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Equational term graph rewriting
 FUNDAMENTA INFORMATICAE
, 1996
"... We present an equational framework for term graph rewriting with cycles. The usual notion of homomorphism is phrased in terms of the notion of bisimulation, which is wellknown in process algebra and concurrency theory. Specifically, a homomorphism is a functional bisimulation. We prove that the bis ..."
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Cited by 75 (8 self)
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We present an equational framework for term graph rewriting with cycles. The usual notion of homomorphism is phrased in terms of the notion of bisimulation, which is wellknown in process algebra and concurrency theory. Specifically, a homomorphism is a functional bisimulation. We prove that the bisimilarity class of a term graph, partially ordered by functional bisimulation, is a complete lattice. It is shown how Equational Logic induces a notion of copying and substitution on term graphs, or systems of recursion equations, and also suggests the introduction of hidden or nameless nodes in a term graph. Hidden nodes can be used only once. The general framework of term graphs with copying is compared with the more restricted copying facilities embodied in the µrule, and translations are given between term graphs and µexpressions. Using these, a proof system is given for µexpressions that is complete for the semantics given by infinite tree unwinding. Next, orthogonal term graph rewrite ...
Optimal Derivations in Weak Lambdacalculi and in Orthogonal Terms Rewriting Systems.
, 1991
"... We introduce the new framework of Labeled Terms Rewriting Systems (T l RS), a general framework to express sharing in Term Rewriting Systems (TRS). For Orthogonal T l RS, an important subclass of T l RS, we characterize optimal derivations. This result is applied to weak calculi, showing the ..."
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Cited by 31 (0 self)
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We introduce the new framework of Labeled Terms Rewriting Systems (T l RS), a general framework to express sharing in Term Rewriting Systems (TRS). For Orthogonal T l RS, an important subclass of T l RS, we characterize optimal derivations. This result is applied to weak calculi, showing the optimality of the lazy strategy, that is, the callbyname with sharing strategy. The result is also valid in the presence of ffi rules, as in PCF. Orthogonal T l RS is also useful as a calculus for proving syntactic properties of functional languages. 1 Compilation of the calculus Most compilers for functional languages translate their source language into some enriched calculus [17], and then, compile this intermediate language to a lowlevel language, such as mutually recursive supercombinators, as in LML [2, 10], or categorical combinators, as in CAML [4]. These lowlevel languages define different forms of weak fireduction. We now describe two of these lowlevel languages, superc...
Correspondence between Operational and Denotational Semantics
 Handbook of Logic in Computer Science
, 1995
"... This course introduces the operational and denotational semantics of PCF and examines the relationship between the two. Topics: Syntax and operational semantics of PCF, Activity Lemma, undefinability of parallel or; Context Lemma (first principles proof) and proof by logical relations Denotational ..."
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Cited by 24 (0 self)
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This course introduces the operational and denotational semantics of PCF and examines the relationship between the two. Topics: Syntax and operational semantics of PCF, Activity Lemma, undefinability of parallel or; Context Lemma (first principles proof) and proof by logical relations Denotational semantics of PCF induced by an interpretation; (standard) Scott model, adequacy, weak adequacy and its proof (by a computability predicate) Domain Theory up to SFP and Scott domains; non full abstraction of the standard model, definability of compact elements and full abstraction for PCFP (PCF + parallel or), properties of orderextensional (continuous) models of PCF, Milner's model and Mulmuley's construction (excluding proofs) Additional topics (time permitting): results on pure simplytyped lambda calculus, Friedman 's Completeness Theorem, minimal model, logical relations and definability, undecidability of lambda definability (excluding proof), dIdomains and stable functions Homepa...
Projecting Sequential Algorithms on Strongly Stable Functions
 Annals of Pure and Applied Logic
, 1993
"... We relate two sequential models of PCF: the sequential algorithm model due to Berry and Curien and the strongly stable model due to Bucciarelli and the author. More precisely, we show that all the morphisms araising in the strongly stable model of PCF are sequential in the sense that they are the ..."
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Cited by 23 (2 self)
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We relate two sequential models of PCF: the sequential algorithm model due to Berry and Curien and the strongly stable model due to Bucciarelli and the author. More precisely, we show that all the morphisms araising in the strongly stable model of PCF are sequential in the sense that they are the "extensional projections" of some sequential algorithms. We define a model of PCF where morphisms are "extensional" sequential algorithms and prove that any equation between PCF terms which holds in this model also holds in the strongly stable model.
On Strong Stability and HigherOrder Sequentiality
 IN PROC. 9TH SYMP. LOGIC IN COMP. SCI. (LICS
, 1994
"... We propose a definition by reducibility of sequentiality for the interpretations of higherorder programs and prove the equivalence between this notion and strong stability. ..."
