Functional Programming 1 Transactional Events : Technical Appendix ∗

Lemma 11 If {〈θ1, e1〉, . . . , 〈θk, ek〉} {〈θ1, e1〉, . . . , 〈θk, ek〉} according to the semantics of Figure 3, the set of trails {〈θ1, ρ1〉, . . . , 〈θk, ρk〉} is committable, and P is a set of search threads, each with a thread identifier in {θ1, . . . , θk}, then {〈θ1, e1, ρ1〉, . . . , 〈θk, ek, ρk〉}]P − → {〈θ1, e1, ρ1〉, . . . , 〈θk, ek, ρk〉}]P ′ according to the semantics of Figure 9, the set of trails {〈θ1, ρ1〉, . . . , 〈θk, ρk〉} is committable, and P ′ is a set of search threads, each with a thread identifier in {θ1, . . . , θk}.