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We address the problem of dening an algebraic framework for modularization supporting separate type-checking. In order to do that we introduce the notions of abstract type system and logic of constraints and we present a canonical construction of a model part, on top of a logic of constraints. This canonical construction works under standard assumptions on the underlying type system. We show...
The conditions under which a formal system for reasoning about structural specications, built over one logical system could be reused for reasoning about structured specications built over another logical system are formulated and studied. Following Goguen and Burstall, the notion of a logical system is formalized as an institution and extended to a D-institution. A new function between classes of...
Recently there has been a growing interest towards algebraic structures that are able to express formalisms different from the standard, tree-like presentation of terms. Many of these approaches reveal a specic interest towards their application in the “distributed and concurrent systems” field, but an exhaustive comparison between them is diffcult because their presentations can be quite dissimilar...
Combined logics have recently deserved much attention. In this paper we develop a detailed study of a form of combination that generalises the temporalisation construction proposed in [16]. It consists of replacing an atomic part (formal parameter) of one (parameterised) logic by another (actual parameter) logic. We provide a categorial characterisation of parameterisation and illustrate it with an...
Hidden algebra is a behavioural algebraic specification formalism for objects. It captures their constructional aspect, concerned with the initialisation and evolution of their states, as well as their observational aspect, concerned with the observable b ehaviour of such states. When attention is restricted to the observational aspect, final/cofree constructions provide suitable denotations for the...
Multi-algebras allow to model nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results. We propose a functorial presentation of various categories of multi-algebras and partial algebras, analogous to the classical presentation of algebras over a signature Σ as cartesian functors from the algebraic theory of Σ, Th(Σ), to Set...
Graph transformation systems have been introduced for the formal specification of software systems. States are thereby modeled as graphs, and computations as graph derivations according to the rules of the specification. Operations on graph derivations provide means to reason about the distribution and composition of computations. In this paper we discuss the development of an algebra of graph derivations...
We propose a definition of hierarchical heterogeneous formal specifications, where each module is specified according to its own homogeneous logic. We focus on the specification structure which we represent by a term in order to take benefit of classical knowledge on terms. For example, substitutions solve implementation sharing of modules. Then, we show how proof mechanisms can be expressed inside...
We investigate the rewrite relation over graphs induced by constructor-based weakly orthogonal graph rewriting systems. It is well known that this relation is not confluent in general whereas it is confluent in the case of weakly orthogonal term rewriting systems. We show, however, that the considered relation is always confluent, as well as confluent modulo bisimilarity, for a large class of graphs...
Spatial and temporal renement relations between typed graph transformation systems have been introduced in [6,7]. In a spatial renement a transformation rule is rened by an amalgamation of rules while in a temporal renement it is rened by a sequence of rules: in both cases, the renement relation supports the modeling of implementation. In the rst part of this paper, we further investigate the properties...
Narrowing is a method for solving equations in the equational theories of term rewriting systems. Unification and rewriting, the central operations in narrowing, are often implemented on graph-like data structures to exploit sharing of common subexpressions. In this paper, we study the completeness of narrowing in graph-based implementations. We show that the well-known condition for the completeness...
The ELAN system is an environment for specifying and prototyping constraint solvers, theorem provers and deduction systems in general. It also provides a framework for experimenting their combination. The ELAN language is based on rewriting logic and evaluation of labelled conditional rewrite rules. ELAN has two originalities with respect to several other algebraic languages, namely to handle non-deterministic...
A Rasiowa-Sikorski system is a sequence-type formalization of logics based on building decomposition trees of formulae labelled with sequences of formulae. Proofs are nite decomposition trees with leaves having “fundamental“, valid labels. The system is dual to the tableau system. The author gives examples of applying the R-S formalism to various C.S and A.I. logic, including a logic for reasoning...
We translate OBJ3 to CASL. At the level of basic specifications, we set up several institution representations between the underlying institutions. They correspond to different methodological views of OBJ3. The translations can be the basis for automated tools translating OBJ3 to CASL.
Casl is an expressive language for the specification of functional requirements and modular design of software. It has been designed by CoFI, the international Common Framework Initiative for algebraic specification and development. It is based on a critical selection of features that have already been explored in various contexts, including subsorts, partial functions, first-order logic, and structured...
In the area of Petri nets, many different developments have taken place within the last 30 years, in academia as well as in practice. For an adequate use in practice, a coherent and application oriented combination of various types and techniques for Petri nets is necessary. In order to attain a formal basis for different classes of Petri nets we introduce the concept of abstract Petri nets. The essential...
We develop an application of the reflective properties of rewriting logic to the specification of the management process of broadband telecommunications networks. The application is illustrated by a process that modifies the demand of a service between two nodes in the network. The strategy language selected for controlling the process is based on the one presented in [2] which has been enhanced with...
Methods are needed to help using formal specifications in a practical way. We present a specification method that takes into account both the specification of concurrent activity and the specification of the data types involved. It is applied here to LOTOS specification, but it may be used for other formalisms. Our method is both constraint oriented (for the processes decomposition into parallel subprocesses)...
The situation calculus (SC) is a formalism for reasoning about action. Within SC, the notion of state of a given situation is usually characterized by the set of fluents that hold in that situation. However, this concept is insufficient for system specification. To overcome this limitation, an extension of SC is proposed, the situation and state calculus (SSC), where the concept of state is primitive,...
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