A program derivation is said to be polytypic if some of its parameters are data types. Polytypic program derivations necessitate a general, non-inductive deenition of`data type'. Here we propose such a dee-nition: a data type is a relator that has membership. It is shown how this deenition implies various other properties that are shared by all data types. In particular, all data types have a u...

with the property that for any pair r, s of elements of R either r = s or there is very little free cancellation in forming the product rs. The classical example of such a group is the fundamental group of a closed orientable 2-manifold of genus k. The study of this group has given rise both to the theory of one-relator groups, initiated by Magnus ([3]), and to the theory of small cancellation ...