Formalisation in Constructive Type Theory of Barendregt's Variable Convention for Generic Structures with Binders
Abstract
We introduce a universe of regular datatypes with variable binding information, for which we define generic formation and elimination (i.e. induction /recursion) operators. We then define a generic alphaequivalence relation over the types of the universe based on nameswapping, and derive iteration and induction principles which work modulo alphaconversion capturing Barendregt's Variable Convention. We instantiate the resulting framework so as to obtain the Lambda Calculus and System F, for which we derive substitution operations and substitution lemmas for alphaconversion and substitution composition. The whole work is carried out in Constructive Type Theory and machinechecked by the system Agda.
 Publication:

arXiv eprints
 Pub Date:
 July 2018
 DOI:
 10.48550/arXiv.1807.01870
 arXiv:
 arXiv:1807.01870
 Bibcode:
 2018arXiv180701870C
 Keywords:

 Computer Science  Programming Languages;
 Computer Science  Logic in Computer Science
 EPrint:
 In Proceedings LFMTP 2018, arXiv:1807.01352