Total order

A total order is a binary relation (<=) on some set X which is antisymmetric, transitive, and total.

• Antisymmetric: if a <= b and b <= a then a == b
• Transitivity: if a <= b and b <= c then a <= c
• Totality: a <= b or b <= a

Applied to concurrency, the definition of total order becomes quite handy. Actions such as operation on the same atomic variable or transaction build a total order. This mean, all threads see the effects of these actions in the same order.