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27
FreshML: Programming with Binders Made Simple
, 2003
"... FreshML extends ML with elegant and practical constructs for declaring and manipulating syntactical data involving binding operations. Userdeclared FreshML datatypes involving binders are concrete, in the sense that values of these types can be deconstructed by matching against patterns naming boun ..."
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Cited by 78 (23 self)
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FreshML extends ML with elegant and practical constructs for declaring and manipulating syntactical data involving binding operations. Userdeclared FreshML datatypes involving binders are concrete, in the sense that values of these types can be deconstructed by matching against patterns naming bound variables explicitly. Such matching may have a computational effect in which bound names get swapped with freshly generated names. Previous work on FreshML used a complicated static type system inferring information about the `freshness' of names for expressions in order to tame such effects. The main contribution of this paper is to show (perhaps surprisingly) that a much simpler type system without freshness inference, coupled with name swapping and a conventional treatment of fresh name generation, suffices for FreshML's crucial correctness propertynamely that values of datatypes involving binders are operationally equivalent if and only if they represent #equivalent pieces of objectlevel syntax. This correctness result is established via a novel denotational semantics. FreshML without static freshness inference is no more impure than ML and our experiences programming in it show that it supports a programming style pleasingly close to informal practice when it comes to dealing with syntax modulo #equivalence.
Nominal Unification
 Theoretical Computer Science
, 2003
"... We present a generalisation of firstorder unification to the practically important case of equations between terms involving binding operations. A substitution of terms for variables solves such an equation if it makes the equated terms #equivalent, i.e. equal up to renaming bound names. For the a ..."
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Cited by 52 (20 self)
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We present a generalisation of firstorder unification to the practically important case of equations between terms involving binding operations. A substitution of terms for variables solves such an equation if it makes the equated terms #equivalent, i.e. equal up to renaming bound names. For the applications we have in mind, we must consider the simple, textual form of substitution in which names occurring in terms may be captured within the scope of binders upon substitution. We are able to take a `nominal' approach to binding in which bound entities are explicitly named (rather than using nameless, de Bruijnstyle representations) and yet get a version of this form of substitution that respects #equivalence and possesses good algorithmic properties. We achieve this by adapting an existing idea and introducing a key new idea. The existing idea is terms involving explicit substitutions of names for names, except that here we only use explicit permutations (bijective substitutions). The key new idea is that the unification algorithm should solve not only equational problems, but also problems about the freshness of names for terms. There is a simple generalisation of the classical firstorder unification algorithm to this setting which retains the latter's pleasant properties: unification problems involving #equivalence and freshness are decidable; and solvable problems possess most general solutions.
TQL: A Query Language for Semistructured Data Based on the Ambient Logic
 Mathematical Structures in Computer Science
, 2003
"... this paper we present TQL, a query language for semistructured data that is based on the ambient logic ..."
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Cited by 25 (1 self)
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this paper we present TQL, a query language for semistructured data that is based on the ambient logic
Spatial Logics for Bigraphs
 In Proceedings of ICALP’05, volume 3580 of LNCS
, 2005
"... Abstract. Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, picalculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper)graph for connections. With the aim of describing bigraphical structur ..."
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Cited by 21 (2 self)
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Abstract. Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, picalculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper)graph for connections. With the aim of describing bigraphical structures, we introduce a general framework for logics whose terms represent arrows in monoidal categories. We then instantiate the framework to bigraphical structures and obtain a logic that is a natural composition of a place graph logic and a link graph logic. We explore the concepts of separation and sharing in these logics and we prove that they generalise some known spatial logics for trees, graphs and tree contexts. 1
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 15 (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.
Behavioral and Spatial Observations in a Logic for the πCalculus
, 2004
"... In addition to behavioral properties, spatial logics can talk about other key properties of concurrent systems such as secrecy, freshness, usage of resources, and distribution. We study an expressive spatial logic for systems specified in the synchronous πcalculus with recursion, based on a small s ..."
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Cited by 11 (1 self)
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In addition to behavioral properties, spatial logics can talk about other key properties of concurrent systems such as secrecy, freshness, usage of resources, and distribution. We study an expressive spatial logic for systems specified in the synchronous πcalculus with recursion, based on a small set of behavioral and spatial observations. We give coinductive and equational characterizations of the equivalence induced on processes by the logic, and conclude that it strictly lies between structural congruence and strong bisimulation. We then show that modelchecking is decidable for a useful class of processes that includes the finitecontrol fragment of the πcalculus.
