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Map calculus: Initial application scenarios and experiments based on Otter
, 1998
"... Properties of a few familiar structures (natural numbers, nested lists, lattices) are formally specified in TarskiGivant's map calculus, with the aim of bringing to light new translation techniques that may bridge the gap between firstorder predicate calculus and the map calculus. It is also highl ..."
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Properties of a few familiar structures (natural numbers, nested lists, lattices) are formally specified in TarskiGivant's map calculus, with the aim of bringing to light new translation techniques that may bridge the gap between firstorder predicate calculus and the map calculus. It is also highlighted to what extent a stateoftheart theoremprover for firstorder logic, namely Otter, can be exploited not only to emulate, but also to reason about, map calculus. 3 1 Introduction Everybody remembers that Boole's Laws of thought (1854), Frege's Begriffsschrift (1879), and the WhiteheadRussell's Principia Mathematica (1910) have been three major milestones in the development of contemporary logic (cf. [3, 8, 15, 4]). Only a few people are aware that very important prePrincipia milestones were laid down by C.S. Peirce and E. Schroder and culminated in the monumental work [11, 12] on the Algebra der Logik . The "rather capricious line of historical development" of the algebraic for...
NonDeterministic Extensions of Untyped λcalculus
 INFO. AND COMP
, 1995
"... The main concern of this paper is the study of the interplay between functionality and non determinism. Indeed the first question we ask is whether the analysis of parallelism in terms of sequentiality and non determinism, which is usual in the algebraic treatment of concurrency, remains correct in ..."
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The main concern of this paper is the study of the interplay between functionality and non determinism. Indeed the first question we ask is whether the analysis of parallelism in terms of sequentiality and non determinism, which is usual in the algebraic treatment of concurrency, remains correct in presence of functional application and abstraction. We identify non determinism in the setting of λcalculus with the absence of the ChurchRosser property plus the inconsistency of the equational theory obtained by the symmetric closure of the reduction relation. We argue in favour of a distinction between non determinism and parallelism, due to the conjunctive nature of the former in contrast to the disjunctive character of the latter. This is the basis of our analysis of the operational and denotational semantics of non deterministiccalculus, which is the classical calculus plus a choice operator, and of our election of bounded indeterminacy as the semantical counterpart of conjunctive non determinism. This leads to operational semantics based on...
Interaction of Agents and Environments
"... . A new abstract model of interaction between agents and environments considered as objects of different types is introduced. Agents are represented by means of labelled transition systems considered up to bisimilarity. The equivalence of agents is characterised in terms of an algebra of behaviours ..."
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. A new abstract model of interaction between agents and environments considered as objects of different types is introduced. Agents are represented by means of labelled transition systems considered up to bisimilarity. The equivalence of agents is characterised in terms of an algebra of behaviours which is a continuous algebra with approximation and two operations: nondeterministic choice and prefixing. Environments are introduced as agents supplied with an insertion function which takes the behaviour of an agent and the behaviour of an environment as arguments and returns the new behaviour of an environment. Arbitrary continuous functions can be used as insertion functions, and we use functions defined by means of rewriting logic as computable ones. The transformation of environment behaviours defined by the insertion function also defines a new type of agent equivalence  insertion equivalence. Two behaviours are insertion equivalent if they define the same transformation of an en...
On the Finitary Bisimulation
 Nils Klarlund, Madhavan Mukund, and Milind Sohoni
, 1995
"... is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS ..."
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Cited by 4 (0 self)
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is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS
Sort Inference in the ACTRESS Compiler Generator
 In [44
, 1994
"... . Actress accepts the actionsemantic description of a source language, and from it generates a compiler. The generated compiler translates its source program to an action, performs sort inference on this action, (optionally) simplifies it by transformations, and finally translates it to object code ..."
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. Actress accepts the actionsemantic description of a source language, and from it generates a compiler. The generated compiler translates its source program to an action, performs sort inference on this action, (optionally) simplifies it by transformations, and finally translates it to object code. The sort inference phase provides valuable information for the subsequent transformation and code generation phases. In this paper we study the problem of sort inference on actions. 1 Introduction Actress is an actionsemantics directed compiler generator [4]. It accepts a formal description of the syntax and action semantics [10, 16] of a particular programming language, called the source language, and automatically generates a compiler that translates the source language to C object code. The generated compiler first translates each source program to an action, called the program action. Then it sortchecks the program action. Finally, it transforms the program action, and translates it...
