diff options
Diffstat (limited to 'plugins/micromega')
| -rw-r--r-- | plugins/micromega/RMicromega.v | 315 | ||||
| -rw-r--r-- | plugins/micromega/coq_micromega.ml | 313 | ||||
| -rw-r--r-- | plugins/micromega/g_micromega.ml4 | 1 |
3 files changed, 190 insertions, 439 deletions
diff --git a/plugins/micromega/RMicromega.v b/plugins/micromega/RMicromega.v index 2352d78d6..30e475b71 100644 --- a/plugins/micromega/RMicromega.v +++ b/plugins/micromega/RMicromega.v @@ -18,7 +18,7 @@ Require Import Refl. Require Import Raxioms RIneq Rpow_def DiscrR. Require Import QArith. Require Import Qfield. - +Require Import Qreals. Require Setoid. (*Declare ML Module "micromega_plugin".*) @@ -38,15 +38,8 @@ Proof. exact Rplus_opp_r. Qed. -Add Ring Rring : Rsrt. Open Scope R_scope. -Lemma Rmult_neutral : forall x:R , 0 * x = 0. -Proof. - intro ; ring. -Qed. - - Lemma Rsor : SOR R0 R1 Rplus Rmult Rminus Ropp (@eq R) Rle Rlt. Proof. constructor; intros ; subst ; try (intuition (subst; try ring ; auto with real)). @@ -59,142 +52,41 @@ Proof. apply (Rlt_irrefl m) ; auto. apply Rnot_le_lt. auto with real. destruct (total_order_T n m) as [ [H1 | H1] | H1] ; auto. - intros. - rewrite <- (Rmult_neutral m). - apply (Rmult_lt_compat_r) ; auto. -Qed. - -Definition IQR := fun x : Q => (IZR (Qnum x) * / IZR (' Qden x))%R. - - -Lemma Rinv_elim : forall x y z, - y <> 0 -> (z * y = x <-> x * / y = z). -Proof. - intros. - split ; intros. - subst. - rewrite Rmult_assoc. - rewrite Rinv_r; auto. - ring. - subst. - rewrite Rmult_assoc. - rewrite (Rmult_comm (/ y)). - rewrite Rinv_r ; auto. - ring. -Qed. - -Ltac INR_nat_of_P := - match goal with - | H : context[INR (Pos.to_nat ?X)] |- _ => - revert H ; - let HH := fresh in - assert (HH := pos_INR_nat_of_P X) ; revert HH ; generalize (INR (Pos.to_nat X)) - | |- context[INR (Pos.to_nat ?X)] => - let HH := fresh in - assert (HH := pos_INR_nat_of_P X) ; revert HH ; generalize (INR (Pos.to_nat X)) - end. - -Ltac add_eq expr val := set (temp := expr) ; - generalize (eq_refl temp) ; - unfold temp at 1 ; generalize temp ; intro val ; clear temp. - -Ltac Rinv_elim := - match goal with - | |- context[?x * / ?y] => - let z := fresh "v" in - add_eq (x * / y) z ; - let H := fresh in intro H ; rewrite <- Rinv_elim in H - end. - -Lemma Rlt_neq : forall r , 0 < r -> r <> 0. -Proof. - red. intros. - subst. - apply (Rlt_irrefl 0 H). + now apply Rmult_lt_0_compat. Qed. +Notation IQR := Q2R (only parsing). Lemma Rinv_1 : forall x, x * / 1 = x. Proof. intro. - Rinv_elim. - subst ; ring. - apply R1_neq_R0. + rewrite Rinv_1. + apply Rmult_1_r. Qed. -Lemma Qeq_true : forall x y, - Qeq_bool x y = true -> - IQR x = IQR y. +Lemma Qeq_true : forall x y, Qeq_bool x y = true -> IQR x = IQR y. Proof. - unfold IQR. - simpl. - intros. - apply Qeq_bool_eq in H. - unfold Qeq in H. - assert (IZR (Qnum x * ' Qden y) = IZR (Qnum y * ' Qden x))%Z. - rewrite H. reflexivity. - repeat rewrite mult_IZR in H0. - simpl in H0. - revert H0. - repeat