Abstract

We are convinced that in a treatment of part ial functions and convergence of computations it is convenient to have an intuitionist 's mind. This conviction comes from the development of the abstract theory for categories of part ial maps. It was begun by Eilenberg & Kelly [1966], but it laid forgotten for a long while. The idea was then brought back to life by the new approach to Scott domains of Plotkin [1986] which concurred with a renewed approach to the categorical theory for part ial maps (see those references listed in the bibliography with either ~partiat or dominical in their title). In particular~ the author's D.Phil. thesis (Rosolini [1986]) shows how to represent any (essentially small) category of part ial maps in a suitable topos.

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