*)
+(******************** OTHER USEFUL TACTICS **********************)
+(* Galla: moved in variousTactics.ml
+
+let rewrite_tac ~term:equality ~status:(proof,goal) =
+ let module C = Cic in
+ let module U = UriManager in
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,gty = List.find (function (m,_,_) -> m=goal) metasenv in
+ let eq_ind_r,ty,t1,t2 =
+ match CicTypeChecker.type_of_aux' metasenv context equality with
+ C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
+ when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind") ->
+ let eq_ind_r =
+ C.Const
+ (U.uri_of_string "cic:/Coq/Init/Logic/eq_ind_r.con",[])
+ in
+ eq_ind_r,ty,t1,t2
+ | C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
+ when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind") ->
+ let eqT_ind_r =
+ C.Const
+ (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind_r.con",[])
+ in
+ eqT_ind_r,ty,t1,t2
+ | _ ->
+ raise
+ (ProofEngineTypes.Fail
+ "Rewrite: the argument is not a proof of an equality")
+ in
+ let pred =
+ let gty' = CicSubstitution.lift 1 gty in
+ let t1' = CicSubstitution.lift 1 t1 in
+ let gty'' =
+ ProofEngineReduction.replace_lifting
+ ~equality:ProofEngineReduction.alpha_equivalence
+ ~what:t1' ~with_what:(C.Rel 1) ~where:gty'
+ in
+ C.Lambda (C.Name "dummy_for_rewrite", ty, gty'')
+ in
+prerr_endline ("#### Sintetizzato: " ^ CicPp.ppterm pred);
+ let fresh_meta = ProofEngineHelpers.new_meta proof in
+ let irl =
+ ProofEngineHelpers.identity_relocation_list_for_metavariable context in
+ let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
+
+ let (proof',goals) =
+ PrimitiveTactics.exact_tac
+ ~term:(C.Appl
+ [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
+ ~status:((curi,metasenv',pbo,pty),goal)
+ in
+ assert (List.length goals = 0) ;
+ (proof',[fresh_meta])
+;;
+
+
+let rewrite_simpl_tac ~term ~status =
+ Tacticals.then_ ~start:(rewrite_tac ~term)
+ ~continuation:
+ (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~term:None)
+ ~status
+;;
+*)
+
+(******************** THE FOURIER TACTIC ***********************)
(* La tactique Fourier ne fonctionne de manière sûre que si les coefficients
des inéquations et équations sont entiers. En attendant la tactique Field.
let debug x = print_string ("____ "^x) ; flush stdout;;
let debug_pcontext x =
- let str = ref "" in
- List.iter (fun y -> match y with Some(Cic.Name(a),_) -> str := !str ^ a ^ " " | _ ->()) x ;
- debug ("contesto : "^ (!str) ^ "\n")
+ let str = ref "" in
+ List.iter (fun y -> match y with Some(Cic.Name(a),_) -> str := !str ^
+ a ^ " " | _ ->()) x ;
+ debug ("contesto : "^ (!str) ^ "\n")
;;
(******************************************************************************
@param c a rational
@return the new flin
*)
-let flin_add f x c =
- let cx = flin_coef f x in
- Hashtbl.remove f.fhom x;
- Hashtbl.add f.fhom x (rplus cx c);
- f
+let flin_add f x c =
+ match x with
+ Cic.Rel(n) ->(
+ let cx = flin_coef f x in
+ Hashtbl.remove f.fhom x;
+ Hashtbl.add f.fhom x (rplus cx c);
+ f)
+ |_->debug ("Internal error in Fourier! this is not a Rel "^CicPp.ppterm x^"\n");
+ let cx = flin_coef f x in
+ Hashtbl.remove f.fhom x;
+ Hashtbl.add f.fhom x (rplus cx c);
+ f
;;
(**
Adds c to f.fcste
;;
(**
- @return f times a
+ @return a times f
*)
let flin_emult a f =
let f2 = flin_zero() in
(*****************************************************************************)
-(**
- @param t a term
- @return proiection on string of t
-*)
-let rec string_of_term t =
- match t with
- Cic.Cast (t1,t2) -> string_of_term t1
- |Cic.Const (u,boh) -> UriManager.string_of_uri u
- |Cic.Var (u) -> UriManager.string_of_uri u
- | _ -> "not_of_constant"
-;;
-
-(* coq wrapper
-let string_of_constr = string_of_term
-;;
-*)
-
(**
@param t a term
@raise Failure if conversion is impossible
(* coq wrapper
let rational_of_const = rational_of_term;;
*)
-
+let fails f a =
+ try
+ let tmp = (f a) in
+ false
+ with
+ _-> true
+ ;;
let rec flin_of_term t =
let fl_of_binop f l =
let arg1 = (List.hd next) and
arg2 = (List.hd(List.tl next))
in
- try
+ if fails rational_of_term arg1
+ then
+ if fails rational_of_term arg2
+ then
+ ( (* prodotto tra 2 incognite ????? impossibile*)
+ failwith "Sistemi lineari!!!!\n"
+ )
+ else
+ (
+ match arg1 with
+ Cic.Rel(n) -> (*trasformo al volo*)
+ (flin_add (flin_zero()) arg1 (rational_of_term arg2))
+ |_-> (* test this *)
+ let tmp = flin_of_term arg1 in
+ flin_emult (rational_of_term arg2) (tmp)
+ )
+ else
+ if fails rational_of_term arg2
+ then
+ (
+ match arg2 with
+ Cic.Rel(n) -> (*trasformo al volo*)
+ (flin_add (flin_zero()) arg2 (rational_of_term arg1))
+ |_-> (* test this *)
+ let tmp = flin_of_term arg2 in
+ flin_emult (rational_of_term arg1) (tmp)
+
+ )
+ else
+ ( (*prodotto tra razionali*)
+ (flin_add_cste (flin_zero()) (rmult (rational_of_term arg1) (rational_of_term arg2)))
+ )
+ (*try
begin
- let a = rational_of_term arg1 in
+ (*let a = rational_of_term arg1 in
+ debug("ho fatto rational of term di "^CicPp.ppterm arg1^
+ " e ho ottenuto "^string_of_int a.num^"/"^string_of_int a.den^"\n");*)
+ let a = flin_of_term arg1
try
begin
let b = (rational_of_term arg2) in
+ debug("ho fatto rational of term di "^CicPp.ppterm arg2^
+ " e ho ottenuto "^string_of_int b.num^"/"^string_of_int b.den^"\n");
(flin_add_cste (flin_zero()) (rmult a b))
end
with
- _ -> (flin_add (flin_zero()) arg2 a)
+ _ -> debug ("ho fallito2 su "^CicPp.ppterm arg2^"\n");
