This paper describes the polytypic functions in PolyLib, motivates their presence in the library, and gives a rationale for their design. Thus we hope to share our experience with other researchers in the field. We will assume the reader has some familiarity with the field of polytypic programming. Of course, a library is an important part of a programming language. Languages like Java, Delphi, Perl and Haskell are popular partly because of their useful and extensive libraries. For a polytypic programming language it is even more important to have a clear and well-designed library: writing polytypic programs is difficult, and we do not expect many programmers to write polytypic programs. On the other hand, many programmers use polytypic pro...