A Tactic Language for Hiproofs

  • Authors:

  • David Aspinall;Ewen Denney;Christoph Lüth

  • Affiliations:

  • LFCS, School of Informatics, University of Edinburgh, Edinburgh, Scotland EH9 3JZ;RIACS, NASA Ames Research Center, Moffett Field, USA 94035;Deutsches Forschungszentrum für Künstliche Intelligenz, Bremen, Germany

  • Venue:
  • Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
  • Year:
  • 2008

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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.