Abstract
In this paper, we introduce Speedith which is a diagrammatic theorem prover for the language of spider diagrams. Spider diagrams are a well-known logic for which there is a sound and complete set of inference rules. Speedith provides a way to input diagrams, transform them via the diagrammatic inference rules, and prove diagrammatic theorems. It is designed as a program that plugs into existing general purpose theorem provers. This allows for seamless formal verification of diagrammatic proof steps within established proof assistants such as Isabelle. We describe the general structure of Speedith, the diagrammatic language, the automatic mechanism that draws the diagrams when inference rules are applied on them, and how formal diagrammatic proofs are constructed.
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
Jamnik, M., Bundy, A., Green, I.: On Automating Diagrammatic Proofs of Arithmetic Arguments. JOLLI 8(3), 297–321 (1999)
Winterstein, D., Bundy, A., Gurr, C.: Dr.Doodle: A Diagrammatic Theorem Prover. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 331–335. Springer, Heidelberg (2004)
Kortenkamp, U., Richter-Gebert, J.: Using automatic theorem proving to improve the usability of geometry software. In: MUI (2004)
Stapleton, G., Masthoff, J., Flower, J., Fish, A., Southern, J.: Automated Theorem Proving in Euler Diagram Systems. JAR 39(4), 431–470 (2007)
Howse, J., Stapleton, G., Taylor, J.: Spider Diagrams. LMS JCM 8, 145–194 (2005)
Gordon, M.J., Milner, A.J., Wadsworth, C.P.: Edinburgh LCF. LNCS, vol. 78. Springer, Heidelberg (1979)
Howse, J., Stapleton, G., Flower, J., Taylor, J.: Corresponding Regions in Euler Diagrams. In: Hegarty, M., Meyer, B., Narayanan, N.H. (eds.) Diagrams 2002. LNCS (LNAI), vol. 2317, pp. 76–90. Springer, Heidelberg (2002)
Urbas, M., Jamnik, M.: Heterogeneous Proofs: Spider Diagrams Meet Higher-Order Provers. In: van Eekelen, M., Geuvers, H., Schmaltz, J., Wiedijk, F. (eds.) ITP 2011. LNCS, vol. 6898, pp. 376–382. Springer, Heidelberg (2011)
Wenzel, M., Paulson, L.C., Nipkow, T.: The Isabelle Framework. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds.) TPHOLs 2008. LNCS, vol. 5170, pp. 33–38. Springer, Heidelberg (2008)
Stapleton, G., Zhang, L., Howse, J., Rodgers, P.: Drawing Euler Diagrams with Circles. In: Goel, A.K., Jamnik, M., Narayanan, N.H. (eds.) Diagrams 2010. LNCS, vol. 6170, pp. 23–38. Springer, Heidelberg (2010)
Dau, F.: Constants and Functions in Peirce’s Existential Graphs. In: Priss, U., Polovina, S., Hill, R. (eds.) ICCS 2007. LNCS (LNAI), vol. 4604, pp. 429–442. Springer, Heidelberg (2007)
Kent, S.: Constraint diagrams: Visualizing invariants in object oriented modelling. In: OOPSLA. SIGPLAN, vol. 32, pp. 327–341. ACM (1997)
Keslter, H., Muller, A., Kraus, J., Buchholz, M., Gress, T., Liu, H., Kane, D., Zeeberg, B., Weinstein, J.: Vennmaster: Area-proportional Euler diagrams for functional go analysis of microarrays. BMC Bioinformatics 9(67) (2008)
De Chiara, R., Hammar, M., Scarano, V.: A system for virtual directories using euler diagrams. ENTCS 134, 33–53 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Urbas, M., Jamnik, M., Stapleton, G., Flower, J. (2012). Speedith: A Diagrammatic Reasoner for Spider Diagrams. In: Cox, P., Plimmer, B., Rodgers, P. (eds) Diagrammatic Representation and Inference. Diagrams 2012. Lecture Notes in Computer Science(), vol 7352. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31223-6_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-31223-6_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31222-9
Online ISBN: 978-3-642-31223-6
eBook Packages: Computer ScienceComputer Science (R0)