Writing your functions/methods without side effects - so they're pure functions - makes it easier to reason about the correctness of your program.
It also makes it easy to compose those functions to create new behaviour.
It also makes certain optimisations possible, where the compiler can for instance memoise the results of functions, or use Common Subexpression Elimination.
Edit: at Benjol's request: Because a lot of your state's stored in the stack (data flow, not control flow, as Jonas has called it here), you can parallelise or otherwise reorder the execution of those parts of your computation that are independent of each other. You can easily find those independent parts because one part doesn't provide inputs to the other.
In environments with debuggers that let you roll back the stack and resume computing (like Smalltalk), having pure functions means that you can very easily see how a value changes, because the previous states are available for inspection. In a mutation-heavy calculation, unless you explicitly add do/undo actions to your structure or algorithm, you cannot see the history of the computation. (This ties back to the first paragraph: writing pure functions makes it easier to inspect the correctness of your program.)
I actually think that return type polymorphism is one of the best features of type classes. After having used it for a while, it is sometimes hard for me to go back to OOP style modeling where I don't have it.
Consider the encoding of algebra. In Haskell we have a type class Monoid (ignoring mconcat)
class Monoid a where
mempty :: a
mappend :: a -> a -> a
How could we encode this as an interface in an OO language? The short answer is we can't. That's because the type of mempty is (Monoid a) => a aka, return type polymorphism. Having the ability to model algebra is incredibly useful IMO.*
You start your post with the complaint about "Referential Transparency." This raises an important point: Haskell is a value oriented language. So expressions like read 3 don't have to be understood as things that compute values, they can also be understood as values. What this means is that the real issue is not return type polymorphism: it is values with polymorphic type ([] and Nothing). If the language should have these, then it really has to have polymorphic return types for consistency.
Should we be able to say [] is of type forall a. [a]? I think so. These features are very useful, and they make the language much simpler.
If Haskell had subtype polymorphism [] could be a subtype for all [a]. The problem is, that I don't know of a way of encoding that without having the type of the empty list be polymorphic. Consider how it would be done in Scala (it is shorter than doing it in the canonical statically typed OOP language, Java)
abstract class List[A]
case class Nil[A] extends List[A]
case class Cons[A](h: A. t: List[A]) extends List[A]
Even here, Nil() is an object of type Nil[A] **
Another advantage of return type polymorphism is that it makes the Curry-Howard embedding much simpler.
Consider the following logical theorems:
t1 = forall P. forall Q. P -> P or Q
t2 = forall P. forall Q. P -> Q or P
We can trivially capture these as theorems in Haskell:
data Either a b = Left a | Right b
t1 :: a -> Either a b
t1 = Left
t2 :: a -> Either b a
t2 = Right
To sum up: I like return type polymorphism, and only think it breaks referential transparency if you have a limited notion of values (although this is less compelling in the ad hoc type class case). On the other hand, I do find your points about MR and type defaulting compelling.
*. In the comments ysdx points out this isn't strictly true: we could re-implement type classes by modeling the algebra as another type. Like the java:
abstract class Monoid<M>{
abstract M empty();
abstract M append(M m1, M m2);
}
You then have to pass objects of this type around with you. Scala has a notion of implicit parameters which avoids some, but in my experience not all, of the overhead of explicitly managing these things. Putting your utility methods (factory methods, binary methods, etc) on a separate F-bounded type turns out to be an incredibly nice way of managing things in an OO language that has support for generics. That said, I'm not sure I would have groked this pattern if I didn't have experience modeling things with typeclasses, and I'm not sure other people will.
It also has limitations, out of the box there is no way to get an object that implements the typeclass for an arbitrary type. You have to either pass the values explicitly, use something like Scala's implicits, or use some form of dependency injection technology. Life gets ugly. On the other hand, it is nice that you can have multiple implementations for the same type. Something can be a Monoid in multiple ways. Also, carrying around these structures separately has IMO a more mathematically modern, constructive, feel to it. So, although I still generally prefer the Haskell way of doing this, I probably overstated my case.
Typeclasses with return type polymorphism makes this kind of thing easy to handle. That doesn't meen it is the best way to do it.
**. Jörg W Mittag points out this isn't really the canonical way of doing this in Scala. Instead, we would follow the standard library with something more like:
abstract class List[+A] ...
case class Cons[A](head: A, tail: List[A]) extends List[A] ...
case object Nil extends List[Nothing] ...
This takes advantage of Scala's support for bottom types, as well as covariant type paramaters. So, Nil is of type Nil not Nil[A]. At this point we are pretty far from Haskell, but it is interesting to note how Haskell represents the bottom type
undefined :: forall a. a
That is, it isn't the subtype of all types, it is polymorphically(sp) a member of all types.
Yet more return type polymorphism.
Best Answer
Let's begin with a definition for referential transparency:
What that means is that (for example) you can replace 2 + 5 with 7 in any part of the program, and the program should still work. This process is called substitution. Substitution is valid if, and only if, 2 + 5 can be replaced with 7 without affecting any other part of the program.
Let's say that I have a class called
Baz, with the functionsFooandBarin it. For simplicity, we'll just say thatFooandBarboth return the value that is passed in. SoFoo(2) + Bar(5) == 7, as you would expect. Referential Transparency guarantees that you can replace the expressionFoo(2) + Bar(5)with the expression7anywhere in your program, and the program will still function identically.But what if
Fooreturned the value passed in, butBarreturned the value passed in, plus the last value provided toFoo? That's easy enough to do if you store the value ofFooin a local variable within theBazclass. Well, if the initial value of that local variable is 0, the expressionFoo(2) + Bar(5)will return the expected value of7the first time you invoke it, but it will return9the second time you invoke it.This violates referential transparency two ways. First, Bar can not be counted on to return the same expression each time it is called. Second, a side-effect has occurred, namely that calling Foo influences the return value of Bar. Since you can no longer guarantee that
Foo(2) + Bar(5)will equal 7, you can no longer substitute.This is what Referential Transparency means in practice; a referentially transparent function accepts some value, and returns some corresponding value, without affecting other code elsewhere in the program, and always returns the same output given the same input.