Partial type constructors in practice

Abstract

Type constructors in functional programming languages are total: a Haskell programmer can equally readily construct lists of any element type. In practice, however, not all applications of type constructors are equally sensible: collections may only make sense for orderable elements, or embedded DSLs might only make sense for serializable return types. Jones et al. proposed a theory of partial type constructors, which guarantees that type applications are sensible, and extends higher-order abstractions to apply equally well to partial and total type constructors. This paper evaluates the practicality of partial type constructors, in terms of both language design and implementation. We extend GHC, the most widely used Haskell compiler, with support for partial type constructors, and test our extension on the compiler itself and its libraries. We show that introducing partial type constructors has a minimal impact on most code, but raises important questions in language and library design.