Speedith: a diagrammatic reasoner for spider diagrams

Authors:
Matej Urbas;Mateja Jamnik;Gem Stapleton;Jean Flower
Affiliations:
Computer Laboratory, University of Cambridge, UK;Computer Laboratory, University of Cambridge, UK;School of Computing, Engineering and Mathematics, University of Brighton, UK;Autodesk, UK
Venue:
Diagrams'12 Proceedings of the 7th international conference on Diagrammatic Representation and Inference
Year:
2012

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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.