Algèbre galactique, un procédé de calcul formel, relatif aux semi-fonctions, à l'inclusion et à l'égalité

Abstract : Universal algebra is one of the theoretical foundations of computer science. Nevertheless we cannot apply it directIy to reasoning about many mathematical objects (such as fields) or about most programs (because of exceptions) : we cannot consider any proper semi-function (partial function); we cannot distinguish any proper subset of the carrier. So we would like a more general theory. After having re-examined partial algebra and order-sorted algebra, each one being only a part of what is wished for, I have looked for and eventually discovered a broader calculus, G algebra, connected with equality (universal alg.), semi-functions (partial alg.), subsets and inclusion (order-sorted alg.). This calculus is a formallogic which has these characteristics: each term has a meaning (no nonsense); each item of information is coded as formula (not as a "declaration"); typing is proving (not parsing). And which has these properties: the logic is complete (completeness theorem); G algebra is a homogeneous, clean superset of universal algebra; in each class of models there are a free algebra and an initial algebra.
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Aristide Mégrelis. Algèbre galactique, un procédé de calcul formel, relatif aux semi-fonctions, à l'inclusion et à l'égalité. Autre [cond-mat.other]. Université Henri Poincaré - Nancy 1, 1990. Français. ⟨NNT : 1990NAN10396⟩. ⟨tel-01754373⟩

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