Ergo is a little engine of proof dedicated to program verification. It fully supports quantifiers and directly handles polymorphic sorts. Its core component is CC(X), a new combination scheme for the theory of uninterpreted symbols parameterized by a built-in theory X. In order to make a sound integration in a proof assistant possible, Ergo is capable of generating proof traces for CC(X). Alternatively, Ergo can also be called interactively as a simple oracle without further verification. It is currently used to prove correctness of C and Java programs as part of the Why platform.
SMT solvers can decide the satisfiability of ground formulas modulo a combination of built-in theories. Adding a built-in theory to a given SMT solver is a complex and time consuming task that requires internal knowledge of the solver. However, many theories (arrays [13], reachability [11]), can be easily expressed using first-order formulas. Unfortunately, since universal quantifiers are not handled in a complete way by SMT solvers, these axiomatics cannot be used as decision procedures.In this paper, we show how to extend a generic SMT solver to accept a custom theory description and behave as a decision procedure for that theory, provided that the described theory is complete and terminating in a precise sense. The description language consists of first-order axioms with triggers, an instantiation mechanism that is found in many SMT solvers. This mechanism, which usually lacks a clear semantics in existing languages and tools, is rigorously defined here; this definition can be used to prove completeness and termination of the theory. We demonstrate using the theory of arrays, how such proofs can be achieved in our formalism.
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We give a hands-on introduction to the tools GNATtest and GNATprove, both developed at AdaCore in the Hi-Lite research project. They allow to do verification of Ada 2012 contracts through testing and formal verification, and also allow a combination of the results of both tools.
The tutorial will contain a very short introduction to Ada 2012, and attendees will write a small example on which they can play with GNATtest to develop test cases, and GNATprove to do some formal verification.
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