Light types for polynomial time computation in lambda calculus

We present a polymorphic type system for lambda calculus ensuring that well-typed programs can be executed in polynomial time: dual light affine logic (DLAL). DLAL has a simple type language with a linear and an intuitionistic type arrow, and one modality. It corresponds to a fragment of light affin...

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Bibliographic Details
Published in:Information and computation Vol. 207; no. 1; pp. 41 - 62
Main Authors: Baillot, Patrick, Terui, Kazushige
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 2009
Elsevier
Subjects:
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
General logic
Implicit computational complexity
Lambda calculus
Light linear logic
Linear logic
Logic and foundations
Mathematical logic, foundations, set theory
Mathematics
Miscellaneous
Polynomial time complexity
Programming theory
Sciences and techniques of general use
Theoretical computing
Type system
Light linear logic
Linear logic
Type system
Polynomial time complexity
Lambda calculus
Implicit computational complexity
Polynomial
Translation
Computer theory
Polynomial time
Polynomial function
Computation time
Proof
Logic
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:We present a polymorphic type system for lambda calculus ensuring that well-typed programs can be executed in polynomial time: dual light affine logic (DLAL). DLAL has a simple type language with a linear and an intuitionistic type arrow, and one modality. It corresponds to a fragment of light affine logic (LAL). We show that contrarily to LAL, DLAL ensures good properties on lambda-terms (and not only on proof-nets): subject reduction is satisfied and a well-typed term admits a polynomial bound on the length of any of its beta reduction sequences. We also give a translation of LAL into DLAL and deduce from it that all polynomial time functions can be represented in DLAL.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2008.08.005