Quotient Polymorphism

Abstract

Quotient types increase the power of type systems by allowing types to include equational properties. However, two key practical issues arise: code being duplicated, and valid code being rejected. Specifically, function definitions often need to be repeated for each quotient of a type, and valid functions may be rejected if they include subterms that do not respect the quotient. This article addresses these reusability and expressivity issues by introducing a notion of quotient polymorphism that we call choice polymorphism. We give practical examples of its use, develop the underlying theory, and implement it in Quotient Haskell.