Positive Dedalus programs tolerate non-causality

•We provide an initial investigation of the CRON conjecture by J.M. Hellerstein.•This conjecture relates causality of message delivery to program monotonicity.•We formalize the conjecture for the language Dedalus, that is inspired by Datalog.•We show that positive programs remain correct when messages are sent into the past.

Declarative networking is a recent approach to programming distributed applications with languages inspired by Datalog. A recent conjecture posits that the delivery of messages should respect causality if and only if they are used in non-monotone derivations. We present our results about this conjecture in the context of Dedalus, a Datalog-variant for distributed programming. We show that both directions of the conjecture fail under a strong semantical interpretation. But on a more syntactical level, we show that positive Dedalus programs can tolerate non-causal messages, in the sense that they compute the correct answer even when messages can be sent into the past.