+ (flin_add (flin_zero()) arg2 a)
end
with
- _-> (flin_add (flin_zero()) arg1 (rational_of_term arg2 ))
+ _-> debug ("ho fallito1 su "^CicPp.ppterm arg1^"\n");
+ (flin_add(flin_zero()) arg1 (rational_of_term arg2))
+ *)
end
|"cic:/Coq/Reals/Rdefinitions/Rinv.con"->
let a=(rational_of_term (List.hd next)) in
|_-> assert false
end
|_-> assert false)
- with _ -> flin_add (flin_zero()) t r1
+ with _ -> debug("eccezione = "^CicPp.ppterm t^"\n");flin_add (flin_zero()) t r1
;;
(* coq wrapper
(flin_of_term arg2);
hstrict=true}]
|"cic:/Coq/Reals/Rdefinitions/Rgt.con" ->
- [{hname=h;
+ [{hname=h;
htype="Rgt";
hleft=arg2;
hright=arg1;
(flin_of_term arg1);
hstrict=true}]
|"cic:/Coq/Reals/Rdefinitions/Rle.con" ->
- [{hname=h;
+ [{hname=h;
htype="Rle";
hleft=arg1;
hright=arg2;
(flin_of_term arg2);
hstrict=false}]
|"cic:/Coq/Reals/Rdefinitions/Rge.con" ->
- [{hname=h;
+ [{hname=h;
htype="Rge";
hleft=arg2;
hright=arg1;
|_->assert false)(* match u *)
| Cic.MutInd (u,i,o) ->
(match UriManager.string_of_uri u with
- "cic:/Coq/Init/Logic_Type/eqT.con" ->
+ "cic:/Coq/Init/Logic_Type/eqT.ind" ->
let t0= arg1 in
let arg1= arg2 in
let arg2= List.hd(List.tl (List.tl next)) in
Hashtbl.iter (fun x c ->
try (Hashtbl.find hvar x;())
with _-> nvar:=(!nvar)+1;
- Hashtbl.add hvar x (!nvar))
+ Hashtbl.add hvar x (!nvar);
+ debug("aggiungo una var "^
+ string_of_int !nvar^" per "^
+ CicPp.ppterm x^"\n"))
f.hflin.fhom)
lineq1;
(*print_hash hvar;*)
debug("Il numero di incognite e' "^string_of_int (!nvar+1)^"\n");
let sys= List.map (fun h->
let v=Array.create ((!nvar)+1) r0 in
- Hashtbl.iter (fun x c -> v.(Hashtbl.find hvar x)<-c)
+ Hashtbl.iter (fun x c -> v.(Hashtbl.find hvar x) <- c)
h.hflin.fhom;
((Array.to_list v)@[rop h.hflin.fcste],h.hstrict))
lineq1 in
- debug ("chiamo unsolvable sul sistema di "^ string_of_int (List.length sys) ^"\n");
+ debug ("chiamo unsolvable sul sistema di "^
+ string_of_int (List.length sys) ^"\n");
print_sys sys;
unsolvable sys
;;
-(******************************************************************************
+(*****************************************************************************
Construction de la preuve en cas de succès de la méthode de Fourier,
i.e. on obtient une contradiction.
*)
-let _R0 = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/R0.con") 0 ;;
-let _R1 = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/R1.con") 0 ;;
-let _Rinv = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rinv.con") 0 ;;
-let _Rle_mult_inv_pos = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_mult_inv_pos.con") 0 ;;
-let _Rle_not_lt = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_not_lt.con") 0 ;;
-let _Rle_zero_1 = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_zero_1.con") 0 ;;
-let _Rle_zero_pos_plus1 = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_zero_pos_plus1.con") 0 ;;
-let _Rle_zero_zero = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_zero_zero.con") 0 ;;
-let _Rlt_mult_inv_pos = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/_Rlt_mult_inv_pos.con") 0 ;;
-let _Rlt_not_le = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rlt_not_le.con") 0 ;;
-let _Rlt_zero_1 = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rlt_zero_1.con") 0 ;;
-let _Rlt_zero_pos_plus1 = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rlt_zero_pos_plus1.con") 0 ;;
-let _Rmult = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rmult.con") 0 ;;
-let _Rminus = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rminus.con") 0 ;;
-
-let _Rnot_lt0 = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rnot_lt0.con") 0 ;;
-let _Ropp = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Ropp.con") 0 ;;
-let _Rplus = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rplus.con") 0 ;;
-let _Rfourier_not_ge_lt = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_ge_lt.con") 0 ;;
-let _Rfourier_not_gt_le = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_gt_le.con") 0 ;;
-let _Rfourier_not_le_gt = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_le_gt.con") 0 ;;
-let _Rfourier_not_lt_ge = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_lt_ge.con") 0 ;;
-let _Rfourier_gt_to_lt =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_gt_to_lt.con") 0 ;;
-
-let _Rfourier_ge_to_le =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_ge_to_le.con") 0 ;;
-let _Rfourier_lt_lt =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_lt_lt.con") 0 ;;
-let _Rfourier_lt_le =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_lt_le.con") 0 ;;
-let _Rfourier_le_lt =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_le_lt.con") 0 ;;
-let _Rfourier_le_le =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_le_le.con") 0 ;;
-
-let _Rfourier_eqLR_to_le=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_eqLR_to_le.con") 0 ;;
-
-let _Rfourier_eqRL_to_le=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_eqRL_to_le.con") 0 ;;
-let _Rlt = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rlt.con") 0 ;;
-let _Rle = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rle.con") 0 ;;
-let _not = Cic.Const (UriManager.uri_of_string "cic:/Coq/Init/Logic/not.con") 0;;
-
-let _sym_eqT = Cic.Const(UriManager.uri_of_string "/Coq/Init/Logic_Type/Equality_is_a_congruence/sym_eqT.con") 0 ;;
-
-let _Rfourier_lt=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_lt.con") 0 ;;
