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Proving Correctness of Imperative Programs by Linearizing Constrained Horn Clauses | | Emanuele De Angelis
; Fabio Fioravanti
; Alberto Pettorossi
; Maurizio Proietti
; | | Date: |
21 Jul 2015 | | Abstract: | We present a method for verifying the correctness of imperative programs
which is based on the automated transformation of their specifications. Given a
program prog, we consider a partial correctness specification of the form
${varphi}$ prog ${psi}$, where the assertions $varphi$ and $psi$ are
predicates defined by a set Spec of possibly recursive Horn clauses with linear
arithmetic (LA) constraints in their premise (also called constrained Horn
clauses). The verification method consists in constructing a set PC of
constrained Horn clauses whose satisfiability implies that ${varphi}$ prog
${psi}$ is valid. We highlight some limitations of state-of-the-art
constrained Horn clause solving methods, here called LA-solving methods, which
prove the satisfiability of the clauses by looking for linear arithmetic
interpretations of the predicates. In particular, we prove that there exist
some specifications that cannot be proved valid by any of those LA-solving
methods. These specifications require the proof of satisfiability of a set PC
of constrained Horn clauses that contain nonlinear clauses (that is, clauses
with more than one atom in their premise). Then, we present a transformation,
called linearization, that converts PC into a set of linear clauses (that is,
clauses with at most one atom in their premise). We show that several
specifications that could not be proved valid by LA-solving methods, can be
proved valid after linearization. We also present a strategy for performing
linearization in an automatic way and we report on some experimental results
obtained by using a preliminary implementation of our method. | | Source: | arXiv, 1507.5877 | | Services: | Forum | Review | PDF | Favorites | |
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