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Processes, Terms and Cycles: Steps on the Road to Infinity: by Aart Middeldorp, Vincent van Oostrom, Femke van Raamsdonk,

By Aart Middeldorp, Vincent van Oostrom, Femke van Raamsdonk, Roel de Vrijer

This Festschrift is devoted to Jan Willem Klop at the get together of his sixtieth birthday. the quantity includes a complete of 23 medical papers via shut buddies and co-workers, written particularly for this ebook. The papers are diverse in nature: a few record on new examine, others have the nature of a survey, and back others are as a rule expository. each contribution has been completely refereed no less than two times. in lots of instances the 1st around of referee experiences resulted in major revision of the unique paper, which was once back reviewed. The articles particularly concentration upon the lambda calculus, time period rewriting and method algebra, the fields to which Jan Willem Klop has made basic contributions.

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3). The definition of 0 and a. on G(Act) is exactly as on G | However, defining the + on G(Act) as in Def. 3 would yield counterintuitive results. Namely we would have g + h = m, as in the top row of Fig. 1. However, m is able to first do a number of a-actions from g and then a b from h; this is inconsistent with the idea that g + h should from the initial state onwards behave either as g or as h. In fact, strong bisimulation equivalence would fail to be a congruence for this definition of +, for g ↔ g ρ , yet m ↔ k.

Proof. Let a semantic context C[·] be an expression build from process graphs | and the hole [·] through application of operators from L, and in g ∈ G(Act) | which the hole occurs exactly once. If C[·] is a semantic context and g ∈ G(Act), then C[g] denotes the process graph obtained by evaluating the expression C[·] in which g is substituted for the hole [·]. Alternatively, a semantic context can be regarded as a unary operator on process graphs: a primitive context is obtained from an operator in L by instantiating all but one of its arguments by process graphs; and a general semantic context is the composition of any number (possibly 0) of primitive contexts.

By the Bernardi-de Jongh-Sambin uniqueness theorem, τ α must be provably equivalent to β. We turn to the case that all non-modalized occurrences of p are positive. Suppose that p is not in φ and not in the domain and not in the range of τ . We construct φp p in such a way that φpp = φp, all occurrences of p are non-modalized and positive and all occurrences of p are boxed. By our preceding results α is, modulo provable equivalence, the fixed point of φ⊥p. Consider τ φp p. It is easy to see that [p := p]τ φp p = τ φpp = τ φp.

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