Solving Horn Clauses on Inductive Data Types Without Induction

Angelis, Emanuele De; Fioravanti, Fabio; Pettorossi, Alberto; Proietti, Maurizio

doi:10.1017/s1471068418000157

Cited by 23 publications

(53 citation statements)

References 36 publications

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“…Concerning the mechanization of our transformation technique, we need to extend the Elimination Algorithm [10] with a suitable automated mechanism for introducing difference predicates and/or auxiliary queries. As shown in Sections 3 and 4, this mechanism can be based on the result of matching the clauses obtained by unfolding (see clause 12 in the InsertionSort example, and clause 12 in the Rotate example) against the predicate definitions introduced in previous transformation steps (see clause 9 in both examples).…”

Section: Discussionmentioning

confidence: 99%

“…However, proving the satisfiability of the clauses obtained by that translation is, in many cases, a much harder task. In a series of papers [5,7,8,9,10,16,19] it has been shown that by combining various transformation techniques, such as Specialization and Predicate Pairing, we can derive equisatisfiable sets of clauses where the efficacy of the CHC solvers is significantly improved. This approach avoids the burden of implementing very sophisticated solving strategies depending on the class of satisfiability problems to be solved.…”

Section: Discussionmentioning

confidence: 99%

“…The technique we present in this paper for the proof of Property Sum, avoids the explicit introduction of this lemma, and thus the use of the induction principle on lists. Let us start off by considering the translation of the functional program InsertionSort and Property Sum into a set of CHCs as explained in the literature [10,25]. In our example, by that translation we get the following set of clauses 1 : In these clauses, sumlist(L, M), insertionSort(L, SL), and ins(X, L, L1) hold iff sumlist L = M, insertionSort L = SL, and ins X L = L1, respectively, hold in program InsertionSort.…”

Section: Horn Clause Satisfiability For Program Verificationmentioning

confidence: 99%

“…The first one consists in the incorporation into the CHC solvers of appropriate induction principles [22,25]. The second one consists in transforming the given set of CHCs into a new set where inductively defined data structures are removed, and whose satisfiability implies the satisfiability of the original clauses [10,19].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we will follow this second approach and, in particular, we will consider the Elimination Algorithm presented in a previous work of ours [10], which implements a transformation strategy for removing inductively defined data structures and is based on the familiar fold/unfold rules [12,24]. Thus, if the clauses derived by the Elimination Algorithm have all their constraints in the LIA or Bool theory, then there is no need to modify the CHC solvers for performing the required satisfiability proofs.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Lemma Generation for Horn Clause Satisfiability: A Preliminary Study

Angelis

Fioravanti

Pettorossi

et al. 2019

Electron. Proc. Theor. Comput. Sci.

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It is known that the verification of imperative, functional, and logic programs can be reduced to the satisfiability of constrained Horn clauses (CHCs), and this satisfiability check can be performed by using CHC solvers, such as Eldarica and Z3. These solvers perform well when they act on simple constraint theories, such as Linear Integer Arithmetic and the theory of Booleans, but their efficacy is very much reduced when the clauses refer to constraints on inductively defined structures, such as lists or trees. Recently, we have presented a transformation technique for eliminating those inductively defined data structures, and hence avoiding the need for incorporating induction principles into CHC solvers. However, this technique may fail when the transformation requires the use of lemmata whose generation needs ingenuity. In this paper we show, through an example, how during the process of transforming CHCs for eliminating inductively defined structures one can introduce suitable predicates, called difference predicates, whose definitions correspond to the lemmata to be introduced. Through a second example, we show that, whenever difference predicates cannot be introduced, we can introduce, instead, auxiliary queries which also correspond to lemmata, and the proof of these lemmata can be done by showing the satisfiability of those queries.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Horn Clause Satisfiability For Program Verificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Lemma Generation for Horn Clause Satisfiability: A Preliminary Study

Angelis

Fioravanti

Pettorossi

et al. 2019

Electron. Proc. Theor. Comput. Sci.

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Fold/Unfold Transformations for Fixpoint Logic

Kobayashi

Fedyukovich²,

Gupta

2020

Tools and Algorithms for the Construction and Analysis of Systems

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Fixpoint logics have recently been drawing attention as common foundations for automated program verification. We formalize fold/unfold transformations for fixpoint logic formulas and show how they can be used to enhance a recent fixpoint-logic approach to automated program verification, including automated verification of relational and temporal properties. We have implemented the transformations in a tool and confirmed its effectiveness through experiments.

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Removing Algebraic Data Types from Constrained Horn Clauses Using Difference Predicates

Angelis

Fioravanti

Pettorossi

et al. 2020

Automated Reasoning

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We address the problem of proving the satisfiability of Constrained Horn Clauses (CHCs) with Algebraic Data Types (ADTs), such as lists and trees. We propose a new technique for transforming CHCs with ADTs into CHCs where predicates are defined over basic types, such as integers and booleans, only. Thus, our technique avoids the explicit use of inductive proof rules during satisfiability proofs. The main extension over previous techniques for ADT removal is a new transformation rule, called differential replacement, which allows us to introduce auxiliary predicates corresponding to the lemmas used when making inductive proofs. We present an algorithm that applies the new rule, together with the traditional folding/unfolding rules, for the automatic removal of ADTs. We prove that if the set of the transformed clauses is satisfiable, then so is the set of the original clauses. By an experimental evaluation, we show that the use of the new rule significantly improves the effectiveness of ADT removal, and that our approach is competitive with respect to a state-of-the-art tool that extends the CVC4 solver with induction.

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Solving Horn Clauses on Inductive Data Types Without Induction

Cited by 23 publications

References 36 publications

Lemma Generation for Horn Clause Satisfiability: A Preliminary Study

Lemma Generation for Horn Clause Satisfiability: A Preliminary Study

Fold/Unfold Transformations for Fixpoint Logic

Removing Algebraic Data Types from Constrained Horn Clauses Using Difference Predicates

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