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A Unified Treatment of Structural Definitions on Syntax for Capture-avoiding Substitution, Context Application, Named Substitution, Partial Differentiation, and So On by Hirschowitz, Tom; Lafont, Ambroise is a scholarly article available to read on EtoBox.

What is A Unified Treatment of Structural Definitions on Syntax for Capture-avoiding Substitution, Context Application, Named Substitution, Partial Differentiation, and So On about?

We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad morphismsfrom basic data. These tools automate ubiquitous standard patternslike (1) defining auxiliary functions in successive, potentiallydependent layers, and (2) proving properties of auxiliary functions byinduction on syntax. We cover significant examples from theliterature, including the standard lambda-calculus withcapture-avoiding substitution, a lambda-calculus with bindingevaluation contexts, the lambda-mu-calculus with named substitution, andthe differential lambda-calculus.

Author

Hirschowitz, Tom; Lafont, Ambroise

Published

2022

Language

EN