Embedding a demonic semilattice in a relation algebra

Desharnais, Jules; Belkhiter, Nadir; Sghaier, Salah Ben Mohamed; Tchier, Fairouz; Jaoua, Ali; Mili, Ali; Zaguia, Nejib

doi:10.1016/0304-3975(94)00271-j

Cited by 37 publications

(21 citation statements)

References 19 publications

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“…Definition 1. A relation R on a set T is a subset of the Cartesian product of T with itself, that is, R C T x T. Among the possible operations on relations, we select the following': The name of the demonic meet comes from the fact that it is the meet operator of a refinement semilattice used to give a so-called demonic semantics to programming languages [5,11,12]. This is a partial operator; the definedness condition dam(Q) n dam(R) = dom(Q n R) means that, for any argument in their common domain, Q and R must agree on at least one result.…”

Section: Relationsmentioning

confidence: 99%

Integration of sequential scenarios

DesharnaisJules

FrappierMarc

KhédriRidha

et al. 1997

SIGSOFT Softw. Eng. Notes

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We give a formal relation-based definition of scenarios and we show how different scenarios can be integrated to obtain a more global view of user-system interactions. We restrict ourselves to the seqzlenlial case, meaning that we suppose that there is only one user (thus, the scenarios we wish to integrate cannot occur concurrently). Our view of scenarios is state-based, rather than event-based, like most of the other approaches, and can be grafted to the well-established specification language Z. Also, the end product of scenario integration, the specification of the functional aspects of the system, is given as a relation; this specification can be refined using independently developed methods. Our formal description is coupled with a diagram-based, transition-system like, presentation of scenarios, which is better suited to communication between clients and specifiers.

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Section: Relationsmentioning

confidence: 99%

Integration of sequential scenarios

DesharnaisJules

FrappierMarc

KhédriRidha

et al. 1997

SIGSOFT Softw. Eng. Notes

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“…Here is an example of these operations: on the intersection of their domains (the second row), the operands agree on the middle value and thus the meet is defined. This is not the case for It is shown in [14] that it is a complete join semilattice. Let f be a monotonic function (with respect to ) having at least one fixed point.…”

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confidence: 97%

“…We give the definitions and needed properties of these operations, and illustrate them with simple examples. For more details on relational demonic semantics and demonic operators, see [6,7,8,9,14]. Definition 4.1.…”

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confidence: 99%

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Demonic semantics: using monotypes and residuals

Tchier

2000

International Journal of Mathematics and Mathematical Sciences

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Relations and relational operators can be used to define the semantics of programming languages. The operations ∨ and • serve to give angelic semantics by defining a program to go right when there is a possibility to go right. On the other hand, the demonic operations and do the opposite: if there is a possibility to go wrong, a program whose semantics is given by these operators will go wrong; it is the demonic semantics. This type of semantics is known at least since Dijkstra's introduction of the language of guarded commands. Recently, there has been a growing interest in demonic relational semantics of sequential programs. Usually, a construct is given an ad hoc semantic definition based on an intuitive understanding of its behavior. In this note, we show how the notion of relational flow diagram (essentially a matrix whose entries are relations on the set of states of the program), introduced by Schmidt, can be used to give a single demonic definition for a wide range of programming constructs. This research had originally been carried out by J. Desharnais and F. Tchier (1996) in the same framework of the binary homogeneous relations. We show that all the results can be generalized by using the monotypes and the residuals introduced by Desharnais et al. (2000).2000 Mathematics Subject Classification: 18C10, 18C50, 68Q55, 68Q65, 03B70, 06B35.1. Introduction. The approaches to semantics are categorized as operational, axiomatic, or denotational. We will be concerned with the operational and the denotational semantics of nondeterministic programs. The operational semantics is described by the relation between the initial and final states. In our case, we consider the worst execution of the program; that is, we suppose that the program behaves as badly as possible according to the demonic relational semantics . Usually this last one is given an ad hoc semantics definition based on an intuitive understanding of the behavior of the program. Denotational semantics has been introduced by Scott and Strachey. To give the denotational semantics, we associate to a program a mathematical object. In our case, this object is a flow diagram which is a graph whose arrows are weighted by the different steps of the program. The operations are "the demonic choice" and "demonic composition." In this note, we show how the notion of the flow diagram can be exploited to give single demonic operational semantics (with only demonic operators) for a wide range of programming constructs.

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“…Again, we generalize from the case of relation algebra to general KAs. For more details on relational demonic semantics and demonic operators, see [4,5,6,7,9,21]. It is easy to show that is indeed a partial ordering.…”

Section: Refinement Orderingmentioning

confidence: 99%

Kleene under a Demonic Star

Desharnais

Möller

Tchier

2000

Algebraic Methodology and Software Technology

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Abstract. In relational semantics, the input-output semantics of a program is a relation on its set of states. We generalize this in considering elements of Kleene algebras as semantical values. In a nondeterministic context, the demonic semantics is calculated by considering the worst behavior of the program. In this paper, we concentrate on while loops. Calculating the semantics of a loop is difficult, but showing the correctness of any candidate abstraction is much easier. For deterministic programs, Mills has described a checking method known as the while statement verification rule. A corresponding programming theorem for nondeterministic iterative constructs is proposed, proved and applied to an example. This theorem can be considered as a generalization of the while statement verification rule to nondeterministic loops.

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Embedding a demonic semilattice in a relation algebra

Cited by 37 publications

References 19 publications

Integration of sequential scenarios

Integration of sequential scenarios

Demonic semantics: using monotypes and residuals

Kleene under a Demonic Star

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