ms

metric spaces.

A MetricSpace is a set together with a notion of distance between elements. Distance is computed by a function dist which has the following four laws:

1. non-negative: forall x y. dist x y >= 0

2. identity of indiscernibles: forall x y. dist x y == 0 <=> x == y

3. symmetry: forall x y. dist x y == dist y x

4. triangle inequality: forall x y z. dist x z <= dist x y + dist y z

See the Wikipedia article on metric spaces for more details.