Linear Dependent Types in a Call-by-Value Scenario

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.