A Tactic Language for the System Coq

We propose a new tactic language for the system Coq, which is intended to enrich the current tactic combinators (tacticals). This language is based on a functional core with recursors and matching operators for Coq terms but also for proof contexts. It can be used directly in proof scripts or in toplevel de nitions (tactic de nitions). We show that the implementation of this language involves considerable changes in the interpretation of proof scripts, essentially due to the matching operators. We give some examples which solve small proof parts locally and some others which deal with non-trivial problems. Finally, we discuss the status of this meta-language with respect to the Coq language and the implementation language of Coq.