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 @l-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 [email protected]?PCF"V, whose types reflect the complexity of evaluating terms in the CEK machine. [email protected]?PCF"V 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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