1 Jan
2015
1 Jan
'15
8:58 a.m.
Tom Ellis wrote:
Is there a type with an Eq instance for which on Ord instance could not also be provided (i.e. I'm interested in Clark's "converse")?
Of course. One of the very many examples is Complex. One can say we can compare complex numbers, by their absolute value. That is true; however we end up in a position where compare x y returns EQ but x==y returns False. In general, Ord represents total order. There are many structures on which total order cannot be established. Take nodes in the tree, the Tree data type. One can compare nodes by taking a parent to be less than any of its children. But then two brothers are not comparable. Searching for "partial orders" and pre-orders gives many more examples.