In Haskell, type classes can act like functions from types to terms. However, unlike for functions, there is no way for the programmer to ask the compiler to verify that classes pattern-match exhaustively on their arguments, and their usage must always be marked by a constraint even when they are exhaustive.

This paper introduces the notion of \emph{total type classes} and, more generally, \emph{total constraints}, which allow the programmer to describe a set of instances whose existence can be verified by inspecting the instance declarations of the class, instead of on a case-by-case basis when a specific instance is demanded. To achieve this functionality, our implementation records the missing constraints during typechecking and then modifies the typechecked program, rewriting it as though the programmer had included the constraints.