IMP with exceptions over decorated logic

In this paper, we facilitate the reasoning about impure programming languages, by annotating terms with “decorations” that describe what computational (side) effect evaluation of a term may involve. In a point-free categorical language, called the “decorated logic”, we formalize the mutable state and the exception effects first separately, and then combined, exploiting a nice duality between them. The combined decorated logic is used as the target language for the denotational semantics of the IMP+Exc imperative programming language, and allows us to prove equivalences between programs written in IMP+Exc. The combined logic is encoded in Coq, and this encoding is used to certify some program equivalence proofs.