2008/12/22 Andrew Wagner :

The problem here is even slightly deeper than you might realize. For example, what if you have a list of functions. How do you compare two functions to each other to see if they're equal? There is no good way really to do it! So, not only is == not completely polymorphic, but it CAN'T be.

There is a nice solution for this, however, and it's very simple:

contain :: Eq a -> [a] -> Bool

Please note that the syntax here should be: contain :: Eq a => a -> [a] -> Bool Denis

On 22 Dec 2008, at 15:18, Andrew Wagner wrote:

Yes, of course, sorry for the typo.

On Mon, Dec 22, 2008 at 9:17 AM, Denis Bueno wrote: 2008/12/22 Andrew Wagner :

...

The problem here is even slightly deeper than you might realize. For example, what if you have a list of functions. How do you compare two functions to each other to see if they're equal? There is no good way really to do it! So, not only is == not completely polymorphic, but it CAN'T be.

There is a nice solution for this, however, and it's very simple:

contain :: Eq a -> [a] -> Bool

Please note that the syntax here should be:

contain :: Eq a => a -> [a] -> Bool

Denis

Of note, unless this is an exercise, such a function already exists -- it's called elem. How do you find such a function? You search on haskell.org/hoogle. http://haskell.org/hoogle/?hoogle=Eq+a+%3D%3E+a+-%3E+%5Ba%5D+-%3E+Bool Bob

There are two ways to fix this. Let me see if I can get my syntax right this time :) 1.) Let GHC work out the Eq instance: data Shape = Square | Triangle | Circle deriving Eq 2.) Tell GHC how to do it explicitly: data Shape = Square | Triangle | Circle instance Eq Shape where Square == Square = True Triangle == Triangle = True Circle == Circle = True _ == _ = False Note that the last line here means that any other comparisons are false. On Mon, Dec 22, 2008 at 9:35 AM, Raeck Zhao wrote:

Thank you very much for your reply! It is really helpful!

But I just found another 'problem', I just realize that the list does not support the user-defined data type? the list is also depending on the Eq function?

For example,

data Shape = Square | Triangle | Circle

when I type either

[Square, Triangle, Circle]

or

Square == Square

there are errors!

So there is no way to construct a truly polymorphic List? any way to extend the list to support some user-defined data type?

Or... I define the Shape in a wrong way actually?

Thanks

Raeck

------------------------------ Date: Mon, 22 Dec 2008 09:02:53 -0500 From: wagner.andrew@gmail.com To: raeck@msn.com Subject: Re: [Haskell-cafe] Defining a containing function on polymorphic list CC: haskell-cafe@haskell.org; beginners@haskell.org

The problem here is even slightly deeper than you might realize. For example, what if you have a list of functions. How do you compare two functions to each other to see if they're equal? There is no good way really to do it! So, not only is == not completely polymorphic, but it CAN'T be.

There is a nice solution for this, however, and it's very simple:

contain :: Eq a -> [a] -> Bool contain x [] = False contain x (y:ys) = if x == y then True else contain x ys

The "Eq a" in the type signature says that 'a' must be a member of the 'Eq' typeclass. That says, in turn, that 'a' must have == defined for it. Fortunately, most types have, or can easily derive that definition. Here is the definition of the typeclass:

class Eqhttp://haskell.org/ghc/docs/latest/html/libraries/base/Data-Eq.html#t:Eqa where (==)http://haskell.org/ghc/docs/latest/html/libraries/base/Data-Eq.html#v:%3D%3D:: a -> a -> Boolhttp://haskell.org/ghc/docs/latest/html/libraries/ghc-prim/GHC-Bool.html#t:B... (/=)http://haskell.org/ghc/docs/latest/html/libraries/base/Data-Eq.html#v:/%3D:: a -> a -> Boolhttp://haskell.org/ghc/docs/latest/html/libraries/ghc-prim/GHC-Bool.html#t:B... That is, for 'a' to be a member of 'Eq', it must have a == operator which can take 2 values of that type and return a Boolean, saying whether or not they're equal, and it must also have a definition for the /= operator, which is "not equal". These two are also defined in terms of each other, so if you define ==, you get /= for free, and vice versa.

That's probably more information than you needed to know, but I hope it helps.

2008/12/22 Raeck Zhao

...

contain :: a -> [a] -> Bool contain x [] = False contain x (y:ys) = if x == y then True else contain x ys it seems that

I am trying to define a containing function to see if a value is one of the elements within a list which is polymorphic, but failed with the following codes: the problem is the 'operator' == does not support a polymorphic check? Any way can solve the problem? or any alternative solution to achieve the purpose? Thanks! Raeck

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2008/12/22 Raeck Zhao

Thank you very much for your reply! It is really helpful!

But I just found another 'problem', I just realize that the list does not support the user-defined data type? the list is also depending on the Eq function?

For example,

data Shape = Square | Triangle | Circle

when I type either

[Square, Triangle, Circle]

This is perfectly legal, but GHCi won't be able to print it, because there is no Show instance for Shape. You can declare one: instance Show Shape where show Square = "Square" show Triagle = "Triangle" show Circle = "Circle" This can be generated automatically when you declare the type, by using: data Shape = Square | Triangle | Circle deriving (Show)

or

Square == Square

Similarly, to use (==), you need an Eq instance, which can be defined much in the same way as the Show instance above (deriving also works on Eq -- don't generalize too hastily; not all classes work with deriving). Luke

-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA512 On Tue, Dec 23, 2008 at 10:48 PM, Henning Thielemann wrote:

Andrew Wagner schrieb:

...

The problem here is even slightly deeper than you might realize. For example, what if you have a list of functions. How do you compare two functions to each other to see if they're equal? There is no good way really to do it! So, not only is == not completely polymorphic, but it CAN'T be.

There is a nice solution for this, however, and it's very simple:

contain :: Eq a -> [a] -> Bool contain x [] = False contain x (y:ys) = if x == y then True else contain x ys

Would HLint jump in here and suggest: contain x (y:ys) = x == y || contain x ys ? Or even "replace 'contain' by 'elem'" ?

I just tried it out. hlint makes no suggestions. Incidentally, your syntax is wrong. Should be: contain :: (Eq a) => a -> [a] -> Bool contain _ [] = False contain x (y:ys) = if x == y then True else contain x ys - -- gwern -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.9 (GNU/Linux) iEYEAREKAAYFAklRtvAACgkQvpDo5Pfl1oKTLQCgixTp95VA8ccRxuWTpIgXVo2k +XkAniyWDU6f1sSCzdUuJIq4pAcgDS0K =Uhkz -----END PGP SIGNATURE-----

Hi Raeck, as I see what types you defined, don't you doing School of Expression? (In summer I made my way to FAL chapter, but I had no time more (school), but I will definitely finish that book:) Fero