Abstract

. We investigate a calculus with positive inductive and coinductive types , which we call ¯; , using logical relations. We show that parametric theories have the strong categorical properties, that the representable functors and natural transformations have the expected properties. Finally we apply the theory to show that terms of functorial type are almost canonical and that monotone inductive definitions can be reduced to positive in some cases. 1 Introduction We investigate a calculus with positive inductive and coinductive types, which we call ¯; , using logical relations. Here ¯ is used to construct the usual datatypes as initial algebras, where -types are used for lazy types as terminal coalgebras. A calculus related to ¯; has for example been investigated by Geuvers [Geu92], but he does not consider nested ¯-types. Loader introduces the strictly positive fragment (and only ¯-types) in [Loa97] and shows that the theory of the PER model is maximal consistent. The restr...

Citations

112	A logic for parametric polymorphism - Plotkin, Abadi - 1993
5	The !+1 -rule - Buchholz - 1981