Second order function formalization

Question

I need to work on a optimizer for a language whose operator are second order functions.

They are the well known ones filter, map, reduce, fold, foreach etc. etc.

I need to formalize as much as possible the language. I mean I would like to have at the end a description such this:

"Filter is function from this domain to that codomain, it has this and that properties, under some condition also this property holds"

Can you suggest me some publication/book where this work has been (at least partially) done?