INR_nat_of_P. intros. - apply Rinv_elim in H2 ; [| apply Rlt_neq ; auto]. - rewrite <- H2. - field. - split ; apply Rlt_neq ; auto. + now apply Qeq_eqR, Qeq_bool_eq. Qed. Lemma Qeq_false : forall x y, Qeq_bool x y = false -> IQR x <> IQR y. Proof. intros. - apply Qeq_bool_neq in H. - intro. apply H. clear H. - unfold Qeq,IQR in *. - simpl in *. - revert H0. - repeat Rinv_elim. - intros. - subst. - assert (IZR (Qnum x * ' Qden y)%Z = IZR (Qnum y * ' Qden x)%Z). - repeat rewrite mult_IZR. - simpl. - rewrite <- H0. rewrite <- H. - ring. - apply eq_IZR ; auto. - INR_nat_of_P; intros; apply Rlt_neq ; auto. - INR_nat_of_P; intros ; apply Rlt_neq ; auto. + apply Qeq_bool_neq in H. + contradict H. + now apply eqR_Qeq. Qed. - - Lemma Qle_true : forall x y : Q, Qle_bool x y = true -> IQR x <= IQR y. Proof. intros. - apply Qle_bool_imp_le in H. - unfold Qle in H. - unfold IQR. - simpl in *. - apply IZR_le in H. - repeat rewrite mult_IZR in H. - simpl in H. - repeat INR_nat_of_P; intros. - assert (Hr := Rlt_neq r H). - assert (Hr0 := Rlt_neq r0 H0). - replace (IZR (Qnum x) * / r) with ((IZR (Qnum x) * r0) * (/r * /r0)). - replace (IZR (Qnum y) * / r0) with ((IZR (Qnum y) * r) * (/r * /r0)). - apply Rmult_le_compat_r ; auto. - apply Rmult_le_pos. - unfold Rle. left. apply Rinv_0_lt_compat ; auto. - unfold Rle. left. apply Rinv_0_lt_compat ; auto. - field ; intuition. - field ; intuition. + now apply Qle_Rle, Qle_bool_imp_le. Qed. - - Lemma IQR_0 : IQR 0 = 0. Proof. - compute. apply Rinv_1. + apply Rmult_0_l. Qed. Lemma IQR_1 : IQR 1 = 1. @@ -202,160 +94,6 @@ Proof. compute. apply Rinv_1. Qed. -Lemma IQR_plus : forall x y, IQR (x + y) = IQR x + IQR y. -Proof. - intros. - unfold IQR. - simpl in *. - rewrite plus_IZR in *. - rewrite mult_IZR in *. - simpl. - rewrite Pos2Nat.inj_mul. - rewrite mult_INR. - rewrite mult_IZR. - simpl. - repeat INR_nat_of_P. - intros. field. - split ; apply Rlt_neq ; auto. -Qed. - -Lemma IQR_opp : forall x, IQR (- x) = - IQR x. -Proof. - intros. - unfold IQR. - simpl. - rewrite opp_IZR. - ring. -Qed. - -Lemma IQR_minus : forall x y, IQR (x - y) = IQR x - IQR y. -Proof. - intros. - unfold Qminus. - rewrite IQR_plus. - rewrite IQR_opp. - ring. -Qed. - - -Lemma IQR_mult : forall x y, IQR (x * y) = IQR x * IQR y. -Proof. - unfold IQR ; intros. - simpl. - repeat rewrite mult_IZR. - rewrite Pos2Nat.inj_mul. - rewrite mult_INR. - repeat INR_nat_of_P. - intros. field ; split ; apply Rlt_neq ; auto. -Qed. - -Lemma IQR_inv_lt : forall x, (0 < x)%Q -> - IQR (/ x) = / IQR x. -Proof. - unfold IQR ; simpl. - intros. - unfold Qlt in H. - revert H. - simpl. - intros. - unfold Qinv. - destruct x. - destruct Qnum ; simpl in *. - exfalso. auto with zarith. - clear H. - repeat INR_nat_of_P. - intros. - assert (HH := Rlt_neq _ H). - assert (HH0 := Rlt_neq _ H0). - rewrite Rinv_mult_distr ; auto. - rewrite Rinv_involutive ; auto. - ring. - apply Rinv_0_lt_compat in H0. - apply Rlt_neq ; auto. - simpl in H. - exfalso. - rewrite Pos.mul_comm in