Haskell: map runST

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I have a binding for a type [ST s (Int, [Int])] and I am trying to apply runST to each element using map as follows:

name :: [ST s (Int, [Int])] --Of Course there is a real value here
map runST name

This gives me an error message

Couldn't match expected type `forall s. ST s b0'
    with actual type `ST s0 (Int, [Int])'
Expected type: [forall s. ST s b0]
  Actual type: [ST s0 (Int, [Int])]
In the second argument of `map', namely `name'
In the expression: map runST name

There must be something I am misunderstanding. I am aware of runST and function composition, but am unsure if this applies.

Thanks for everyones time!

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