In System F, what is the difference between the following 3 types: 
Reproduced in text here:
∀X.((X → X) → (X → X))
∀X.((X → X) → ∀X.(X → X))
((∀X.X → X) → (∀X.X → X))
Is the second one more general than the first?
Which is the difference between these polymorphic types?
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Depends on how tight
forallquantifier binds. Lets assume that it binds on next terminal expression (variable or()-block).The first will become
(X0 -> X0) -> (X0 -> X0)whereX0is a fresh type variable.The second will become
(X0 -> X0) -> forall X1. (X1 -> X1)whereX0andX1are fresh.The third -
(bot -> X) -> (bot -> X)whereXis the old binding and bot is the uninhabitedforall X. X.