Abstract
We describe a system to prove properties of programs. The key feature of this approach is a method to automatically synthesize inductive invariants of the loops contained in the program. The method is generic, i.e., it applies to a large set of programming languages and application domains; and lazy, in the sense that it only generates invariants that allow one to derive the required properties. It relies on an existing system called GPiD for abductive reasoning modulo theories [14], and on the platform for program verification Why3 [16]. Experiments show evidence of the practical relevance of our approach.
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Notes
- 1.
An implicant of a formula \(\psi \) is a formula \(\phi \) such that \(\phi \models \psi \). It is the dual notion of that of implicates.
- 2.
However, Theorem 2 only holds if the proof procedure is terminating and complete.
- 3.
This can be checked by computing the weakest precondition of \(\phi \) w.r.t. Lines 1, 2. The obtained formula is \(\mathbf {head}(\mathbf {list}(1,\mathbf {nil})) = \mathbf {length}(\mathbf {list}(1,\mathbf {nil}))\) which is equivalent to \(\top \) (w.r.t. the usual definitions of \(\mathbf {list}\) and \(\mathbf {head}\)).
- 4.
- 5.
Those are the three solvers the Why3 documentation recommends to work with as an initial setup. (see also http://why3.lri.fr/@External Provers.).
- 6.
The AltErgo interface provided by the tool uses an SMTlib2 interface that is under heavy development and that, in practice, does not work well with the examples we send it.
- 7.
The translation was done by hand.
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Echenim, M., Peltier, N., Sellami, Y. (2019). Ilinva: Using Abduction to Generate Loop Invariants. In: Herzig, A., Popescu, A. (eds) Frontiers of Combining Systems. FroCoS 2019. Lecture Notes in Computer Science(), vol 11715. Springer, Cham. https://doi.org/10.1007/978-3-030-29007-8_5
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