[Haskell-cafe] One-way and two-way monads.

[Kwanghoon Choi]

Dear All,

List and IO are both monads when appropriate operations are defined. 

The IO monad, which is a one-way monad, does not have a function of
type IO a -> a, in general, except an unsafe function 
"unsafePerformIO :: IO a -> a". A two-way monad, such as List, has such 
a function "head :: [a] -> a".

My rough question is:
  Is there any intersting theory on the relationship between one-way monads
  and two-way monads? For example, a restriction on the IO monad would offer
  a *safe* "unsafePerformIO", and so the IO monad would become a two-way 
  monad. 

Does this question make sense at all?


Thanks in advance.

Kwanghoon Choi