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Cited by 4 (0 self)
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We propose a definition by reducibility of sequentiality for the interpretations of higherorder programs and prove the equivalence between this notion and strong stability.
The sigmaSemantics: A Comprehensive Semantics for Functional Programs
, 1997
"... A comprehensive semantics for functional programs is presented, which generalizes the wellknown callbyvalue and callbyname semantics. By permitting a separate choice between callby value and callbyname for every argument position of every function and parameterizing the semantics by this cho ..."
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A comprehensive semantics for functional programs is presented, which generalizes the wellknown callbyvalue and callbyname semantics. By permitting a separate choice between callby value and callbyname for every argument position of every function and parameterizing the semantics by this choice we abstract from the parameterpassing mechanism. Thus common and distinguishing features of all instances of the &semantics, especially callbyvalue and callbyname semantics, are highlighted. Furthermore, a property can be validated for all instances of the &semantics by a single proof. This is employed for proving the equivalence of the given denotational (fixedpoint based) and two operational (reduction based) definitions of the &semantics. We present and apply means for very simple proofs of equivalence with the denotational &semantics for a large class of reductionbased &semantics. Our basis are simple firstorder constructorbased functional programs with patterns. Keyw...
The ςSemantics: A Comprehensive Semantics for Functional Programs
, 1996
"... A comprehensive semantics for functional programs is presented, which generalizes the wellknown callbyvalue and callbyname semantics. By permitting a separate choice between callby value and callbyname for every argument position of every function and parameterizing the semantics by this ch ..."
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A comprehensive semantics for functional programs is presented, which generalizes the wellknown callbyvalue and callbyname semantics. By permitting a separate choice between callby value and callbyname for every argument position of every function and parameterizing the semantics by this choice we abstract from the parameterpassing mechanism. Thus common and distinguishing features of all instances of the ςsemantics, especially callbyvalue and callbyname semantics, are highlighted. Furthermore, a property can be validated for all instances of the ςsemantics by a single proof. This is employed for proving the equivalence of the given denotational (fixedpoint based) and two operational (reduction based) definitions of the ςsemantics. We present and apply means for very simple proofs of equivalence with the denotational ςsemantics for a large class of reductionbased ςsemantics. Our basis are simple firstorder
Locally Boolean Domains and Universal Models for Infinitary Sequential Languages
"... genehmigte ..."
G. Markowsky
"... Abstract: Various authors (especially Scott, Egli, and Constable) have introduced concepts of “basis ” for various classes of partially ordered sets (posets). This paper studies a basis concept directly analogous to the concept of a basis for a vector space. The new basis concept includes that of Eg ..."
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Abstract: Various authors (especially Scott, Egli, and Constable) have introduced concepts of “basis ” for various classes of partially ordered sets (posets). This paper studies a basis concept directly analogous to the concept of a basis for a vector space. The new basis concept includes that of Egli and Constable as a special case, and one of their theorems is a corollary of our results. This paper also summarizes some previously reported but little known results of wide utility. For example, if every linearly ordered subset (chain) in a poset has a least upper bound (supremum), so does every directed subset. Given posets P and Q, it is often useful to construct maps g:P + Q that are c./zuinc.onrinLlous: supremums of nonempty chains are preserved. Chaincontinuity is analogous to topological continuity and is generally much more difficult to verify than isofonicity: the preservation of the order relation. Th15 paper introduces the concept of an exrc,n.cion hasis: a subset B of P such that any is0tonefiBQ has a unique chaincontinuous extension,g:P+Q. Two characterizations of the chaincomplete posets that have extension bases are obtained. These results are then applied to the problem of constructing an extension basis for the poset [P + Q] of chaincontinuous maps from P to Q, given extension bases for P and Q. This is not always possible, but it becomes possible when a mild (and independently motivated) restriction is imposed on either P or Q. A lattice structure is not needed. 1.
Series VI: Fundamenta Informaticæ III.1 (1980), 105–118 Completions of ordered magmas
, 1978
"... Abstract.We give a completion theorem for ordered magmas (i.e. ordered algebras with monotone operations) in a general form. Particular instances of this theorem are already known, and new results follow. The semantics of programming languages is the motivation of such investigations. Key wordscompl ..."
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Abstract.We give a completion theorem for ordered magmas (i.e. ordered algebras with monotone operations) in a general form. Particular instances of this theorem are already known, and new results follow. The semantics of programming languages is the motivation of such investigations. Key wordscomplete partial orders, semantics of programming languages. Introduction. When defining recursive functions by systems of equations (Kleene [5]), one introduces an order relation which means that a partial result approximates another one. This partial order is complete (i.e. every ascending chain admits a least upper bound), thus allowing a minimal solution to be defined for the system. This matter has been rebuilt by Scott, and many authors after him, within the framework of complete lattices; that last theory has been developed for its own sake by several authors, among which Birkhoff [1].