  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 \L, a many-reduction from solvability of
Diophantine equations to the halting problem of L, and a polynomial-time
simulation of Turing machines in L.
