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
Reduction-free normalisation for a polymorphic system
LICS '96 Proceedings of the 11th 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
Explicit substitutions and higher-order syntax
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
Second-Order and Dependently-Sorted Abstract Syntax
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Category Theoretic Semantics for Typed Binding Signatures with Recursion
Fundamenta Informaticae - Logic for Pragmatics
A Categorical Model of the Fusion Calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Universal algebra for termination of higher-order rewriting
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
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Discrete generalised polynomial functors
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Multiversal Polymorphic Algebraic Theories: Syntax, Semantics, Translations, and Equational Logic
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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Abstract syntax with variable binding is known to be characterised as an initial algebra in a presheaf category. This paper extends it to the case of polymorphic typed abstract syntax with binding. We consider two variations, secondorder and higher-order polymorphic syntax. The central idea is to apply Fiore's initial algebra characterisation of typed abstract syntax with binding repeatedly, i.e. first to the type structure and secondly to the term structure of polymorphic system. In this process, we use the Grothendieck construction to combine differently staged categories of polymorphic contexts