  In distributed systems where strong consistency is costly when not
impossible, causal consistency provides a valuable abstraction to represent
program executions as partial orders. In addition to the sequential program
order of each computing entity, causal order also contains the semantic links
between the events that affect the shared objects -- messages emission and
reception in a communication channel , reads and writes on a shared register.
Usual approaches based on semantic links are very difficult to adapt to other
data types such as queues or counters because they require a specific analysis
of causal dependencies for each data type. This paper presents a new approach
to define causal consistency for any abstract data type based on sequential
specifications. It explores, formalizes and studies the differences between
three variations of causal consistency and highlights them in the light of
PRAM, eventual consistency and sequential consistency: weak causal consistency,
that captures the notion of causality preservation when focusing on convergence
; causal convergence that mixes weak causal consistency and convergence; and
causal consistency, that coincides with causal memory when applied to shared
memory.
