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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Models of a Non-associative Composition
verfasst von : Guillaume Munch-Maccagnoni
Erschienen in: Foundations of Software Science and Computation Structures
Verlag: Springer Berlin Heidelberg
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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
where
is a category of duploids and duploid functors, and
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.