H. - compute in H. - discriminate. -Qed. - -Lemma Qinv_opp : forall x, (- (/ x) = / ( -x))%Q. -Proof. - destruct x ; destruct Qnum ; reflexivity. -Qed. - -Lemma Qopp_involutive_strong : forall x, (- - x = x)%Q. -Proof. - intros. - destruct x. - unfold Qopp. - simpl. - rewrite Z.opp_involutive. - reflexivity. -Qed. - -Lemma Ropp_0 : forall r , - r = 0 -> r = 0. -Proof. - intros. - rewrite <- (Ropp_involutive r). - apply Ropp_eq_0_compat ; auto. -Qed. - -Lemma IQR_x_0 : forall x, IQR x = 0 -> x == 0%Q. -Proof. - destruct x ; simpl. - unfold IQR. - simpl. - INR_nat_of_P. - intros. - apply Rmult_integral in H0. - destruct H0. - apply eq_IZR_R0 in H0. - subst. - reflexivity. - exfalso. - apply Rinv_0_lt_compat in H. - rewrite <- H0 in H. - apply Rlt_irrefl in H. auto. -Qed. - - -Lemma IQR_inv_gt : forall x, (0 > x)%Q -> - IQR (/ x) = / IQR x. -Proof. - intros. - rewrite <- (Qopp_involutive_strong x). - rewrite <- Qinv_opp. - rewrite IQR_opp. - rewrite IQR_inv_lt. - repeat rewrite IQR_opp. - rewrite Ropp_inv_permute. - auto. - intro. - apply Ropp_0 in H0. - apply IQR_x_0 in H0. - rewrite H0 in H. - compute in H. discriminate. - unfold Qlt in *. - destruct x ; simpl in *. - auto with zarith. -Qed. - -Lemma IQR_inv : forall x, ~ x == 0 -> - IQR (/ x) = / IQR x. -Proof. - intros. - assert ( 0 > x \/ 0 < x)%Q. - destruct x ; unfold Qlt, Qeq in * ; simpl in *. - rewrite Z.mul_1_r in *. - destruct Qnum ; simpl in * ; intuition auto. - right. reflexivity. - left ; reflexivity. - destruct H0. - apply IQR_inv_gt ; auto. - apply IQR_inv_lt ; auto. -Qed. - Lemma IQR_inv_ext : forall x, IQR (/ x) = (if Qeq_bool x 0 then 0 else / IQR x). Proof. @@ -366,18 +104,13 @@ Proof. destruct x ; simpl. unfold Qeq in H. simpl in H. - replace Qnum with 0%Z. - compute. rewrite Rinv_1. - reflexivity. - rewrite <- H. ring. + rewrite Zmult_1_r in H. + rewrite H. + apply Rmult_0_l. intros. - apply IQR_inv. - intro. - rewrite <- Qeq_bool_iff in H0. - congruence. + now apply Q2R_inv, Qeq_bool_neq. Qed. - Notation to_nat := N.to_nat. Lemma QSORaddon : @@ -391,10 +124,10 @@ Proof. constructor ; intros ; try reflexivity. apply IQR_0. apply IQR_1. - apply IQR_plus. - apply IQR_minus. - apply IQR_mult. - apply IQR_opp. + apply Q2R_plus. + apply Q2R_minus. + apply Q2R_mult. + apply Q2R_opp. apply Qeq_true ; auto. apply R_power_theory. apply Qeq_false. @@ -453,13 +186,13 @@ Proof. apply IQR_1. reflexivity. unfold IQR. simpl. rewrite Rinv_1. reflexivity. - apply IQR_plus. - apply IQR_minus. - apply IQR_mult. + apply Q2R_plus. + apply Q2R_minus. + apply Q2R_mult. rewrite <- IHc. apply IQR_inv_ext. rewrite <- IHc. - apply IQR_opp. + apply Q2R_opp. Qed. Require Import EnvRing. diff --git a/plugins/micromega/coq_micromega.ml b/plugins/micromega/coq_micromega.ml index e4b58a56f..eb26c5431 100644 --- a/plugins/micromega/coq_micromega.ml +++ b/plugins/micromega/coq_micromega.ml @@ -20,6 +20,8 @@ open Pp open Mutils open Goptions +module Term = EConstr + (** * Debug flag *) @@ -330,6 +332,8 @@ struct open Coqlib open Term + open Constr + open EConstr (** * Location of the Coq libraries. @@ -364,6 +368,7 @@ struct [["Coq";"Reals" ; "Rdefinitions"]; ["Coq";"Reals" ; "Rpow_def"] ; ["Coq";"Reals" ; "Raxioms"] ; + ["Coq";"QArith"; "Qreals"] ; ] let z_modules = [["Coq";"ZArith";"BinInt"]] @@ -373,6 +378,7 @@ struct * ZMicromega.v *) + let gen_constant_in_modules s m n = EConstr.of_constr (gen_constant_in_modules s m n) let init_constant = gen_constant_in_modules "ZMicromega" init_modules let constant = gen_constant_in_modules "ZMicromega" coq_modules let bin_constant = gen_constant_in_modules "ZMicromega" bin_module @@ -383,7 +389,6 @@ struct let coq_and = lazy (init_constant "and") let coq_or = lazy (init_constant "or") let coq_not = lazy (init_constant "not") - let coq_not_gl_ref = (Nametab.locate ( Libnames.qualid_of_string "Coq.Init.Logic.not")) let coq_iff = lazy (init_constant "iff") let coq_True = lazy (init_constant "True") @@ -480,7 +485,7 @@ struct let coq_Rinv = lazy (r_constant "Rinv") let coq_Rpower = lazy (r_constant "pow") let coq_IZR = lazy (r_constant "IZR") - let coq_IQR = lazy (constant "IQR") + let coq_IQR = lazy (r_constant "Q2R") let coq_PEX = lazy (constant "PEX" ) @@ -599,12 +604,12 @@ struct (* A simple but useful getter function *) - let get_left_construct term = - match Term.kind_of_term term with - | Term.Construct((_,i),_) -> (i,[| |]) - | Term.App(l,rst) -> - (match Term.kind_of_term l with - | Term.Construct((_,i),_) -> (i,rst) + let get_left_construct sigma term = + match EConstr.kind sigma term with + | Constr.Construct((_,i),_) -> (i,[| |]) + | Constr.App(l,rst) -> + (match EConstr.kind sigma l with + | Constr.Construct((_,i),_) -> (i,rst) | _ -> raise ParseError ) | _ -> raise ParseError @@ -613,11 +618,11 @@ struct (* parse/dump/print from numbers up to expressions and formulas *) - let rec parse_nat term = - let (i,c) = get_left_construct term in + let rec parse_nat sigma term = + let (i,c) = get_left_construct sigma term in match i with | 1 -> Mc.O - | 2 -> Mc.S (parse_nat (c.(0))) + | 2 -> Mc.S (parse_nat sigma (c.(0))) | i -> raise ParseError let pp_nat o n = Printf.fprintf o "%i" (CoqToCaml.nat n) @@ -627,11 +632,11 @@ struct | Mc.O -> Lazy.force coq_O | Mc.S p -> Term.mkApp(Lazy.force coq_S,[| dump_nat p |]) - let rec parse_positive term = - let (i,c) = get_left_construct term in + let rec parse_positive sigma term = + let (i,c) = get_left_construct sigma term in match i with - | 1 -> Mc.XI (parse_positive c.(0)) - | 2 -> Mc.XO (parse_positive c.(0)) + | 1 -> Mc.XI (parse_positive sigma c.(0)) + | 2 -> Mc.XO (parse_positive sigma c.(0)) | 3 -> Mc.XH | i -> raise ParseError @@ -661,12 +666,12 @@ struct let dump_pair t1 t2 dump_t1 dump_t2 (x,y) = Term.mkApp(Lazy.force coq_pair,[| t1 ; t2 ; dump_t1 x ; dump_t2 y|]) - let parse_z term = - let (i,c) = get_left_construct term in + let parse_z sigma term = + let (i,c) = get_left_construct sigma term in match i with | 1 -> Mc.Z0 - | 2 -> Mc.Zpos (parse_positive c.