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
Abstract Syntax and Variable Binding for Linear Binders
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
A New Approach to Abstract Syntax Involving Binders
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
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
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
A unified category-theoretic formulation of typed binding signatures
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 Categorical Model of the Fusion Calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
A unifying model of variables and names
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
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Fiore, Plotkin and Turi provided a definition of binding signature and characterised the presheaf of terms generated from a binding signature by an initiality property. Tanaka did for linear binders what Fiore et al did for cartesian binders. They used presheaf categories to model variable binders for contexts, with leading examples given by the untyped ordinary and linear λ-calculi. Here, we give an axiomatic framework that includes their works on cartesian and linear binders, and moreover their assorted variants, notably including the combined cartesian and linear binders of the Logic of Bunched Implications. We provide a definition of binding signature in general, extending the previous ones and yielding a definition for the first time for the example of Bunched Implications, and we characterise the presheaf of terms generated from the binding signature. The characterisation requires a subtle analysis of a strength of a binding signature over a substitution monoidal structure on the presheaf category.