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A congruence rule format for namepassing process calculi from mathematical structural operational semantics
 In Proc. LICS’06
, 2006
"... We introduce a GSOSlike rule format for namepassing process calculi. Specifications in this format correspond to theories in nominal logic. The intended models of such specifications arise by initiality from a general categorical model theory. For operational semantics given in this rule format, a ..."
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We introduce a GSOSlike rule format for namepassing process calculi. Specifications in this format correspond to theories in nominal logic. The intended models of such specifications arise by initiality from a general categorical model theory. For operational semantics given in this rule format, a natural behavioural equivalence — a form of open bisimilarity — is a congruence.
About permutation algebras, (pre)sheaves and named sets
 In Higher Order and Symbolic Computation
, 2006
"... Abstract. In this paper, we survey some wellknown approaches proposed as general models for calculi dealing with names (like e.g. process calculi with namepassing). We focus on (pre)sheaf categories, nominal sets, permutation algebras and named sets. We study the relationships among these models, w ..."
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Abstract. In this paper, we survey some wellknown approaches proposed as general models for calculi dealing with names (like e.g. process calculi with namepassing). We focus on (pre)sheaf categories, nominal sets, permutation algebras and named sets. We study the relationships among these models, which allow for transferring techniques and constructions from one model to the other.
A Dependent Type Theory with Names and Binding
 In Proceedings of the 2004 Computer Science Logic Conference, number 3210 in Lecture notes in Computer Science
, 2004
"... We consider the problem of providing formal support for working with abstract syntax involving variable binders. Gabbay and Pitts have shown in their work on FraenkelMostowski (FM) set theory how to address this through firstclass names: in this paper we present a dependent type theory for prog ..."
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Cited by 18 (1 self)
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We consider the problem of providing formal support for working with abstract syntax involving variable binders. Gabbay and Pitts have shown in their work on FraenkelMostowski (FM) set theory how to address this through firstclass names: in this paper we present a dependent type theory for programming and reasoning with such names. Our development is based on a categorical axiomatisation of names, with freshness as its central notion. An associated adjunction captures constructions known from FM theory: the freshness quantifier N , namebinding, and unique choice of fresh names. The Schanuel topos  the category underlying FM set theory  is an instance of this axiomatisation.
Coalgebraic modal logic beyond Sets
 In MFPS XXIII
, 2007
"... Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be ..."
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Cited by 14 (4 self)
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Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be
A unifying model of variables and names
 Foundations of Software Science and Computational Structures, vol. 3441, Lect. Notes in Comp. Sci
, 2005
"... Abstract. We investigate a category theoretic model where both “variables” and “names”, usually viewed as separate notions, are particular cases of the more general notion of distinction. The key aspect of this model is to consider functors over the category of irreflexive, symmetric finite relation ..."
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Abstract. We investigate a category theoretic model where both “variables” and “names”, usually viewed as separate notions, are particular cases of the more general notion of distinction. The key aspect of this model is to consider functors over the category of irreflexive, symmetric finite relations. The models previously proposed for the notions of “variables ” and “names ” embed faithfully in the new one, and initial algebra/final coalgebra constructions can be transferred from the formers to the latter. Moreover, the new model admits a definition of distinctionaware simultaneous substitutions. As a substantial application example, we give the first semantic interpretation of MillerTiu’s FOλ ∇ logic. 1
Mathematical models of computational and combinatorial structures. Invited address for Foundations
 of Software Science and Computation Structures (FOSSACS 2005
, 2005
"... Abstract. The general aim of this talk is to advocate a combinatorial perspective, together with its methods, in the investigation and study of models of computation structures. This, of course, should be taken in conjunction with the wellestablished views and methods stemming from algebra, category ..."