-let _Rfourier_le=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_le.con") 0 ;;
-
-let _False = Cic.MutConstruct(UriManager.uri_of_string "cic:/Coq/Init/Datatypes/bool.ind") 0 1 0 ;;
-
-let _Rinv_R1 = Cic.Const(UriManager.uri_of_string "cic:/Coq/Reals/Rbase/Rinv_R1.con" ) 0;;
-
-
-let _Rnot_lt_lt =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rnot_lt_lt.con") 0 ;;
-let _Rnot_le_le =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rnot_le_le.con") 0 ;;
-
-
-
-
+let _eqT = Cic.MutInd(UriManager.uri_of_string
+ "cic:/Coq/Init/Logic_Type/eqT.ind") 0 [] ;;
+let _False = Cic.MutInd (UriManager.uri_of_string
+ "cic:/Coq/Init/Logic/False.ind") 0 [] ;;
+let _not = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/Init/Logic/not.con") [];;
+let _R0 = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/Reals/Rdefinitions/R0.con") [] ;;
+let _R1 = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/Reals/Rdefinitions/R1.con") [] ;;
+let _R = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/Reals/Rdefinitions/R.con") [] ;;
+let _Rfourier_eqLR_to_le=Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rfourier_eqLR_to_le.con") [] ;;
+let _Rfourier_eqRL_to_le=Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rfourier_eqRL_to_le.con") [] ;;
+let _Rfourier_ge_to_le =Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rfourier_ge_to_le.con") [] ;;
+let _Rfourier_gt_to_lt =Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rfourier_gt_to_lt.con") [] ;;
+let _Rfourier_le=Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rfourier_le.con") [] ;;
+let _Rfourier_le_le =Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rfourier_le_le.con") [] ;;
+let _Rfourier_le_lt =Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rfourier_le_lt.con") [] ;;
+let _Rfourier_lt=Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rfourier_lt.con") [] ;;
+let _Rfourier_lt_le =Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rfourier_lt_le.con") [] ;;
+let _Rfourier_lt_lt =Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rfourier_lt_lt.con") [] ;;
+let _Rfourier_not_ge_lt = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rfourier_not_ge_lt.con") [] ;;
+let _Rfourier_not_gt_le = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rfourier_not_gt_le.con") [] ;;
+let _Rfourier_not_le_gt = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rfourier_not_le_gt.con") [] ;;
+let _Rfourier_not_lt_ge = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rfourier_not_lt_ge.con") [] ;;
+let _Rinv = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/Reals/Rdefinitions/Rinv.con") [] ;;
+let _Rinv_R1 = Cic.Const(UriManager.uri_of_string
+ "cic:/Coq/Reals/Rbase/Rinv_R1.con" ) [] ;;
+let _Rle = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/Reals/Rdefinitions/Rle.con") [] ;;
+let _Rle_mult_inv_pos = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rle_mult_inv_pos.con") [] ;;
+let _Rle_not_lt = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rle_not_lt.con") [] ;;
+let _Rle_zero_1 = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rle_zero_1.con") [] ;;
+let _Rle_zero_pos_plus1 = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rle_zero_pos_plus1.con") [] ;;
+(*let _Rle_zero_zero = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rle_zero_zero.con") [] ;;*)
+let _Rlt = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/Reals/Rdefinitions/Rlt.con") [] ;;
+let _Rlt_mult_inv_pos = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rlt_mult_inv_pos.con") [] ;;
+let _Rlt_not_le = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rlt_not_le.con") [] ;;
+let _Rlt_zero_1 = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rlt_zero_1.con") [] ;;
+let _Rlt_zero_pos_plus1 = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rlt_zero_pos_plus1.con") [] ;;
+let _Rminus = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/Reals/Rdefinitions/Rminus.con") [] ;;
+let _Rmult = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/Reals/Rdefinitions/Rmult.con") [] ;;
+let _Rnot_le_le =Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rnot_le_le.con") [] ;;
+let _Rnot_lt0 = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rnot_lt0.con") [] ;;
+let _Rnot_lt_lt =Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/fourier/Fourier_util/Rnot_lt_lt.con") [] ;;
+let _Ropp = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/Reals/Rdefinitions/Ropp.con") [] ;;
+let _Rplus = Cic.Const (UriManager.uri_of_string
+ "cic:/Coq/Reals/Rdefinitions/Rplus.con") [] ;;
+
+(******************************************************************************)
let is_int x = (x.den)=1
;;
let rec int_to_real_aux n =
match n with
0 -> _R0 (* o forse R0 + R0 ????? *)
+ | 1 -> _R1
| _ -> Cic.Appl [ _Rplus ; _R1 ; int_to_real_aux (n-1) ]
;;
(* preuve que 0<n*1/d
*)
-let tac_zero_inf_pos gl (n,d) =
+let tac_zero_inf_pos (n,d) ~status =
(*let cste = pf_parse_constr gl in*)
- let tacn=ref (PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ) in
- let tacd=ref (PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ) in
- for i=1 to n-1 do
- tacn:=(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_zero_pos_plus1) ~continuation:!tacn); done;
- for i=1 to d-1 do
- tacd:=(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_zero_pos_plus1) ~continuation:!tacd); done;
- (Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_mult_inv_pos) ~continuations:[!tacn;!tacd])
