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Relating Typability and Expressiveness in FiniteRank Intersection Type Systems (Extended Abstract)
 In Proc. 1999 Int’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 ..."
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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. ...
LAL is square: Representation and expressiveness in light affine logic
 In Proc. Workshop on Implicit Computational Complexity
, 2002
"... Abstract. We focus on how the choice of inputoutput representation has a crucial impact on the expressiveness of socalled “logics of polynomial time. ” Our analysis illustrates this dependence in the context of Light Affine Logic (LAL), which is both a restricted version of Linear Logic, and a pri ..."
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Cited by 3 (2 self)
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Abstract. We focus on how the choice of inputoutput representation has a crucial impact on the expressiveness of socalled “logics of polynomial time. ” Our analysis illustrates this dependence in the context of Light Affine Logic (LAL), which is both a restricted version of Linear Logic, and a primitive functional programming language with restricted sharing of arguments. By slightly relaxing representation conventions, we derive doublyexponential expressiveness bounds for this “logic of polynomial time. ” We emphasize that squaring is the unifying idea that relates upper bounds on cut elimination for LAL with lower bounds on representation. Representation issues arise in the simulation of DTIME[2 2n], where we construct a uniform family of proofnets encoding a Turing Machine; specifically, the dependence on n only affects the number of enclosing boxes. A related technical improvement is the simulation of DTIME[n k]indepthO(log k) LAL proofnets. The resulting upper bounds on cut elimination then satisfy the properties of a
Reflections on complexity of ML type reconstruction
, 1997
"... This is a collection of some more or less chaotic remarks on the ML type system, definitely not sufficient to fill a research paper of reasonable quality, but perhaps interesting enough to be written down as a note. At the beginning the idea was to investigate the complexity of type reconstruction a ..."
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Cited by 1 (0 self)
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This is a collection of some more or less chaotic remarks on the ML type system, definitely not sufficient to fill a research paper of reasonable quality, but perhaps interesting enough to be written down as a note. At the beginning the idea was to investigate the complexity of type reconstruction and typability in bounded order fragments of ML. Unexpectedly the problem turned out to be hard, and finally I obtained only partial results. I do not feel like spending more time on this topic, so the text is not polished, the proofs  if included at all  are only sketched and of rather poor mathematical quality. I believe however, that some remarks, especially those of "philosophical" nature, shed some light on the ML type system and may be of some value to the reader interested especially in the interaction between theory and practice of ML type reconstruction. 1 Introduction The ML type system was developed by Robin Milner in the late seventies [26, 3], but was influenced by much ol...