A Language-Independent Proof System for Mutual Program Equivalence

Programming languages should be formally specified in order to reason about programs written in them. We show that, given two formally specified programming languages, it is possible to construct the formal semantics of an aggregated language, in which programs consist of pairs of programs from the initial languages. The construction is based on algebraic techniques and it can be used to reduce relational properties (such as equivalence of programs) to reachability properties (in the aggregated language).

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“…The theorem is not new (see for example [17]). A proof can also be found in our technical report [5].…”

Section: Model Amalgamationsupporting

confidence: 54%

A Theoretical Foundation for Programming Languages Aggregation

Ciobâcă

Lucanu

Rusu

et al. 2015

Recent Trends in Algebraic Development Techniques

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“…There have been proposed program logics for relational verification [5,6,14,24]. In particular, the relational refinement type system proposed in [6] can be applied to differential privacy and other relational security verification problems of higher-order functional programs.…”

Section: Related Workmentioning

confidence: 99%

Automating Induction for Solving Horn Clauses

Unno

Torii

Sakamoto

2017

Computer Aided Verification

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Verification problems of programs written in various paradigms (such as imperative, logic, concurrent, functional, and objectoriented ones) can be reduced to problems of solving Horn clause constraints on predicate variables that represent unknown inductive invariants. This paper presents a novel Horn constraint solving method based on inductive theorem proving: the method reduces Horn constraint solving to validity checking of first-order formulas with inductively defined predicates, which are then checked by induction on the derivation of the predicates. To automate inductive proofs, we introduce a novel proof system tailored to Horn constraint solving and use an SMT solver to discharge proof obligations arising in the proof search. The main advantage of the proposed method is that it can verify relational specifications across programs in various paradigms where multiple function calls need to be analyzed simultaneously. The class of specifications includes practically important ones such as functional equivalence, associativity, commutativity, distributivity, monotonicity, idempotency, and non-interference. Furthermore, our novel combination of Horn clause constraints with inductive theorem proving enables us to naturally and automatically axiomatize recursive functions that are possibly non-terminating, non-deterministic, higher-order, exception-raising, and over non-inductively defined data types. We have implemented a relational verification tool for the OCaml functional language based on the proposed method and obtained promising results in preliminary experiments.

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“…Relational verification has been extensively studied, and still receives much attention as a relevant problem in the field of software engineering [4,6,7,16,20,21,23,30,32,39,40,41]. In particular, during the software development process it may be helpful to prove that the semantics of a new program version has some specified relation with the semantics of an old version.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

“…A method that, like ours, is parametric with respect to the semantics of the programming languages in which the programs to be verified are written, is proposed by S. Ciobâcă et al [7], who present a language-independent deductive system for proving mutual equivalence of programs.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Predicate Pairing with Abstraction for Relational Verification

Angelis

Fioravanti

Pettorossi

et al. 2018

Logic-Based Program Synthesis and Transformation

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Relational verification is a technique that aims at proving properties that relate two different program fragments, or two different program runs. It has been shown that constrained Horn clauses (CHCs) can effectively be used for relational verification by applying a CHC transformation, called predicate pairing, which allows the CHC solver to infer relations among arguments of different predicates. In this paper we study how the effects of the predicate pairing transformation can be enhanced by using various abstract domains based on linear arithmetic (i.e., the domain of convex polyhedra and some of its subdomains) during the transformation. After presenting an algorithm for predicate pairing with abstraction, we report on the experiments we have performed on over a hundred relational verification problems by using various abstract domains. The experiments have been performed by using the VeriMAP transformation and verification system, together with the Parma Polyhedra Library (PPL) and the Z3 solver for CHCs.

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A Language-Independent Proof System for Mutual Program Equivalence

Cited by 10 publications

References 18 publications

A Theoretical Foundation for Programming Languages Aggregation

A Theoretical Foundation for Programming Languages Aggregation

Automating Induction for Solving Horn Clauses

Predicate Pairing with Abstraction for Relational Verification

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