+ let pall str ~status:(proof,goal) t =
+ debug ("tac "^str^" :\n" );
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
+ debug ("th = "^ CicPp.ppterm t ^"\n");
+ debug ("ty = "^ CicPp.ppterm ty^"\n");
+ in
+ let tacn=ref
+ (fun ~status -> pall "n0" ~status _Rlt_zero_1 ;
+ PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ~status ) in
+ let tacd=ref
+ (fun ~status -> pall "d0" ~status _Rlt_zero_1 ;
+ PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ~status ) in
+
+
+ for i=1 to n-1 do
+ tacn:=(Tacticals.then_ ~start:(fun ~status -> pall ("n"^string_of_int i)
+ ~status _Rlt_zero_pos_plus1;
+ PrimitiveTactics.apply_tac ~term:_Rlt_zero_pos_plus1 ~status)
+ ~continuation:!tacn);
+ done;
+ for i=1 to d-1 do
+ tacd:=(Tacticals.then_ ~start:(fun ~status -> pall "d"
+ ~status _Rlt_zero_pos_plus1 ;PrimitiveTactics.apply_tac
+ ~term:_Rlt_zero_pos_plus1 ~status) ~continuation:!tacd);
+ done;
+
+
+
+debug("TAC ZERO INF POS\n");
+
+(Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_mult_inv_pos)
+ ~continuations:[
+ !tacn ;
+ !tacd ]
+ ~status)
;;
-
(* preuve que 0<=n*1/d
*)
-let tac_zero_infeq_pos gl (n,d) =
- (*let cste = pf_parse_constr gl in*)
- let tacn = ref (if n=0 then
- (PrimitiveTactics.apply_tac ~term:_Rle_zero_zero )
- else
- (PrimitiveTactics.apply_tac ~term:_Rle_zero_1 ))
- in
- let tacd=ref (PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ) in
- for i=1 to n-1 do
- tacn:=(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rle_zero_pos_plus1) ~continuation:!tacn); done;
- for i=1 to d-1 do
- tacd:=(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_zero_pos_plus1) ~continuation:!tacd); done;
- (Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rle_mult_inv_pos) ~continuations:[!tacn;!tacd])
+let tac_zero_infeq_pos gl (n,d) ~status =
+ (*let cste = pf_parse_constr gl in*)
+ debug("inizio tac_zero_infeq_pos\n");
+ let tacn = ref
+ (*(if n=0 then
+ (PrimitiveTactics.apply_tac ~term:_Rle_zero_zero )
+ else*)
+ (PrimitiveTactics.apply_tac ~term:_Rle_zero_1 )
+ (* ) *)
+ in
+ let tacd=ref (PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ) in
+ for i=1 to n-1 do
+ tacn:=(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac
+ ~term:_Rle_zero_pos_plus1) ~continuation:!tacn);
+ done;
+ for i=1 to d-1 do
+ tacd:=(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac
+ ~term:_Rlt_zero_pos_plus1) ~continuation:!tacd);
+ done;
+ let r =
+ (Tacticals.thens ~start:(PrimitiveTactics.apply_tac
+ ~term:_Rle_mult_inv_pos) ~continuations:[!tacn;!tacd]) ~status in
+ debug("fine tac_zero_infeq_pos\n");
+ r
;;
(* preuve que 0<(-n)*(1/d) => False
*)
-let tac_zero_inf_false gl (n,d) =
- if n=0 then (PrimitiveTactics.apply_tac ~term:_Rnot_lt0)
+let tac_zero_inf_false gl (n,d) ~status=
+ debug("inizio tac_zero_inf_false\n");
+ if n=0 then
+ (debug "1\n";let r =(PrimitiveTactics.apply_tac ~term:_Rnot_lt0 ~status) in
+ debug("fine\n");
+ r)
else
- (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rle_not_lt)
- ~continuation:(tac_zero_infeq_pos gl (-n,d)))
+ (debug "2\n";let r = (Tacticals.then_ ~start:(
+ fun ~status:(proof,goal as status) ->
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,ty =List.find (function (m,_,_) -> m=goal) metasenv in
+ debug("!!!!!!!!!1: unify "^CicPp.ppterm _Rle_not_lt^" with "
+ ^ CicPp.ppterm ty ^"\n");
+ let r = PrimitiveTactics.apply_tac ~term:_Rle_not_lt ~status in
+ debug("!!!!!!!!!2\n");
+ r
+ )
+ ~continuation:(tac_zero_infeq_pos gl (-n,d))) ~status in
+ debug("fine\n");
+ r
+ )
;;
-(* preuve que 0<=(-n)*(1/d) => False
+(* preuve que 0<=n*(1/d) => False ; n est negatif
*)
-let tac_zero_infeq_false gl (n,d) =
- (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_not_le)
- ~continuation:(tac_zero_inf_pos gl (-n,d)))
+let tac_zero_infeq_false gl (n,d) ~status:(proof,goal as status)=
+debug("stat tac_zero_infeq_false\n");
+let r =
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,ty =List.find (function (m,_,_) -> m=goal) metasenv in
+
+ debug("faccio fold di " ^ CicPp.ppterm
+ (Cic.Appl
+ [_Rle ; _R0 ;
+ Cic.Appl
+ [_Rmult ; int_to_real n ; Cic.Appl [_Rinv ; int_to_real d]]
+ ]
+ ) ^ "\n") ;
+ debug("apply di _Rlt_not_le a "^ CicPp.ppterm ty ^"\n");
+ (*CSC: Patch to undo the over-simplification of RewriteSimpl *)
+ Tacticals.then_
+ ~start:
+ (ReductionTactics.fold_tac ~reduction:CicReduction.whd
+ ~also_in_hypotheses:false
+ ~term:
+ (Cic.Appl
+ [_Rle ; _R0 ;
+ Cic.Appl
+ [_Rmult ; int_to_real n ; Cic.Appl [_Rinv ; int_to_real d]]
+ ]
+ )
+ )
+ ~continuation:
+ (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_not_le)
+ ~continuation:(tac_zero_inf_pos (-n,d))) ~status in
+ debug("end tac_zero_infeq_false\n");
+ r
+(*PORTING
+ Tacticals.id_tac ~status
+*)
;;
(* *********** ********** ******** ??????????????? *********** **************)
-let mkMeta (proof,goal) =
-let curi,metasenv,pbo,pty = proof in
-let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
-Cic.Meta (ProofEngineHelpers.new_meta proof)
- (ProofEngineHelpers.identity_relocation_list_for_metavariable context)
-;;
-
let apply_type_tac ~cast:t ~applist:al ~status:(proof,goal) =
- let new_m = mkMeta (proof,goal) in
- PrimitiveTactics.apply_tac ~term:(Cic.Appl ((Cic.Cast (new_m,t))::al)) ~status:(proof,goal)
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
+ let fresh_meta = ProofEngineHelpers.new_meta proof in
+ let irl =
+ ProofEngineHelpers.identity_relocation_list_for_metavariable context in
