Procedural Representation of CIC Proof Terms

Abstract

We propose an effective procedure, the first one to our knowledge, for translating a proof term of the Calculus of Inductive Constructions (CIC), into a tactical expression of the high-level specification language of a CIC-based proof assistant like coq (Coq development team 2008) or matita (Asperti et al., J Autom Reason 39: 2007). This procedure, which should not be considered definitive at its present stage, is intended for translating the logical representation of a proof coming from any source, i.e. from a digital library or from another proof development system, into an equivalent proof presented in the proof assistant's editable high-level format. To testify to effectiveness of our procedure, we report on its implementation in matita and on the translation of a significant set of proofs (Guidi, ACM Trans Comput Log 2009) from their logical representation as coq 7.3.1 (Coq development team 2002) CIC proof terms to their high-level representation as tactical expressions of matita's user interface language.

Nonuniform Coercions via Unification Hints

“…This affects in a positive way not only the type checking time, thanks to the smaller size of proof terms, but also the output quality of any procedure manipulating proof terms. For example in [10] and [6] the authors reconstruct a proof script, respectively based on a procedural and a declarative tactic language, starting from a proof term. Another example is [8,7] where an explanation of a proof in natural language is obtained solely processing a proof term.…”

The formal system λδ

“…In[Guidi 2007b] we present an effective procedure for transforming a CIC proof term is a sequence of basic proof steps. We already implemented this procedure in the proof assistant matita.ACM Transactions on Computational Logic, Vol.…”