A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely capture the functional behaviour of PCF programs (i.e. how the output relates to the input) but also some of their intensional properties, namely the complexity of evaluating them with Krivine's Machine. dlPCF is designed around dependent types and linear logic and is parametrized on the underlying language of index terms, which can be tuned so as to sacrifice completeness for tractability.
Linear Dependent Types and Relative Completeness / Ugo Dal Lago; Marco Gaboardi. - In: LOGICAL METHODS IN COMPUTER SCIENCE. - ISSN 1860-5974. - ELETTRONICO. - 8:4(2012), pp. 1-44. [10.2168/LMCS-8(4:11)2012]
Linear Dependent Types and Relative Completeness
DAL LAGO, UGO;
2012
Abstract
A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely capture the functional behaviour of PCF programs (i.e. how the output relates to the input) but also some of their intensional properties, namely the complexity of evaluating them with Krivine's Machine. dlPCF is designed around dependent types and linear logic and is parametrized on the underlying language of index terms, which can be tuned so as to sacrifice completeness for tractability.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