+ let metasenv' = (fresh_meta,context,t)::metasenv in
+ let proof' = curi,metasenv',pbo,pty in
+ let proof'',goals =
+ PrimitiveTactics.apply_tac
+ (*~term:(Cic.Appl ((Cic.Cast (Cic.Meta (fresh_meta,irl),t))::al)) (* ??? *)*)
+ ~term:(Cic.Appl ((Cic.Meta (fresh_meta,irl))::al)) (* ??? *)
+ ~status:(proof',goal)
+ in
+ proof'',fresh_meta::goals
;;
let my_cut ~term:c ~status:(proof,goal)=
let curi,metasenv,pbo,pty = proof in
let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
- apply_type_tac ~cast:(Cic.Prod(Cic.Name "Anonymous",c,ty)) ~applist:[mkMeta(proof,goal)] ~status:(proof,goal)
+
+debug("my_cut di "^CicPp.ppterm c^"\n");
+
+
+ let fresh_meta = ProofEngineHelpers.new_meta proof in
+ let irl =
+ ProofEngineHelpers.identity_relocation_list_for_metavariable context in
+ let metasenv' = (fresh_meta,context,c)::metasenv in
+ let proof' = curi,metasenv',pbo,pty in
+ let proof'',goals =
+ apply_type_tac ~cast:(Cic.Prod(Cic.Name "Anonymous",c,
+ CicSubstitution.lift 1 ty)) ~applist:[Cic.Meta(fresh_meta,irl)]
+ ~status:(proof',goal)
+ in
+ (* We permute the generated goals to be consistent with Coq *)
+ match goals with
+ [] -> assert false
+ | he::tl -> proof'',he::fresh_meta::tl
;;
let exact = PrimitiveTactics.exact_tac;;
-let tac_use h = match h.htype with
- "Rlt" -> exact ~term:h.hname
- |"Rle" -> exact ~term:h.hname
- |"Rgt" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_gt_to_lt)
- ~continuation:(exact ~term:h.hname))
- |"Rge" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_ge_to_le)
- ~continuation:(exact ~term:h.hname))
- |"eqTLR" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_eqLR_to_le)
- ~continuation:(exact ~term:h.hname))
- |"eqTRL" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_eqRL_to_le)
- ~continuation:(exact ~term:h.hname))
- |_->assert false
+let tac_use h ~status:(proof,goal as status) =
+debug("Inizio TC_USE\n");
+let curi,metasenv,pbo,pty = proof in
+let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
+debug ("hname = "^ CicPp.ppterm h.hname ^"\n");
+debug ("ty = "^ CicPp.ppterm ty^"\n");
+
+let res =
+match h.htype with
+ "Rlt" -> exact ~term:h.hname ~status
+ |"Rle" -> exact ~term:h.hname ~status
+ |"Rgt" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac
+ ~term:_Rfourier_gt_to_lt)
+ ~continuation:(exact ~term:h.hname)) ~status
+ |"Rge" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac
+ ~term:_Rfourier_ge_to_le)
+ ~continuation:(exact ~term:h.hname)) ~status
+ |"eqTLR" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac
+ ~term:_Rfourier_eqLR_to_le)
+ ~continuation:(exact ~term:h.hname)) ~status
+ |"eqTRL" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac
+ ~term:_Rfourier_eqRL_to_le)
+ ~continuation:(exact ~term:h.hname)) ~status
+ |_->assert false
+in
+debug("Fine TAC_USE\n");
+res
;;
| _ -> c
;;
-let find_in_context id context =
+(*let find_in_context id context =
let rec find_in_context_aux c n =
match c with
[] -> failwith (id^" not found in context")
[] -> []
| Some(Cic.Name(h),Cic.Decl(t))::next -> (
let n = find_in_context h cont in
- [(Cic.Rel(n),t)] @ filter_real_hyp next cont)
+ debug("assegno "^string_of_int n^" a "^CicPp.ppterm t^"\n");
+ [(Cic.Rel(n),t)] @ filter_real_hyp next cont)
| a::next -> debug(" no\n"); filter_real_hyp next cont
+;;*)
+let filter_real_hyp context _ =
+ let rec filter_aux context num =
+ match context with
+ [] -> []
+ | Some(Cic.Name(h),Cic.Decl(t))::next ->
+ (
+ (*let n = find_in_context h cont in*)
+ debug("assegno "^string_of_int num^" a "^h^":"^CicPp.ppterm t^"\n");
+ [(Cic.Rel(num),t)] @ filter_aux next (num+1)
+ )
+ | a::next -> filter_aux next (num+1)
+ in
+ filter_aux context 1
;;
+
(* lifts everithing at the conclusion level *)
let rec superlift c n=
match c with
[] -> []
- | Some(name,Cic.Decl(a))::next -> [Some(name,Cic.Decl(CicSubstitution.lift n a))] @ superlift next (n+1)
- | Some(name,Cic.Def(a))::next -> [Some(name,Cic.Def(CicSubstitution.lift n a))] @ superlift next (n+1)
+ | Some(name,Cic.Decl(a))::next -> [Some(name,Cic.Decl(
+ CicSubstitution.lift n a))] @ superlift next (n+1)
+ | Some(name,Cic.Def(a))::next -> [Some(name,Cic.Def(
+ CicSubstitution.lift n a))] @ superlift next (n+1)
| _::next -> superlift next (n+1) (*?? ??*)
;;
-(* this may not work *)
-let equality_replace a b =
- let _eqT_ind = Cic.Const( UriManager.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind.con" ) 0 in
- PrimitiveTactics.apply_tac ~term:(Cic.Appl [_eqT_ind;a;b])
+let equality_replace a b ~status =
+debug("inizio EQ\n");
+ let module C = Cic in
+ let proof,goal = status in
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
+ let a_eq_b = C.Appl [ _eqT ; _R ; a ; b ] in
+ let fresh_meta = ProofEngineHelpers.new_meta proof in
+ let irl =
+ ProofEngineHelpers.identity_relocation_list_for_metavariable context in
+ let metasenv' = (fresh_meta,context,a_eq_b)::metasenv in
+debug("chamo rewrite tac su"^CicPp.ppterm (C.Meta (fresh_meta,irl)));
+ let (proof,goals) =
+ VariousTactics.rewrite_simpl_tac ~term:(C.Meta (fresh_meta,irl))
+ ~status:((curi,metasenv',pbo,pty),goal)
+ in
+ let new_goals = fresh_meta::goals in
+debug("fine EQ -> goals : "^string_of_int( List.length new_goals) ^" = "
+ ^string_of_int( List.length goals)^"+ meta\n");
+ (proof,new_goals)
;;
-(* unused *)
let tcl_fail a ~status:(proof,goal) =
match a with
- 1 -> raise (ProofEngineTypes.Fail "???????")
