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Syntactic Multicategories and Categorical Combinators for Linear Logic
, 1993
"... ) Eike Ritter Valeria de Paiva Computer Laboratory University of Cambridge 1 Introduction This paper contributes to the area of "categorical combinatory logic" or "categorical combinators", following the steps of Curien [Cur93] and Ritter [Rit92]. We provide a precise syntactic formulation of the n ..."
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) Eike Ritter Valeria de Paiva Computer Laboratory University of Cambridge 1 Introduction This paper contributes to the area of "categorical combinatory logic" or "categorical combinators", following the steps of Curien [Cur93] and Ritter [Rit92]. We provide a precise syntactic formulation of the notion of a multicategory (a recent reference is Lambek [Lam89]) and based on that we give categorical combinators for (multiplicative) Intuitionistic Linear Logic, following the general approach of Ritter for the Calculus of Constructions [Rit92]. Multicategories are usually thought of as "just like categories, except that instead of arrows A ! B one has multiarrows An ; : : : ; A 1 ! B". There is a wellknown correspondence between multicategories and (rudimentary) linear logic in such a way that a multimap f : An ; : : : ; A 1 ! B above corresponds to a term denoting a proof of B from the assumptions x i : A i . But the picture of a multicategory referred to above is lacking in two accou...
Categorical Logic
, 2001
"... This document provides an introduction to the interaction between category theory and mathematical logic which is slanted towards computer scientists. ..."
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This document provides an introduction to the interaction between category theory and mathematical logic which is slanted towards computer scientists.