Generating induction principles and subterm relations for inductive types using MetaCoq

06/25/2020

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by   Bohdan Liesnikov, et al.

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We implement three Coq plugins regarding inductive types in MetaCoq. The first plugin is a simple syntax transformation generating alternative constructors for inductive types by abstracting over concrete indices in the types of the constructors. The second plugin re-implements Coq's Scheme Induction command in MetaCoq, and extends it to nested inductive types, e.g. types like rose trees which use list in their definition, similar to the Elpi-plugin by Tassi. The third plugin implements the Derive Subterm command provided by the Equations package in MetaCoq.