+ 1 -> raise (ProofEngineTypes.Fail "fail-tactical")
|_-> (proof,[goal])
;;
+let assumption_tac ~status:(proof,goal)=
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
+ let num = ref 0 in
+ let tac_list = List.map
+ ( fun x -> num := !num + 1;
+ match x with
+ Some(Cic.Name(nm),t) -> (nm,exact ~term:(Cic.Rel(!num)))
+ | _ -> ("fake",tcl_fail 1)
+ )
+ context
+ in
+ Tacticals.try_tactics ~tactics:tac_list ~status:(proof,goal)
+;;
+
(* !!!!! fix !!!!!!!!!! *)
let contradiction_tac ~status:(proof,goal)=
- proof,[goal]
+ Tacticals.then_
+ (*inutile sia questo che quello prima della chiamata*)
+ ~start:PrimitiveTactics.intros_tac
+ ~continuation:(Tacticals.then_
+ ~start:(VariousTactics.elim_type_tac ~term:_False)
+ ~continuation:(assumption_tac))
+ ~status:(proof,goal)
;;
(* ********************* TATTICA ******************************** *)
-let rec fourier ~status:(proof,goal)=
- let curi,metasenv,pbo,pty = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
+let rec fourier ~status:(s_proof,s_goal)=
+ let s_curi,s_metasenv,s_pbo,s_pty = s_proof in
+ let s_metano,s_context,s_ty = List.find (function (m,_,_) -> m=s_goal)
+ s_metasenv in
- debug ("invoco fourier_tac sul goal "^string_of_int(goal)^" e contesto :\n");
- debug_pcontext context;
+ debug ("invoco fourier_tac sul goal "^string_of_int(s_goal)^" e contesto :\n");
+ debug_pcontext s_context;
- (* il goal di prima dovrebbe essere ty
-
- let goal = strip_outer_cast (pf_concl gl) in *)
-
let fhyp = String.copy "new_hyp_for_fourier" in
- (* si le but est une inéquation, on introduit son contraire,
- et le but à prouver devient False *)
-
- try (let tac =
- match ty with
- Cic.Appl ( Cic.Const(u,boh)::args) ->
- (match UriManager.string_of_uri u with
- "cic:/Coq/Reals/Rdefinitions/Rlt.con" ->
- (Tacticals.then_
- ~start:(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_not_ge_lt)
- ~continuation:(PrimitiveTactics.intros_tac ~name:fhyp))
- ~continuation:fourier)
- |"cic:/Coq/Reals/Rdefinitions/Rle.con" ->
- (Tacticals.then_
- ~start:(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_not_gt_le)
- ~continuation:(PrimitiveTactics.intros_tac ~name:fhyp))
- ~continuation:fourier)
- |"cic:/Coq/Reals/Rdefinitions/Rgt.con" ->
- (Tacticals.then_
- ~start:(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_not_le_gt)
- ~continuation:(PrimitiveTactics.intros_tac ~name:fhyp))
- ~continuation:fourier)
- |"cic:/Coq/Reals/Rdefinitions/Rge.con" ->
- (Tacticals.then_
- ~start:(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_not_lt_ge)
- ~continuation:(PrimitiveTactics.intros_tac ~name:fhyp))
- ~continuation:fourier)
- |_->assert false)
- |_->assert false
- in tac (proof,goal) )
- with _ ->
-
- (* les hypothèses *)
+
+(* here we need to negate the thesis, but to do this we need to apply the right
+theoreme,so let's parse our thesis *)
+
+ let th_to_appl = ref _Rfourier_not_le_gt in
+ (match s_ty with
+ Cic.Appl ( Cic.Const(u,boh)::args) ->
+ (match UriManager.string_of_uri u with
+ "cic:/Coq/Reals/Rdefinitions/Rlt.con" -> th_to_appl :=
+ _Rfourier_not_ge_lt
+ |"cic:/Coq/Reals/Rdefinitions/Rle.con" -> th_to_appl :=
+ _Rfourier_not_gt_le
+ |"cic:/Coq/Reals/Rdefinitions/Rgt.con" -> th_to_appl :=
+ _Rfourier_not_le_gt
+ |"cic:/Coq/Reals/Rdefinitions/Rge.con" -> th_to_appl :=
+ _Rfourier_not_lt_ge
+ |_-> failwith "fourier can't be applyed")
+ |_-> failwith "fourier can't be applyed");
+ (* fix maybe strip_outer_cast goes here?? *)
+
+ (* now let's change our thesis applying the th and put it with hp *)
+
+ let proof,gl =
+ Tacticals.then_
+ ~start:(PrimitiveTactics.apply_tac ~term:!th_to_appl)
+ ~continuation:PrimitiveTactics.intros_tac
+ ~status:(s_proof,s_goal) in
+ let goal = if List.length gl = 1 then List.hd gl
+ else failwith "a new goal" in
+
+ debug ("port la tesi sopra e la nego. contesto :\n");
+ debug_pcontext s_context;
+
+ (* now we have all the right environment *)
+
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
+
+
+ (* now we want to convert hp to inequations, but first we must lift
+ everyting to thesis level, so that a variable has the save Rel(n)
+ in each hp ( needed by ineq1_of_term ) *)
(* ? fix if None ?????*)
- let new_context = superlift context 1 in
- let hyps = filter_real_hyp new_context new_context in
+ (* fix change superlift with a real name *)
+
+ let l_context = superlift context 1 in
+ let hyps = filter_real_hyp l_context l_context in
+
debug ("trasformo in diseq. "^ string_of_int (List.length hyps)^" ipotesi\n");
+
let lineq =ref [] in
+
+ (* transform hyps into inequations *)
+
List.iter (fun h -> try (lineq:=(ineq1_of_term h)@(!lineq))
with _-> ())
hyps;
- (* lineq = les inéquations découlant des hypothèses *)
-
- debug ("applico fourier a "^ string_of_int (List.length !lineq)^" disequazioni\n");
+ debug ("applico fourier a "^ string_of_int (List.length !lineq)^
+ " disequazioni\n");
let res=fourier_lineq (!lineq) in
- let tac=ref Ring.id_tac in
- if res=[] then (print_string "Tactic Fourier fails.\n";flush stdout)
