February 2017
Appeared at ICFP 2017
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.
@inproceedings{Elliott-2017-compiling-to-categories,
author = {Conal Elliott},
title = {Compiling to categories},
booktitle = {Proceedings of the ACM on Programming Languages (ICFP)},
year = {2017},
url = {http://conal.net/papers/compiling-to-categories}
}