Towards Complete Reasoning about Axiomatic Specifications

Jacobs, Swen; Kunčak, Viktor

doi:10.1007/978-3-642-18275-4_20

Cited by 17 publications

(10 citation statements)

References 19 publications

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“…When axiomatizing properties of a desired function f of type σ 1 × · · · × σ n → σ, a particularly well-behaved class are single-invocation properties (see, e.g., [13]). These properties include, in particular, standard function contracts, so they can be used to synthesize a function implementation given its postcondition as a relation between the arguments and the result of the function.…”

Section: Refutation-based Synthesismentioning

confidence: 99%

Counterexample-Guided Quantifier Instantiation for Synthesis in SMT

Reynolds

Deters

Kunčak

et al. 2015

Computer Aided Verification

Self Cite

103

131

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Satisfiability Modulo Theories (SMT) solvers have emerged as prominent tools in formal methods applications. While originally targeted towards quantifier-free inputs, SMT solvers are now often used for handling quantified formulas in automated theorem proving and software verification applications. The most common technique for handling quantified formulas in modern SMT solvers in quantifier instantiation. This paper gives an overview of recent advances in quantifier instantiation in SMT. In addition to the well-known technique known as E-matching, we discuss the use of conflicts and models for accelerating the search for (un)satisfiably. We further mention new instantiation-based techniques that are specialized to background theories such as linear real and integer arithmetic, and future work in this direction.

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Section: Refutation-based Synthesismentioning

confidence: 99%

Counterexample-Guided Quantifier Instantiation for Synthesis in SMT

Reynolds

Deters

Kunčak

et al. 2015

Computer Aided Verification

Self Cite

103

131

View full text Add to dashboard Cite

show abstract

“…This requires more involved and specialized techniques [RDK + 15, KKKS13, JK11] that usually pose additional restrictions on the synthesis conjectures or the search space. As an example, popular synthesis techniques require the synthesis conjectures to be a single invocation property [JK11]. The here presented approach does not pose such restrictions.…”

Section: Function Synthesismentioning

confidence: 99%

Extensional Paramodulation for Higher-Order Logic and Its Effective Implementation Leo-III

Steen

2019

Künstl Intell

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In this thesis the theoretical foundations and the practical components for implementing an effective automated theorem proving system for higher-order logic are presented. A primary focus of this thesis is the provision of evidence that a paramodulation-based proof calculus can effectively be employed for performant equational reasoning in Extensional Type Theory (higher-order logic). To that end, a sound and complete paramodulation calculus for extensional higherorder logic with Henkin semantics is presented. The completeness proof hereby unifies and simplifies existing abstract consistency techniques for a formulation of higher-order logic that is based on primitive equality as sole logical connective. In the practically motivated main part of this thesis, the design and architecture of the new higher-order theorem prover Leo-III is presented. Leo-III is based on the above paramodulation calculus and implements additional practically motivated inference rules including equational simplification routines such as heuristic rewriting and support for reasoning with choice. The system encompasses a flexible mechanism for asynchronous cooperation with first-order reasoning systems, a powerful proof search procedure and a sophisticated and efficient set of underlying data structures. Pragmatic and practically significant features of Leo-III are discussed, including its native support for polymorphic higher-order logic and reasoning in higher-order quantified modal logics. An evaluation on a heterogeneous set of benchmark problems confirms that Leo-III is one of the most effective and versatile higher-order automated reasoning systems to date. vii The dissertation project was conducted within the "Leo-III" project funded by the German Research Foundation (DFG) under grant BE 2501/11-1, and the project "Consistent Rational Argumentation in Politics" funded by the Volkswagenstiftung. All source code related to work presented in this thesis is publicly available (under BSD-3 license) at https://github.com/leoprover/Leo-III.

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“…These methods concern limited properties and may be used in the early stages of the library development to infer internal invariant properties. Extension of fully automatic techniques to cover functional specification abstractions like sets or bags are based either on shape analysis, e.g., [7,14] or on logic fragments supported by SMT decision procedures [16,18,37,38]. These functional specifications capture essential mathematical properties of the data structure but do not deal with properties of iterators over them.…”

Section: Related Workmentioning

confidence: 99%

A Verified Implementation of the Bounded List Container

Cauderlier

Sighireanu

2018

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. This paper contributes to the trend of providing fully verified container libraries. We consider an implementation of the bounded doubly linked list container which manages the list in a fixed size, heap allocated array. The container provides constant time methods to update the list by adding, deleting, and changing elements, as well as cursors for list traversal and access to elements. The library is implemented in C, but we wrote the code and its specification by imitating the ones provided by GNAT for the standard library of Ada 2012. The proof of functional correctness is done using VeriFast, which provides an auto-active verification environment for Separation Logic extended with algebraic data types. The specifications proved entail the contracts of the Ada library and include new features. The verification method we used employs a precise algebraic model of the data structure and we show that it facilitates the verification and captures entirely the library contracts. This case study may be of interest for other verification platforms, thus we highlight the intricate points of its proof.

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Towards Complete Reasoning about Axiomatic Specifications

Cited by 17 publications

References 19 publications

Counterexample-Guided Quantifier Instantiation for Synthesis in SMT

Counterexample-Guided Quantifier Instantiation for Synthesis in SMT

Extensional Paramodulation for Higher-Order Logic and Its Effective Implementation Leo-III

A Verified Implementation of the Bounded List Container

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