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Abstract. The general aim of this talk is to advocate a combinatorial perspective, together with its methods, in the investigation and study of models of computation structures. This, of course, should be taken in conjunction with the wellestablished views and methods stemming from algebra, category theory, domain theory, logic, type theory, etc. In support of this proposal I will show how such an approach leads to interesting connections between various areas of computer science and mathematics; concentrating on one such example in some detail. Specifically, I will consider the line of my research involving denotational models of the pi calculus and algebraic theories with variablebinding operators, indicating how the abstract mathematical structure underlying these models fits with that of Joyal’s combinatorial species of structures. This analysis suggests both the unification and generalisation of models, and in the latter vein I will introduce generalised species of structures and their calculus. These generalised species encompass and generalise various of the notions of species used in combinatorics. Furthermore, they have a rich mathematical structure (akin to models of Girard’s linear logic) that can be described purely within Lawvere’s generalised logic. Indeed, I will present and treat the cartesian closed structure, the linear structure, the differential structure, etc. of generalised species axiomatically in this mathematical framework. As an upshot, I will observe that the setting allows for interpretations of computational calculi (like the lambda calculus, both typed and untyped; the recently introduced differential lambda calculus of Ehrhard and Regnier; etc.) that can be directly seen as translations into a more basic elementary calculus of interacting agents that compute by communicating and operating upon structured data.
Bialgebraic Methods and Modal Logic in Structural Operational Semantics
 Electronic Notes in Theoretical Computer Science
, 2007
"... Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various ..."
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Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various kinds of operational descriptions in a uniform fashion. In this paper, bialgebraic semantics is combined with a coalgebraic approach to modal logic in a novel, general approach to proving the compositionality of process equivalences for languages defined by structural operational semantics. To prove compositionality, one provides a notion of behaviour for logical formulas, and defines an SOSlike specification of modal operators which reflects the original SOS specification of the language. This approach can be used to define SOS congruence formats as well as to prove compositionality for specific languages and equivalences. Key words: structural operational semantics, coalgebra, bialgebra, modal logic, congruence format 1
πcalculus in logical form
 Logic in Computer Science, LICS 2007
, 2007
"... Abramsky’s logical formulation of domain theory is extended to encompass the domain theoretic model for picalculus processes of Stark and of Fiore, Moggi and Sangiorgi. This is done by defining a logical counterpart of categorical constructions including dynamic name allocation and name exponentiati ..."
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Abramsky’s logical formulation of domain theory is extended to encompass the domain theoretic model for picalculus processes of Stark and of Fiore, Moggi and Sangiorgi. This is done by defining a logical counterpart of categorical constructions including dynamic name allocation and name exponentiation, and showing that they are dual to standard constructs in functor categories. We show that initial algebras of functors defined in terms of these constructs give rise to a logic that is sound, complete, and characterises bisimilarity. The approach is modular, and we apply it to derive a logical formulation of picalculus. The resulting logic is a modal calculus with primitives for input, free output and bound output. 1.
A study of substitution, using nominal techniques and FraenkelMostowki sets
"... FraenkelMostowski (FM) set theory delivers a model of names and alphaequivalence. This model, now generally called the ‘nominal ’ model, delivers inductive datatypes of syntax with alphaequivalence — rather than inductive datatypes of syntax, quotiented by alphaequivalence. The treatment of name ..."
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FraenkelMostowski (FM) set theory delivers a model of names and alphaequivalence. This model, now generally called the ‘nominal ’ model, delivers inductive datatypes of syntax with alphaequivalence — rather than inductive datatypes of syntax, quotiented by alphaequivalence. The treatment of names and alphaequivalence extends to the entire sets universe. This has proven useful for developing ‘nominal ’ theories of reasoning and programming on syntax with alphaequivalence, because a sets universe includes elements representing functions, predicates, and behaviour. Often, we want names and alphaequivalence to model captureavoiding substitution. In this paper we show that FM set theory models captureavoiding subsitution for names in much the same way as it models alphaequivalence; as an operation valid for the entire sets universe which coincides with the usual (inductively defined) operation on inductive datatypes. In fact, more than one substitution action is possible (they all agree on sets representing