Linearity in the Non-deterministic Call-by-Value Setting

  • Alejandro Díaz-Caro
  • Barbara Petit
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7456)


We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity present in such formalisms. After proving the subject reduction and the strong normalisation properties, we propose a translation of this calculus into the System F with pairs, which corresponds to a non linear fragment of linear logic. The translation provides a deeper understanding of the linearity in our setting.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alejandro Díaz-Caro
    • 1
  • Barbara Petit
    • 2
  1. 1.Université Paris 13, Sorbonne Paris Cité, LIPNVilletaneuseFrance
  2. 2.FOCUS (INRIA) – Università di BolognaItaly

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