How to write a monad that prints “step i of N” when executing each statement in the monad?

Question

I\'m not even sure this is possible in any kind of monad; does it violate monad laws? But it seems like something that should be possible in some kind of construct or other. S

Answer 1

I assume that you want the steps to be displayed automatically, without having to sprinkle you code with logging statements.

The problem of doing this with monads is that they are too flexible: at any point, the "shape" of the rest of the computation can depend on values obtained during the computation itself. This is made explicit in the type of (>>=), which is m a -> (a -> m b) -> m b.

As a consequence, there is no fixed number N of total steps that you can know before running the computation.

However, Haskell offers two other abstractions which trade some of the power and flexibility of monads for the chance to perform a greater amount of "static" analysis beforehand: applicative functors and arrows.

Applicative functors, while hugely useful, are perhaps too "weak" for your needs. You can´t write a function inside an applicative functor that, when applied to a value, prints that value to console. This is explained in the paper "Idioms are oblivious, arrows are meticulous, monads are promiscuous" which contains some enlightening examples of the limits of each abstraction (applicative functors are called "idioms" in that paper.)

Arrows offer a better compromise between expressive power and amenability to static analysis. The "shape" of arrow computations is fixed in a static pipeline. Data obtained during the computation can influence effects later in the pipeline (for example, you can print a value obtained by a previous effect in the computation) but not change the shape of the pipeline, or the number of steps.

So, if you could express your computation using Kleisli arrows (the arrows of a monad), perhaps you could write some kind of arrow transformer (not monad transformer) which added automated logging capabilities.

The arrows package offers a number of arrow transformers. I think StaticArrow could be used to automatically track the total number of steps. But you would still need to write some functionality to actually emit the messages.

Edit: Here's an example of how to keep count of the number of steps in a computation, using arrows:

module Main where

import Data.Monoid
import Control.Monad
import Control.Applicative
import Control.Arrow
import Control.Arrow.Transformer
import Control.Arrow.Transformer.Static

type SteppedIO a b = StaticArrow ((,) (Sum Int)) (Kleisli IO) a b

step :: (a -> IO b) -> SteppedIO a b
step cmd = wrap (Sum 1, Kleisli cmd)

countSteps :: SteppedIO a b -> Int
countSteps = getSum . fst . unwrap

exec :: SteppedIO a b -> a -> IO b
exec =  runKleisli . snd . unwrap 

program :: SteppedIO () ()
program =
    step (\_ -> putStrLn "What is your name?")  
    >>>
    step (\_ -> getLine)
    >>>
    step (putStrLn . mappend "Hello, ")

main :: IO ()
main = do
    putStrLn $ "Number of steps: " ++ show (countSteps program)
    exec program ()

Notice that the effect of step 3 is influenced by a value produced in step 2. This can't be done using applicatives.

We do use the (,) (Sum Int) applicative, required by StaticArrow to encode the static information (here, just the number of steps).

Displaying the steps as they are executed would require a bit more work.

Edit#2 If we are dealing with a sequence of commands in which no effect depends on a value produced by a previous effect, then we can avoid using arrows and count the steps using only applicative functors:

module Main where

import Data.Monoid
import Control.Applicative
import Data.Functor.Compose

type SteppedIO a = Compose ((,) (Sum Int)) IO a

step :: IO a -> SteppedIO a
step cmd = Compose (Sum 1, cmd)

countSteps :: SteppedIO a -> Int
countSteps = getSum . fst . getCompose

exec :: SteppedIO a -> IO a
exec =  snd . getCompose

program :: SteppedIO () 
program =
    step (putStrLn "aaa") 
    *>  
    step (putStrLn "bbb")
    *>
    step (putStrLn "ccc")

main :: IO ()
main = do
    putStrLn $ "Number of steps: " ++ show (countSteps program)
    exec program 

Data.Functor.Compose comes from the transformers package.

Edit#3 The following code extends the previous Applicative step counting solution, using the pipes package to actually emit notifications. The arrow-based solution could be adapted in a similar manner.

module Main where

import Data.Monoid
import Control.Applicative
import Control.Monad.State
import Data.Functor.Compose
import Pipes
import Pipes.Lift

type SteppedIO a = Compose ((,) (Sum Int)) (Producer () IO) a

step :: IO a -> SteppedIO a
step cmd = Compose (Sum 1, yield () *> lift cmd)

countSteps :: SteppedIO a -> Int
countSteps = getSum . fst . getCompose

exec :: SteppedIO a -> Producer () IO a
exec =  snd . getCompose

stepper :: MonadIO m => Int -> Consumer () m a
stepper n = evalStateP 0 $ forever $ do 
    await
    lift $ modify succ
    current <- lift get
    liftIO $ putStrLn $ "step " ++ show current ++ " of " ++ show n

program :: SteppedIO () 
program = *** does not change relative to the previous example ***

main :: IO ()
main = runEffect $ exec program >-> stepper (countSteps program)