Linda based Applicative and Imperative Process Algebras
"... The classical algebraic approach to the specification and verification of concurrent systems is tuned to distributed programs that rely on asynchronous communications and permit explicit data exchange. An applicative process algebra, obtained by embedding the Linda primitives for interprocess com ..."
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The classical algebraic approach to the specification and verification of concurrent systems is tuned to distributed programs that rely on asynchronous communications and permit explicit data exchange. An applicative process algebra, obtained by embedding the Linda primitives for interprocess communication in a CCS/CSPlike language, and an imperative one, obtained from the applicative variant by adding a construct for explicit assignment of values to variables, are introduced. The testing framework is used to define behavioural equivalences for both languages and sound and complete proof systems for them are described together with a fully abstract denotational model (namely, a variant of Strong Acceptance Trees). Keywords: Concurrency, Asynchronous Communications, Process Algebras, Formal Semantics. 1
On Sets of Terms: A Study of a Generalisation Relation and of Its Algorithmic Properties
, 1996
"... . Signatures, as introduced to cope with semantics of programming languages, provide an interesting framework for knowledge representation. They allow structured and recursive properties that attribute representation does not permit, and at the same time seem to be algorithmically treatable. We reca ..."
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. Signatures, as introduced to cope with semantics of programming languages, provide an interesting framework for knowledge representation. They allow structured and recursive properties that attribute representation does not permit, and at the same time seem to be algorithmically treatable. We recall how a generalisation relation on terms can be introduced by means of the classical special symbol W, whose meaning is "indeterminate", and the partial order inductively defined on the terms. This formalism can nevertheless not take into account negation or disjunction. We provide in this paper a generalisation relation on sets of terms to withdraw these restrictions. This relation has different definitions (syntactical, settheoretic, and based on a closed world assumption) that are proved to be equivalent for specific classes of signatures. They yield an equivalence relation whose canonical form is studied. We also study the combinatorial and algorithmic issues of the generalisation rela...
Complexity as a Basis for Comparing Semantic Models of Concurrency
, 1995
"... . We investigate some aspects of interexpressiveness of languages and their (denotational) semantic models by viewing semantic functions from a complexitytheory viewpoint. We classify semantic functions as polynomial or finite if a language term of size n produces a metalanguage object respectivel ..."
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. We investigate some aspects of interexpressiveness of languages and their (denotational) semantic models by viewing semantic functions from a complexitytheory viewpoint. We classify semantic functions as polynomial or finite if a language term of size n produces a metalanguage object respectively polynomially bounded in n or finite. Languages involving concurrency manifest most interest which we associate to the fact that their semantic models in general lack style abstraction. The paper provides a quantifiable reason why labelled event structures form a more reasonable model for the choice and concurrency operators of CCS than do synchronisation trees. Similarly we show the representation of conflict by places within (at least occurrence forms of) Petrinets is exponentially larger than the relational representation within corresponding event structures. An application is a criterion for selection of semantic models for realworld algorithmic purposes; for example, `model checki...
On Sets of Terms: A Study of a Generalisation Relation and of Its Algorithmic Properties
, 1996
"... Signatures, as introduced to cope with semantics of programming languages, provide an interesting framework for knowledge representation. They allow structured and recursive properties that attribute representation does not permit, and at the same time seem to be algorithmically treatable. We rec ..."
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Signatures, as introduced to cope with semantics of programming languages, provide an interesting framework for knowledge representation. They allow structured and recursive properties that attribute representation does not permit, and at the same time seem to be algorithmically treatable. We recall how a generalisation relation on terms can be introduced by means of the classical special symbol W, whose meaning is "indeterminate", and the partial order inductively defined on the terms. This formalism can nevertheless not take into account negation or disjunction. We provide in this paper a generalisation relation on sets of terms to withdraw these restrictions. This relation has different definitions (syntactical, settheoretic, and based on a closed world assumption) that are proved to be equivalent for specific classes of signatures. They yield an equivalence relation whose canonical form is studied. We also study the combinatorial and algorithmic issues of the generalisation relation: the following problems are proved to be decidable (on finite data) but generally at least NPcomplete: Does set A generalise set B? Are sets A and B equivalent? Is set B the canonical form of set A? Compute the negation of set A.... In the case where one of the sets contains only terms maximal for the generalisation relation, the first three problems are shown to be polynomial.