pp. 140–161. Springer, Heidelberg (1995)
Appel, A.W., Felty, A.P.: Dependent types ensure partial correctness of theorem provers. Journal of Functional Programming 14, 3–19 (2004)
Delahaye, D.: A tactic language for the system Coq. In: Parigot, M., Voronkov, A. (eds.) LPAR 2000. LNCS (LNAI), vol. 1955, pp. 85–95. Springer, Heidelberg (2000)
Kirchner, F.: Coq tacticals and PVS strategies: A small-step semantics. In: Archer, M., et al. (eds.) Design and Application of Strategies/Tactics in Higher Order Logics. NASA, pp. 69–83 (September 2003)
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, pp. 167–184. Springer, Heidelberg (1999)
Griffin, T.G.: Notational Definition and Top-down Refinement for Interactive Proof Development Systems. PhD thesis, Cornell University (1988)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aspinall, D., Denney, E., Lüth, C. (2008). A Tactic Language for Hiproofs. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds) Intelligent Computer Mathematics. CICM 2008. Lecture Notes in Computer Science(), vol 5144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85110-3_30
Download citation
DOI: https://doi.org/10.1007/978-3-540-85110-3_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85109-7
Online ISBN: 978-3-540-85110-3
eBook Packages: Computer ScienceComputer Science (R0)