Abstract

category-theoretic accounts of these issues can be found in [Fio93, HJ95]. In type theory. In [CP92], Crole and Pitts introduced a higher-order typed predicate logic for fixed-point computations. This was done by exploiting Moggi's treatment of computations using monads [Mog91], and by introducing the key notion of fixpoint object . Fixpoint objects were partly inspired by Martin-Lof's non-standard "iteration type" [ML83], and give a categorical characterisation of general recursion at higher types similar to the characterisation of primitive recursion at higher types in terms of Lawvere's concept of natural number object [LS86]. A type-theoretic approach to domain theory is that of [Plo93]. There, rather than considering directly possible categorical structure, the idea is to work within a type theory pursuing the analogies: intuitionistic exponential = function space, and linear exponential = strict function space. More precisely, the basic setting is that of second-order intuition...

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