On algebraic abstractions for concurrent separation logics

Concurrent separation logic is distinguished by transfer of state ownership upon parallel composition and framing. The algebraic structure that underpins partial commutative monoids (PCMs). Extant research considers primarily from the logical perspective while comparatively less attention drawn to considerations. This paper provides an formalization in concurrent means structure-preserving functions (i.e., morphisms) between PCMs, associated notion separating relations. Morphisms structures are a standard concept algebra category theory, but haven't seen ubiquitous use before. Separating binary relations generalize disjointness characterize inputs on which morphisms preserve structure. two abstractions facilitate verification enabling concise ways writing specs, providing abstract views threads' states preserved under transfer, user-level construction new PCMs out existing ones.