FW: RE [Haskell-cafe] Monad Description For Imperative Programmer

peterv bf3 at telenet.be
Thu Aug 2 07:01:05 EDT 2007

IMHO although this is a great explanation of what a monad is (as far as I understand it), for newbies I think it helps a lot to first look at the specific cases where monads are used and why they are invented, as explained in http://sigfpe.blogspot.com/2006/08/you-could-have-invented-monads-and.html and then looking at http://haskell.org/haskellwiki/IO_inside for the IO thingy.

However, one thing which I find annoying is that a "classic pure" function cannot evaluate an IO function unless you use unsafePerformIO; one must "promote" (?demote) the pure function into the IO monad.

For example, as an exercise I tried to convert the Monte Carlo experiment as demonstrated in http://mitpress.mit.edu/sicp/full-text/sicp/book/node53.html into Haskell (warning: newbie code ahead, should be much nicer when I once become a real Haskeller in a million years ;-)

In the code below I had to change the monteCarlo1 into a completely different monteCarlo2 in order to use the IO random facility. Okay, this is "expected behavior", but for an imperative programmer, this is quite a shock!

Any ways of "promoting" such a pure function into the monadic one automatically? I tried playing with "liftM", without succes.

import Data.Ratio
import Data.List
import System.Random
import Control.Monad

-- Monte Carlo using "pure" functions
monteCarlo1 :: Integral n => n -> (a -> (a,Bool)) -> a -> Ratio n
monteCarlo1 trials experiment startValue = trialsPassed % trials
  where trialsPassed = genericLength $ filter id outcomes
        outcomes = snd $ unzip $ genericTake trials $ iterate (experiment . fst) (experiment startValue)

cesaroTest1 :: StdGen -> (StdGen, Bool)
cesaroTest1 gen0 = (gen2, (gcd rand1 rand2) == 1)
                  where (rand1, gen1) = random gen0
                        (rand2, gen2) = random gen1

estimatePi1 trials = sqrt $ 6 / (fromRational $ monteCarlo1 trials cesaroTest1 (mkStdGen 0))

-- Monte Carlo using monadic IO
-- no genericReplicateM, so must use Int
monteCarlo2 :: Int -> IO Bool -> IO (Ratio Integer)
monteCarlo2 trials experiment = do
  outcomes <- replicateM trials experiment
  return $ fromIntegral (genericLength $ filter id outcomes) % fromIntegral trials

cesaroTest2 = do
  rand1 <- getStdRandom random
  rand2 <- getStdRandom random
  return $ (gcd rand1 rand2) == 1

estimatePi2 trials = do
  mc <- monteCarlo2 trials cesaroTest2
  return $ sqrt $ 6 / (fromRational mc)

main = let pi1 = estimatePi1 50000 in
       do pi2 <- estimatePi2 50000
          putStrLn (show pi1) >> putStrLn (show pi2)

-----Original Message-----
From: haskell-cafe-bounces at haskell.org [mailto:haskell-cafe-bounces at haskell.org] On Behalf Of Claus Reinke
Sent: Thursday, August 02, 2007 12:18 AM
To: haskell-cafe at haskell.org
Subject: Re: FW: RE [Haskell-cafe] Monad Description For Imperative Programmer

a Monad is a type constructor with two operations, implementing
a standard interface and following a few simple rules.

the Monad type class tells you the interface (what operations
you've got, and their types), the Monad laws tell you what all
types implementing that interface should have in common. 

the monadic interface gives you two operations, one to throw
things into a monad thing (return), and one to chain two monad 
things together (>>=). the chaining explicitly caters for information
flowing from the first to the second parameter of (>>=). 

the monad laws tell you two useful facts about monad things 
thrown together in that way: whatever it is the monad does, 
anything just thrown into it will take no part in that action,
and whichever way you use that chaining operation, the 
structure of chaining is irrelevant, only the ordering of chained
monad things matters.

there are usually other ways to create 'primitive' monadic things,
which can be combined into complex monadic structures using 
the operations from the Monad interface.

there is usually a way to interpret monadic structures built in
this way (a 'run' operation of some kind).

that's it, i think?-)


    examples include:

    - i/o: primitive monadic things are basic i/o operations, 
        the 'run' operation is outside the language, applied to
        'Main.main', and interprets (abstract) IO monad structures
        sequentially, starting with the leftmost innermost i/o 
        operation in the structure and applying the second
        argument of (>>=) to the result of executing the first.

    - []: primitive monadic things are lists, the 'run' operation
        is the identity, ie, the lists are directly exposed as data
        structures, return creates a singleton list, (>>=) applies
        its second argument to each element of its first argument
        and concatenates the results (concatMap).

    - State: primitive monadic things are operations on a state
        type, returning a result and a state; return returns its 
        parameter, passing its input state unchanged, (>>=) applies 
        its first parameter to the input state, applies its second 
        parameter to the result value and result state of the first. 
        'run' is runState and applies a (possibly) complex monadic 
        thing to an input state, returning a result and a (modified) 

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