Linear dependent types were introduced recently 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.
Linear dependent types in a call-by-value scenario
DAL LAGO, UGO;
2014
Abstract
Linear dependent types were introduced recently 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.