Lilac: A Modal Separation Logic for Conditional Probability

We present Lilac, a separation logic for reasoning about probabilistic programs where separating conjunction captures independence. Inspired by an analogy with mutable state sampling corresponds to dynamic allocation, we show how probability spaces over fixed, ambient sample space appear be the natural analogue of heap fragments, and new combining operation on them such that behave like heaps measurability random variables behaves ownership. This forms basis our model separation, produces many pleasant properties. In particular, Lilac has frame rule identical ordinary one, naturally accommodates advanced features continuous quantitative properties programs. Then propose modality based disintegration theory conditional probability. resulting modal validates examples from prior work, give formal verification intricate weighted algorithm whose correctness depends crucially independence structure.