Combining the Syntactic and Semantic Representations of Mizar Proofs

Abstract

The Mizar system provides two representations of the proofs present in its library. The syntactic representation preserves the human-friendly rich Mizar language, where the meaning of structures and expressions is still influenced by their context. The semantic one, on the other hand, explicitly reflects the meaning of all elements present in the proof scripts, however many features of the Mizar language are eliminated. In this article, we overcome the limitations of both representations of proofs, by proposing a method combining them. We show that we can simultaneously maintain the richness of the language and provide access to the derived proof information. We discuss how such combined information closer corresponds to that present in other proof assistant languages, for example that of Isabelle /Isar.