(0)) - | 3 -> Mc.Zneg (parse_positive c.(0)) + | 2 -> Mc.Zpos (parse_positive sigma c.(0)) + | 3 -> Mc.Zneg (parse_positive sigma c.(0)) | i -> raise ParseError let dump_z x = @@ -686,10 +691,10 @@ struct Term.mkApp(Lazy.force coq_Qmake, [| dump_z q.Micromega.qnum ; dump_positive q.Micromega.qden|]) - let parse_q term = - match Term.kind_of_term term with - | Term.App(c, args) -> if Constr.equal c (Lazy.force coq_Qmake) then - {Mc.qnum = parse_z args.(0) ; Mc.qden = parse_positive args.(1) } + let parse_q sigma term = + match EConstr.kind sigma term with + | Constr.App(c, args) -> if EConstr.eq_constr sigma c (Lazy.force coq_Qmake) then + {Mc.qnum = parse_z sigma args.(0) ; Mc.qden = parse_positive sigma args.(1) } else raise ParseError | _ -> raise ParseError @@ -719,27 +724,27 @@ struct | Mc.CInv t -> Term.mkApp(Lazy.force coq_CInv, [| dump_Rcst t |]) | Mc.COpp t -> Term.mkApp(Lazy.force coq_COpp, [| dump_Rcst t |]) - let rec parse_Rcst term = - let (i,c) = get_left_construct term in + let rec parse_Rcst sigma term = + let (i,c) = get_left_construct sigma term in match i with | 1 -> Mc.C0 | 2 -> Mc.C1 - | 3 -> Mc.CQ (parse_q c.(0)) - | 4 -> Mc.CPlus(parse_Rcst c.(0), parse_Rcst c.(1)) - | 5 -> Mc.CMinus(parse_Rcst c.(0), parse_Rcst c.(1)) - | 6 -> Mc.CMult(parse_Rcst c.(0), parse_Rcst c.(1)) - | 7 -> Mc.CInv(parse_Rcst c.(0)) - | 8 -> Mc.COpp(parse_Rcst c.(0)) + | 3 -> Mc.CQ (parse_q sigma c.(0)) + | 4 -> Mc.CPlus(parse_Rcst sigma c.(0), parse_Rcst sigma c.(1)) + | 5 -> Mc.CMinus(parse_Rcst sigma c.(0), parse_Rcst sigma c.(1)) + | 6 -> Mc.CMult(parse_Rcst sigma c.(0), parse_Rcst sigma c.(1)) + | 7 -> Mc.CInv(parse_Rcst sigma c.(0)) + | 8 -> Mc.COpp(parse_Rcst sigma c.(0)) | _ -> raise ParseError - let rec parse_list parse_elt term = - let (i,c) = get_left_construct term in + let rec parse_list sigma parse_elt term = + let (i,c) = get_left_construct sigma term in match i with | 1 -> [] - | 2 -> parse_elt c.(1) :: parse_list parse_elt c.(2) + | 2 -> parse_elt sigma c.(1) :: parse_list sigma parse_elt c.(2) | i -> raise ParseError let rec dump_list typ dump_elt l = @@ -872,9 +877,9 @@ struct dump_op o ; dump_expr typ dump_constant e2|]) - let assoc_const x l = + let assoc_const sigma x l = try - snd (List.find (fun (x',y) -> Constr.equal x (Lazy.force x')) l) + snd (List.find (fun (x',y) -> EConstr.eq_constr sigma x (Lazy.force x')) l) with Not_found -> raise ParseError @@ -896,37 +901,36 @@ struct coq_Qeq, Mc.OpEq ] - let has_typ gl t1 typ = - let ty = Retyping.get_type_of (Tacmach.pf_env gl) (Tacmach.project gl) t1 in - Constr.equal ty typ - + type gl = { env : Environ.env; sigma : Evd.evar_map } let is_convertible gl t1 t2 = - Reductionops.is_conv (Tacmach.pf_env gl) (Tacmach.project gl) t1 t2 + Reductionops.is_conv gl.env gl.sigma t1 t2 let parse_zop gl (op,args) = - match kind_of_term op with - | Const (x,_) -> (assoc_const op zop_table, args.(0) , args.