Generic Haskell is an extension of Haskell that supports datatypegeneric programming. The central idea of Generic Haskell is to interpret a type by a function, the so-called instance of a generic function at that type. Since types in Haskell include parametric types such as 'list of', Generic Haskell represents types by terms of the simply-typed lambda calculus. This paper puts the idea of interpreting types as functions on a firm theoretical footing, exploiting the fact that the simply-typed...