Abstract
Proof animation is a way of executing proofs to find errors in the formalization of proofs. It is intended to be “testing in proof engineering”. Although the realizability interpretation as well as the functional interpretation based on limit-computations were introduced as means for proof animation, they were unrealistic as an architectural basis for actual proof animation tools. We have found game theoretical semantics corresponding to these interpretations, which is likely to be the right architectural basis for proof animation.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Akama, Y., Berardi, S., Hayashi, S., Kohlenbach, U.: An arithmetical hierarchy of the law of excluded middle and related principles.
Berardi, S.: Classical logic as Limit Completion. In: A constructive model for non-recursive maps (2001) (submitted), available at http://www.di.unito.it/~stefano/
Berardi, S., Coquand, T., Hayashi, S.: Games with 1-Backtracking (2005) (submitted)
Coquand, T.: A Semantics of Evidence for Classical Arithmetic. In: Géard Huet, G., Plotkin, C., Jones (eds.) Proceedings of the Second Workshop on Logical Frameworks (1991) (a preliminary version of [5])
Coquand, T.: A Semantics of Evidence for Classical Arithmetic. Journal of Symbolic Logic 60(1), 325–337 (1995)
Hayashi, S., Nakano, H.: PX: A Computational Logic. The MIT Press, Cambridge (1988); available free from the author’s web page in PDF format.
Hayashi, S., Nakata, M.: Towards Limit Computable Mathematics, in Types for Proofs and Programs. In: Callaghan, P., Luo, Z., McKinna, J., Pollack, R. (eds.) TYPES 2000. LNCS, vol. 2277, pp. 125–144. Springer, Heidelberg (2001)
Hayashi, S., Sumitomo, R., Shii, K.: Towards Animation of Proofs - Testing Proofs by Examples. Theoretical Computer Science 272, 177–195 (2002)
Hayashi, S.: Mathematics based on Incremental Learning, -Excluded middle and Inductive inference. Theoretical Computer Science (to appear)
Hilbert, D.: Über die Theorie der algebraische Formen. Mathematische Annalen 36, 473–531 (1890)
Hilbert, D.: Theory of Algebraic Invariants, translated by Laubenbacher, R.L. Cambridge University Press, Cambridge (1993)
Hintikka, J., Kulas, J.: The Game of Language. Reidel, Dordrechtz (1983)
Hintikka, J., Sandu, G.: Game-Theoretical Semantics. In: van Benthem Jan, F.A.K., et al. (eds.) Handbook of Logic and Language, Part I (1999)
Kohlenbach, U., Oliva, P.: Proof mining: a systematic way of analysing proofs in Mathematics. In: Proceedings of the Steklov Institute of Mathematics, vol.242, pp. 136–164 (2003)
Nakata, M., Hayashi, S.: Realizability Interpretation for Limit Computable Mathematics. Scientiae Mathematicae Japonicae 5, 421–434 (2001)
Sommerville, I.: Software engineering, 6th edn. Addison Wesley, Reading (2000)
Sanjay, J., Osherson, D., Royer, J.S., Sharma, A.: Systems That Learn - 2nd Edition: An Introduction to Learning Theory (Learning, Development, and Conceptual Change). The MIT Press, Cambridge (1999)
Toftdal, M.: A Calibration of Ineffective Theorems of Analysis in a Hierarchy of Semi-Classical Logical Principles. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 1188–1200. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hayashi, S. (2005). Can Proofs Be Animated By Games?. In: Urzyczyn, P. (eds) Typed Lambda Calculi and Applications. TLCA 2005. Lecture Notes in Computer Science, vol 3461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11417170_3
Download citation
DOI: https://doi.org/10.1007/11417170_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25593-2
Online ISBN: 978-3-540-32014-2
eBook Packages: Computer ScienceComputer Science (R0)