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Combining First Order Algebraic Rewriting Systems, Recursion and Extensional Lambda Calculi
 Intern. Conf. on Automata, Languages and Programming (ICALP), volume 820 of Lecture Notes in Computer Science
, 1994
"... It is well known that confluence and strong normalization are preserved when combining leftlinear algebraic rewriting systems with the simply typed lambda calculus. It is equally well known that confluence fails when adding either the usual extensional rule for j, or recursion together with the usu ..."
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Cited by 16 (8 self)
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It is well known that confluence and strong normalization are preserved when combining leftlinear algebraic rewriting systems with the simply typed lambda calculus. It is equally well known that confluence fails when adding either the usual extensional rule for j, or recursion together with the usual contraction rule for surjective pairing. We show that confluence and normalization are modular properties for the combination of leftlinear algebraic rewriting systems with typed lambda calculi enriched with expansive extensional rules for j and surjective pairing. For that, we use a translation technique allowing to simulate expansions without expansion rules. We also show that confluence is maintained in a modular way when adding fixpoints. This result is also obtained by a simple translation technique allowing to simulate bounded recursion with fi reduction. 1 Introduction Confluence and strong normalization for the combination of lambda calculus and algebraic rewriting systems have...
EtaExpansions in Dependent Type Theory  The Calculus of Constructions
 Proceedings of the Third International Conference on Typed Lambda Calculus and Applications (TLCA'97
, 1997
"... . Although the use of expansionary jrewrite has become increasingly common in recent years, one area where jcontractions have until now remained the only possibility is in the more powerful type theories of the cube. This paper rectifies this situation by applying jexpansions to the Calculus of ..."
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Cited by 13 (0 self)
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. Although the use of expansionary jrewrite has become increasingly common in recent years, one area where jcontractions have until now remained the only possibility is in the more powerful type theories of the cube. This paper rectifies this situation by applying jexpansions to the Calculus of Constructions  we discuss some of the difficulties posed by the presence of dependent types, prove that every term rewrites to a unique long fijnormal form and deduce the decidability of fijequality, typeability and type inhabitation as corollaries. 1 Introduction Extensional equality for the simply typed calculus requires jconversion, whose interpretation as a rewrite rule has traditionally been as a contraction x : T:fx ) f where x 6 2 FV(t). When combined with the usual fireduction, the resulting rewrite relation is strongly normalising and confluent, and thus reduction to normal form provides a decision procedure for the associated equational theory. However jcontractions beh...
Constructor subtyping
, 1999
"... Constructor subtyping is a form of subtyping in which an inductive type is viewed as a subtype of another inductive type Ï if Ï has more constructors than. As suggested in [5, 12], its (potential) uses include proof assistants and functional programming languages. In this paper, we introduce and ..."
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Cited by 7 (3 self)
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Constructor subtyping is a form of subtyping in which an inductive type is viewed as a subtype of another inductive type Ï if Ï has more constructors than. As suggested in [5, 12], its (potential) uses include proof assistants and functional programming languages. In this paper, we introduce and study the properties of a simply typed Î»calculus with record types and datatypes, and which supports record subtyping and constructor subtyping. In the first part of the paper, we show that the calculus is confluent and strongly normalizing. In the second part of the paper, we show that the calculus admits a wellbehaved theory of canonical inhabitants, provided one adopts expansive extensionality rules, includingexpansion, surjective pairing, and a suitable expansion rule for datatypes. Finally, in the third part of the paper, we extend our calculus with unbounded recursion and show that confluence is preserved.
A Unified Framework for BindingTime Analysis
 Colloquium on Formal Approaches in Software Engineering (FASE '97), volume 1214 of Lect
, 1997
"... . Bindingtime analysis is a crucial part of offline partial evaluation. It is often specified as a nonstandard type system. Many typebased bindingtime analyses are reminiscent of simple type systems with additional features like recursive types. We make this connection explicit by expressing bind ..."
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Cited by 7 (3 self)
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. Bindingtime analysis is a crucial part of offline partial evaluation. It is often specified as a nonstandard type system. Many typebased bindingtime analyses are reminiscent of simple type systems with additional features like recursive types. We make this connection explicit by expressing bindingtime analysis with annotated type systems that separate the concerns of type inference from those of bindingtime annotation. The separation enables us to explore a design space for bindingtime analysis by varying the underlying type system and the annotation strategy independently. The result is a classification of different monovariant bindingtime analyses which allows us to compare their relative power. Due to the systematic approach we uncover some novel analyses. A partial evaluator separates the computation of a source program into two or more stages [7, 20]. Using the (static) input of the first stage it transforms a source program into a specialized residual program. Application...
Eta Expansions in System F
 LIENSDMI, Ecole Normale Superieure
, 1996
"... The use of expansionary jrewrite rules in various typed calculi has become increasingly common in recent years as their advantages over contractive jrewrite rules have become apparent. Not only does one obtain the decidability of fijequality, but rewrite relations based on expansions give a natu ..."
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Cited by 6 (0 self)
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The use of expansionary jrewrite rules in various typed calculi has become increasingly common in recent years as their advantages over contractive jrewrite rules have become apparent. Not only does one obtain the decidability of fijequality, but rewrite relations based on expansions give a natural interpretation of long fijnormal forms, generalise more easily to other type constructors, retain key properties when combined with other rewrite relations, and are supported by a categorical theory of reduction. This paper extends the initial results concerning the simply typed calculus to System F, that is, we prove strong normalisation and confluence for a rewrite relation consisting of traditional fireductions and jexpansions satisfying certain restrictions. Further, we characterise the second order long fijnormal forms as precisely the normal forms of the restricted rewrite relation. These results are an important step towards showing that jexpansions are compatible with the m...
Reasoning about Layered, Wildcard and Product Patterns
 ALP '94, volume 850 of LNCS
, 1994
"... We study the extensional version of the simply typed calculus with product types and fixpoints enriched with layered, wildcard and product patterns. Extensionality is expressed by the surjective pairing axiom and a generalization of the jconversion to patterns. We obtain a confluent reduction syst ..."
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Cited by 3 (2 self)
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We study the extensional version of the simply typed calculus with product types and fixpoints enriched with layered, wildcard and product patterns. Extensionality is expressed by the surjective pairing axiom and a generalization of the jconversion to patterns. We obtain a confluent reduction system by turning the extensional axioms as expansion rules, and then adding some restrictions to these expansions in order to avoid reduction loops. Confluence is proved by composition of modular properties of the extensional and nonextensional subsystems of the reduction calculus. 1 Introduction Patternmatching function definitions is one of the most popular features of functional languages, allowing to specify the behavior of functions by cases, according to the form of their arguments. Lefthand sides of function definitions are usually expressed using Layered, Wildcard and Product Patterns (LWPP), as for example the following Caml Light [ea93] program where the function cons new pair ta...