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177
A new approach to abstract syntax with variable binding
 Formal Aspects of Computing
, 2002
"... Abstract. The permutation model of set theory with atoms (FMsets), devised by Fraenkel and Mostowski in the 1930s, supports notions of ‘nameabstraction ’ and ‘fresh name ’ that provide a new way to represent, compute with, and reason about the syntax of formal systems involving variablebinding op ..."
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Cited by 287 (63 self)
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Abstract. The permutation model of set theory with atoms (FMsets), devised by Fraenkel and Mostowski in the 1930s, supports notions of ‘nameabstraction ’ and ‘fresh name ’ that provide a new way to represent, compute with, and reason about the syntax of formal systems involving variablebinding operations. Inductively defined FMsets involving the nameabstraction set former (together with Cartesian product and disjoint union) can correctly encode syntax modulo renaming of bound variables. In this way, the standard theory of algebraic data types can be extended to encompass signatures involving binding operators. In particular, there is an associated notion of structural recursion for defining syntaxmanipulating functions (such as capture avoiding substitution, set of free variables, etc.) and a notion of proof by structural induction, both of which remain pleasingly close to informal practice in computer science. 1.
Fresh Logic
 Journal of Applied Logic
, 2007
"... Abstract. The practice of firstorder logic is replete with metalevel concepts. Most notably there are metavariables ranging over formulae, variables, and terms, and properties of syntax such as alphaequivalence, captureavoiding substitution and assumptions about freshness of variables with resp ..."
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Cited by 219 (28 self)
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Abstract. The practice of firstorder logic is replete with metalevel concepts. Most notably there are metavariables ranging over formulae, variables, and terms, and properties of syntax such as alphaequivalence, captureavoiding substitution and assumptions about freshness of variables with respect to metavariables. We present oneandahalfthorder logic, in which these concepts are made explicit. We exhibit both sequent and algebraic specifications of oneandahalfthorder logic derivability, show them equivalent, show that the derivations satisfy cutelimination, and prove correctness of an interpretation of firstorder logic within it. We discuss the technicalities in a wider context as a casestudy for nominal algebra, as a logic in its own right, as an algebraisation of logic, as an example of how other systems might be treated, and also as a theoretical foundation
Nominal Logic: A First Order Theory of Names and Binding
 Information and Computation
, 2001
"... This paper formalises within firstorder logic some common practices in computer science to do with representing and reasoning about syntactical structures involving named bound variables (as opposed to nameless terms, explicit substitutions, or higher order abstract syntax). It introduces Nominal L ..."
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Cited by 219 (15 self)
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This paper formalises within firstorder logic some common practices in computer science to do with representing and reasoning about syntactical structures involving named bound variables (as opposed to nameless terms, explicit substitutions, or higher order abstract syntax). It introduces Nominal Logic, a version of firstorder manysorted logic with equality containing primitives for renaming via nameswapping and for freshness of names, from which a notion of binding can be derived. Its axioms express...
Separation and Information Hiding
, 2004
"... We investigate proof rules for information hiding, using the recent formalism of separation logic. In essence, we use the separating conjunction to partition the internal resources of a module from those accessed by the module's clients. The use of a logical connective gives rise to a form of d ..."
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Cited by 184 (19 self)
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We investigate proof rules for information hiding, using the recent formalism of separation logic. In essence, we use the separating conjunction to partition the internal resources of a module from those accessed by the module's clients. The use of a logical connective gives rise to a form of dynamic partitioning, where we track the transfer of ownership of portions of heap storage between program components. It also enables us to enforce separation in the presence of mutable data structures with embedded addresses that may be aliased.
Mechanized metatheory for the masses: The POPLmark challenge
 In Theorem Proving in Higher Order Logics: 18th International Conference, number 3603 in LNCS
, 2005
"... Abstract. How close are we to a world where every paper on programming languages is accompanied by an electronic appendix with machinechecked proofs? We propose an initial set of benchmarks for measuring progress in this area. Based on the metatheory of System F<:, a typed lambdacalculus with se ..."
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Cited by 161 (14 self)
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Abstract. How close are we to a world where every paper on programming languages is accompanied by an electronic appendix with machinechecked proofs? We propose an initial set of benchmarks for measuring progress in this area. Based on the metatheory of System F<:, a typed lambdacalculus with secondorder polymorphism, subtyping, and records, these benchmarks embody many aspects of programming languages that are challenging to formalize: variable binding at both the term and type levels, syntactic forms with variable numbers of components (including binders), and proofs demanding complex induction principles. We hope that these benchmarks will help clarify the current state of the art, provide a basis for comparing competing technologies, and motivate further research. 1
A Metalanguage for Programming with Bound Names Modulo Renaming
 Mathematics of Program Construction, volume 1837 of Lecture Notes in Computer Science
, 2000
"... This paper describes work in progress on the design of an MLstyle metalanguage FreshML for programming with recursively defined functions on userdefined, concrete data types whose constructors may involve variable binding. Up to operational equivalence, values of such FreshML data types can faithf ..."
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Cited by 95 (21 self)
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This paper describes work in progress on the design of an MLstyle metalanguage FreshML for programming with recursively defined functions on userdefined, concrete data types whose constructors may involve variable binding. Up to operational equivalence, values of such FreshML data types can faithfully encode terms modulo alphaconversion for a wide range of object languages in a straightforward fashion. The design of FreshML is `semantically driven', in that it arises from the model of variable binding in set theory with atoms given by the authors in [7]. The language has a type constructor for abstractions over names ( = atoms) and facilities for declaring locally fresh names. Moreover, recursive definitions can use a form of patternmatching on bound names in abstractions. The crucial point is that the FreshML type system ensures that these features can only be used in welltyped programs in ways that are insensitive to renaming of bound names.
Accomplishments and Research Challenges in MetaProgramming
 In 2nd Int. Workshop on Semantics, Applications, and Implementation of Program Generation, LNCS 2196
, 2000
"... this paper into several sections. As an overview, in Section 2, I try and classify metaprograms into groups. The purpose of this is to provide a common vocabulary which we can use to describe metaprogramming systems in the rest of the paper ..."
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Cited by 84 (6 self)
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this paper into several sections. As an overview, in Section 2, I try and classify metaprograms into groups. The purpose of this is to provide a common vocabulary which we can use to describe metaprogramming systems in the rest of the paper
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 70 (28 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.
Some lambda calculus and type theory formalized
 Journal of Automated Reasoning
, 1999
"... Abstract. We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified, proof of standardization for beta reduction, that does not mention ..."
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Cited by 64 (10 self)
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Abstract. We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified, proof of standardization for beta reduction, that does not mention redex positions or residuals. Then we outline the meta theory of Pure Type Systems, leading to the strengthening lemma. One novelty is our use of named variables for the formalization. Along the way we point out what we feel has been learned about general issues of formalizing mathematics, emphasizing the search for formal definitions that are convenient for formal proof and convincingly represent the intended informal concepts.
A Spatial Logic for Concurrency (Part II)
 IN CONCUR2002: CONCURRENCY THEORY (13TH INTERNATIONAL CONFERENCE), LECTURE NOTES IN COMPUTER SCIENCE
, 1998
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