Fully Abstract Denotational Models for Nonuniform Concurrent Languages

AbstractThis paper investigates full abstraction of denotational model w.r.t. operational ones for two concurrent languages. The languages are nonuniform in the sense that the meaning of atomic statements generally depends on the current state. The first language, L1, has parallel composition but no communication, whereas the second one, L2, has CSP-like communications in addition. For each of Li (i = 1, 2), an operational model Oi is introduced in terms of a Plotkin-style transition system, while a denotational model Di for Li is defined compositionally using interpreted operations of the language, with meanings of recursive programs as fixed points in appropriate complete metric spaces. The full abstraction is shown by means of a context with parallel composition: Given two statements s1 and s2 with different denotational meanings, a suitable statement T is constructed such that the operational meanings of s1 ∥ T and s2 ∥ T are distinct. A combinatorial method for constructing such T is proposed. Thereby the full abstraction of D1 and D2 w.r.t. O1 and O2, respectively, is established. That is, Di is most abstract of those models C which are compositional and satisfy Oi = α ∘ C for some abstraction function α (i = 1, 2)