The Power of Linear Functions

  • Sandra Alves
  • Maribel Fernández
  • Mário Florido
  • Ian Mackie
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4207)


The linear lambda calculus is very weak in terms of expressive power: in particular, all functions terminate in linear time. In this paper we consider a simple extension with Booleans, natural numbers and a linear iterator. We show properties of this linear version of Gödel’s System \(\mathcal{T}\) and study the class of functions that can be represented. Surprisingly, this linear calculus is extremely expressive: it is as powerful as System \(\mathcal{T}\)


Linear Logic Lambda Calculus Closed Term Iterative Type Contraction Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sandra Alves
    • 1
  • Maribel Fernández
    • 2
  • Mário Florido
    • 1
  • Ian Mackie
    • 2
    • 3
  1. 1.Department of Computer Science & LIACCUniversity of PortoPortoPortugal
  2. 2.Department of Computer ScienceKing’s College LondonLondonU.K.
  3. 3.LIX, École PolytechniquePalaiseauFrance

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