This is the artifact accompanying the paper:
Lax-Nominal Inductive Reasoning about Syntax with Bindings
The artifact contains the tool support for defining binding datatypes and proving strong rule induction principles we developed in Isabelle/HOL as well as the case studies we report on in the paper. It works with the latest released version Isabelle2023, which can be downloaded here:
https://isabelle.in.tum.de/website-Isabelle2023/
After downloading Isabelle, a good starting point is to issue the following command
/<Isabelle/installation/path>/bin/isabelle jedit -d . -l Prelim thys/Untyped_Lambda_Calculus/LC_Beta
in the folder of the artifact. This will open Isabelle/jEdit and load our formalization of beta reduction for the untyped lambda calculus and the associated strong rule induction principle.
To let Isabelle check all relevant theories (from the command line, i.e., without running Isabelle/jEdit), one can use the command
/<Isabelle/installation/path>/bin/isabelle build -vD .
We also provide generated HTML documents (folder html) that allow one to browse the formalization without running Isabelle. The file html/index.html provides a good starting point. The formalization is organized into the following "sessions":
| session | description |
|---|---|
| Isabelle_Prelim | administrative session bundling standard Isabelle libraries we use |
| Prelim | miscellaneous extensions to standard libraries, and bindings-specific infrastructure (e.g., countable and uncountable types we use for variables) |
| Binders | main metatheory including the formalization our Thms 10 (called strong_induct in the formalization) and 20 (BE_iinduct) in Generic_Barendregt_Enhanced_Rule_Induction (Sect 4, 7.3, 7.5 and App. F.2), the proof that our results generalize existing results from the literature in Urban_Berghofer_Norrish_Rule_Induction (App. B), and the binding-aware datatype automation in MRBNF_Composition and MRBNF_Recursor and the various ML files, App. F.1) |
| Operations | detailed proof examples for automation of the metatheory |
| Untyped_Lambda_Calculus | formalization of the untyped lambda calculus including beta reduction and parallel beta reduction (Sect 2) |
| Process_Calculus | formalization of the pi calculus transition relation and the associated strong rule induction principle (Sect 7.1 and App. C.3) |
| System_Fsub | formalization of System F with subtyping, the associated strong rule induction principles, and the POPLmark challenge 1A, (Sect 7.2 and App. E) |
| Infinitary_Lambda_Calculus | formalization of Mazza's isomorphism between the untyped lambda calculus and the affine uniform infinitary lambda calculus in Iso_LC_ILC (Sect 7.4 and App. D) |
| System_Fc | formalization of the historic evolution of System Fc |
The session structure resembles the directory structure: theories from session are placed in the directory src/thys/. Exceptions to this rule are the Isabelle_Prelim session which merely bundles existing theories from Isabelle's standard library, and the Binders session whose associated theories are placed directly in the directories src/thys and src/Tools (the latter consists of the ML files implementing the support for datatypes with bindings).