An Inverse Limit Construction of a Domain of Infinite Lists

A domain of infinite lists is constructed by taking the inverse limit of a chain of finite list domains ordered by projection. The resulting space, called L infinity, is shown to be a complete partial order. Its use as a semantic domain for non-terminating programs is illustrated. Infinite lists arise when we want to give meaning to non-terminating, yet answer producing, programs. In applicative languages lazy evaluation enables infinite objects to be progressively computed. Precise formulation of infinite lists is necessary for formal reasoning of such programs.