POPL 2017
Sun 15 - Sat 21 January 2017
Wed 18 Jan 2017 17:20 - 17:45 at Amphitheater 44 - Logic Chair(s): Alexandra Silva

The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for functional or imperative programs over inductively defined data types such as lists and trees. However, as the theory of finite term algebras is not finitely axiomatizable, reasoning about quantified properties over term algebras is challenging.

In this paper we address full first-order reasoning about properties of programs manipulating term algebras, and describe two approaches for doing so by using first-order theorem proving. Our first method is a conservative extension of the theory of term algebras using a finite number of statements, while our second method relies on extending the superposition calculus of first-order theorem provers with additional inference rules.

We implemented our work in the first-order theorem prover Vampire and evaluated it on a large number of inductive datatype benchmarks, as well as game theory constraints. Our experimental results show that our methods are able to find proofs for many hard problems previously unsolved by state-of-the-art methods. We also show that Vampire implementing our methods outperforms existing SMT solvers able to deal with inductive data types.

Wed 18 Jan
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16:30 - 17:45: LogicPOPL at Amphitheater 44
Chair(s): Alexandra SilvaUniversity College London
16:30 - 16:55
Loris D'AntoniUniversity of Wisconsin–Madison, Margus VeanesMicrosoft Research
16:55 - 17:20
Naoki KobayashiUniversity of Tokyo, Japan, Etienne LozesENS Cachan, Florian BruseUniversity of Kassel
17:20 - 17:45
Simon RobillardChalmers University of Technology, Andrei VoronkovUniversity of Manchester, Laura KovacsChalmers University of Technology