In this paper, we introduce Speedith which is an interactive diagrammatic theorem prover for the well-known language of spider diagrams. Speedith provides a way to input spider diagrams, transform them via the diagrammatic inference rules, and prove diagrammatic theorems. Speedith's inference rules are sound and complete, extending previous research by including all the classical logic connectives. In addition to being a stand-alone proof system, Speedith is also designed as a program that plugs into existing general purpose theorem provers. This allows for other systems to access diagrammatic reasoning via Speedith, as well as a formal verification of diagrammatic proof steps within standard sentential proof assistants. 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.

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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.

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Abstract. We present an interactive heterogeneous theorem proving framework, which performs formal reasoning by arbitrarily mixing diagrammatic and sentential proof steps. We use Isabelle to enable formal reasoning with either traditional sentences or spider diagrams. We provide a mechanisation of the theory of abstract spider diagrams and establish a formal link between diagrammatic concepts and the existing theories in Isabelle/HOL.