Linear dependent types in a call-by-value scenario

International audienceLinear dependent types were introduced recently as a formal system that allows to precisely capture both the extensional behavior and the time com-plexity of λ-terms, when the latter are evaluated by Krivine's abstract ma-chine. 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 behaviour of terms can be derived, provided all true index term inequalities can be used as assumptions