A Tactic Language for Hiproofs

David Aspinall, Ewen Denney, Christoph Lüth

In: Serge Autexier , J. Campbell , J. Rubio (Hrsg.). 7th International Conference on Mathematical Knowledge Management (MKM 2007). International Conference on Mathematical Knowledge Management (MKM-2007) befindet sich Conferences on Intelligent Computer Mathematics (CICM 2008) July 28-August 1 Birmingham United Kingdom Seiten 339-354 Lecture Notes in Computer Science (LNCS) 5144 Springer 2008.


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.

mkm08.pdf (pdf, 284 KB )

Deutsches Forschungszentrum für Künstliche Intelligenz
German Research Center for Artificial Intelligence