Locality Results for Certain Extensions of Theories with Bridging Functions

Sofronie-Stokkermans, Viorica

doi:10.1007/978-3-642-02959-2_5

Cited by 24 publications

(44 citation statements)

References 17 publications

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“…functions to compute set or multiset content, size, or height of algebraic data type (ADT) values. We verify that, like [15], the results of [17] can be naturally explained using Ψ -locality. We present a more abstract algorithm than the description in [17], possibly leading to more efficient future implementations.…”

Section: Introductionsupporting

confidence: 71%

“…Several decidability results for recursive functions over algebraic data types are presented in [15,17]. Whereas [15] uses local theory extensions, [17] uses a criterion of sufficient surjectivity, related to the notion of counting constraints of [19].…”

Section: Reasoning About Adts With Abstractionsmentioning

confidence: 99%

“…Whereas [15] uses local theory extensions, [17] uses a criterion of sufficient surjectivity, related to the notion of counting constraints of [19]. In the following, we give a decision procedure that follows [17] but uses local theory extensions.…”

Section: Reasoning About Adts With Abstractionsmentioning

confidence: 99%

“…The results on both single-invocation and many-invocation axioms are particularly useful in the presence of recursively defined functions. Recent results [15,17] show the decidability of theories of algebraic data types with recursive abstraction functions which includes e.g. functions to compute set or multiset content, size, or height of algebraic data type (ADT) values.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Towards Complete Reasoning about Axiomatic Specifications

Jacobs

Kunčak

2011

Lecture Notes in Computer Science

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Abstract. To support verification of expressive properties of functional programs, we consider algebraic style specifications that may relate multiple user-defined functions, and compare multiple invocations of a function for different arguments. We present decision procedures for reasoning about such universally quantified properties of functional programs, using local theory extension methodology. We establish new classes of universally quantified formulas whose satisfiability can be checked in a complete way by finite quantifier instantiation. These classes include single-invocation axioms that generalize standard function contracts, but also certain many-invocation axioms, specifying that functions satisfy congruence, injectivity, or monotonicity with respect to abstraction functions, as well as conjunctions of some of these properties. These manyinvocation axioms can specify correctness of abstract data type implementations as well as certain information-flow properties. We also present a decidability-preserving construction that enables the same function to be specified using different classes of decidable specifications on different partitions of its domain.

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Section: Introductionsupporting

confidence: 71%

Section: Reasoning About Adts With Abstractionsmentioning

confidence: 99%

Section: Reasoning About Adts With Abstractionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Towards Complete Reasoning about Axiomatic Specifications

Jacobs

Kunčak

2011

Lecture Notes in Computer Science

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“…This is especially the case when we consider theories sharing some algebraic constraints [14,16,17,18,20,21]. In order to combine satisfiability procedures for the single theories to handle constraints in their nondisjoint union one needs to rely on powerful methods such as the combination framework of [9,10].…”

Section: Introductionmentioning

confidence: 99%

Modular Termination and Combinability for Superposition Modulo Counter Arithmetic

Ringeissen

Senni

2011

Frontiers of Combining Systems

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Abstract. Modularity is a highly desirable property in the development of satisfiability procedures. In this paper we are interested in using a dedicated superposition calculus to develop satisfiability procedures for (unions of) theories sharing counter arithmetic. In the first place, we are concerned with the termination of this calculus for theories representing data structures and their extensions. To this purpose, we prove a modularity result for termination which allows us to use our superposition calculus as a satisfiability procedure for combinations of data structures. In addition, we present a general combinability result that permits us to use our satisfiability procedures into a non-disjoint combination method a la Nelson-Oppen without loss of completeness. This latter result is useful whenever data structures are combined with theories for which superposition is not applicable, like theories of arithmetic.

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Theory Combination: Beyond Equality Sharing

Bonacina

Fontaine

Ringeissen

et al. 2019

Lecture Notes in Computer Science

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Satisfiability is the problem of deciding whether a formula has a model. Although it is not even semidecidable in first-order logic, it is decidable in some first-order theories or fragments thereof (e.g., the quantifier-free fragment). Satisfiability modulo a theory is the problem of determining whether a quantifier-free formula admits a model that is a model of a given theory. If the formula mixes theories, the considered theory is their union, and combination of theories is the problem of combining decision procedures for the individual theories to get one for their union. A standard solution is the equality-sharing method by Nelson and Oppen, which requires the theories to be disjoint and stably infinite. This paper surveys selected approaches to the problem of reasoning in the union of disjoint theories, that aim at going beyond equality sharing, including: asymmetric extensions of equality sharing, where some theories are unrestricted, while others must satisfy stronger requirements than stable infiniteness; superposition-based decision procedures; and current work on conflict-driven satisfiability (CDSAT).

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Locality Results for Certain Extensions of Theories with Bridging Functions

Cited by 24 publications

References 17 publications

Towards Complete Reasoning about Axiomatic Specifications

Towards Complete Reasoning about Axiomatic Specifications

Modular Termination and Combinability for Superposition Modulo Counter Arithmetic

Theory Combination: Beyond Equality Sharing

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