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HigherOrder Containers
"... Abstract. Containers are a semantic way to talk about strictly positive types. In previous work it was shown that containers are closed under various constructions including products, coproducts, initial algebras and terminal coalgebras. In the present paper we show that, surprisingly, the category ..."
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Abstract. Containers are a semantic way to talk about strictly positive types. In previous work it was shown that containers are closed under various constructions including products, coproducts, initial algebras and terminal coalgebras. In the present paper we show that, surprisingly, the category of containers is cartesian closed, giving rise to a full cartesian closed subcategory of endofunctors. The result has interesting applications syntax. We also show that the category of containers has finite limits, but it is not locally cartesian closed. 1
Substitution in Structural Operational Semantics and valuepassing process calculi
"... Consider a process calculus that allows agents to communicate values. The structural operational semantics involves substitution of values for variables. Existing rule formats, such as the GSOS format, do not allow this kind of explicit substitution in the semantic rules. We investigate how to deriv ..."
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Consider a process calculus that allows agents to communicate values. The structural operational semantics involves substitution of values for variables. Existing rule formats, such as the GSOS format, do not allow this kind of explicit substitution in the semantic rules. We investigate how to derive rule formats for languages with substitution, by using categorical logic to interpret the framework of the GSOS format in different categories. The categories in question are categories of ‘substitution actions’. 1 A simple language for valuepassing To set the scene, fix a set of channel names, and consider a set V of valueexpressions, that includes the channel names. A simple untyped valuepassing process language, VCCS, is given in Figure 1 (c.f. [8]). The precise value expressions of V are not important, but note that since V includes the (static) channel names, VCCS is a very primitive applied πcalculus without restriction or name generation; c.f. [1]. For the sake of illustration, consider the set Vex of value expressions determined by the following grammar: v:: = n  v + v  (v, v)  π1(v)  π2(v)  c (n is a number, c is a channel name). We will always work with value expressions upto the evident equations (2 + 3 = 5; π1(v, w) = v; etc.), rather than explicitly evaluating or normalizing them; this is to simplify the presentation. The following transitions are derivable in VexCCS. (¯c〈3〉.0)  (c(v).¯c〈2 + v〉.0) τ
Thesis description: Namepassing process calculi: operational models and structural operational semantics.
"... My thesis is about foundations for formal semantics of namepassing process calculi. These calculi are languages for describing systems of agents that communicate channel names along named channels. This facility provides a natural way of describing the mobility of communication links. (The πcalcul ..."
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My thesis is about foundations for formal semantics of namepassing process calculi. These calculi are languages for describing systems of agents that communicate channel names along named channels. This facility provides a natural way of describing the mobility of communication links. (The πcalculus of Milner et al. [1992] is a paradigmatic example of such a language.) The thesis is split into two parts, reflecting the two aspects of the foundations of namepassing calculi that are addressed. • Part I of the thesis is dedicated to operational models for namepassing calculi. Conventional operational models, such as labelled transition systems, are inappropriate for namepassing systems. For this reason I develop and relate two different models of namepassing from the literature: indexed labelled transition systems, based on work of Cattani and Sewell [2004], and a coalgebraic approach introduced by Fiore and Turi [2001]. Connections are made with the History Dependent Automata of Montanari and Pistore [2005], and I introduce a new operational model using the nominal logic of Pitts [2003]. • Part II of the thesis concerns structural operational semantics for namepassing calculi. Various work has been done on the meaning of rulebased transition system specifications, and on
Context Positive structural operational semantics and monotone distributive laws
"... We describe a correspondence between (i) rulebased inductive definitions in the Positive GSOS format, i.e. without negative premises, and (ii) distributive laws in the spirit of Turi and Plotkin (LICS’97), that are suitably monotone. This result can be understood as an isomorphism of lattices, in w ..."
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We describe a correspondence between (i) rulebased inductive definitions in the Positive GSOS format, i.e. without negative premises, and (ii) distributive laws in the spirit of Turi and Plotkin (LICS’97), that are suitably monotone. This result can be understood as an isomorphism of lattices, in which the prime elements are the individual rules. We fix a signature, i.e. a set S of operators, each op ∈ S having an arity, ar(op) ∈ N. We also fix a set L of labels. We are concerned with labelled transition relations over the terms of the signature. For an example, we recall a fragment of Milner’s CCS. Fix a set A of actions. There is a binary operation for parallel composition (written xy), a constant for deadlock, and two unary operations for every action a ∈ A, for prefix and coaction prefix. The set of labels contains actions, coactions, and silent steps: L = A + A + 1. x a − → x ′ y ā − → y ′ xy τ − → x ′ y ′ A labelled transition relation over CCS terms is defined by a transition system specification (TSS). This is a set of rules, including the one in the box on the right. Background on the Positive GSOS rule format li j − → yi j  i ≤ ar(op), j ∈ Ji} {xi lik
Higher Order Containers
"... Abstract. Containers are a semantic way to talk about strictly positive types. In previous work it was shown that containers are closed under various constructions including products, coproducts, initial algebras and terminal coalgebras. In the present paper we show that, surprisingly, the category ..."
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Abstract. Containers are a semantic way to talk about strictly positive types. In previous work it was shown that containers are closed under various constructions including products, coproducts, initial algebras and terminal coalgebras. In the present paper we show that, surprisingly, the category of containers is cartesian closed, giving rise to a full cartesian closed subcategory of endofunctors. The result has interesting applications syntax. We also show that while the category of containers has finite limits, it is not locally cartesian closed. 1