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