[Haskell-cafe] Abstraction leak

Jon Cast jcast at ou.edu
Fri Jun 29 16:28:17 EDT 2007

On Friday 29 June 2007, Andrew Coppin wrote:
> ...and again today I found myself trying to do something that would be
> very easy in an imperative language, but I cannot think of a single good
> way of doing it in Haskell. Hopfully somebody can give me some hints.
<snip long and helpful explanation>

Here's my solution (drawn from a library I'll be posting Real Soon Now):

import Control.Monad
import Control.Monad.Trans

data SPMT iota omicron m alpha
  = ReturnSP alpha
   | LiftSP (m (SPMT iota omicron m alpha))
   | GetSP (iota -> SPMT iota omicron m alpha))
   | PutSP omicron (SPMT iota omicron m alpha)
instance Monad m => Monad (SPMT iota omicron m) where
  return x = ReturnSP x
  ReturnSP x >>= f = f x
  LiftSP a >>= f = LiftSP (liftM (>>= f) a)
  GetSP a >>= f = GetSP (\ x -> a x >>= f)
  PutSP x a >>= f = PutSP x (a >>= f)
instance MonadTrans (SPMT iota omicron) where
  lift a = LiftSP (liftM ReturnSP a)

getSP :: SPMT iota omicron m iota
getSP = GetSP ReturnSP

putSP :: omicron -> SPMT iota omicron m ()
putSP x = PutSP x (ReturnSP ())

(^>^) :: Monad m => SPMT iota omicron m alpha -> SPMT omicron omicron' m beta
                 -> SPMT iota omicron' m beta
a ^>^ ReturnSP x = ReturnSP x
a ^>^ LiftSP b = LiftSP (liftM (a ^>^) b)
a ^>^ PutSP x b = PutSP x (a ^>^ b)
LiftSP a ^>^ GetSP b = LiftSP (liftM (^>^ GetSP b) a)
GetSP a ^>^ GetSP b = GetSP (\ x -> a x ^>^ GetSP b)
PutSP x a ^>^ GetSP b = a ^>^ b x

If the signature of SPMT suffices to write decodeRLE and decodeHeader, the 
task of applying RLE decoding just to the header can be implemented by using 
decodeRLE ^>^ decodeHeader in place of just decodeHeader.  Extension to 
situations left un-implemented above I leave for your ingenuity and/or 
release of my library.


Jonathan Cast

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