Abstract

: We establish sufficient and necessary conditions for a natural sink to be a colimit in DCPO. Based on these conditions we show how to construct a colimit for any functor F from a small category " into the category DCPO. This demonstrates that the category DCPO is cocomplete. We also investigate under what conditions the colimit object is algebraic. 0 Introduction Colimits play an important role in modeling subtyping relations. Given a domain of type names D, it is common to interpret it with a functor F from the domain D into the category DCPO, where F assigns to each type name the corresponding dcpo of semantic values. A subtyping relation type 1 <type 2 in D is interpreted as a continuous function from F(type 1 ) into F(type 2 ). It is reasonable to require that if we have a (directed) set of type names Q st. type Q is the lub of Q in D, then the dcpo corresponding to type Q should be the colimit of all the dcpos corresponding to type names in Q. Existence of arbitrary colimits ...

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