[Haskell-beginners] type class question

[Ben]

dear haskellers --

this email is an (il)literate haskell file.

suppose i have class of computations a -> State s b.  for
concreteness, let's say i'm writing a library of on-line statistical
summary functions, like

> {-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances #-}
>
> module Foo where
>
> import Control.Monad
> import Control.Monad.State
> import Control.Monad.State.Class
>
> data RunningAverageState = S Double Int
>
> runningAverage :: Double -> State RunningAverageState Double
> runningAverage v = do
>                    S sum count <- get
>                    let nsum = sum + v
>                        ncount = count + 1
>                    put $ S nsum ncount
>                    return $ nsum / (fromIntegral ncount)
>
> test = take 10 $ evalState (mapM runningAverage [1..]) $ S 0 0

test -> [1.0,1.5,2.0,2.5,3.0,3.5,4.0,4.5,5.0,5.5]

here "on-line" means that we may be taking data from an intermittant
external source, e.g. a data generator IO [Double], say, and want to
be able to feed the summarizer datum one-by-one, and produce
intermediate summaries.  also we may want to be able to serialize our
computation state (with Data.Binary, say) so that we can resume data
collection and summarization later.

naturally i want to create some common higher order operations on
these primitives, like applying them to a stream of data, or combining
them in some way.  it seems that one would want some kind of type
class to define a common interface to them.

> class (MonadState s m) => Summarizer s m | m -> s where
>     initialState :: s
>     runOne :: Double -> m Double
>

where initialize puts some intial state into the system, and runOne
collects and summarizes the next piece of data.  an instance for
runningAverage would look like

> instance Summarizer RunningAverageState (State RunningAverageState) where
>    initialState = S 0 0
>    runOne = runningAverage

but how would i use this, e.g.

> --summarizeMany vs = last $ evalState (mapM runOne vs) initialState

does not compile.

1) what am i doing wrong?  what are the right type class and instance
declarations?

2) is there a better way of expressing this kind of "on-line"
calculation, perhaps in pure (non-monadic) functions?

best, ben