A linear algebra approach to linear metatheory

Linear typed λ-calculi are more delicate than their simply typed siblings when it comes to metatheoretic results like preservation of typing under renaming and substitution. Tracking the usage of variables in contexts places more constraints on how variables may be renamed or substituted. We present a methodology based on linear algebra over semirings, extending McBride's kits and traversals approach for the metatheory of syntax with binding to linear usage-annotated terms. Our approach is readily formalisable, and we have done so in Agda

A theory and its metatheory in FS 0

Feferman has proposed FS0, a theory of finitary inductive systems, as a framework theory suitable for various purposes, including reasoning both in and about encoded theories. I look here at how practical FS0 really is. I formalise of a sequent calculus presentation of classical propositional logic in FS0 and show this can be used for work in both the theory and the metatheory. the latter is illustrated with a discussion of a proof of Gentzen's Hauptsatz

A Sheaf Model of the Algebraic Closure

In constructive algebra one cannot in general decide the irreducibility of a polynomial over a field K. This poses some problems to showing the existence of the algebraic closure of K. We give a possible constructive interpretation of the existence of the algebraic closure of a field in characteristic 0 by building, in a constructive metatheory, a suitable site model where there is such an algebraic closure. One can then extract computational content from this model. We give examples of computation based on this model.Comment: In Proceedings CL&C 2014, arXiv:1409.259