Linear dependent types in a call-by-value scenario

Linear dependent types were introduced recently (Dal Lago and Gaboardi, 2012) [26] as a formal system that allows 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 pa...

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Vydáno v:	Science of computer programming Ročník 84; s. 77 - 100
Hlavní autoři:	Dal Lago, Ugo, Petit, Barbara
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier B.V 01.05.2014 Elsevier
Témata:	Cognitive science Complexity analysis Computer science Implicit computational complexity Linear logic Type systems Linear logic Complexity analysis Type systems Implicit computational complexity
ISSN:	0167-6423, 1872-7964
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Shrnutí:	Linear dependent types were introduced recently (Dal Lago and Gaboardi, 2012) [26] as a formal system that allows 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 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. •A type system for complexity analysis of higher-order functional programs.•Extend previous, related, work to an applied, call-by-value, lambda-calculus.•The type system is not only sound, but relatively complete.•We provide fully-developed nontrivial examples of complexity analyses.
ISSN:	0167-6423 1872-7964
DOI:	10.1016/j.scico.2013.07.010