The strict state-transformer monad. A computation of type ST s a transforms an internal state indexed by s, and returns a value of type a. The s parameter is either

• an uninstantiated type variable (inside invocations of runST), or
• RealWorld (inside invocations of stToIO).

It serves to keep the internal states of different invocations of runST separate from each other and from invocations of stToIO.

The >>= and >> operations are strict in the state (though not in values stored in the state). For example,

runST (writeSTRef _|_ v >>= f) = _|_

Return the value computed by a state transformer computation. The forall ensures that the internal state used by the ST computation is inaccessible to the rest of the program.

Allow the result of a state transformer computation to be used (lazily) inside the computation. Note that if f is strict, fixST f = _|_.

RealWorld is deeply magical. It is primitive, but it is not unlifted (hence ptrArg). We never manipulate values of type RealWorld; it's only used in the type system, to parameterise State#.

A monad transformer embedding strict state transformers in the IO monad. The RealWorld parameter indicates that the internal state used by the ST computation is a special one supplied by the IO monad, and thus distinct from those used by invocations of runST.