Nested collections and polytypism

A point-free calculus of so-called ''collection types'' is presented, similar to the monadic calculus of http://www.cis.upenn.edu/~db/home.html. We observe that our calculus is parametrised by a monad thus making the calculus ''polytypic''. A novel contribution of the paper is to discuss situations in which a single application involves more than one collection type. In particular, we outline the contribution to database research that may be obtained by exploiting current developments in polytypic programming.