Decidability of Freshness, Undecidability of Revelation
 IN PROC. OF INTERNATIONAL CONFERENCE ON FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATIONAL STRUCTURES (FOSSACS), VOLUME 2987 OF LNCS
, 2003
"... We study decidability of a logic for describing processes with restricted names. We choose a minimal fragment of the Ambient Logic, but the techniques we present should apply to every logic which uses Cardelli and Gordon revelation and hiding operators, and Gabbay and Pitts freshness quantifier. We ..."
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Cited by 9 (2 self)
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We study decidability of a logic for describing processes with restricted names. We choose a minimal fragment of the Ambient Logic, but the techniques we present should apply to every logic which uses Cardelli and Gordon revelation and hiding operators, and Gabbay and Pitts freshness quantifier. We start from the static fragment of ambient logic that Calcagno Cardelli and Gordon proved to be decidable. We prove that the addition of a hiding quantifier makes the logic undecidable. Hiding can be decomposed as freshness plus revelation. Quite surprisingly, freshness alone is decidable, but revelation alone is not.
Adjuncts elimination in the static ambient logic
, 2003
"... The Ambient Logic (AL) has been proposed for expressing spatial properties of processes of the Mobile Ambient calculus (MA). Restricting both the calculus and the logic to their static part yields static ambients (SA) and the static ambient logic (SAL), that form a model for queries about semistruct ..."
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Cited by 9 (2 self)
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The Ambient Logic (AL) has been proposed for expressing spatial properties of processes of the Mobile Ambient calculus (MA). Restricting both the calculus and the logic to their static part yields static ambients (SA) and the static ambient logic (SAL), that form a model for queries about semistructured data. SAL also includes the nonstandard fresh quantifier (I). This work adresses the questions of expressiveness and minimality of SAL from the point of view of adjuncts. We define the intensional fragment of the logic (SALint), the logic without adjuncts, and prove that it captures all the expressiveness of the logic. We moreover study the question of adjuncts elimination in SAL ∀ , where I quantifier is replaced by the classical ∀ quantifier. We conclude with a proof of the minimality of SALint.
Elimination of spatial connectives in static spatial logics
, 2003
"... The recent interest for specification on resources yields socalled spatial logics, that is specification languages offering spatial connectives: a separation into two subcomponents of the considered structure, (∗,or ), and its adjunct, the guarantee respect to the extension of the structure (− ∗ , ..."
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Cited by 8 (0 self)
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The recent interest for specification on resources yields socalled spatial logics, that is specification languages offering spatial connectives: a separation into two subcomponents of the considered structure, (∗,or ), and its adjunct, the guarantee respect to the extension of the structure (− ∗ , ⊲). We consider two resource models and their related logics: • the Static Ambient (SA), proposed as a model of semistructured data [4], with the Static Ambient Logic (SAL) that was proposed as a request language, both obtained restricting the Mobile Ambient calculus [5] and logic [6] to their purely static aspects. • the shared mutable data structures adressed by the Separation Logic (SL), as it has been defined in [15] as an adequate assertion language for Hoare style reasoning on imperative programs manipulating pointers. We raise the questions of the expressiveness and the minimality of these logics. Our main contributions are the elimination of adjuncts for SAL, the minimality of the adjunctfree fragment (SALint), and the elimination of both spatial connectives ∗ and − ∗ for SL.
Elimination of Quantifiers and Undecidability in Spatial Logics for Concurrency
, 2004
"... The introduction of spatial logics in concurrency is motivated by a shift of focus from concurrent systems towards distributed systems. Aiming at a deeper understanding of the essence of dynamic spatial logics, we study a minimal spatial logic without quantifiers or any operators talking about names ..."
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Cited by 8 (2 self)
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The introduction of spatial logics in concurrency is motivated by a shift of focus from concurrent systems towards distributed systems. Aiming at a deeper understanding of the essence of dynamic spatial logics, we study a minimal spatial logic without quantifiers or any operators talking about names. The logic just includes the basic spatial operators void, composition and its adjunct, and the next step modality; for the model we consider a tiny fragment of CCS. We show that this core logic can already encode its own extension with quantifiers, and modalities for actions. From this result, we derive several consequences. Firstly, we establish the intensionality of the logic, we characterize the equivalence it induces on processes, and we derive characteristic formulas. Secondly, we show that, unlike in static spatial logics, the composition adjunct adds to the expressiveness of the logic, so that adjunct elimination is not possible for dynamic spatial logics, even quantifierfree. Finally, we prove that both modelchecking and satisfiability problems are undecidable in our logic. We also conclude that our results extend to other calculi, namely the #calculus and the ambient calculus.