On Wed, Apr 14, 2010 at 02:07:52AM -0700, Ashley Yakeley wrote:
>> So the facts that
>> (1) f == g
>> (2) f undefined = 6
>> (3) g undefined = undefined
>> is not a problem?
>
> This is not a problem. f and g represent the same moral function, they
> are just implemented differently. f is smart enough to know that its
> argument doesn't matter, so it doesn't need to evaluate it. g waits
> forever trying to evaluate its function, not knowing it doesn't need it.
Hence they are distinct functions, and should not be determined to be
equal by an equality instance. A compiler will not transform g into f
because said distinction is important and part of the definition of a
function. Not considering 'bottom' a normal value leads to all sorts of
issues when trying to prove properties of a program. Just because they
don't occur at run time, you can't pretend they don't exist when
reasoning about the meaning of a program, any more than you can
reasonably reason about haskell without taking types into account simply
because types don't occur in the run-time representation.
John
--
John Meacham - ⑆repetae.net⑆john⑈ - http://notanumber.net/
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