(1)) + let sigma = gl.sigma in + match EConstr.kind sigma op with + | Const (x,_) -> (assoc_const sigma op zop_table, args.(0) , args.(1)) | Ind((n,0),_) -> - if Constr.equal op (Lazy.force coq_Eq) && is_convertible gl args.(0) (Lazy.force coq_Z) + if EConstr.eq_constr sigma op (Lazy.force coq_Eq) && is_convertible gl args.(0) (Lazy.force coq_Z) then (Mc.OpEq, args.(1), args.(2)) else raise ParseError | _ -> failwith "parse_zop" let parse_rop gl (op,args) = - match kind_of_term op with - | Const (x,_) -> (assoc_const op rop_table, args.(0) , args.(1)) + let sigma = gl.sigma in + match EConstr.kind sigma op with + | Const (x,_) -> (assoc_const sigma op rop_table, args.(0) , args.(1)) | Ind((n,0),_) -> - if Constr.equal op (Lazy.force coq_Eq) && is_convertible gl args.(0) (Lazy.force coq_R) + if EConstr.eq_constr sigma op (Lazy.force coq_Eq) && is_convertible gl args.(0) (Lazy.force coq_R) then (Mc.OpEq, args.(1), args.(2)) else raise ParseError | _ -> failwith "parse_zop" let parse_qop gl (op,args) = - (assoc_const op qop_table, args.(0) , args.(1)) + (assoc_const gl.sigma op qop_table, args.(0) , args.(1)) - let is_constant t = (* This is an approx *) - match kind_of_term t with + let is_constant sigma t = (* This is an approx *) + match EConstr.kind sigma t with | Construct(i,_) -> true | _ -> false @@ -936,9 +940,9 @@ struct | Power | Ukn of string - let assoc_ops x l = + let assoc_ops sigma x l = try - snd (List.find (fun (x',y) -> Constr.equal x (Lazy.force x')) l) + snd (List.find (fun (x',y) -> EConstr.eq_constr sigma x (Lazy.force x')) l) with Not_found -> Ukn "Oups" @@ -950,12 +954,12 @@ struct struct type t = constr list - let compute_rank_add env v = + let compute_rank_add env sigma v = let rec _add env n v = match env with | [] -> ([v],n) | e::l -> - if eq_constr e v + if eq_constr sigma e v then (env,n) else let (env,n) = _add l ( n+1) v in @@ -963,13 +967,13 @@ struct let (env, n) = _add env 1 v in (env, CamlToCoq.positive n) - let get_rank env v = + let get_rank env sigma v = let rec _get_rank env n = match env with | [] -> raise (Invalid_argument "get_rank") | e::l -> - if eq_constr e v + if eq_constr sigma e v then n else _get_rank l (n+1) in _get_rank env 1 @@ -985,9 +989,9 @@ struct * This is the big generic function for expression parsers. *) - let parse_expr parse_constant parse_exp ops_spec env term = + let parse_expr sigma parse_constant parse_exp ops_spec env term = if debug - then Feedback.msg_debug (Pp.str "parse_expr: " ++ Printer.prterm term); + then Feedback.msg_debug (Pp.str "parse_expr: " ++ Printer.pr_leconstr term); (* let constant_or_variable env term = @@ -998,7 +1002,7 @@ struct (Mc.PEX n , env) in *) let parse_variable env term = - let (env,n) = Env.compute_rank_add env term in + let (env,n) = Env.compute_rank_add env sigma term in (Mc.PEX n , env) in let rec parse_expr env term = @@ -1009,12 +1013,12 @@ struct try (Mc.PEc (parse_constant term) , env) with ParseError -> - match kind_of_term term with + match EConstr.kind sigma term with | App(t,args) -> ( - match kind_of_term t with + match EConstr.kind sigma t with | Const c -> - ( match assoc_ops t ops_spec with + ( match assoc_ops sigma t ops_spec with | Binop f -> combine env f (args.