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Section: New Results

Formalized Meta-Theory of Simultaneous Substitutions

Participant : Kaustuv Chaudhuri.

It has long been claimed that a logical framework must have sophisticated built-in support for reasoning about formal substitutions in order to formalize relational meta-theorems such as strong normalization (using a logical relations style argument) or that applicative simulation is a pre-congruence. A number of type-theoretic frameworks in recent years, such as Beluga, have indeed started to incorporate such constructs in their core systems.

We have recently shown how to implement the meta-theory of simultaneous substitutions in the Abella system without any modification or extension of the (trusted) kernel, and without sacrificing any expressivity. The results of this paper will appear in the ACM Conference on Certified Programming in Jannuary 2018.

Our hope is that this work will be continued in the near future to build a specification language based on contextual LF in Abella, similar to how Abella/LF handles (ordinary) LF.