[Haskell-cafe] Re: Re: Re: Wikipedia on first-class object
jonathanccast at fastmail.fm
Sat Dec 29 14:39:59 EST 2007
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
> 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...
More information about the Haskell-Cafe