A Certifying Extraction with Time Bounds from Coq to Call-By-Value Lambda Calculus.

We provide a plugin extracting Coq functions of simple polymorphic types to the (untyped) call-by-value $\lambda$-calculus L. The plugin is implemented in the MetaCoq framework and entirely written in Coq. We provide Ltac tactics to automatically verify the extracted terms w.r.t a logical relation connecting Coq functions with correct extractions and time bounds, essentially performing a certifying translation and running time validation. We provide three case studies: A universal L-term obtained as extraction from the Coq definition of a step-indexed self-interpreter for Ł, a many-reduction from solvability of Diophantine equations to the halting problem of L, and a polynomial-time simulation of Turing machines in L.