Scoped Metatheorems

Proof development systems traditionally structure theories hierarchically: Theorems established in a subtheory hold in all supertheories. While often eective, this is sometimes too restrictive as there are certain facts that are true of some but not all extensions. We present a solution where instead of rst formalizing a theory and then establishing facts, we parameterize each statement with its scope of application. We present this idea abstractly and consider concrete implementations based on parameterized inductive denitions. 1 Introduction It is a truism of software engineering that large programming projects should be factored into modular subdevelopments. The same holds for large formal mathematical projects carried out using computer support in the form of a proof development system, as we see if look at what has been achieved by the user communities of, e.g., Nuprl, HOL, Coq, Isabelle, or Mizar. However the nature of facilities for structuring developments varies from syst..

Scoped Metatheorems

AbstractProof development systems traditionally structure theories hierarchically: Theorems established in a subtheory hold in all supertheories. While often effective, this is sometimes too restrictive as there are certain facts that are true of some but not all extensions. We present a solution where instead of first formalizing a theory and then establishing facts, we parameterize each statement with its scope of application. We present this idea abstractly and consider concrete implementations based on parameterized inductive definitions