There is no magic here. This is merely explicit type specialization from the most general inferred type to something more specific. The denotational semantics of a function whose type is specialized does not change for those values belonging to the more specialized type. ``` f :: forall a. (Num a) => a -> a -> a f x y = x + y g :: Int -> Int -> Int g x y = x + y ```f and g denote (extensionally) the identical function, differing only in their type. g is a specialization of f. It is possible that (operationally) f could be slower if the compiler is not clever enough to avoid passing a type witness dictionary. ``` h :: forall b. b -> Char h = const 'a' k :: () -> Char k = const 'a' data Void m :: Void -> Char m = const 'a' n :: (forall a. a) -> Char n = const 'a' ```h, k, m, and n yield *identical* values for any input compatible with the type of any two of the functions. ``` ```In constrast, whether a function is strict or non-strict is *not* a function of type specialization. Strictness is not reflected in the type system. Compare: ``` u x y = y `seq` const x y v x y = const x y ```Both have type forall a b. a -> b -> a but are denotationally different functions: ``` u 2 undefined = undefined v 2 undefined = 2 Cristiano Paris wrote: ``````On Wed, Sep 16, 2009 at 7:12 PM, Ryan Ingram wrote: ``````Here's the difference between these two types: test1 :: forall a. a -> Int -- The caller of test1 determines the type for test1 test2 :: (forall a. a) -> Int -- The internals of test2 determines what type, or types, to instantiate the argument at `````` I can easily understand your explanation for test2: the type var a is closed under existential (?) quantification. I can't do the same for test1, even if it seems that a is closed under universal (?) quantification as well. ``````Or, to put it another way, since there are no non-bottom objects of type (forall a. a): `````` Why? ``````test1 converts *anything* to an Int. `````` Is the only possible implementation of test1 the one ignoring its argument (apart from bottom of course)? ``````test2 converts *nothing* to an Int -- type-correct implementation -- instantiates the (forall a. a) argument at Int test2 x = x `````` ``````-- type error, the caller chose "a" and it is not necessarily Int -- test1 x = x -- type-correct implementation: ignore the argument test1 _ = 1 `````` Cristiano _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@xxxxxxxxxxx http://www.haskell.org/mailman/listinfo/haskell-cafe `````` _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@xxxxxxxxxxx http://www.haskell.org/mailman/listinfo/haskell-cafe ```