We characterise the polarised evaluation order through a categorical structure where the hypothesis that composition is associative is relaxed. Duploid is the name of the structure, as a reference to Jean-Louis Loday’s duplicial algebras. The main result is a reflection Open image in new window where Open image in new window is a category of duploids and duploid functors, and Open image in new window is the category of adjunctions and pseudo maps of adjunctions. The result suggests that the various biases in denotational semantics: indirect, call-by-value, call-by-name... are ways of hiding the fact that composition is not always associative.


Natural Transformation Linear Logic Direct Model Denotational Semantic Lambda Calculus 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Guillaume Munch-Maccagnoni
    • 1
  1. 1.Sorbonne Paris Cité, PPS, UMR 7126 CNRS, PiR2, INRIA Paris-RocquencourtUniv Paris DiderotParisFrance

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