[Haskell-cafe] Re: instance Eq (a -> b)

[roconnor at theorem.ca]

On Wed, 14 Apr 2010, Ashley Yakeley wrote:

> On 2010-04-14 13:03, Alexander Solla wrote:
>> If you're willing to accept that distinct functions can represent the
>> same "moral function", you should be willing to accept that different
>> "bottoms" represent the same "moral value".
>
> Bottoms should not be considered values. They are failures to calculate 
> values, because your calculation would never terminate (or similar 
> condition).

Let's not get muddled too much in semantics here.

There is some notion of value, let's call it proper value, such that 
bottom is not one.

In other words bottom is not a proper value.

Define a proper value to be a value x such that x == x.

So neither undefined nor (0.0/0.0) are proper values

In fact proper values are not just subsets of values but are also 
quotients.

thus (-0.0) and 0.0 denote the same proper value even though they are 
represented by different Haskell values.

-- 
Russell O'Connor                                      <http://r6.ca/>
``All talk about `theft,''' the general counsel of the American Graphophone
Company wrote, ``is the merest claptrap, for there exists no property in
ideas musical, literary or artistic, except as defined by statute.''