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28
What is a Universal HigherOrder Programming Language?
 In Proc. International Conference on Automata, Languages, and Programming. Lecture Notes in Computer Science
, 1993
"... . In this paper, we develop a theory of higherorder computability suitable for comparing the expressiveness of sequential, deterministic programming languages. The theory is based on the construction of a new universal domain T and corresponding universal language KL. The domain T is universal for ..."
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. In this paper, we develop a theory of higherorder computability suitable for comparing the expressiveness of sequential, deterministic programming languages. The theory is based on the construction of a new universal domain T and corresponding universal language KL. The domain T is universal for observably sequential domains; KL can define all the computable elements of T, including the elements corresponding to computable observably sequential functions. In addition, domain embeddings in T preserve the maximality of finite elementspreserving the termination behavior of programs over the embedded domains. 1 Background and Motivation Classic recursion theory [7, 13, 18] asserts that all conventional programming languages are equally expressive because they can define all partial recursive functions over the natural numbers. This statement, however, is misleading because real programming languages support and enforce a more abstract view of data than bitstrings. In particular, mo...
Typed event Structures and the πcalculus
 In Proc. MFPS’06
, 2006
"... Abstract. We propose a typing system for the true concurrent model of event structures that guarantees an interesting behavioural property known as confusion freeness. A system is confusion free if nondeterministic choices are localised and do not depend on the scheduling of independent components. ..."
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Abstract. We propose a typing system for the true concurrent model of event structures that guarantees an interesting behavioural property known as confusion freeness. A system is confusion free if nondeterministic choices are localised and do not depend on the scheduling of independent components. It is a generalisation of confluence to systems that allow nondeterminism. Ours is the first typing system to control behaviour in a true concurrent model. To demonstrate its applicability, we show that typed event structures give a semantics of linearly typed version of the πcalculi with internal mobility. The semantics we provide is the first event structure semantics of the πcalculus and generalises Winskel’s original event structure semantics of CCS. 1
A constructive denotational semantics for Kahn networks in Coq
, 2007
"... Semantics of programming languages and interactive environments for the development of proofs and programs are two important aspects of Gilles Kahn’s scientific contributions. In his paper “The semantics of a simple language for parallel programming ” [11], he proposed an interpretation of (determin ..."
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Semantics of programming languages and interactive environments for the development of proofs and programs are two important aspects of Gilles Kahn’s scientific contributions. In his paper “The semantics of a simple language for parallel programming ” [11], he proposed an interpretation of (deterministic) parallel programs (now called Kahn networks) as stream transformers based on the theory of complete partial orders (cpos). A restriction of this language to synchronous programs is the basis of the dataflow Lustre language which is used for the development of critical embedded systems [14, 10]. We present a formalization of this seminal paper in the Coq proof assistant [4, 15]. For that purpose, we developed a general library for cpos. Our cpos are defined with an explicit function computing the least upper bound (lub) of an increasing sequence of elements. This is different from what G. Kahn developed for the standard Coq library where only the existence of lubs (for arbitrary directed sets) is required, giving no way to explicitly compute a fixpoint. We define a cpo structure for the type of possibly infinite streams. It is then possible to define formally what is a Kahn network and what is its semantics, achieving the goal of having a concept closed by composition and recursion. The library is illustrated by the example taken from the original paper as well as the Sieve of Eratosthenes, an example of a dynamic network. 1
Probabilistic trueconcurrency models: branching cells and distributed probabilities, in "Information and Computation
, 2006
"... This paper is devoted to trueconcurrency models for probabilistic systems. By this we mean probabilistic models in which Mazurkiewicz traces, not interleavings, are given a probability. Here we address probabilistic event structures. We consider a new class of event structures, called locally finit ..."
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This paper is devoted to trueconcurrency models for probabilistic systems. By this we mean probabilistic models in which Mazurkiewicz traces, not interleavings, are given a probability. Here we address probabilistic event structures. We consider a new class of event structures, called locally finite. Locally finite event structures exhibit “finite confusion”; in particular, under some mild condition, confusionfree event structures are locally finite. In locally finite event structures, maximal configurations can be tiled with branching cells: branching cells are minimal and finite substructures capturing the choices performed while scanning a maximal configuration. A probabilistic event structure (p.e.s.) is a pair (E, P), where E is a prime event structure and P is a probability on the space of maximal configurations of E. We introduce the new class of distributed probabilities for p.e.s.: distributed probabilities are such that random choices in
Concrete Data Structures and Functional Parallel Programming
, 1997
"... We present a framework for designing parallel programming languages whose semantics is functional and where communications are explicit. To this end, we specialize Brookes and Geva's generalized concrete data structures with a notion of explicit data layout and obtain a CCC of distributed structures ..."
