Deriving Comparators and Show Functions in Isabelle/HOL

Introduction

This website provides supporting material for the paper Deriving Comparators and Show Functions in Isabelle/HOL by Christian Sternagel and René Thiemann.

It describes how to access the right versions of Isabelle, the archive of formal proofs, and IsaFoR (Sources). Moreover, it contains links which clearly demonstrate the change of Isabelle files after using the derive command (Theory Changes). And it provides details on our experiments comparing the old generator code with the new one, where linear orders have been replaced by comparators (Experiments).

Sources

The derive command has been made available in the archive of formal proofs (AFP), where the main entries for this paper are Deriving and Show. Running the theories requires Isabelle/HOL (Isabelle2015) and the corresponding AFP. Moreover, experiments with regard to the speed of generated code have been performed using IsaFoR/CeTA.

Theory Changes

We provide evidence on how easy it became to derive linear orders and comparators in comparison to manual proofs.

Experiments

In order to compare the performance of linear orders with the one of comparators in the generated code, we used our formalization IsaFoR which generates CeTA, a certifier that is capable of validating automatically generated proofs of first-order term rewrite systems, like termination and complexity.

To this end, we took 4122 example proofs that have been generated during the international termination competition. Then we validated all of the proofs with two different versions of CeTA. The (old) one where linear orders have been integrated, and a newer one based on comparators. The experiments clearly show the increase of efficiency when using comparators.


ExampleCeTA (linear orders)CeTA (comparators)
Total time16m56.367s3m40.416s
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