Finite Vector Spaces as Model of Simply-Typed Lambda-Calculi

  • Benoît Valiron
  • Steve Zdancewic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8687)


In this paper we use finite vector spaces (finite dimension, over finite fields) as a non-standard computational model of linear logic. We first define a simple, finite PCF-like lambda-calculus with booleans, and then we discuss two finite models, one based on finite sets and the other on finite vector spaces. The first model is shown to be fully complete with respect to the operational semantics of the language. The second model is not complete, but we develop an algebraic extension of the finite lambda calculus that recovers completeness. The relationship between the two semantics is described, and several examples based on Church numerals are presented.


Vector Space Operational Semantic Linear Logic Algebraic Extension Lambda Calculus 
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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Benoît Valiron
    • 1
  • Steve Zdancewic
    • 2
  1. 1.PPS, UMR 7126, Univ Paris Diderot, Sorbonne Paris CitéParisFrance
  2. 2.University of PennsylvaniaPhiladelphiaUS

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