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Abstract: Most often, in a categorical semantics for a programming language, thesubstitution of terms is expressed by composition and finite products. Howeverthis does not deal with the order of evaluation of arguments, which may havemajor consequences when there are side-effects. In this paper Cartesian effectcategories are introduced for solving this issue, and they are compared withstrong monads, Freyd-categories and Haskell-s Arrows. It is proved that aCartesian effect category is a Freyd-category where the premonoidal structureis provided by a kind of binary product, called the sequential product. Theuniversal property of the sequential product provides Cartesian effectcategories with a powerful tool for constructions and proofs. To our knowledge,both effect categories and sequential products are new notions.



Author: Jean-Guillaume Dumas LJK, Dominique Duval LJK, Jean-Claude Reynaud RC

Source: https://arxiv.org/







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