  Sometimes systems of intuitionistic and constructive set theory have been presented with the natural numbers as a separate sort of urelements, that is, primitive objects with no elements (Friedman 1977;  Myhill 1975; Beeson 1985). Constructively, this is a natural choice which is in agreement with ideas expressed, for example, by Bishop (1967) (among others). In Bishop’s monograph the natural numbers are taken as a fundamental concept on which all the other mathematical concepts are based. From a technical point of view, if the natural numbers are taken as primitive and distinct from their set-theoretic representations, the axiom of infinity then takes the form: “there is a set of natural numbers (as urelements)”. A more general form of urelements in constructive set theories have been considered in (Cantini and Crosilla 2008). Here a variant of constructive set theory is proposed which combines  an intensional and partial notion of operation with CZF’s extensional notion of set  (see also Cantini and Crosilla 2010).