Compiling to Categories

It is well-known that the simply typed lambda-calculus is modeled by any cartesian closed category (CCC). This correspondence suggests giving typed functional programs a variety of interpretations, each corresponding to a different category. A convenient way to realize this idea is as a collection of meaning-preserving transformations added to an existing compiler, such as GHC for Haskell. This paper describes such an implementation and demonstrates its use for a variety of interpretations including hardware circuits, automatic differentiation, incremental computation, and interval analysis. Each such interpretation is a category easily defined in Haskell (outside of the compiler). The general technique appears to provide a compelling alternative to deeply embedded domain-specific languages.