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We introduce a new class of abstract structures, which we call generalizedultrametric semilattices, and in which the meet operation of the semilatticecoexists with a generalized distance function in a tightly coordinated way. Weprove a constructive fixed-point theorem for strictly contracting functions ondirected-complete generalized ultrametric semilattices, and introduce acorresponding induction principle. We cite examples of application in thesemantics of logic programming and timed computation, where, until now, theonly tool available has been the non-constructive fixed-point theorem ofPriess-Crampe and Ribenboim for strictly contracting functions on sphericallycomplete generalized ultrametric semilattices.

The Fixed-Point Theory of Strictly Contracting Functions on Generalized Ultrametric Semilattices