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A feasible algorithm for typing in elementary affine logic
 In Proceedings of the 8th International Conference on Typed LambdaCalculi and Applications
, 2005
"... We give a new type inference algorithm for typing lambdaterms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction. Following previous references on this topic, the variant of EAL type system we consider (denoted EAL ⋆ ) is a variant without shari ..."
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Cited by 11 (5 self)
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We give a new type inference algorithm for typing lambdaterms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction. Following previous references on this topic, the variant of EAL type system we consider (denoted EAL ⋆ ) is a variant without sharing and without polymorphism. Our algorithm improves over the ones already known in that it offers a better complexity bound: if a simple type derivation for the term t is given our algorithm performs EAL ⋆ type inference in polynomial time. 1
Complexity of strongly normalising λterms via nonidempotent intersection types
"... We present a typing system for the λcalculus, with nonidempotent intersection types. As it is the case in (some) systems with idempotent intersections, a λterm is typable if and only if it is strongly normalising. Nonidempotency brings some further information into typing trees, such as a bound o ..."
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Cited by 2 (0 self)
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We present a typing system for the λcalculus, with nonidempotent intersection types. As it is the case in (some) systems with idempotent intersections, a λterm is typable if and only if it is strongly normalising. Nonidempotency brings some further information into typing trees, such as a bound on the longest βreduction sequence reducing a term to its normal form. We actually present these results in Klop’s extension of λcalculus, where the bound that is read in the typing tree of a term is refined into an exact measure of the longest reduction sequence. This complexity result is, for longest reduction sequences, the counterpart of de Carvalho’s result for linear headreduction sequences.
Filter models: nonidempotent intersection types, orthogonality and polymorphism
"... This paper revisits models of typed λcalculus based on filters of intersection types: By using nonidempotent intersections, we simplify a methodology that produces modular proofs of strong normalisation based on filter models. Nonidempotent intersections provide a decreasing measure proving a key ..."
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Cited by 1 (1 self)
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This paper revisits models of typed λcalculus based on filters of intersection types: By using nonidempotent intersections, we simplify a methodology that produces modular proofs of strong normalisation based on filter models. Nonidempotent intersections provide a decreasing measure proving a key termination property, simpler than the reducibility techniques used with idempotent intersections. Such filter models are shown to be captured by orthogonality techniques: we formalise an abstract notion of orthogonality model inspired by classical realisability, and express a filter model as one of its instances, along with two termmodels (one of which captures a now common technique for strong normalisation). Applying the above range of model constructions to Currystyle System F describes at different levels of detail how the infinite polymorphism of System F can systematically be reduced to the finite polymorphism of intersection types.
A semantic measure of the execution time in Linear Logic
, 2007
"... We give a semantic account of the execution time (i.e. the number of cutelimination steps leading to the normal form) of an untyped MELL (proof)net. We first prove that: 1) a net is headnormalizable (i.e. normalizable at depth 0) if and only if its interpretation in the multiset based relational ..."
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We give a semantic account of the execution time (i.e. the number of cutelimination steps leading to the normal form) of an untyped MELL (proof)net. We first prove that: 1) a net is headnormalizable (i.e. normalizable at depth 0) if and only if its interpretation in the multiset based relational semantics is not empty and 2) a net is normalizable if and only if its exhaustive interpretation (a suitable restriction of its interpretation) is not empty. We then define a size on every experiment of a net, and we precisely relate the number of cutelimination steps of every stratified reduction sequence to the size of a particular experiment. Finally, we give a semantic measure of execution time: we prove that we can compute the number of cutelimination steps leading to a cut free normal form of the net obtained by connecting two cut free nets by means of a cut link, from the interpretations of the two cut free nets. These results are inspired by similar ones obtained by the first author for the (untyped) lambdacalculus. 1
A Semantic Measure of the Execution Time in Linear Logic
"... We give a semantic account of the execution time (i.e. the number of cut elimination steps leading to the normal form) of an untypedMELL net. We first prove that: 1) a net is headnormalizable (i.e. normalizable at depth 0) if and only if its interpretation in the multiset based relational semantics ..."
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We give a semantic account of the execution time (i.e. the number of cut elimination steps leading to the normal form) of an untypedMELL net. We first prove that: 1) a net is headnormalizable (i.e. normalizable at depth 0) if and only if its interpretation in the multiset based relational semantics is not empty and 2) a net is normalizable if and only if its exhaustive interpretation (a suitable restriction of its interpretation) is not empty. We then give a semantic measure of execution time: we prove that we can compute the number of cut elimination steps leading to a cut free normal form of the net obtained by connecting two cut free nets by means of a cut link, from the interpretations of the two cut free nets. These results are inspired by similar ones obtained by the first author for the untyped lambdacalculus.