Hidden coinduction: 
behavioural correctness proofs for objects

Goguen, Joseph A.; Malcolm, Grant

doi:10.1017/s0960129599002777

Cited by 32 publications

(24 citation statements)

References 39 publications

(57 reference statements)

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“…However, in most of the cases it is possible to consider only a finite set of contexts C Σ ⊆ C {s} Σ instead of the set C {s} Σ , inducing this way the formation of finite specifications SP s (cf. [1,12,19]). …”

Section: Proofmentioning

confidence: 99%

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Observational Refinement Process

Madeira

2008

Electronic Notes in Theoretical Computer Science

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In the algebraic specification of software systems, it is desirable to have freedom in the implementation process, namely for the software reuse. In this paper we will discuss two issues in order to achieve this freedom: we study the observational stepwise refinement process and we propose an alternative formalization of the refinement concept based on the logical translation from the abstract algebraic logic. In the first topic, we go beyond the traditional assumption of maintaining the set of observable sorts during the refinement process by the possibility of changing it between the process steps, i.e., we analise the stepwise refinement with encapsulation and desencapsulation of sorts during the process. In the second topic, we suggest a formalization of the refinement concept where an equation may be mapped into a set of equations, against the refinements based on signature morphisms, where an equation is mapped into another one.

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Section: Proofmentioning

confidence: 99%

“…The study of methods for observational verification of properties can be found, for example, in works of M. Bidoit and R. Hennicker, of J. Goguen, G. Malcolm and G. Roşu, of A. Bouhoula, of R. Diaconescu, of K. Futatsugi, of P. Padawitz among others (cf. [1,15,13,12,21,7,9,20]). …”

Section: Introductionmentioning

confidence: 99%

Observational Refinement Process

Madeira

2008

Electronic Notes in Theoretical Computer Science

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“…CafeOBJ [26,27] is being built at the Japan Institute of Science and Technology under the direction of Prof. Kokichi Futatsugi; it extends OBJ3 with hidden algebra [55,80,68,67] for behavioral specification, and with rewriting logic [113,114] for applications programming. Maude [112,16] is being built at SRI International under the direction of Dr. Jose Meseguer; it extends OBJ with rewriting logic, and has been successfully used for metaprogramming, reflection, and algorithm implementation [17,18].…”

Section: A Brief History Of Objmentioning

confidence: 99%

Introducing OBJ

Goguen

Winkler

Meseguer

et al. 2000

Advances in Formal Methods

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148

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This is an introduction to the philosophy and use of OBJ, emphasizing its operational semantics, with aspects of its history and its logical semantics. Release 2 of OB13 is described in detail, with many examples. OBJ is a wide spectrum first-order functional language that is rigorously based on (order sorted) equationallogic and parameterized programming, supporting a declarative style that facilitates verification and allows OBJ to be used as a theorem prover.Order sorted algebra provides a notion of subsort that rigorously supports mUltiple inheritance, exception handling and overloading. Parameterized programming gives powerful support for design, verification, reuse, and maintenance, using two kinds of module: objects to encapsulate executable code, and in particular to define abstract data types by initial algebra semantics; and (loose) theories to specify both syntactic and semantic properties of modules. SOFTWARE ENGINEERING WITH OBlof module can be parameterized, where actual parameters may be modules. For parameter instantiation, a view binds the formal entities in an interface theory to actual entities in a module, and also asserts that the target module satisfies the semantic conditions of the interface theory. Module expressions allow complex combinations of already defined modules, including sums, instantiations, and transformations; moreover, evaluating a module expression actually constructs the described software (sub)system from the given components. Default views can greatly reduce the effort of instantiating modules, by allowing obvious correspondences to be left out. We argue that first-order parameterized programming includes much of the power of higher-order programming, in a form that is often more convenient.Although OBI executable code normally consists of equations that are interpreted as rewrite rules, OBJ3 objects can also encapsulate Lisp code, e.g., to provide efficient built-in data types, or to augment the system with new capabilities; we describe the syntax of this facility, and provide some examples. In addition, OBI provides rewriting modulo associative, commutative and/or identity equations, as well as user-definable evaluation strategies that allow lazy, eager, and mixed evaluation strategies on an operator-by-operator basis; memoization is also available on an operator-by-operator basis. In addition, OBJ3 supports the application of equations one at a time, either forwards or backwards; this is needed for equational theorem proving. Finally, OBI provides user-definable mixfix syntax, which supports the notational conventions of particular application domains. INTRODUCTIONThis paper motivates and describes the use of OB], based on Release 2.04 of the OBJ3 system. OBJ3 is the latest in a series of OB] systems, each of which has been rigorously based upon equational logic; however, the semantic basis of OB] is not developed here in full detail. The OBJ3 system is implemented in Common Lisp, and is based on ideas from order sorted algebra and parameterized programming. ...

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“…The most relevant to the topic of this paper are the variations developed by Goguen et al (hidden logics [24,25]) and by Bidoit and Hennicker (observational logics [28,3]). These approaches formalize behavioral validity (correctness) as follows: hidden logic is a variant of the equational logic in which some part of the specification is visible and another is hidden.…”

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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Hidden coinduction: behavioural correctness proofs for objects

Cited by 32 publications

References 39 publications

Observational Refinement Process

Observational Refinement Process

Introducing OBJ

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

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