Gödel's system T revisited

Authors:
Sandra Alves;Maribel Fernández;Mário Florido;Ian Mackie
Affiliations:
LIACC - University of Porto, R. do Campo Alegre 1021/1055, 4169-007, Porto, Portugal;Kings College London, Department of Computer Science, Strand, London WC2R 2LS, UK;LIACC - University of Porto, R. do Campo Alegre 1021/1055, 4169-007, Porto, Portugal;LIX, CNRS UMR 7161, École Polytechnique, 91128 Palaiseau Cedex, France
Venue:
Theoretical Computer Science
Year:
2010

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Abstract

The linear lambda calculus, where variables are restricted to occur in terms exactly once, has a very weak expressive power: in particular, all functions terminate in linear time. In this paper we consider a simple extension with natural numbers and a restricted iterator: only closed linear functions can be iterated. We show properties of this linear version of Godel's Tusing a closed reduction strategy, and study the class of functions that can be represented. Surprisingly, this linear calculus offers a huge increase in expressive power over previous linear versions of T, which are 'closed at construction' rather than 'closed at reduction'. We show that a linear Twith closed reduction is as powerful as T.