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Solving Horn Clauses on Inductive Data Types Without Induction

Published online by Cambridge University Press:  10 August 2018

EMANUELE DE ANGELIS Open the ORCID record for EMANUELE DE ANGELIS [Opens in a new window] ,
FABIO FIORAVANTI Open the ORCID record for FABIO FIORAVANTI [Opens in a new window] ,
ALBERTO PETTOROSSI Open the ORCID record for ALBERTO PETTOROSSI [Opens in a new window]  and
MAURIZIO PROIETTI Open the ORCID record for MAURIZIO PROIETTI [Opens in a new window]
EMANUELE DE ANGELIS
Affiliation:
DEC, ‘G. d'Annunzio’ University of Chieti-Pescara, Pescara, Italy (e-mails: emanuele.deangelis@unich.it, fabio.fioravanti@unich.it)
FABIO FIORAVANTI
Affiliation:
DEC, ‘G. d'Annunzio’ University of Chieti-Pescara, Pescara, Italy (e-mails: emanuele.deangelis@unich.it, fabio.fioravanti@unich.it)
ALBERTO PETTOROSSI
Affiliation:
DICII, University of Rome Tor Vergata, Rome, Italy (e-mail: pettorossi@info.uniroma2.it)
MAURIZIO PROIETTI
Affiliation:
CNR-IASI, Rome, Italy (e-mail: maurizio.proietti@iasi.cnr.it)
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Abstract

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We address the problem of verifying the satisfiability of Constrained Horn Clauses (CHCs) based on theories of inductively defined data structures, such as lists and trees. We propose a transformation technique whose objective is the removal of these data structures from CHCs, hence reducing their satisfiability to a satisfiability problem for CHCs on integers and booleans. We propose a transformation algorithm and identify a class of clauses where it always succeeds. We also consider an extension of that algorithm, which combines clause transformation with reasoning on integer constraints. Via an experimental evaluation we show that our technique greatly improves the effectiveness of applying the Z3 solver to CHCs. We also show that our verification technique based on CHC transformation followed by CHC solving, is competitive with respect to CHC solvers extended with induction.

Keywords

Program verificationconstrained Horn clausesconstraint logic programminginductively defined data typesprogram transformation
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 18 , Special Issue 3-4: 34th International Conference on Logic Programming , July 2018 , pp. 452 - 469
Copyright
Copyright © Cambridge University Press 2018 

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