A unified framework and a transparent name-space for the Coq module system

  • Authors:
  • Elie Soubiran

  • Affiliations:
  • INRIA, Paris, France

  • Venue:
  • Proceedings of the 1st Workshop on Modules and Libraries for Proof Assistants
  • Year:
  • 2009

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Abstract

We present an evolution of the Coq module system where we unify both structure (i.e. module implementation) and signature (i.e. module interface) into a single concept called theory. In order to easily derive theories, we equip our system with three theory combinators: application, inclusion and refinement. In this work we also isolate a new notion of Δ-equivalence that characterizes in a decidable way the exact equalities between paths implied by modular construction. This equivalence provides the adequate information to simulate a transparent name-space from the user's point of view and furthermore eases the integration of the non-logical features of Coq. Finally, we give a sketch of conservativity proof relative to the Calculus of Constructions. By emancipating from SML module system legacy, this work contributes to a more flexible and clearer system of modules for Coq.