Lawvere theories

mixphix:

The laws aren’t always so tightly coupled to the signature

What I meant by coupled is: Just by looking at the constructors of EqLaw alone one can not learn how many operations there are in Eq and what their aritites are. You need to look at how the constructors are used in lawful. Yet I agree that Lawvere’s way is far too complicated to be practically useful for Haskell type class hierarchies. I actually do not know whether Lawvere came up with this just for descriptive purposes or whether something genuinely new arose out of it.