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Status of Extraction in Coq version 7.x
======================================
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 (V6.3 and before)
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 <ident>" or the "Recursive Extraction <ident>".
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 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 soon ...
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
(*):
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
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