R. Milner. The -calculus. Undergraduate lecture notes, Cambridge University, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and fv(P ) for the sets of variables free in M and P respectively. An expression is closed if it has no free variables. A closed expression may have free names. 11 3. 2 Commitment We give an operational semantics for the spi calculus by defining a commitment relation, in the style of Milner [Mil95] The definition of commitment depends on some new syntactic forms, abstractions and concretions. An abstraction is an expression of the form (x 1 , x k )P , where k # 0, x 1 , x k are bound variables, and P is a process. A concretion is an expression of the form (#m 1 , ....

R. Milner. The #-calculus. Undergraduate lecture notes, Cambridge University, 1995.

....27 5.1 The Commitment Relation The original semantics of the pi calculus (given in [MPW92] is not based on the notion of reaction, but rather on a labelled transition system. Here we define a labelled transition semantics for the spi calculus, imitating Milner s recent lecture notes [Mil95b]. Despite di#erences in style, this semantics is essentially equivalent to the one of Section 4, so it can be used in proofs about that semantics. In order to define the labelled transition semantics, we need some new syntactic forms: abstractions, concretions, and agents. An abstraction is an ....

....on processes that approximate testing equivalence. In particular, in Section 5.2.3, we define barbed congruence, which is a stronger relation than testing equivalence but is sometimes easier to prove directly. 5.2. 1 Strong bisimilarity We first recall the definition of strong bisimulation [Mil95b]. If R is a relation on closed processes, we define the relation R on closed agents: P R Q i# P R Q (x)P R (x)Q i# P [M x] R Q[M x] for all closed M (##n)#M#P R (# # m)#M#Q i# # m is a permutation of #n and P R Q A strong simulation is a binary relation S # Proc Proc such ....

R. Milner. The #-calculus. Undergraduate lecture notes, Cambridge University, 1995.

....ambient calculus and reviews the strong bisimilarity relation a standard notion of behavioral equivalence induced by commitment. The use of structural congruence to define reduction results in an elegant and compact definition, but also complicates proofs about reduction. As in the calculus [1, 4, 7], the purpose of the commitment relation is to characterise reduction independently of structural congruence. Section 2.1 introduces the commitment relation. In calculus jargon our relation is an early transition system; we discuss how to obtain a late variant of our transition system in ....

Robin Milner. The ß-calculus. Undergraduate lecture notes, Cambridge University, 1995.

....a new technique, based on a hardening relation, for defining the labelled transition system. We employed these tools to prove equational properties of mobile ambients. Our use of concretions to highlight those subprocesses of a process that may participate in a computation follows Milner [10, 11], and is an alternative to the use of membranes and airlocks in the chemical abstract machine of Berry and Boudol [5] Unlike these authors, in the definition of our transition relation we use the hardening relation, rather than the full structural congruence relation, to choose subprocesses to ....

R. Milner. The ß-calculus. Undergraduate lecture notes, Cambridge University, 1995.

....equivalence. 5.1 The Commitment Relation The original semantics of the pi calculus (given in [MPW92] is not based on the notion of reaction, but rather on a labelled transition system. Here we define a labelled transition semantics for the spi calculus, imitating Milner s recent lecture notes [Mil95b]. Despite differences in style, this semantics is essentially equivalent to the one of Section 4, so it can be used in proofs about that semantics. We need some new syntactic forms. An abstraction is an expression of the form (x)P , where x is a bound variable and P is a process. A concretion is ....

....on processes that approximate testing equivalence. In particular, in Section 5.2.3, we define barbed congruence, which is a stronger relation than testing equivalence but is sometimes easier to prove directly. 5.2. 1 Strong bisimilarity We first recall the definition of strong bisimulation [Mil95b]. If R is a relation on closed processes, we define the relation R on closed agents: P R Q iff P R Q (x)P R (x)Q iff P [M=x] R Q[M=y] for all closed M ( n)hMiP R ( m)hMiQ iff m is a permutation of n and P R Q A strong simulation is a binary relation S Proc Theta Proc such that if P S ....

R. Milner. The ß-calculus. Undergraduate lecture notes, Cambridge University, 1995.

....a new technique, based on a hardening relation, for defining the labelled transition system. We employed these tools to prove equational properties of mobile ambients. Our use of concretions to highlight those subprocesses of a process that may participate in a computation follows Milner [11, 12], and is an alternative to the use of membranes and airlocks in the chemical abstract machine of Berry and Boudol [5] Unlike these authors, in the definition of our transition relation we use the hardening relation, rather than the full structural congruence relation, to choose subprocesses to ....

R. Milner. The ß-calculus. Undergraduate lecture notes, Cambridge University, 1995.

....The definition of reaction is rather elegant, but not convenient for proofs (because it relies on an auxiliary notion of structural equivalence) Therefore, we provide an alternative, direct characterisation of reaction. We achieve this by defining a commitment relation, in the style of Milner [Mil95b]. The Reaction Relation The definition of reaction has several phases. First we define a reduction relation on Proc. We require that P (P j P ) that [M is M ] P P , and that case fMgN of fxgN in P P [M=x] we omit similar conditions for let and for the case construct for numerals. ....

.... m is a permutation of n and P R Q A strong simulation is a binary relation S on Proc such that if P S Q and P ff Gamma A then there exists B with Q ff Gamma B and A S B. A relation S is a strong bisimulation if and only if both S and its converse S Gamma1 are strong simulations [Mil95b]. Strong bisimilarity, written s , is the greatest strong bisimulation, namely the union of all strong bisimulations. Strong bisimilarity is a rather fine grained equivalence for the spi calculus. For instance, it discriminates between the processes (K)chfMgK i and (K)chfM 0 gK i, which we ....

R. Milner. The ß-calculus. Undergraduate lecture notes, Cambridge University, 1995.

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R. Milner. The -calculus. Undergraduate lecture notes, Cambridge University, 1995.

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R. Milner. The -calculus. Undergraduate lecture notes, Cambridge University, 1995.

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R. Milner. The #-calculus. Undergraduate lecture notes, Cambridge University, 1995.

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R. Milner. The -calculus. Undergraduate lecture notes, Cambridge University, 1995.

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