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Rushby, N. Shankar, and F von Henke. Formal veriﬁcation for faulttolerant architectures: Prolegomena to the design of PVS. IEEE Transactions on Software Engineering, 21(2):107–125, 1995. 16. A. Simpson. Compositionality via cut-elimination: Hennesy-Milner logic for an arbitrary GSOS. In Proceedings of the Tenth Annual IEEE Symposium on Logic in Computer Science (LICS), pages 420–430, 1995. 17. G. Smith and D. Volpano. Secure information ﬂow in a multi-threaded imperative language. In Proceedings of POPL’98, pages 355–364.
The export interface EXP2 is the same net as the import interface IM P1 of COM P1 . The export transformation exp2 : EXP2 ⇒ BOD2 adds two new operations do1, do2: Object → Object to the signature. The run-transition is removed and replaced by two new transitions act1 and act2 with an intermediate place working (see Fig. 7). We assume that the algebra ABOD2 satisﬁes the equation do2(do1(o)) = do(o) because sequential ﬁring of act1 and act2 should still produce the same result as before. runnable t t t started st(t,o) act1 t st(t,do1(o)) working st(t,o) Fig.
N ψ1 , . . , ψn . e. φ1 ∧ . . ∧ φn ⇒ ψ1 ∨ . . ∨ ψn . Formally, we deﬁne the building blocks of our proof system as follows. Definition 6 (Assertion, Sequent). (i) An assertion γ is either a satisfaction assertion A : φ, where φ is a proposiα tionally closed formula, a transition assertion A1 − → A2 , an atomic formula T assertion σ, a transfer-edge assertion v → v , a call-edge assertion v →C v , or a wellformedness assertion wf(A). (ii) Assertion A : φ is valid for program model M and environment ρ if Aρ ∈ αρ α φ M → A2 is valid for M and ρ if A1 ρ −→M A2 ρ.