[Haskell-cafe] General function to count list elements?

[John A. De Goes]

Two functions are equal iff they have the same domain and range and  
the same outputs for the same inputs. Simple to state, but extremely  
difficult to implement in a useful way, and impossible to implement in  
a perfect way.

If you had a compiler or algorithm capable of determining function  
equality, you could use it to prove or disprove arbitrary theorems in  
mathematics.

Regards,

John A. De Goes
N-BRAIN, Inc.
The Evolution of Collaboration

http://www.n-brain.net    |    877-376-2724 x 101

On Apr 18, 2009, at 9:39 AM, Eugene Kirpichov wrote:

> Could you then provide an example of two functions that *are* equal,
> or, even better, a definition of equality for arbitrary functions?
> Since Haskell may be compiled into C, this must be a definition that
> is implementable in C.
>
> 2009/4/18 michael rice <nowgate at yahoo.com>:
>> Though I haven't tried it out, it's trying to use my function to  
>> count
>> functions.
>>
>> The first argument is the identity function.
>>
>> The second argument is a list of a different form of the identity  
>> function.
>>
>> Though the two identity functions, given the same input, would  
>> produce the
>> same output, I doubt they would be equal.
>>
>> So my guess at an answer would be zero.
>>
>> Michael
>>
>> --- On Sat, 4/18/09, Eugene Kirpichov <ekirpichov at gmail.com> wrote:
>>
>> From: Eugene Kirpichov <ekirpichov at gmail.com>
>> Subject: Re: [Haskell-cafe] General function to count list elements?
>> To: "michael rice" <nowgate at yahoo.com>
>> Cc: haskell-cafe at haskell.org
>> Date: Saturday, April 18, 2009, 11:03 AM
>>
>> What should
>>
>> count (\x -> x) (replicate 10 (\y -> if 1==1 then y else undefined))
>>
>> return?
>>
>> 2009/4/18 michael rice <nowgate at yahoo.com>:
>>> Is there a general function to count list elements. I'm trying this
>>>
>>> count :: a -> [a] -> Int
>>> count x ys = length (filter (== x) ys)
>>>
>>> with this error upon loading
>>>
>>> =============
>>>
>>> [michael at localhost ~]$ ghci count
>>> GHCi, version 6.10.1: http://www.haskell.org/ghc/  :? for help
>>> Loading package ghc-prim ... linking ... done.
>>> Loading package integer ... linking ... done.
>>> Loading package base ... linking ... done.
>>> [1 of 1] Compiling Main             ( count.hs, interpreted )
>>>
>>> count.hs:2:29:
>>>     Could not deduce (Eq a) from the context ()
>>>       arising from a use of `==' at count.hs:2:29-32
>>>     Possible fix:
>>>       add (Eq a) to the context of the type signature for `count'
>>>     In the first argument of `filter', namely `(== x)'
>>>     In the first argument of `length', namely `(filter (== x) ys)'
>>>     In the expression: length (filter (== x) ys)
>>> Failed, modules loaded: none.
>>> Prelude>
>>>
>>> =============
>>>
>>> Not sure what it's trying to tell me other than I need an (Eq a)
>>> somewhere.
>>>
>>> Michael
>>>
>>>
>>>
>>>
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>>>
>>
>>
>>
>> --
>> Eugene Kirpichov
>> Web IR developer, market.yandex.ru
>>
>>
>
>
>
> -- 
> Eugene Kirpichov
> Web IR developer, market.yandex.ru
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