Under consideration for publication in J . Functional Programming 1 Container Types

A program derivation is said to be polytypic if some of its parameters are data types. Often these data types are container types, whose elements store data. Polytypic program derivations necessitate a general, non-inductive deenition of`container (data) type'. Here we propose such a deenition: a container type is a relator that has membership. It is shown how this deenition implies various other properties that are shared by all container types. In particular, all container types have a unique strength, and all natural transformations between container types are strong. Progress in a scientiic dicipline is readily equated with an increase in the volume of knowledge, but the true milestones are formed by the introduction of solid, precise and usable deenitions. Here you will nd the rst generic (`polytypic') deenition of the notion of`container type', a deenition that is remarkably simple and suitable for formal generic proofs (as is amply illustrated in the paper). Among the startling results is the proof that any lax natural transformation between two container types is strong.