8 August Bill Naylor title: "From Untyped to Polymorphically Typed Mathematical Web Services" abstract: In my talk, I shall describe the techniques that I have used to facilitate mathematical web services which use the Aldor Computer Algebra (CA) system as a back end. Aldor has advantages for use as a web service facilitator, including small footprint binaries and fast executables, unusual for CA systems. There are also disadvantages including the mismatch between the strongly typed polymorphic nature of its language and the necessarily untyped nature of communication protocols. I shall talk about how I have overcome this problem, and the techniques I have used to reduce the complexity of some of the algorithms I use. Finally I shall describe the web-based Service Manager I have implemented, and describe how I automatically create Mathematical Service Description Language (MSDL) documents for advertising the capabilities offered by the services.