Linear Dependent Types and Relative Completeness

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...

Full description

Saved in:
Bibliographic Details
Published in:2011 IEEE 26th Annual Symposium on Logic in Computer Science pp. 133 - 142
Main Authors: Dal Lago, Ugo, Gaboardi, M.
Format: Conference Proceeding
Language:English
Published: IEEE 01.06.2011
Subjects:
Complexity theory
Context
implicit computational complexity
Indexes
lambda calculus
Polynomials
relative completeness
Semantics
type systems
Vegetation
ISBN:9781457704512, 145770451X
ISSN:1043-6871
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISBN:9781457704512
145770451X
ISSN:1043-6871
DOI:10.1109/LICS.2011.22