This paper deals with formalizations and verifications in type theory that are abstracted with respect to a class of datatypes; i.e polytypic constructions. The main advantage of these developments are that they can not only be used to define functions in a generic way but also to formally state polytypic theorems and to synthesize polytypic proof objects in a formal way. This opens the door to mechanically proving many useful facts about large classes of datatypes once and for all.

• polytypic.ps