Re: Fwd: [Haskell-cafe] Class

2 Nov 2006


      Am Donnerstag, 2. November 2006 10:57 schrieb Slavomir Kaslev:
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---------- Forwarded message ----------
From: Slavomir Kaslev 
Date: Nov 2, 2006 10:47 AM
Subject: Re: [Haskell-cafe] Class
To: Daniel Fischer 
On 11/2/06, Daniel Fischer  wrote:
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Am Donnerstag, 2. November 2006 00:06 schrieb Slavomir Kaslev:
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Hello.
I am new to Haskell and I am going through "Haskell: The craft of
functional programming". I am trying to grasp haskell's classes and
instances, so here is slightly modified code from the book:
class Show a => Visible a where
    toString :: a -> String
    toString = show
    size :: a -> Int
    size = length . show
instance Visible a => Visible [a] where
    toString = concat . map toString
    size = foldl (+) 0 . map size
vSort :: (Visible a, Ord a) => [a] -> String
vSort = toString . List.sort
^^^^^^^
my ghc complained that List.sort is not in scope, did you import
Data.List as List?
Yes, I did imported Data.List. My mistake for forgetting to add it in the
post.
That was not quite what I meant. If I import Data.List, what is in scope are
plain "sort" and qualified "Data.List.sort", not "List.sort". To have the 
latter in scope, I think you would have to 
import (qualified) Data.List as List
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s = vSort [1..3]
Unfortunetly in ghc it gives the following type error:
    Ambiguous type variable `a' in the constraints:
      `Visible a' arising from use of `vSort' at d:/tmp.hs:83:4-8
      `Enum a' arising from the arithmetic sequence `1 .. 3' at
d:/tmp.hs:83:10-15
      `Num a' arising from the literal `3' at d:/tmp.hs:83:14
      `Ord a' arising from use of `vSort' at d:/tmp.hs:83:4-8
    Probable fix: add a type signature that fixes these type
variable(s) Failed, modules loaded: none.
As you can see, Visible is nothing more than an adapter to the Show
class. How I got thing so far, [1..3] :: (Num a, Enum a) => [a], has a
Show instance so does class Num (which 'subclasses' Show). Therefore,
I can't see any reason why toString function can't call show from
those instances.
First problem: class Visible has no instances yet, so even if you
disambiguate the type by writing e.g.
s = vSort [1 :: Int .. 3], you'll get an error message:
Visible.hs:20:4:
    No instance for (Visible Int)
      arising from use of `vSort' at Visible.hs:20:4-8
    Probable fix: add an instance declaration for (Visible Int)
    In the definition of `s': s = vSort ([1 :: Int .. 3])
Visible 'subclasses' Show. Doesn't this mean that Visible should be
defined for all types with Show instances? I don't want to write
Visible Int, if ghc has already defined a Show Int instance.
No, quite reverse, that Visible is a subclass of Show means that all instances 
of Visible must also be instances of Show. Perhaps the notation

class Show a => Visible a where

mislead you, as it may be read that Show implies Visible, while it actually 
means that Visible _requires_ Show.
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And the second problem:
The typechecker has no means of determining which type 1 should have.
By virtue of the fact that numeric literals are overloaded in Haskell, it
has type Num a => a. The use of enumFromTo adds the Enum a constraint and
vSort adds Ord and Visible, however there may be many types satisfying
these constraints and ghc says it's up to you to select one.
And even if there is only one instance of Visible declared, ghc (nor, as
far as I know, any other Haskell implementation) won't select that
because there might, somewhere in a long-forgotten directory, lie a
module dormant in which another instance satisfying all constraints is
declared.
To sum up: instance selection is left to the user, the compiler does only
type _inference_. Often that determines which instance fits, but
sometimes you have to give an expression type signature to tell the
compiler what to choose.
I agree with second problem you pointed out. Thanks for mentioning it.
--
Slavomir Kaslev
No sweat,
Daniel