[Haskell-cafe] Re: Re: Re[2]: Wikipedia on first-class object

[Jonathan Cast]

On 29 Dec 2007, at 10:14 AM, Ben Franksen wrote:

> Jonathan Cast wrote:
>> On 28 Dec 2007, at 3:13 PM, Ben Franksen wrote:
>>> Bulat Ziganshin wrote:
>>>> Hello Yitzchak,
>>>> Thursday, December 27, 2007, 12:10:21 PM, you wrote:
>>>>> In particular,
>>>>> two functions are equal only if they produce
>>>>> the same value for every input, and in general it is
>>>>> impossible for a computer to check that.
>>>>
>>>> "for a computer" is superfluous here. people are not smarter than
>>>> computers and can't do anything that's impossible for computers
>>>
>>> I don't think my computer can be sorry, but I know I can be.
>>>
>>> And don't forget that there are 'undecidable' problems.
>>
>> Which I have never yet seen decided by a person...
>
> In many cases, equality of functions has been decided by humans, as  
> has
> termination of programs. Of course this doesn't prove that humans  
> can, in
> principle, decide equality for any pair of functions. But neither  
> has the
> opposite been proved.

It hasn't been proved that we can't build a device that can decide  
equality for arbitrary functions, either.  It's simply that no one  
has ever succeeded in imagining a definition of `decidable' that  
includes that particular relation.  I rather strongly suspect that  
anything decidable by humans must be decidable in some sense...

jcc