Functional programming and mathematical objects

We discuss the application of the Haskell/Gofer type classes and constructor classes to the implementation and teaching of the manipulation techniques in the domain of formal mathematical expressions. We show also how the lazy evaluation paradigms simplify the construction and the presentation of several algorithms dealing with iterative data types, such as power series or formal Pade expansion. We shown the. application of higher order functions to algebra and geometry, and specifically - to the construction of parametric surfaces.