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|
(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(*i camlp4deps: "parsing/grammar.cma" i*)
(* $Id$ *)
(* This file is the interface between the c-c algorithm and Coq *)
open Evd
open Proof_type
open Names
open Libnames
open Nameops
open Inductiveops
open Declarations
open Term
open Tacmach
open Tactics
open Tacticals
open Ccalgo
open Tacinterp
open Ccproof
open Pp
open Util
open Format
exception Not_an_eq
let fail()=raise Not_an_eq
let constant dir s = lazy (Coqlib.gen_constant "CC" dir s)
let f_equal_theo = constant ["Init";"Logic"] "f_equal"
let congr_theo = constant ["cc";"CC"] "Congr_nodep"
let congr_dep_theo = constant ["cc";"CC"] "Congr_dep"
(* decompose member of equality in an applicative format *)
let rec decompose_term env t=
match kind_of_term t with
App (f,args)->
let tf=decompose_term env f in
let targs=Array.map (decompose_term env) args in
Array.fold_left (fun s t->Appli (s,t)) tf targs
| Construct c->
let (_,oib)=Global.lookup_inductive (fst c) in
let nargs=mis_constructor_nargs_env env c in
Constructor (c,nargs,nargs-oib.mind_nparams)
| _ ->(Symb t)
(* decompose equality in members and type *)
let eq_type_of_term term=
match kind_of_term term with
App (f,args)->
(try
let ref = reference_of_constr f in
if ref=Coqlib.glob_eq && (Array.length args)=3
then (args.(0),args.(1),args.(2))
else fail()
with
Not_found -> fail ())
| _ ->fail ()
(* read an equality *)
let read_eq env term=
let (_,t1,t2)=eq_type_of_term term in
(decompose_term env t1,decompose_term env t2)
(* rebuild a term from applicative format *)
let rec make_term=function
Symb s->s
| Constructor(c,_,_)->mkConstruct c
| Appli (s1,s2)->make_app [(make_term s2)] s1
and make_app l=function
Symb s->applistc s l
| Constructor(c,_,_)->applistc (mkConstruct c) l
| Appli (s1,s2)->make_app ((make_term s2)::l) s1
(* store all equalities from the context *)
let rec read_hyps env=function
[]->[]
| (id,_,e)::hyps->let q=(read_hyps env hyps) in
try (id,(read_eq env e))::q with Not_an_eq -> q
(* build a problem ( i.e. read the goal as an equality ) *)
let make_prb gl=
let env=pf_env gl in
(read_hyps env gl.it.evar_hyps,read_eq env gl.it.evar_concl)
(* indhyps builds the array of arrays of constructor hyps for (ind largs) *)
let build_projection (cstr:constructor) nargs argind ttype default atype gls=
let (h,argv) = destApplication ttype in
let ind=destInd h in
let (mib,mip) = Global.lookup_inductive ind in
let n = mip.mind_nparams in
(* assert (n=(Array.length argv));*)
let lp=Array.length mip.mind_consnames in
let types=mip.mind_nf_lc in
let ci=(snd cstr)-1 in
let branch i=
let ti=Term.prod_appvect types.(i) argv in
let rc=fst (Sign.decompose_prod_assum ti) in
let head=
if i=ci then mkRel (1+nargs-argind) else default in
Sign.it_mkLambda_or_LetIn head rc in
let branches=Array.init lp branch in
let casee=mkRel 1 in
let pred=mkLambda(Anonymous,ttype,atype) in
let env=pf_env gls in
let case_info=make_default_case_info (pf_env gls) RegularStyle ind in
let body= mkCase(case_info, pred, casee, branches) in
let id=pf_get_new_id (id_of_string "t") gls in
mkLambda(Name id,ttype,body)
(* generate an adhoc tactic following the proof tree *)
let rec proof_tac uf axioms=function
Ax id->exact_check (mkVar id)
| SymAx id->tclTHEN symmetry (exact_check (mkVar id))
| Refl t->reflexivity
| Trans (p1,p2)->let t=(make_term (snd (type_proof axioms p1))) in
(tclTHENS (transitivity t)
[(proof_tac uf axioms p1);(proof_tac uf axioms p2)])
| Congr (p1,p2)->
fun gls->
let (f1,f2)=(type_proof axioms p1)
and (x1,x2)=(type_proof axioms p2) in
let tf1=make_term f1 and tx1=make_term x1
and tf2=make_term f2 and tx2=make_term x2 in
let typf=pf_type_of gls tf1 and typx=pf_type_of gls tx1
and typfx=pf_type_of gls (mkApp(tf1,[|tx1|])) in
let id=pf_get_new_id (id_of_string "f") gls in
let appx1=mkLambda(Name id,typf,mkApp(mkRel 1,[|tx1|])) in
let lemma1=
mkApp(Lazy.force f_equal_theo,[|typf;typfx;appx1;tf1;tf2|])
and lemma2=
mkApp(Lazy.force f_equal_theo,[|typx;typfx;tf2;tx1;tx2|]) in
(tclTHENS (transitivity (mkApp(tf2,[|tx1|])))
[tclTHEN (apply lemma1) (proof_tac uf axioms p1);
tclFIRST
[tclTHEN (apply lemma2) (proof_tac uf axioms p2);
reflexivity;
fun gls ->
errorlabstrm "CC"
(Pp.str
"CC doesn't know how to handle dependent equality.")]]
gls)
| Inject (prf,cstr,nargs,argind) as gprf->
(fun gls ->
let ti,tj=type_proof axioms prf in
let ai,aj=type_proof axioms gprf in
let cti=make_term ti in
let ctj=make_term tj in
let cai=make_term ai in
let ttype=pf_type_of gls cti in
let atype=pf_type_of gls cai in
let proj=build_projection cstr nargs argind ttype cai atype gls in
let injt=
mkApp (Lazy.force f_equal_theo,[|ttype;atype;proj;cti;ctj|]) in
tclTHEN (apply injt) (proof_tac uf axioms prf) gls)
(* wrap everything *)
let cc_tactic gls=
Library.check_required_library ["Coq";"Init";"Logic"];
let prb=
try make_prb gls with
Not_an_eq ->
errorlabstrm "CC" (str "Goal is not an equality") in
match (cc_proof prb) with
None->errorlabstrm "CC" (str "CC couldn't solve goal")
| Some (p,uf,axioms)->proof_tac uf axioms p gls
(* Tactic registration *)
TACTIC EXTEND CC
[ "CC" ] -> [ cc_tactic ]
END
|
