D. Baelde, K. Chaudhuri, A. Gacek, D. Miller, G. Nadathur, A. Tiu, Y. Wang
Journal of Formalized Reasoning. Vol 7, No 2, pp. 1-89
The Abella interactive theorem prover is based on an intuitionistic logic that allows for inductive and co-inductive reasoning over relations. Abella supports the lambda-tree approach to treating syntax containing binders: it allows simply typed lambda-terms to be used to represent such syntax and it provides higher-order (pattern) unification, the nabla quantifier, and nominal constants for reasoning about these representations. As such, it is a suitable vehicle for formalizing the meta-theory of formal systems such as logics and programming languages. This tutorial exposes Abella incrementally, starting with its capabilities at a first-order logic level and gradually presenting more sophisticated features, ending with the support it offers to the two-level logic approach to meta-theoretic reasoning. Along the way, we show how Abella can be used prove theorems involving natural numbers, lists, and automata, as well as involving typed and untyped lambda-calculi and the pi-calculus.