It is well known that type classes in Haskell are open. A user may at any time extend a visible type class by providing a new instance. There are situations where such an extensibility is undesirable. We may want to prevent the user from adding an instance to our class for some specific type -- or for all types (except some finite set of types). This messages shows that this problem is solvable in Haskell with common extensions. The code in this message has been tested with GHC 6.2.1, GHC 6.3.20041106 snapshot, and Hugs -98 (Nov 2003). We first discuss the problem of excluding specific ground types from a type class. That problem easily reduces to the one of defining a class that has no instances and cannot have ones. We then describe excluding non-ground types in the presence of overlapping (and perhaps, incoherent) instance extensions. The latter solution shows how to close a class -- that is, preclude adding any further instances to it. Completely closing the class has a price to pay: the principal type of an expression that involves closed class methods exists and _can_ be inferred -- but cannot be explicitly written. The essence of the technique can be expressed by a well-known phrase How to replace failure by a [long...] list of successes On Thu Nov 11 10:57:42 EST 2004 Ben Rudiak-Gould wrote on Haskell Cafe:
Except how would you prevent the user from declaring an instance for PrivateState RealWorld? Oh well.
Let us indeed consider preventing the user from declaring an instance of our class for a specific ground type. The answer is simple: we declare that instance ourselves. But we make that instance _statically_ unusable. Here's a simple example:
{-# OPTIONS -fglasgow-exts #-} {-# OPTIONS -fallow-undecidable-instances #-}
module C1 where
class C a where op:: a -> String instance C Int where op x = show x instance C Char where op x = "char"
Suppose we wish to define two instances of that class, C Int and C Char, and prevent the user from declaring an instance of C for a string. So, we define that instance ourselves:
instance Fail String => C String where op = error "thou shall not be"
class Fail a
test1 = op (1::Int) test2 = op 'z' --test3 = op "str"
Here class Fail has no instances (we shall discuss how to guarantee that in a moment). If we uncomment out the test3 line, we get a type error. Thus we have reduced the problem of excluding certain types from a typeclass to the problem of excluding all types from one particular typeclass: Fail. How can we prevent the user from adding instances to Fail? Again, we define the most general instance the class Fail may have:
instance Fail [a] => Fail a
If the test3 line stays commented out, the code typechecks and test1 and test2 work as expected. However, if we now uncomment the test3 line, we get the truly impressive type error message (I like the way it looks in Hugs). If overlapping instances extension is off, any attempt to add another instance to class Fail will be rejected by the compiler, because it will be overlapping with our general instance. Let us now turn to a more complex problem of the exclusion of non-ground types in the presence of overlapping instances. For example, suppose we wish to prevent any instances of class C for lists of any type. If overlapping instances are allowed, writing instance Fail [a] => C [a] will not do us much good, because the user may still introduce "instance C [Int]" for specific ground types like Int. Although overlapping (let alone incoherent) instance extensions seem to be quite permissive, there is still a law they must obey: the law of functional dependencies. That law lets us effectively close a class. Indeed, functional dependencies are already a tool to semi-close a class, to disallow a broad subset of instances (the ones that fail the dependency). Our solution requires adding a dummy type parameter to the type class. Note that the signatures of class methods are not affected.
{-# OPTIONS -fglasgow-exts #-} {-# OPTIONS -fallow-undecidable-instances #-} {-# OPTIONS -fallow-overlapping-instances #-} {-# OPTIONS -fallow-incoherent-instances #-}
We activate all extensions
module C2 (C(..)) where
data Private a -- NOT exported
class C a b | a->b where op:: a -> String instance C Int (Private Int) where op x = show x instance C Char (Private Char) where op x = "char" test1 = op (1::Int) test2 = op 'z'
Here we add a dummy class parameter 'b'. Note that the method signature remains the same -- and so all the uses of the method. To preclude the instantiation of the class for any list, we make the instance ourselves:
instance C [[a]] (Private [[a]]) => C [a] (Private [a]) where op = error "thou shall not be"
The user may try to add a new instance, say instance C [Int] ??? but what can he put instead of ??? Functional dependencies leave *only* one choice: (Private [Int]) -- but the type constructor Private is not exported from C2 and not available. So, effectively the user is prevented from adding any instance of class C for a list of any type -- and the one instance there is, is statically unusable. We can see that if we try to evaluate `op "str"'. We get even more spectacular type error. We can extend that idea to completely close the class C to any new instances -- whatever they may be. We merely need to add to our module C2:
instance C [a] (Private [a]) => C a (Private a) where op = error "thou shall not be"
The class is closed. But there is a price to pay. We can write
module C3 where import C2
test4 x = op x ++ "abc"
We can evaluate "test4 'c'", we can get the compiler to infer the principal type for test4 and to show it to us *C3> :t test4 test4 :: forall a. (C a (C2.Private a)) => a -> [Char] but we cannot write that type signature ourselves, because the type constructor C2.Private is not exported. If we wish to give test4 signature, we must use particular instantiations of class C, e.g., "test4:: Int -> String"