- (* l'algorithme de Fourier a réussi: on va en tirer une preuve Coq *)
- else (
-
+ let tac=ref Tacticals.id_tac in
+ if res=[] then
+ (print_string "Tactic Fourier fails.\n";flush stdout;
+ failwith "fourier_tac fails")
+ else
+ (
match res with (*match res*)
[(cres,sres,lc)]->
- (* lc=coefficients multiplicateurs des inéquations
- qui donnent 0<cres ou 0<=cres selon sres *)
-
+
+ (* in lc we have the coefficient to "reduce" the system *)
print_string "Fourier's method can prove the goal...\n";flush stdout;
+ debug "I coeff di moltiplicazione rit sono: ";
let lutil=ref [] in
- debug "I coeff di moltiplicazione rit sono: ";
List.iter
(fun (h,c) -> if c<>r0 then (lutil:=(h,c)::(!lutil);
- Fourier.print_rational(c);print_string " ")
+ (* DBG *)Fourier.print_rational(c);print_string " "(* DBG *))
)
(List.combine (!lineq) lc);
- print_string (" quindi lutil e' lunga "^string_of_int (List.length (!lutil))^"\n");
- (* on construit la combinaison linéaire des inéquation *)
-
-
+
+ print_string (" quindi lutil e' lunga "^
+ string_of_int (List.length (!lutil))^"\n");
+
+ (* on construit la combinaison linéaire des inéquation *)
+
(match (!lutil) with (*match (!lutil) *)
- (h1,c1)::lutil ->
- debug ("elem di lutil ");Fourier.print_rational c1;print_string "\n";
- let s=ref (h1.hstrict) in
- (* let t1=ref (mkAppL [|parse "Rmult";parse (rational_to_real c1);h1.hleft|]) in
- let t2=ref (mkAppL [|parse "Rmult";parse (rational_to_real c1);h1.hright|]) in*)
- let t1 = ref (Cic.Appl [_Rmult;rational_to_real c1;h1.hleft] ) in
- let t2 = ref (Cic.Appl [_Rmult;rational_to_real c1;h1.hright]) in
-
- List.iter (fun (h,c) ->
+ (h1,c1)::lutil ->
+ debug ("elem di lutil ");Fourier.print_rational c1;print_string "\n";
+
+ let s=ref (h1.hstrict) in
+
+
+ let t1 = ref (Cic.Appl [_Rmult;rational_to_real c1;h1.hleft] ) in
+ let t2 = ref (Cic.Appl [_Rmult;rational_to_real c1;h1.hright]) in
+
+ List.iter (fun (h,c) ->
s:=(!s)||(h.hstrict);
- t1:=(Cic.Appl [_Rplus;!t1;Cic.Appl [_Rmult;rational_to_real c;h.hleft ] ]);
- t2:=(Cic.Appl [_Rplus;!t2;Cic.Appl [_Rmult;rational_to_real c;h.hright] ]))
+ t1:=(Cic.Appl [_Rplus;!t1;Cic.Appl
+ [_Rmult;rational_to_real c;h.hleft ] ]);
+ t2:=(Cic.Appl [_Rplus;!t2;Cic.Appl
+ [_Rmult;rational_to_real c;h.hright] ]))
lutil;
- let ineq=Cic.Appl [(if (!s) then _Rlt else _Rle);!t1;!t2 ] in
- let tc=rational_to_real cres in
-
-
- (* puis sa preuve *)
- debug "inizio a costruire tac1\n";
- let tac1=ref ( if h1.hstrict then
- (Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_lt)
- ~continuations:[tac_use h1;tac_zero_inf_pos goal
- (rational_to_fraction c1)])
- else
- (Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le)
- ~continuations:[tac_use h1;tac_zero_inf_pos goal
- (rational_to_fraction c1)]))
- in
- s:=h1.hstrict;
-
- List.iter (fun (h,c) ->
- (if (!s) then
- (if h.hstrict then
- tac1:=(Tacticals.thens ~start:(PrimitiveTactics.apply_tac
- ~term:_Rfourier_lt_lt)
- ~continuations:[!tac1;tac_use h;
- tac_zero_inf_pos goal
- (rational_to_fraction c)])
- else
- tac1:=(Tacticals.thens ~start:(PrimitiveTactics.apply_tac
- ~term:_Rfourier_lt_le)
- ~continuations:[!tac1;tac_use h;
- tac_zero_inf_pos goal
- (rational_to_fraction c)])
- )
- else
- (if h.hstrict then
- tac1:=(Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le_lt)
- ~continuations:[!tac1;tac_use h;
- tac_zero_inf_pos goal
- (rational_to_fraction c)])
- else
- tac1:=(Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le_le)
- ~continuations:[!tac1;tac_use h;
- tac_zero_inf_pos goal
- (rational_to_fraction c)])));
- s:=(!s)||(h.hstrict))
- lutil;(*end List.iter*)
-
- let tac2= if sres then
- tac_zero_inf_false goal (rational_to_fraction cres)
- else
- tac_zero_infeq_false goal (rational_to_fraction cres)
- in
- tac:=(Tacticals.thens ~start:(my_cut ~term:ineq)
- ~continuations:[Tacticals.then_ (* ?????????????????????????????? *)
- ~start:(PrimitiveTactics.change_tac ~what:ty ~with_what:(Cic.Appl [ _not; ineq] ))
- ~continuation:(Tacticals.then_
- ~start:(PrimitiveTactics.apply_tac
- ~term:(if sres then _Rnot_lt_lt else _Rnot_le_le))
- ~continuation:(Tacticals.thens
- ~start:(equality_replace (Cic.Appl [_Rminus;!t2;!t1] ) tc)
- ~continuations:[tac2;(Tacticals.thens
- ~start:(equality_replace (Cic.Appl[_Rinv;_R1]) _R1)
- ~continuations:
-(* en attendant Field, ça peut aider Ring de remplacer 1/1 par 1 ... *)
- [Tacticals.try_tactics
- (* ???????????????????????????? *)
- ~tactics:[ "ring", Ring.ring_tac ; "id", Ring.id_tac]
- ;
- Tacticals.then_
- ~start:(PrimitiveTactics.apply_tac ~term:_sym_eqT)
- ~continuation:(PrimitiveTactics.apply_tac ~term:_Rinv_R1)
- ]
-
- )
- ] (* end continuations before comment *)
- )
- );
- !tac1]
- );(*end tac:=*)
- tac:=(Tacticals.thens ~start:(PrimitiveTactics.cut_tac ~term:_False)
- ~continuations:[Tacticals.then_
- (* ???????????????????????????????
- in coq era intro *)
- ~start:(PrimitiveTactics.intros_tac ~name:(String.copy "??"))
