Why context is not considered when selecting typeclass instance in Haskell?

Question

I understand that when having

instance (Foo a) => Bar a
instance (Xyy a) => Bar a

GHC doesn\'t consider the contexts, and the instanc

Answer 1

Adding backtracking would make instance resolution require exponential time, in the worst case.

Essentially, instances become logical statements of the form

P(x) => R(f(x)) /\ Q(x) => R(f(x))

which is equivalent to

(P(x) \/ Q(x)) => R(f(x))

Computationally, the cost of this check is (in the worst case)

c_R(n) = c_P(n-1) + c_Q(n-1)

assuming P and Q have similar costs

c_R(n) = 2 * c_PQ(n-1)

which leads to exponential growth.

To avoid this issue, it is important to have fast ways to choose a branch, i.e. to have clauses of the form

((fastP(x) /\ P(x)) \/ (fastQ(x) /\ Q(x))) => R(f(x))

where fastP and fastQ are computable in constant time, and are incompatible so that at most one branch needs to be visited.

Haskell decided that this "fast check" is head compatibility (hence disregarding contexts). It could use other fast checks, of course -- it's a design decision.