Linear Dependent Types in a Call-by-Value Scenario

Ugo Dal Lago 1, 2 Barbara Petit 3
2 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
Abstract : Linear dependent types allow to precisely capture both the extensional behavior and the time complexity of λ-terms, when the latter are evaluated by Krivine's abstract machine. In this work, we show that the same paradigm can be applied to call-by-value computation. A system of linear dependent types for Plotkin's PCF is introduced, called dlPCFv whose types reflect the complexity of evaluating terms in the so-called CEK machine. dlPCFv is proved to be sound, but also relatively complete: every true statement about the extensional and intentional behavior of terms can be derived, provided all true index term inequalities can be used as assumptions.
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https://hal.inria.fr/hal-00909317
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Submitted on : Tuesday, November 26, 2013 - 10:46:37 AM
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Ugo Dal Lago, Barbara Petit. Linear Dependent Types in a Call-by-Value Scenario. Science of Computer Programming, Elsevier, 2013, ⟨10.1016/j.scico.2013.07.010⟩. ⟨hal-00909317⟩

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