Status of Extraction in Coq V7.0 final. ====================================== J.C. Filliâtre P. Letouzey Extraction code has been completely rewritten since version V6.3. This work is still not finished, but most parts of it are already usable. In consequence it is included in the Coq V7.0 final release. But don't be mistaken: THIS WORK IS STILL EXPERIMENTAL ! 1) Principles The main goal of the new extraction is to handle any Coq term, even those upon sort Type, and to produce code that always compiles. Thus it will never answer something like "Not an ML type", but rather a dummy term like the ML unit. Translation between Coq and ML is based upon the following principles: - Terms of sort Prop don't have any computational meaning, so they are merged in one ML term "prop", which is for the moment the ML constant (). This part is done according to P. Letouzey's work (*). - Terms that are arities (i.e. something of shape ( : )( : )...s with s a sort ) don't have any ML counterpart, since they are types of types transformers. We have also a special constant "arity" to represent them if needed. - A Coq term gives a ML term or a ML type depending of its type: a term of type an arity will give a ML type, and otherwise a ML term. And the rest of the translation is (almost) straightforward: an inductive gives an inductive, etc... This gives ML code that have no special reason to typecheck, due to the incompatibilities between Coq and ML typing systems. In fact most of the time everything goes right. For example, it is sufficient to extract and compile everything in the "theories" directory (cf test subdirectory). The last feature (not yet implemented) is to ensure that the extracted code will typecheck. This will be done soon by adding some "Obj.magic" calls in the code. 2) Differences with previous extraction 2.a) The pros The ability to extract every Coq term, as explain in the previous paragraph. The ability to extract from a file an ML module (cf Extraction Module in the documentation) You can have a taste of extraction directly at the toplevel by using the "Extraction " or the "Recursive Extraction ". This toplevel extraction was already there in V6.3, but was printing Fw terms. It now prints in an Ocaml-like syntax. The optimization done on extracted code has been mostly ported between V6.3 and V7, and in particular the mechanism of automatic expansion. 2.b) The cons The only language currently available is Ocaml. Haskell extraction will be added as soon as possible. At the opposite, Caml Light is definitely dead. The presence of some parasite "unit" or "prop" as dummy arguments in functions. This denotes the rests of a proof part. The previous extraction was able to remove them totally, but this is no more possible due to extraction upon Type. For example, let's take this pathological term: (if b then Set else Prop) : Type The only way to know if this is an Set (to keep) or a Prop (to remove) is to compute the boolean b, and we do not want to do that during extraction. There is no more "ML import" feature. You can compensate by using Axioms, and then "Extract Constant ..." Still no assurance of typechecking, since there is still no "Obj.magic" yet. Coming really soon ... Absolutely no benchmarking nor profiling nor optimizing has been done on the new extraction code. 3) Examples The file "test-extraction.v" is made of some examples used while debugging. In the subdirectory "test", you can test extraction on the Coq theories. Go there. "make tree" to make a local copy of the "theories" tree "make" to extract & compile most of the theories file "make reals" to extract & compile a realization of the Reals axioms (*): Exécution de termes de preuves: une nouvelle méthode d'extraction pour le Calcul des Constructions Inductives, Pierre Letouzey, DEA thesis, 2000, http://www.eleves.ens.fr/home/letouzey/download/rapport_dea.ps.gz Any feedback is welcome: Pierre.Letouzey@lri.fr Jean.Christophe.Filliatre@lri.fr coq@pauillac.inria.fr