Why are polymorphic values not inferred in Haskell?

Question

Numeric literals have a polymorphic type:

*Main> :t 3 3 :: (Num t) => t 

But if I bind a variable to such a literal, the polymorphism is lost:

x = 3 ... *Main> :t x x :: Integer 

If I define a function, on the other hand, it is of course polymorphic:

f x = 3 ... *Main> :t f f :: (Num t1) => t -> t1 

I could provide a type signature to ensure the x remains polymorphic:

x :: Num a => a x = 3 ... *Main> :t x x :: (Num a) => a 

But why is this necessary? Why isn't the polymorphic type inferred?

Answer 1

It's the monomorphism restriction which says that all values, which are defined without parameters and don't have an explicit type annotation, should have a monomorphic type. This restriction can be disabled in ghc and ghci using -XNoMonomorphismRestriction.

The reason for the restriction is that without this restriction long_calculation 42 would be evaluated twice, while most people would probably expect/want it to only be evaluated once:

longCalculation :: Num a => a -> a longCalculation = ...  x = longCalculation 42  main = print $ x + x