Automatically Deriving Schematic Theorems for Dynamic Contexts

Abstract

Hypothetical judgments go hand-in-hand with higher-order abstract syntax for meta-theoretic reasoning. The dynamic assumptions of these judgments often have a simple regular structure of repetitions of related assumptions; reflecting on this regular structure can let us derive a number of structural properties about the elements of the context automatically. We present an extension of the Abella theorem prover with a new mechanism for defining particular kinds of regular context relations, called schemas, and tacticals to derive theorems from these schemas as needed. Importantly, our extension leaves the trusted kernel of Abella unchanged. We show that these tacticals can eliminate many commonly encountered kinds of administrative lemmas that would otherwise have to be proven manually, which is a common source of complaints from Abella users.