Proof-Producing Translation from Gallina to CakeML

Users of theorem provers often desire to to extract their verified code to a

  more efficient, compiled language. Coq's current extraction mechanism provides

  this facility but does not provide a formal guarantee that the extracted code

  has the same semantics as the logic it is extracted from. Providing such a

  guarantee requires a formal semantics for the target code. The CakeML

  project, implemented in HOL4, provides a formally defined syntax and semantics

  for a subset of SML and includes a proof-producing translator from

  higher-order logic to CakeML. We use the CakeML definition to develop a

  certifying extractor to CakeML from Gallina using the translation and proof techniques

  of the HOL4 CakeML translator. We also address how differences

  between HOL4 (higher-order logic) and Coq (calculus of constructions) effect

  the implementation details of the Coq translator.