A new theory of data types which allows for the definition of types as initial algebras of certain functors Fam(C) → Fam(C) is presented. This theory, which we call positive inductive-recursive definitions, is a generalisation of Dybjer and Setzer’s theory of inductive-recursive definitions within which C had to be discrete — our work can therefore be seen as lifting this restriction. This is a...

representations of contexts, recall, assign specific values to variables (§3.3.6). This includes the standards variable s. Hence the inductive premise is false given any abstract context c. (For instance, if we assume a context c1 such that sc1(rich) = 100, then n = 99 provides a counterinstance: x99’s degree of wealth isn’t at least as great as the degree standard of richness in c1, but x100’s...

BACKGROUND AND AIMS Survival of many herbaceous species in Mediterranean habitats during the dry, hot summer depends on the induction of summer dormancy by changes in environmental conditions during the transition between the winter (growth) season to the summer (resting) season, i.e. longer days, increasing temperature and drought. In Poa bulbosa, a perennial geophytic grass, summer dormancy i...