Why do all Haskell typeclasses have laws?

Question

All the typeclasses in Typeclassopedia have associated laws, such as associativity or commutativity for certain operators. The definition of a \"law\" seems to be a constraint t

Answer 1

Yes and no. For instance the Show class does not have any laws associated with it, and it is certainly useful.

However, typeclasses express interfaces. An interface needs to satisfy more than being just a bunch of functions - you want these functions to fulfill a specification. The specification is normally more complicated than what can be expressed in Haskell's type system. For example, take the Eq class. It only needs to provide us with a function, the type of which has to be a -> a -> Bool. That's the most that Haskell's type system will allow us to require from an instance of an Eq type. However, we would normally expect more from this function - you would probably want it to be an equivalence relation (reflexive, symmetric and transitive). So then you state these requirements as separate "laws".