Why isn't Validation a Monad?

Question

an example use case:

def div2(i: Int): Validation[String, Int] = 
    if (i%2 == 0) Validation.success(i/2)
    else Validation.failure(\"odd\")

def div4(i:         


        

Answer 1

The issue is that the applicative functor as implied by the monad does not equal the actual applicative functor

Answer 2

As discussed in the Scalaz group, the problem seems to be that ap would accumulate errors whereas (pseudo-)monadic composition would only operate on the value part of Validation.

Therefore, one cannot be expressed in terms of the other and thus no monad instance exists for Validation.