SMT solvers are efficient tools to decide the satisfiability of ground formulas, including a number of built-in theories such as congruence, linear arithmetic, arrays, and bit-vectors. Adding a theory to that list requires delving into the implementation details of a given SMT solver, and is done mainly by the developers of the solver itself. For many useful theories, one can alternatively provide a first-order axiomatization. However, in the presence of quantifiers, SMT solvers are incomplete and exhibit unpredictable behavior. Consequently, this approach can not provide us with a complete and terminating treatment of the theory of interest. In this paper, we propose a framework to solve this problem, based on the notion of instantiation patterns, also known as triggers. Triggers are annotations that suggest instances which are more likely to be useful in proof search. They are implemented in all SMT solvers that handle first-order logic and are included in the SMT-LIB format. In our framework, the user provides a theory axiomatization with triggers, along with a proof of completeness and termination properties of this axiomatization, and obtains a sound, complete, and terminating solver for her theory in return. We describe and prove a corresponding extension of the traditional Abstract DPLL Modulo Theory framework. Implementing this mechanism in a given SMT solver requires a one-time development effort. We believe that this effort is not greater than that of adding a single decision procedure to the same SMT solver. We have implemented the proposed extension in the Alt-Ergo prover and we discuss some implementation details in the paper. To show that our framework can handle complex theories, we prove completeness and termination of a feature-rich axiomatization of doubly-linked lists. Our tests show that our approach results in a better performance of the solver on goals that stem from the verification of programs manipulating doubly-linked lists.

In the context of deductive program verification, ghost code is part of the program that is added for the purpose of specification. Ghost code must not interfere with regular code, in the sense that it can be erased without observable difference in the program outcome. In particular, ghost data cannot participate in regular computations and ghost code cannot mutate regular data or diverge. The idea exists in the folklore since the early notion of auxiliary variables and is implemented in many state-of-the-art program verification tools. However, a rigorous definition and treatment of ghost code is surprisingly subtle and few formalizations exist.

In this article, we describe a simple ML-style programming language with mutable state and ghost code. Non-interference is ensured by a type system with effects, which allows, notably, the same data types and functions to be used in both regular and ghost code. We define the procedure of ghost code erasure and we prove its safety using bisimulation. A similar type system, with numerous extensions which we briefly discuss, is implemented in the program verification environment Why3.

Keywords: Why3

Keywords: Coq proof assistant ; formal proof ; decision procedure ; interval arithmetic ; floating-point arithmetic ; nonlinear arithmetic

In this paper we present an approach to specify programs performing iterations. The idea is to specify iteration in terms of the nite sequence of the elements enumerated so far, and only those. In particular, we are able to deal with non-deterministic and possibly innite iteration. We show how to cope with the issue of an iteration no longer being consistent with mutable data. We validate our proposal using the deductive verication tool Why3 and two iteration paradigms, namely cursors and higher-order iterators. For each paradigm, we verify several implementations of iterators and client code. This is done in a modular way, i.e., the client code only relies on the specication of the iteration.

In the context of deductive verication, it is customary today to handle programs with pointers using either separation logic, dynamic frames, or explicit memory models. Yet we can observe that in numerous programs, a large amount of code ts within the scope of Hoare logic, provided we can statically control aliasing. When this is the case, the code correctness can be reduced to simpler verication conditions which do not require any explicit memory model. This makes verication conditions more amenable both to automated theorem proving and to manual inspection and debugging. In this paper, we devise a method of such static aliasing control for a programming language featuring nested data structures with mutable components. Our solution is based on a type system with singleton regions and eects, which we prove to be sound.