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Proving congruence of bisimulation in functional programming languages
 Information and Computation
, 1996
"... Email: howe research.att.com We give a method for proving congruence of bisimulationlike equivalences in functional programming languages. The method applies to languages that can be presented as a set of expressions together with an evaluation relation. We use this method to show that some genera ..."
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Cited by 106 (1 self)
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Email: howe research.att.com We give a method for proving congruence of bisimulationlike equivalences in functional programming languages. The method applies to languages that can be presented as a set of expressions together with an evaluation relation. We use this method to show that some generalizations of Abramsky's applicative bisimulation are congruences whenever evaluation can be specified by a certain natural form of structured operational semantics. One of the generalizations handles nondeterminism and diverging computations.] 1996 Academic Press, Inc. 1.
Relational Reasoning about Contexts
 HIGHER ORDER OPERATIONAL TECHNIQUES IN SEMANTICS, PUBLICATIONS OF THE NEWTON INSTITUTE
, 1998
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Discrimination by Parallel Observers: the Algorithm
 LICS '97 , IEEE Comp. Soc
, 1998
"... The main result of the paper is a constructive proof of the following equivalence: two pure terms are observationally equivalent in the lazy concurrent calculus iff they have the same L'evyLongo trees. An algorithm which allows to build a context discriminating any two pure terms with differe ..."
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Cited by 6 (3 self)
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The main result of the paper is a constructive proof of the following equivalence: two pure terms are observationally equivalent in the lazy concurrent calculus iff they have the same L'evyLongo trees. An algorithm which allows to build a context discriminating any two pure terms with different L'evyLongo trees is described. It follows that contextual equivalence coincides with behavioural equivalence (bisimulation) as considered by Sangiorgi. Another consequence is that the discriminating power of concurrent lambda contexts is the same as that of BoudolLaneve's contexts with multiplicities. 3 1 Introduction The aim of this paper is to improve our understanding of what is the "meaning" of a term in the lazy calculus. To explain our result let us begin with the following few observations borrowed from the paper [2] of Abramsky and Ong. In the ordinary calculus, the most natural understanding of evaluation to a "value" is reduction to a normal form. It is however wellk...
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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Cited by 6 (0 self)
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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...
Action Semantics Reasoning About Functional Programs
 Mathematical Structures in Computer Science
, 1996
"... syntax The algebraic definition of abstract syntax trees below can, more or less, be read as a BNF grammar. Emphatic brackets, [[: : : ]], indicate nodes in an abstract syntax tree. grammar: ffl Expression = Identifier "true" "false" [[ "" Identifier "." Expression ]] [[ Expression Expression ]] ..."
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Cited by 5 (2 self)
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syntax The algebraic definition of abstract syntax trees below can, more or less, be read as a BNF grammar. Emphatic brackets, [[: : : ]], indicate nodes in an abstract syntax tree. grammar: ffl Expression = Identifier "true" "false" [[ "" Identifier "." Expression ]] [[ Expression Expression ]] [[ "rec" Identifier "." Expression ]] [[ "if" Expression "then" Expression "else" Expression ]] . Action semantics reasoning about functional programs 3 ffl Identifier = [[ letter + ]] . 2.2. Semantic functions Action semantic descriptions are syntaxdirected in the denotational style: compositional semantic functions map abstract syntax into meaning and are defined inductively by semantic equations. There is one universal semantic domain, namely action, the sort of actions. Actions are expressed in a notation that looks a little like informal English prose but, in fact, it is a completely formal combinatorbased notation. The verbose notation should be suggestive of the meaning of th...
A Filter Model for Concurrent λCalculus
 SIAM J. Comput
, 1998
"... Type free lazy calculus is enriched with angelic parallelism and demonic nondeterminism. Callbyname and callbyvalue abstractions are considered and the operational semantics is stated in terms of a must convergence predicate. We introduce a type assignment system with intersection and union typ ..."
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Cited by 4 (1 self)
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Type free lazy calculus is enriched with angelic parallelism and demonic nondeterminism. Callbyname and callbyvalue abstractions are considered and the operational semantics is stated in terms of a must convergence predicate. We introduce a type assignment system with intersection and union types and we prove that the induced logical semantics is fully abstract.
A Convex Powerdomain over Lattices: its Logic and λCalculus
, 1997
"... . To model at the same time parallel and nondeterministic functional calculi we define a powerdomain functor P such that it is an endofunctor over the category of algebraic lattices. P is locally continuous and we study the initial solution D 1 of the domain equation D = P([D ! D]? ). We derive f ..."
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Cited by 1 (1 self)
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. To model at the same time parallel and nondeterministic functional calculi we define a powerdomain functor P such that it is an endofunctor over the category of algebraic lattices. P is locally continuous and we study the initial solution D 1 of the domain equation D = P([D ! D]? ). We derive from the algebras of P the logic of D 1 , that is the axiomatic description of its compact elements. We then define a calculus and a type assignment system using the logic of D 1 as the related type theory. We prove that the filter model of this calculus, which is isomorphic to D 1 , is fully abstract with respect to the observational preorder of the calculus. Keywords: calculus, Nondeterminism, Full Abstraction, Powerdomain Construction, Intersection Type Disciplines. 1. Introduction One of the main issues in the design of programming languages is the achievement of a good compromise between the multiplicity of control structures and data types and the unicity of the mathematica...