Information and Computation
ALGOL-like languages (v.2)
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
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
Journal of Functional 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
Binding signatures for generic contexts
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Pseudo-distributive laws and axiomatics for variable binding
Higher-Order and Symbolic Computation
Higher-order semantic labelling for inductive datatype systems
Proceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming
Category Theoretic Semantics for Typed Binding Signatures with Recursion
Fundamenta Informaticae - Logic for Pragmatics
Modules over monads and initial semantics
Information and Computation
Modules over monads and linearity
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Category Theoretic Semantics for Typed Binding Signatures with Recursion
Fundamenta Informaticae - Logic for Pragmatics
Hi-index | 0.00 |
We generalise Fiore et al's account of variable binding for untyped cartesian contexts and Tanaka's account of variable binding for untyped linear contexts to give an account of variable binding for simply typed axiomatically defined contexts. In line with earlier work by us, we axiomatise the notion of context by means of a pseudo-monad S on Cat: Fiore et al implicitly used the pseudo-monad Tfp for small categories with finite products, and Tanaka implicitly used the pseudo-monad Tsm for small symmetric monoidal categories. But here we also extend from untyped variable binding to typed variable binding. Given a set A of types, this involves generalising from Fiore et al's use of [F,Set] to [(SA)op,SetA]. We define a substitution monoidal structure on [(SA)op,SetA], give a definition of binding signature at this level of generality, and extend initial algebra semantics to this typed, axiomatic setting. This generalises and axiomatises previous work by Fiore et al and later authors in particular cases. In particular, it includes the Logic of Bunched Implications and variants, and it yields an improved axiomatic definition of binding signature even in the case of untyped binders.