In this wikipedia article on Turing Completeness it states that:
The untyped lambda calculus is Turing complete, but many typed lambda calculi, including System F, are not. The value of typed systems is based in their ability to represent most typical computer programs while detecting more errors.
What is an example of a total computable function that is uncomputable by system F?
In addition, since hindley-milner is:
A restriction of System F
because of the fact that:
type checking is undecidable for a Curry-style variant of System F, that is, one that lacks explicit typing annotations.
Does this mean that the lambda calculus underlying hindley-milner type systems is not turing complete as well?
If this is true, since haskell is clearly turing complete and we know that it's basis is the lambda calculus and the hindley-milner type system, what features that are not present in the lambda calculus are added in order to make haskell turing complete?