Mutability is attained by using the ST monad. The ST monad uses mutable memory, but since it does not allow other interactions with the outside world, its value can be extracted (unlike the IO monad). When you are done with the modification of the vector, it can be frozen to obtain a pure vector.
The IO monad can also be used, but not if you want to return a pure value.
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Yes. For example, the vector package provides mutable arrays:
http://hackage.haskell.org/package/vector-0.7.0.1
Mutability is attained by using the ST monad. The ST monad uses mutable memory, but since it does not allow other interactions with the outside world, its value can be extracted (unlike the IO monad). When you are done with the modification of the vector, it can be frozen to obtain a pure vector.
The IO monad can also be used, but not if you want to return a pure value.
A good tutorial can be found at:
http://www.haskell.org/haskellwiki/Numeric_Haskell:_A_Vector...
I used mutable vectors in the ST monad in maximum entropy training software, and they are really performant.
What blew my mind about the ST monad is that despite its promise of single-threading, it still allows for recursive division of labor.
I was like, "Wait. Wait. Waaaiiiitt. How does it do that?"