[Haskell-cafe] Extending Type Classes

[Henning Thielemann]

  The problem of refinement of type classes annoys me from time to time 
when I work on the NumericPrelude. It is an experimental type class 
hierarchy for mathematical types. Sometimes a new data type T shall be 
implemented and it turns out that you can implement only a part of all 
methods of a certain class. Then a natural step is to split the class into 
two classes A and B: 'A' contains the methods we can implement for T and 
'B' contains the remaining methods and 'B' is a sub-class of 'A'.
  First, this means that all client code has to be rewritten. Second, code 
for instances becomes very lengthy, because over the time code tends to 
contain one instances for every method. However the many small instances 
actually carry information: Every instance has its specialised 
constraints. E.g. you would certainly try to use only Applicative 
constraints in an Applicative instance and not Monad constraints. However, 
if there is a way to define Applicative and Monad instances in one go, the 
Applicative instance may get Monad constraints.