Online partial evaluation for shift and reset
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A fresh approach to representing syntax with static binders in functional programming
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A spatial logic for concurrency (part I)
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A unified category theoretic approach to variable binding
MERLIN '03 Proceedings of the 2003 ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
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Coalgebraic minimization of HD-automata for the π-calculus using polymorphic types
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Structured coalgebras and minimal HD-automata for the π-calculus
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Manipulating Trees with Hidden Labels
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Structuring Operational Semantics: Simplification and Computation
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A general mathematics of names
Information and Computation
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Multiple-labelled transition systems for nominal calculi and their logics†
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A Name Abstraction Functor for Named Sets
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Functorial Coalgebraic Logic: The Case of Many-sorted Varieties
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Term Equational Systems and Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
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Modules over monads and initial semantics
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Normalization by evaluation for the computational lambda-calculus
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Modules over monads and linearity
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Families of Symmetries as Efficient Models of Resource Binding
Electronic Notes in Theoretical Computer Science (ENTCS)
On universal algebra over nominal sets
Mathematical Structures in Computer Science
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Mathematical models of computational and combinatorial structures
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Binding signatures for generic contexts
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The ∇-calculus. functional programming with higher-order encodings
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A characterisation of languages on infinite alphabets with nominal regular expressions
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LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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The Fraenkel-Mostowski permutation model of set theory with atoms (FM-sets) can serve as the semantic basis of meta-logics for specifying and reasoning about formal systems involving name binding, alpha-conversion, capture avoiding substitution, and so on. We show that in FM-set theory one can express statements quantifying over `fresh' names and we use this to give a novel set-theoretic interpretation of name abstraction. Inductively defined FM-sets involving this name-abstraction set former (together with cartesian product and disjoint union) can correctly encode object-level syntax modulo alpha-conversion. 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 syntax-manipulating 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.