Behavioural theories and the proof of behavioural properties

Bidoit, Michel; Hennicker, Rolf

doi:10.1016/0304-3975(96)00039-4

Cited by 51 publications

(52 citation statements)

References 9 publications

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“…In [9], the notion of constructive data refinement is formalised in terms of the existence of a pre-logical relation. They demonstrate that an implementation of 3 The proof of theorem 3 does not rely on particular properties of combinatory algebras. Thus we can expect that it holds over lambda applicative structures.…”

Section: Definition 10 (Observational Pre-logical Relationsmentioning

confidence: 98%

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Behavioural Equivalence and Indistinguishability in Higher-Order Typed Languages

Katsumata

2003

Recent Trends in Algebraic Development Techniques

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Abstract. We extend the study of the relationship between behavioural equivalence and the indistinguishability relation [4,7] to the simply typed lambda calculus, where higher-order types are available. The relationship between these two notions is established in terms of factorisability [4]. The main technical tool of this study is pre-logical relations [8], which give a precise characterisation of behavioural equivalence. We then consider a higher-order logic to reason about models of the simply typed lambda calculus, and relate the resulting standard satisfaction relation to behavioural satisfaction.

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Section: Definition 10 (Observational Pre-logical Relationsmentioning

confidence: 98%

“…Subsequent work by Bidoit and Hennicker [3] discussed a proof method for showing behavioural equivalence in first order logic, and considered finitary axiomatisation of behavioural equality. The above work is extended by Hofmann and Sannella [8] to higher-order logic.…”

Section: Related Workmentioning

confidence: 99%

Behavioural Equivalence and Indistinguishability in Higher-Order Typed Languages

Katsumata

2003

Recent Trends in Algebraic Development Techniques

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“…¿From around 1997, the CafeOBJ group at JAIST [3] started to extend the proof score method (1) to apply to distributed and real-time systems, such as classical distributed (and/or real-time) algorithms, component-based software, railway signal systems, secure protocols, etc., (2) to make the method applicable to practical size problems, and (3) to automate the method. As a result, the proof score method using reduction (rewriting) has become a promising way to do serious proofs.…”

Section: Development Of Proof Scoresmentioning

confidence: 99%

“…Behavioral (also called observational) logic is a natural approach to verifying such systems. Three major approaches in this area are: coalgebra (e.g., see the overview [22]); the "observational logic" of Bidoit and Henniker [2,21]; and hidden algebra [15,7], on which our own work is based.…”

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confidence: 99%

Verifying Design with Proof Scores

Futatsugi

Goguen

Ogata

2008

Verified Software: Theories, Tools, Experiments

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Abstract. Verifying design instead of code can be an effective and practical approach to obtaining verified software. This paper argues that proof scores are an attractive method for verifying design, in that they achieve a balance in which the respective capabilities of humans and machines are utilized optimally. Verifying Code or DesignAlthough creation of a verifying compiler is a difficult challenge, recent developments suggest that there are ways to make it easier. Systems that generate lexical analyzers and parsers already have a long history (e.g. Lex and Yacc), and recent work of Sorin Lerner [23] shows that the same can be done for compiler backends; there is also work suggesting that code generation modules can be automatically generated (e.g. using intermediate languages). Unfortunately, a great number of different compilers are needed in today's software world, and the underlying machine architectures are evolving, as are the languages, so it would be difficult to create verifying compilers for all useful combinations of language and platform, and code verification for such tools still remains very difficult. Major impediments include the unsolvability of discovering loop invariants, the potential unsolvability of loop once they are found, and the further difficulties raised by interactivity, nondeterminism, concurrency, distribution, active agents, and unreliable communication.A long term approach is to use high level, application specific source languages, in order to greatly simplify source program verification by eliminating many obscure features of current languages. In the meantime, a currently feasible approach is to verify the design of software, instead of its code; experience shows that design verification often leads to better design, and nearly always leads to greater conceptual clarity. An aditional motivation is that the main sources of errors in software are in areas other than code, namely, requirements, specification, and design. The Proof Score ApproachThe goal of verification in software engineering is to increase confidence in the correctness of computer-based systems. For software verification to be genuinely

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“…The idea of using the satisfaction relation on hidden terms for determining behavioral equivalence was also introduced by Reichel in the 80's [51] and it seems to be a useful way of defining equivalence between hidden terms. In fact, in applied settings, there are some well designed pieces of software that may fail to satisfy their requirements strictly, but do satisfy them behaviorally, i.e., under any program executed on the system (see [6,3,9]). More formally, in such approach, the standard equality predicate is augmented by behavioral equivalence (two data elements representing states are said to be behaviorally equivalent if every function returns the same visible value when executed on the same visible input).…”

Section: Introductionmentioning

confidence: 99%

Behavioral equivalence of hidden k-logics: An abstract algebraic approach

Babenyshev¹,

Martins²

2016

Journal of Applied Logic

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This work advances a research agenda which has as its main aim the application of Abstract Algebraic Logic (AAL) methods and tools to the specification and verification of software systems. It uses a generalization of the notion of an abstract deductive system to handle multi-sorted deductive systems which differentiate visible and hidden sorts. Two main results of the paper are obtained by generalizing properties of the Leibniz congruencethe central notion in AAL.In this paper we discuss a question we posed in [2] about the relationship between the behavioral equivalences of equivalent hidden logics. We also present a necessary and sufficient intrinsic condition for two hidden logics to be equivalent.

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Behavioural theories and the proof of behavioural properties

Cited by 51 publications

References 9 publications

Behavioural Equivalence and Indistinguishability in Higher-Order Typed Languages

Behavioural Equivalence and Indistinguishability in Higher-Order Typed Languages

Verifying Design with Proof Scores

Behavioral equivalence of hidden k-logics: An abstract algebraic approach

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