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Algebraic Approaches to Nondeterminism  an Overview
 ACM Computing Surveys
, 1997
"... this paper was published as Walicki, M.A. and Meldal, S., 1995, Nondeterministic Operators in Algebraic Frameworks, Tehnical Report No. CSLTR95664, Stanford University ..."
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Cited by 23 (3 self)
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this paper was published as Walicki, M.A. and Meldal, S., 1995, Nondeterministic Operators in Algebraic Frameworks, Tehnical Report No. CSLTR95664, Stanford University
A Complete Calculus for the Multialgebraic and Functional Semantics of Nondeterminism
, 1995
"... : The current algebraic models for nondeterminism focus on the notion of possibility rather than necessity, and con sequently equate (nondeterministic) terms that one intuitively would not consider equal. Furthermore, existing models for nondeterminism depart radically from the standard models for ( ..."
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Cited by 22 (9 self)
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: The current algebraic models for nondeterminism focus on the notion of possibility rather than necessity, and con sequently equate (nondeterministic) terms that one intuitively would not consider equal. Furthermore, existing models for nondeterminism depart radically from the standard models for (equational) specifications of deterministic operators. One would prefer that a specification language for nondeterministic operators be based on an extension of the standard model concepts, preferably in such a way that the reasoning system for (possibly nondeterministic) operators becomes the standard equational one whenever restricted to the deterministic operators  the objective should be to minimize the departure from the standard frameworks. In this paper we define a specification language for nondeterministic operators and multialgebraic semantics. The first complete reasoning system for such specifications is introduced. We also define a transformation of specifications of nondeterm...
Structured Specifications and Implementation of Nondeterministic Data Types
, 1995
"... The use of nondeterminism in specifications, as distinct from underspecification, is motivated by an example in the context of data refinement. A simple formalism for specifying nondeterministic data types is introduced. Its semantics is given in terms of the existing formalisms of relations, multia ..."
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Cited by 8 (5 self)
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The use of nondeterminism in specifications, as distinct from underspecification, is motivated by an example in the context of data refinement. A simple formalism for specifying nondeterministic data types is introduced. Its semantics is given in terms of the existing formalisms of relations, multialgebras, sets of functions and oracles by means of appropriate translation rules. Nondeterministic data refinement is studied from the syntactic and semantic perspective, and the correctness of the suggested proof obligations is proved. More general, the implementation relation and parameterisation of nondeterministic data types are discussed and the standard theorems of vertical and horizontal composition are generalized to the nondeterministic case.
Abstraction Barriers in Equational Proof
 In Proc. of AMAST'98, volume 1548 of LNCS
, 1998
"... ion Barriers in Equational Proof Jo Erskine Hannay LFCS, Division of Informatics, University of Edinburgh, Scotland joh@dcs.ed.ac.uk Abstract. Module constructs in programming languages have protection mechanisms hindering unauthorised external access to internal operators of data types. In some c ..."
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Cited by 1 (1 self)
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ion Barriers in Equational Proof Jo Erskine Hannay LFCS, Division of Informatics, University of Edinburgh, Scotland joh@dcs.ed.ac.uk Abstract. Module constructs in programming languages have protection mechanisms hindering unauthorised external access to internal operators of data types. In some cases, granting external access to internal operators would result in serious violation of a data type's specified external properties. In order to reason consistently about specifications of such data types, it is necessary in general to incorporate a notion of protective abstraction barrier in proof strategies as well. We show how this can be done in equational calculus by simply restricting the congruence axiom, and see how the motivation for this naturally arises from FI and FRI approaches to specification refinement. 1 Introduction Many programming languages have encapsulation mechanisms that hide internal detail of data types. Besides providing abstraction from uninteresting detail, th...
Relative Equational Specification and Semantics
, 1997
"... Abstract: Standard concepts of initial and final algebra semantics are generalised in a modular hierarchical manner. The resulting relative formalism allows a unified view on the relationship between initial and final algebra semantics and gives a dualised notion of consistency. Using this, a modula ..."
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Abstract: Standard concepts of initial and final algebra semantics are generalised in a modular hierarchical manner. The resulting relative formalism allows a unified view on the relationship between initial and final algebra semantics and gives a dualised notion of consistency. Using this, a modular hierarchical approach to proof by consistency is taken by which only toplevel equations need be considered at any level. The formalism also allows nonhomogeneous specification schemes and different proof methods at each level.