Develop operational Markov chain semantics for iid statements in ReDiP

Develop the operational Markov chain construction that handles ReDiP programs containing the iid increment statement +={X}{iid{D}{Y}}, thereby extending the small-step operational semantics to include iid and enabling soundness results for such programs.

Background

The paper proves soundness of the automata-based semantics by relating it to an operational small-step semantics formulated as a Markov chain. While a new Sample rule is added to cover random increments by a distribution D, the authors explicitly exclude programs that use the iid construct +={X}{iid{D}{Y}} from this operational treatment.

They state that constructing the operational semantics for iid is deferred, which leaves a gap in the current operational framework for handling iid within ReDiP.

References

In the subsequent discussion, we will disregard programs containing iid instructions, the construction of which is left for future work.

— Weighted Automata for Exact Inference in Discrete Probabilistic Programs (2509.15074 - Geißler et al., 18 Sep 2025) in Section 5: Soundness Relative to Operational Semantics, introductory paragraph before Definition 5.1