Abella: A System for Reasoning about Relational Specifications

David Baelde (1) , Kaustuv Chaudhuri (2) , Andrew Gacek (3) , Dale Miller (2) , Gopalan Nadathur (4) , Alwen Tiu (5) , Yuting Wang (4)

1 LSV - Laboratoire Spécification et Vérification [Cachan]
2 PARSIFAL - Proof search and reasoning with logic specifications
3 Rockwell Collins
4 Department of Computer Science and Engineering [Minneapolis]
5 School of Computer Engineering [Singapore]

The Abella interactive theorem prover is based on an intuitionistic logic that allows for inductive and co-inductive reasoning over relations. Abella supports the λ-tree approach to treating syntax containing binders: it allows simply typed λ-terms to be used to represent such syntax and it provides higher-order (pattern) unification, the ∇ 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 λ-calculi and the π-calculus.

Domaines: Logique en informatique [cs.LO]

David Baelde, Kaustuv Chaudhuri, Andrew Gacek, Dale Miller, Gopalan Nadathur, et al.. Abella: A System for Reasoning about Relational Specifications. Journal of Formalized Reasoning, 2014, Special Issue: User Tutorials 2, 7 (2), pp.1-89. ⟨10.6092/issn.1972-5787/4650⟩. ⟨hal-01102709⟩