Unique fixed points vs. least fixed points

AbstractThe aim of this paper is to compare two approaches to the semantics of programming languages: the least fixed point approach, and the unique fixed point approach. Briefly speaking, we investigate here the problem of existence of extensions of algebras with the unique fixed point property to ordered algebras with the least fixed point property, that preserve the fixed point solutions. We prove that such extensions always exist, the construction of a free extension is given. It is also shown that in some cases there is no ‘faithful’ extension, i.e. some elements of a carrier are always collapsed