A Semantic Basis for Proof Queries and Transformations

We extend the query language PrQL, designed for inspecting machine representations of proofs, to also allow transformation of proofs. PrQL natively supports hiproofs which express proof structure using hierarchically nested labelled trees, which we claim is a natural way of taming the complexity of huge proofs. Query-driven transformations enable manipulation of this structure, in particular, to transform proofs produced by interactive theorem provers into forms that assist their understanding, or that could be consumed by other tools. In this paper we motivate and define basic transformation operations, using an abstract denotational semantics of hiproofs and queries. This extends our previous semantics for queries based on syntactic tree representations.We define update operations that add and remove sub-proofs, and manipulate the hierarchy to group and ungroup nodes. We show that