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Cited by 4 (3 self)
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We present a framework for designing parallel programming languages whose semantics is functional and where communications are explicit. To this end, we specialize Brookes and Geva's generalized concrete data structures with a notion of explicit data layout and obtain a CCC of distributed structures called arrays. We find that arrays' symmetric replicated structures, suggested by the dataparallel SPMD paradigm, are incompatible with sum types. We then outline a functional language with explicitlydistributed (monomorphic) concrete types, including higherorder, sum and recursive ones. In this language, programs can be as large as the network and can observe communication events in other programs. Such flexibility is missing from current dataparallel languages and amounts to a fusion with their socalled annotations, directives or metalanguages. 1 Explicit communications and functional programming Faced with the mismatch between parallel programming languages and the requirements o...
Modes of Convergence for Term Graph Rewriting
"... Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour is impaired by the lack of an appropriate count ..."
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Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour is impaired by the lack of an appropriate counterpart of infinitary rewriting on the side of term graphs. We aim to fill this gap by devising two modes of convergence based on a partial order resp. a metric on term graphs. The thus obtained structures generalise corresponding modes of convergence that are usually studied in infinitary term rewriting. We argue that this yields a common framework in which both term rewriting and term graph rewriting can be studied. In order to substantiate our claim, we compare convergence on term graphs and on terms. In particular, we show that the resulting infinitary calculi of term graph rewriting exhibit the same correspondence as we know it from term rewriting: Convergence via the partial order is a conservative extension of the metric convergence.
Stable computational semantics of conflictfree rewrite systems (Draft). Available at http://www.sys.uea.ac.uk/~zurab
, 2000
"... Abstract. We study orderings ✂S on reductions in the style of Lévy reflecting the growth of information w.r.t. (super)stable sets S of ‘values’ (such as headnormal forms or Böhmtrees). We show that sets of coinitial reductions ordered by ✂S form finitary ωalgebraic complete lattices, and hence f ..."
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Cited by 3 (3 self)
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Abstract. We study orderings ✂S on reductions in the style of Lévy reflecting the growth of information w.r.t. (super)stable sets S of ‘values’ (such as headnormal forms or Böhmtrees). We show that sets of coinitial reductions ordered by ✂S form finitary ωalgebraic complete lattices, and hence form computation and Scott domains. As a consequence, we obtain a relativized version of the computational semantics proposed by Boudol for term rewriting systems. Furthermore, we give a pure domaintheoretic characterization of the orderings ✂S in the spirit of Kahn and Plotkin’s concrete domains. These constructions are carried out in the framework of Stable Deterministic Residual Structures, which are abstract reduction systems with an axiomatized residual relations on redexes, that model all orthogonal (or conflictfree) reduction systems as well as many other interesting computation structures. 1
Probabilistic πCalculus and Event Structures
"... This paper proposes two semantics of a probabilistic variant of the πcalculus: an interleaving semantics in terms of Segala automata and a true concurrent semantics, in terms of probabilistic event structures. The key technical point is a use of types to identify a good class of nondeterministic p ..."
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Cited by 2 (2 self)
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This paper proposes two semantics of a probabilistic variant of the πcalculus: an interleaving semantics in terms of Segala automata and a true concurrent semantics, in terms of probabilistic event structures. The key technical point is a use of types to identify a good class of nondeterministic probabilistic behaviours which can preserve a compositionality of the parallel operator in the event structures and the calculus. We show an operational correspondence between the two semantics. This allows us to prove a “probabilistic confluence” result, which generalises the confluence of the linearly typed πcalculus.
Modularity and Expressibility for Nets of Relations
, 1996
"... Modularity reflects the Frege Principle: any two expressions expr 1 and expr 2 which have the same meaning (semantics) can be replaced by each other in every appropriate context C[ ] without changing the meaning of the overall expression. In [18] we identified observable relations and nets of obser ..."
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Modularity reflects the Frege Principle: any two expressions expr 1 and expr 2 which have the same meaning (semantics) can be replaced by each other in every appropriate context C[ ] without changing the meaning of the overall expression. In [18] we identified observable relations and nets of observable relations as appropriate tools for the investigation of dataflow networks over nondeterministic agents. The observable relations are the InputOutput behaviors of (in general nondeterministic) dataflow agents. Moreover, the semantics of nets of observable relations is consistent with the inputoutput behavior of dataflow agents. In [18, 19] we showed that the main source of the BrockAckerman anomaly [2] is in the semantics of nets of relations. But it turns out that this semantics is not modular. The central objective of this paper is the characterization of modular classes of relations and hence indirectly the set of dataflow nets without anomalies. Another major theme which plays a ...
Reasoning with powerdomains in Isabelle/HOLCF
 In Otmane Ait Mohamed, César Muñoz, and Sofiène Tahar, editors, Theorem Proving in HigherOrder Logics (TPHOLs 2008): Emerging Trends
, 2008
"... Abstract. This paper presents the first fullymechanized formalization of powerdomains, implemented view of powerdomains to the user, hiding the complicated implementation details. The library also provides proof automation, in the form of sets of rewrite rules for solving equalities and inequalitie ..."
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Abstract. This paper presents the first fullymechanized formalization of powerdomains, implemented view of powerdomains to the user, hiding the complicated implementation details. The library also provides proof automation, in the form of sets of rewrite rules for solving equalities and inequalities on powerdomains. 1