Relational parametricity and local variables
POPL '93 Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Information and Computation
Introduction to ALGOL-like languages
ALGOL-like Languages, Volume 1
Semantic analysis of normalisation by evaluation for typed lambda calculus
Proceedings of the 4th ACM SIGPLAN international conference on Principles and practice of declarative programming
Semantical Analysis of Higher-Order Abstract Syntax
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Abstract Syntax and Variable Binding
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
A framework for typed HOAS and semantics
Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming
Nominal logic, a first order theory of names and binding
Information and Computation - TACS 2001
Journal of Functional Programming
A definitional approach to primitivexs recursion over higher order abstract syntax
MERLIN '03 Proceedings of the 2003 ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
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
Profunctors, open maps and bisimulation
Mathematical Structures in Computer Science
A unified category-theoretic formulation of typed binding signatures
Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Toward a general theory of names: binding and scope
Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Pseudo-distributive laws and axiomatics for variable binding
Higher-Order and Symbolic Computation
A Unified Category-theoretic Semantics for Binding Signatures in Substructural Logics
Journal of Logic and Computation
Polymorphic abstract syntax via Grothendieck construction
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
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We generalise Fiore et al's account of variable binding for untyped cartesian contexts to give an account of binding for either variables or names that may be typed. We do this in an enriched setting, allowing the incorporation of recursion into the analysis. Extending earlier work by us, we axiomatise the notion of context by defining and using the notion of an enriched pseudo-monad S on V-Cat, with leading examples of V given by Set and ωCpo, the latter yielding an account of recursion. Fiore et al implicitly used the pseudo-monad T$_{fp}$ on Cat for small categories with finite products. Given a set A of types, our extension to typed binders and enrichment involves generalising from Fiore et al's use of [F, Set] to [(SA)$^{op}$, V$^{A}$]. We define a substitution monoidal structure on [(SA)$^{op}$, V$^{A}$], allowing us to give a definition of binding signature at this level of generality, and extend initial algebra semantics to the typed, enriched axiomatic setting. This generalises and axiomatises previouswork by Fiore et al and later authors in particular cases. In particular, it includes the Logic of Bunched Implications and variants, infinitary examples, and structures not previously considered such as those generated by finite limits.