Models of a Non-Associative Composition

Guillaume Munch-Maccagnoni 1, 2
2 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, Inria Paris-Rocquencourt, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique : UMR7126
Abstract : 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 Adj→Dupl where Dupl is a category of duploids and duploid functors, and Adj 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 a way of hiding the fact that composition is not always associative.
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Guillaume Munch-Maccagnoni. Models of a Non-Associative Composition. FOSSACS 2014 - 17th International Conference on Foundations of Software Science and Computation Structures, Apr 2014, Grenoble, France. pp.396-410, ⟨10.1007/978-3-642-54830-7_26⟩. ⟨hal-00996729⟩

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