[Haskell-cafe] show in monad

[Jos Kusiek]

You simply cannot do that. To be more precise, you cannot use show 
inside the bind operator on Prob (but you could use it in flatten). 
Deriving Show creates a Show instance which looks something like that:

instance Show a => Show (Prob a) where ...

This instance needs "a" to instanciate Show, so you can only use show 
with Prob types, where "a" is an instance of Show itself, e. g. Prob 
Int. Your flatten function does not guarantee that "a" is an instance of 
Show. The type says, any type for "a" will do it. You can easily 
restrict that with a class constraint:

flatten :: Show a => Prob (Prob a) -> Prob a

But now you have a problem with the bind operator. You can no longer use 
flatten here. The bind operator for Prob has the following type:

(>>=) :: Prob a -> (a -> Prob b) -> Prob b

There are no constraints here and you cannot add any constraints. The 
type is predefined by the Monad class. So it is not guaranteed, that 
this Prob type has a show function and you cannot guarantee it in any 
way. So you cannot use show on your first parameter type (Prob a) or 
your result type (Prob b) inside the bind or any function that is called 
by bind.

On 28.02.19 11:00, Damien Mattei wrote:
> just for tracing the monad i have this :
>
> import Control.Monad
>
> import Data.Ratio
> import Data.List (all)
> import Debug.Trace
>
> newtype Prob a = Prob { getProb :: [(a,Rational)] } deriving Show
>
> instance Functor Prob where
>     fmap f (Prob xs) = trace " Functor Prob "
>                        Prob $ map (\(x,p) -> (f x,p)) xs
>
>
> t
>
>
> flatten :: Prob (Prob a) -> Prob a
> flatten (Prob xs) = trace (" flatten " ++ show xs)
>                     Prob $ concat $ map multAll xs
>   where multAll (Prob innerxs,p) = trace " multAll "
>                                    map (\(x,r) -> (x,p*r)) innerxs
>
>
> instance Applicative Prob where
>    pure = trace " Applicative Prob return " return
>    (<*>) = trace " Applicative Prob ap " ap
>
> instance Monad Prob where
>   return x = trace " Monad Prob return "
>              Prob [(x,1%1)]
>   m >>= f = trace " Monad Prob >>= "
>             flatten (fmap f m)
>   fail _ = trace " Monad Prob fail "
>            Prob []
>
>
> {-
> instance Applicative Prob where
>
>   pure a = Prob [(a,1%1)]
>
>   Prob fs <*> Prob as = Prob [(f a,x*y) | (f,x) <- fs, (a,y) <- as]
>
>
> instance Monad Prob where
>
>   Prob as >>= f = Prob [(b,x*y) | (a,x) <- as, let Prob bs = f a, 
> (b,y) <- bs]
>
> -}
>
>
>
> in this :
>
> flatten :: Prob (Prob a) -> Prob a
> flatten (Prob xs) = trace (" flatten " ++ show xs)
>                     Prob $ concat $ map multAll xs
>   where multAll (Prob innerxs,p) = trace " multAll "
>                                    map (\(x,r) -> (x,p*r)) innerxs
>
>
> i have this error:
>
> [1 of 1] Compiling Main             ( monade.hs, interpreted )
>
> monade.hs:22:43: error:
>     • No instance for (Show a) arising from a use of ‘show’
>       Possible fix:
>         add (Show a) to the context of
>           the type signature for:
>             flatten :: forall a. Prob (Prob a) -> Prob a
>     • In the second argument of ‘(++)’, namely ‘show xs’
>       In the first argument of ‘trace’, namely ‘(" flatten " ++ show xs)’
>       In the expression: trace (" flatten " ++ show xs) Prob
>    |
> 22 | flatten (Prob xs) = trace (" flatten " ++ show xs)
>    |                                           ^^^^^^^
> Failed, no modules loaded.
>
> how can i implement a show for xs ?
> regards,
> damien
>
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-- 
Dipl.-Inf. Jos Kusiek

Technische Universität Dortmund
Fakultät 4 - Informatik / Lehrstuhl 1 - Logik in der Informatik
Otto-Hahn-Straße 12, Raum 3.020
44227 Dortmund

Tel.: +49 231-755 7523

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