- (* ????????????????????????????? *)
-
- ~continuation:contradiction_tac;!tac])
-
-
- |_-> assert false)(*match (!lutil) *)
- |_-> assert false); (*match res*)
+ let ineq=Cic.Appl [(if (!s) then _Rlt else _Rle);!t1;!t2 ] in
+ let tc=rational_to_real cres in
- debug ("finalmente applico t1\n");
- (!tac ~status:(proof,goal))
+(* ora ho i termini che descrivono i passi di fourier per risolvere il sistema *)
+
+ debug "inizio a costruire tac1\n";
+ Fourier.print_rational(c1);
+
+ let tac1=ref ( fun ~status ->
+ if h1.hstrict then
+ (Tacticals.thens
+ ~start:(
+ fun ~status ->
+ debug ("inizio t1 strict\n");
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,ty = List.find
+ (function (m,_,_) -> m=goal) metasenv in
+ debug ("th = "^ CicPp.ppterm _Rfourier_lt ^"\n");
+ debug ("ty = "^ CicPp.ppterm ty^"\n");
+ PrimitiveTactics.apply_tac ~term:_Rfourier_lt ~status)
+ ~continuations:[tac_use h1;tac_zero_inf_pos
+ (rational_to_fraction c1)]
+ ~status
+ )
+ else
+ (Tacticals.thens
+ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le)
+ ~continuations:[tac_use h1;tac_zero_inf_pos
+ (rational_to_fraction c1)] ~status
+ )
+ )
+
+ in
+ s:=h1.hstrict;
+ List.iter (fun (h,c) ->
+ (if (!s) then
+ (if h.hstrict then
+ (debug("tac1 1\n");
+ tac1:=(Tacticals.thens
+ ~start:(PrimitiveTactics.apply_tac
+ ~term:_Rfourier_lt_lt)
+ ~continuations:[!tac1;tac_use h;tac_zero_inf_pos
+ (rational_to_fraction c)])
+ )
+ else
+ (debug("tac1 2\n");
+ Fourier.print_rational(c1);
+ tac1:=(Tacticals.thens
+ ~start:(
+ fun ~status ->
+ debug("INIZIO TAC 1 2\n");
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,ty = List.find (function (m,_,_) -> m=goal)
+ metasenv in
+ debug ("th = "^ CicPp.ppterm _Rfourier_lt_le ^"\n");
+ debug ("ty = "^ CicPp.ppterm ty^"\n");
+ PrimitiveTactics.apply_tac ~term:_Rfourier_lt_le ~status)
+ ~continuations:[!tac1;tac_use h;tac_zero_inf_pos
+ (rational_to_fraction c)])
+ )
+ )
+ else
+ (if h.hstrict then
+ (debug("tac1 3\n");
+ tac1:=(Tacticals.thens
+ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le_lt)
+ ~continuations:[!tac1;tac_use h;tac_zero_inf_pos
+ (rational_to_fraction c)])
+ )
+ else
+ (debug("tac1 4\n");
+ tac1:=(Tacticals.thens
+ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le_le)
+ ~continuations:[!tac1;tac_use h;tac_zero_inf_pos
+ (rational_to_fraction c)])
+ )
+ )
+ );
+ s:=(!s)||(h.hstrict)) lutil;(*end List.iter*)
+
+ let tac2 =
+ if sres then
+ tac_zero_inf_false goal (rational_to_fraction cres)
+ else
+ tac_zero_infeq_false goal (rational_to_fraction cres)
+ in
+ tac:=(Tacticals.thens
+ ~start:(my_cut ~term:ineq)
+ ~continuations:[(*Tacticals.id_tac;Tacticals.id_tac*)(**)Tacticals.then_
+ ~start:(fun ~status:(proof,goal as status) ->
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,ty = List.find (function (m,_,_) -> m=goal)
+ metasenv in
+ PrimitiveTactics.change_tac ~what:ty
+ ~with_what:(Cic.Appl [ _not; ineq]) ~status)
+ ~continuation:(Tacticals.then_
+ ~start:(PrimitiveTactics.apply_tac ~term:
+ (if sres then _Rnot_lt_lt else _Rnot_le_le))
+ ~continuation:(Tacticals.thens
+ ~start:(
+ fun ~status ->
+ debug("t1 ="^CicPp.ppterm !t1 ^"t2 ="^CicPp.ppterm !t2 ^"tc="^ CicPp.ppterm tc^"\n");
+ let r = equality_replace (Cic.Appl [_Rminus;!t2;!t1] ) tc
+ ~status
+ in
+ (match r with (p,gl) ->
+ debug("eq1 ritorna "^string_of_int(List.length gl)^"\n" ));
+ r)
+ ~continuations:[(Tacticals.thens
+ ~start:(
+ fun ~status ->
+ let r = equality_replace (Cic.Appl[_Rinv;_R1]) _R1 ~status in
+ (match r with (p,gl) ->
+ debug("eq2 ritorna "^string_of_int(List.length gl)^"\n" ));
+ r)
+ ~continuations:
+ [PrimitiveTactics.apply_tac ~term:_Rinv_R1
+ ;Tacticals.try_tactics
+ ~tactics:[ "ring", (fun ~status ->
+ debug("begin RING\n");
+ let r = Ring.ring_tac ~status in
+ debug ("end RING\n");
+ r)
+ ; "id", Tacticals.id_tac]
+ ])
+ ;(*Tacticals.id_tac*)
+ Tacticals.then_
+ ~start:
+ (
+ fun ~status:(proof,goal as status) ->
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,ty = List.find (function (m,_,_) -> m=
+ goal) metasenv in
+ (* check if ty is of type *)
+ let w1 =
+ debug("qui c'e' gia' l'or "^CicPp.ppterm ty^"\n");
+ (match ty with
+ Cic.Prod (Cic.Anonymous,a,b) -> (Cic.Appl [_not;a])
+ |_ -> assert false)
+ in
+ let r = PrimitiveTactics.change_tac ~what:ty ~with_what:w1 ~status in
+ debug("fine MY_CHNGE\n");
+ r
+
+ )
+ ~continuation:(*PORTINGTacticals.id_tac*)tac2]))
+ ;(*Tacticals.id_tac*)!tac1]);(*end tac:=*)
+
+ |_-> assert false)(*match (!lutil) *)
+ |_-> assert false); (*match res*)
+ debug ("finalmente applico tac\n");
+ (
+ let r = !tac ~status:(proof,goal) in
+ debug("\n\n]]]]]]]]]]]]]]]]]) That's all folks ([[[[[[[[[[[[[[[[[[[\n\n");r
+
+ )
;;
let fourier_tac ~status:(proof,goal) = fourier ~status:(proof,goal);;
+
projects / helm.git / blobdiff