On 03:53 Thu 15 Apr , roconnor@theorem.ca wrote:
On Wed, 14 Apr 2010, Ashley Yakeley wrote:
On 2010-04-14 14:58, Ashley Yakeley wrote:
On 2010-04-14 13:59, roconnor@theorem.ca wrote:
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.
The trouble is, there are functions that can distinguish -0.0 and 0.0. Do we call them bad functions, or are the Eq instances for Float and Double broken?
I'd call them disrespectful functions, or maybe nowadays I might call them improper functions. The "good" functions are respectful functions or proper functions.
<snip from other post>
Try using the (x == y) ==> (f x = g y) test yourself.
Your definitions seem very strange, because according to this, the functions f :: Double -> Double f x = 1/x and g :: Double -> Double g x = 1/x are not equal, since (-0.0 == 0.0) yet f (-0.0) /= g (0.0). -- Nick Bowler, Elliptic Technologies (http://www.elliptictech.com/)