Linear dependent types in a call-by-value scenario.

Abstract: 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 -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 is introduced, called , whose types reflect the complexity of evaluating terms in the machine. 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. [Copyright &y& Elsevier]