Well, this definition, although correct, contradicts the OP's claim that \x->x /= \y->if 1==1 then y else undefined :) I'm leading the OP to the thought that necessity Eq constraint and lack of an Eq instance for functions (and thus non-existence of a universally polymorphic 'count' function) is something dictated by the nature of the world, not by the nature of Haskell. 2009/4/18 John A. De Goes <john@n-brain.net>:
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@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@gmail.com> wrote:
From: Eugene Kirpichov <ekirpichov@gmail.com> Subject: Re: [Haskell-cafe] General function to count list elements? To: "michael rice" <nowgate@yahoo.com> Cc: haskell-cafe@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@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@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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