[Haskell-cafe] question - which monad to use?

[Tamas K Papp]

On Mon, Oct 02, 2006 at 11:35:40AM -0400, Tamas K Papp wrote:
> Matthias,
> 
> Sorry if I was not clear in stating the problem.  Your solution works
> nicely, but I would like to try writing a monad.  This is what I came
> up with:
> 
> type Failure = String
> data Computation a = Computation (Either Failure a) [a]
> 
> instance Monad Computation where
>     (Computation (Left e) h) >>= f = Computation (Left e) h -- do not proceed
>     (Computation (Right a) h) >>= f = let r = f a -- result
>                                           h' = case r of
>                                                  Left e -> h
>                                                  Right a' -> a':h
>                                       in
>                                         Computation r h'
>     return (s,c) = Computation (Right (s,c)) [(s,c)]

sorry, I pasted an older version.  This line should be

    return a = Computation (Right a) [a]

> Basically, I want the >>= operator to call f on the last result, if it
> is not a failure, and append the new result to the list (if it didn't
> fail).
> 
> However, I am getting the following error message:
> 
> /home/tpapp/doc/research/pricespread/Main.hs:62:58:
>     Couldn't match the rigid variable `b' against the rigid variable `a'
>       `b' is bound by the type signature for `>>='
>       `a' is bound by the type signature for `>>='
>       Expected type: [b]
>       Inferred type: [a]
>     In the second argument of `Computation', namely `h'
>     In the definition of `>>=':
> 	>>= (Computation (Left e) h) f = Computation (Left e) h
> 
> I don't know what the problem is.
> 
> Thanks,
> 
> Tamas
> 
> On Mon, Oct 02, 2006 at 03:54:23PM +0200, Matthias Fischmann wrote:
> 
> > hi, i don't fully understand your problem, but perhaps you could use
> > iterate to produce a list or type [Result a], ie, of all computation
> > steps, and then use this function to extract either result or error
> > from the list:
> > 
> > 
> > type Failmessage = Int
> > data Result a = Root a | Failure Failmessage  deriving (Show)
> > 
> > f :: [Result a] -> Either a (Int, [Result a])
> > f cs = f [] cs
> >     where
> >     f (Root r:_) [] = Left r
> >     f l [Failure i] = Right (i, reverse l)
> >     f l (x:xs)      = f (x:l) xs
> > 
> > cs = [Root 1.2, Root 1.4, Root 1.38, Root 1.39121]
> > cs' = [Root 1.2, Root 1.4, Root 1.38, Failure 1]
> > 
> > -- f cs  ==> Left 1.39121
> > -- f cs' ==> Right (1,[Root 1.2,Root 1.4,Root 1.38])
> > 
> > 
> > (although this way you probably have the list still floating around
> > somewhere if you process the error returned by f, so f should probably
> > just drop the traversed part of the list.)
> > 
> > hth,
> > matthias
> > 
> > 
> > 
> > On Sun, Oct 01, 2006 at 06:00:43PM -0400, Tamas K Papp wrote:
> > > To: Haskell Cafe <haskell-cafe at haskell.org>
> > > From: Tamas K Papp <tpapp at Princeton.EDU>
> > > Date: Sun, 1 Oct 2006 18:00:43 -0400
> > > Subject: [Haskell-cafe] question - which monad to use?
> > > 
> > > Hi,
> > > 
> > > I have a computation where a function is always applied to the
> > > previous result.  However, this function may not return a value (it
> > > involves finding a root numerically, and there may be no zero on the
> > > interval).  The whole problem has a parameter c0, and the function is
> > > also parametrized by the number of steps that have been taken
> > > previously.
> > > 
> > > To make things concrete,
> > > 
> > > type Failmessage = Int          -- this might be something more complex
> > > data Result a = Root a | Failure Failmessage -- guess I could use Either too
> > > 
> > > f :: Double -> Int -> Double 0 -> Result Double
> > > f c0 0 _ = c0
> > > f c0 j x = {- computation using x, parameters calculated from c0 and j -}
> > > 
> > > Then
> > > 
> > > c1 = f c0 0 c0
> > > c2 = f c0 1 c1
> > > c3 = f c0 2 c2
> > > ...
> > > 
> > > up to cn.
> > > 
> > > I would like to
> > > 
> > > 1) stop the computation when a Failure occurs, and store that failure
> > > 
> > > 2) keep track of intermediate results up to the point of failure, ie
> > > have a list [c1,c2,c3,...] at the end, which would go to cn in the
> > > ideal case of no failure.
> > > 
> > > I think that a monad would be the cleanest way to do this.  I think I
> > > could try writing one (it would be a good exercise, I haven't written
> > > a monad before).  I would like to know if there is a predefined one
> > > which would work.
> > > 
> > > Thank you,
> > > 
> > > Tamas
> > > _______________________________________________
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> > -- 
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> > 
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