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Relating Typability and Expressiveness in FiniteRank Intersection Type Systems (Extended Abstract)
 In Proc. 1999 Intâ€™l Conf. Functional Programming
, 1999
"... We investigate finiterank intersection type systems, analyzing the complexity of their type inference problems and their relation to the problem of recognizing semantically equivalent terms. Intersection types allow something of type T1 /\ T2 to be used in some places at type T1 and in other places ..."
Abstract

Cited by 22 (9 self)
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We investigate finiterank intersection type systems, analyzing the complexity of their type inference problems and their relation to the problem of recognizing semantically equivalent terms. Intersection types allow something of type T1 /\ T2 to be used in some places at type T1 and in other places at type T2 . A finiterank intersection type system bounds how deeply the /\ can appear in type expressions. Such type systems enjoy strong normalization, subject reduction, and computable type inference, and they support a pragmatics for implementing parametric polymorphism. As a consequence, they provide a conceptually simple and tractable alternative to the impredicative polymorphism of System F and its extensions, while typing many more programs than the HindleyMilner type system found in ML and Haskell. While type inference is computable at every rank, we show that its complexity grows exponentially as rank increases. Let K(0, n) = n and K(t + 1, n) = 2^K(t,n); we prove that recognizing the pure lambdaterms of size n that are typable at rank k is complete for dtime[K(k1, n)]. We then consider the problem of deciding whether two lambdaterms typable at rank k have the same normal form, Generalizing a wellknown result of Statman from simple types to finiterank intersection types. ...
Postponement, Conservation and Preservation of Strong Normalisation for Generalised Reduction
"... Postponement of K contractions and the conservation theorem do not hold for ordinary but have been established by de Groote for a mixture of with another reduction relation. In this paper, de Groote's results are generalised for a single reduction relation e which generalises . We show morever, t ..."
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Postponement of K contractions and the conservation theorem do not hold for ordinary but have been established by de Groote for a mixture of with another reduction relation. In this paper, de Groote's results are generalised for a single reduction relation e which generalises . We show morever, that e has the Preservation of Strong Normalisation property. Keywords: Generalised reduction, Postponement of Kcontractions, Generalised Conservation, Preservation of Strong Normalisation. 1 The calculus with generalized reduction In the term (( x : y :N)P )Q, the abstraction starting with x and the argument P form the redex ( x : y :N)P . When this redex is contracted, the abstraction starting with y and Q will in turn form a redex. It is important to note that Q (or some residual of Q) is the only argument that the abstraction (or some residual of the abstraction) starting with y can ever have. This fact has been exploited by many researchers. Reduction has been ex...
Higher Order Unification via ...Style of Explicit Substitution
"... A higher order unification (HOU) method based on the ...style of explicit substitution is proposed. The method is based on the treatment introduced by Dowek, Hardin and Kirchner in [DHK95] using the ...style of explicit substitution. Correctness and completeness properties of the proposed approach ..."
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A higher order unification (HOU) method based on the ...style of explicit substitution is proposed. The method is based on the treatment introduced by Dowek, Hardin and Kirchner in [DHK95] using the ...style of explicit substitution. Correctness and completeness properties of the proposed approach are shown and advantages of the method, inherited from the qualities of the ... calculus, are pointed out.