From Object-Orientation to Formal Methods: Essays in Memory by Olaf Owe, Stein Krogdahl, Tom Lyche

By Olaf Owe, Stein Krogdahl, Tom Lyche

After Ole-Johan’s retirement in the beginning of the hot millennium, a few of us had idea and mentioned creating a “Festschrift” in his honor. whilst Donald Knuth took the initiative via sending us the ?rst contribution, the p- cess started to roll! In early 2002 an modifying staff was once shaped, together with Kristen Nygaard, who had identified Ole-Johan on account that their pupil days, and with whom he had built the Simula language. Then we invited a few favorite researchers accustomed to Ole-Johan to post contributions for a booklet hon- ing Ole-Johan at the get together of his seventieth birthday. Invitees incorporated a number of individuals of the IFIP 2. three operating staff, a discussion board that Ole-Johan valuable and enjoyedparticipating in throughouthis profession. inspite of the shortdeadline, the reaction to the invites used to be overwhelmingly optimistic. the unique inspiration used to be to accomplish the booklet particularly fast to make it a present he might learn and revel in, simply because by way of then he had had melanoma for 3 years, and his overall healthiness used to be steadily deteriorating. Kristen were frequently traveling Ole-Johan,who used to be within the hospitalat that point, and so they have been workingon their Turing award speech. Ole-Johan was once grati?ed to listen to concerning the contributions to this publication, yet modestly expressed the sensation that there has been no specified have to adopt a e-book undertaking on his behalf. Peacefully accepting his future, Ole- Johan died on June 29, 2002.

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From OO to FM (Dahl Festschrift), LNCS 2635, pp. 26–57, 2004. c Springer-Verlag Berlin Heidelberg 2004 An Algebraic Theory of Actors 27 autonomous agent which has intentions, resources, contain message monitors and a scheduler [19]. Later work by Hewitt and his associates developed a more abstract model of parallelism based on causal relations between asynchronous events at different actors – where an event represents the sending or receiving of a message [10, 16]. The formulation of the Actor Model that most people refer to is based on the transition system in Agha [1].

The first consists of two actors x and y, a message targeted to x, and a message targeted to an actor An Algebraic Theory of Actors 35 z that is external to the sub-configuration. The actor y is a receptionist, while x is hidden. The second sub-configuration, also contains two actors x and z, and a message targeted to an external actor w. Note that although the name x is used to denote two different actors, the uniqueness property of actor names is not violated in R because the scopes of the two restrictions of x do not intersect.

E. reflexive and transitive, and ρ is an equivalence relation. Further, note that the larger the parameter ρ, the smaller ❁ ❁ the observer set that is used to decide ∼ρ . Hence if ρ1 ⊂ ρ2 , we have P ∼ρ1 Q ❁ ❁ ❁ implies P ∼ρ2 Q. However, P ∼ρ2 Q need not imply P ∼ρ1 Q. For instance, ❁ ❁ ❁ 0 {x} xx, but only 0 ∼∅ xx and xx∼/∅ 0. Similarly, xx {x,y} yy, but xx∼/∅ yy ❁ ❁ ❁ and yy∼/∅ xx. However, P ∼ρ2 Q implies P ∼ρ1 Q if fn(P ) ∪ fn(Q) ⊂ ρ1 . ❁ ❁ Theorem 3. Let ρ1 ⊂ ρ2 . Then P ∼ρ1 Q implies P ∼ρ2 Q.

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