[TYPES] CPO semantics of recursive types

[Malcolm Tyrrell]

Hello,

I have a question concerning the denotational semantics of
recursive types using complete partial orders.

For a programming language, the domain for a function type T->U is
defined as the space of all continuous functions from the domain of T
to the domain of U. I understand that recursively defined domains
have solutions in this semantics.

I am working with a specification language, and the domains I'm using
for function types T->U is the space of all *monotonic* functions from
the domain of T to the domain of U. Can anyone tell me (or even better,
point me to a reference) whether this has any ramifications for the
existence of recursively defined domains?

Thanks for any help,

Malcolm.