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Finite semantics of polymorphism, complexity and the power of type fixpoints

Abstract : Many applications of denotational semantics, such as higher-order model checking or the complexity of normaliza-tion, rely on finite semantics for monomorphic type systems. We present two constructions of finite semantics for second-order Multiplicative-Additive Linear Logic (MALL2) and study their properties. We apply this to understand the gap in expressive power between MALL2 and its extension with type fixpoints, and to obtain an implicit characterization of regular languages in Elementary Linear Logic. Furthermore, some semantic results established here lay the groundwork for a sequel paper proposing a new approach to sub-polynomial implicit complexity.
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https://hal.archives-ouvertes.fr/hal-01979009
Contributor : Lê Thành Dũng Nguyễn <>
Submitted on : Saturday, January 12, 2019 - 12:05:52 PM
Last modification on : Thursday, June 18, 2020 - 12:46:02 PM
Long-term archiving on: : Saturday, April 13, 2019 - 12:39:40 PM

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  • HAL Id : hal-01979009, version 1

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Lê Thành Dũng Nguyễn, Thomas Seiller, Paolo Pistone, Lorenzo Tortora de Falco. Finite semantics of polymorphism, complexity and the power of type fixpoints. 2019. ⟨hal-01979009⟩

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