(0),args.(1)) | Opp -> let (expr,env) = parse_expr env args.(0) in (Mc.PEopp expr, env) @@ -1026,12 +1030,12 @@ struct (power , env) with e when CErrors.noncritical e -> (* if the exponent is a variable *) - let (env,n) = Env.compute_rank_add env term in (Mc.PEX n, env) + let (env,n) = Env.compute_rank_add env sigma term in (Mc.PEX n, env) end | Ukn s -> if debug then (Printf.printf "unknown op: %s\n" s; flush stdout;); - let (env,n) = Env.compute_rank_add env term in (Mc.PEX n, env) + let (env,n) = Env.compute_rank_add env sigma term in (Mc.PEX n, env) ) | _ -> parse_variable env term ) @@ -1074,60 +1078,60 @@ struct (* coq_Rdiv , (fun x y -> Mc.CMult(x,Mc.CInv y)) ;*) ] - let rec rconstant term = - match Term.kind_of_term term with + let rec rconstant sigma term = + match EConstr.kind sigma term with | Const x -> - if Constr.equal term (Lazy.force coq_R0) + if EConstr.eq_constr sigma term (Lazy.force coq_R0) then Mc.C0 - else if Constr.equal term (Lazy.force coq_R1) + else if EConstr.eq_constr sigma term (Lazy.force coq_R1) then Mc.C1 else raise ParseError | App(op,args) -> begin try (* the evaluation order is important in the following *) - let f = assoc_const op rconst_assoc in - let a = rconstant args.(0) in - let b = rconstant args.(1) in + let f = assoc_const sigma op rconst_assoc in + let a = rconstant sigma args.(0) in + let b = rconstant sigma args.(1) in f a b with ParseError -> match op with - | op when Constr.equal op (Lazy.force coq_Rinv) -> - let arg = rconstant args.(0) in + | op when EConstr.eq_constr sigma op (Lazy.force coq_Rinv) -> + let arg = rconstant sigma args.(0) in if Mc.qeq_bool (Mc.q_of_Rcst arg) {Mc.qnum = Mc.Z0 ; Mc.qden = Mc.XH} then raise ParseError (* This is a division by zero -- no semantics *) else Mc.CInv(arg) - | op when Constr.equal op (Lazy.force coq_IQR) -> Mc.CQ (parse_q args.(0)) - | op when Constr.equal op (Lazy.force coq_IZR) -> Mc.CZ (parse_z args.(0)) + | op when EConstr.eq_constr sigma op (Lazy.force coq_IQR) -> Mc.CQ (parse_q sigma args.(0)) + | op when EConstr.eq_constr sigma op (Lazy.force coq_IZR) -> Mc.CZ (parse_z sigma args.(0)) | _ -> raise ParseError end | _ -> raise ParseError - let rconstant term = + let rconstant sigma term = if debug - then Feedback.msg_debug (Pp.str "rconstant: " ++ Printer.prterm term ++ fnl ()); - let res = rconstant term in + then Feedback.msg_debug (Pp.str "rconstant: " ++ Printer.pr_leconstr term ++ fnl ()); + let res = rconstant sigma term in if debug then (Printf.printf "rconstant -> %a\n" pp_Rcst res ; flush stdout) ; res - let parse_zexpr = parse_expr - zconstant + let parse_zexpr sigma = parse_expr sigma + (zconstant sigma) (fun expr x -> - let exp = (parse_z x) in + let exp = (parse_z sigma x) in match exp with | Mc.Zneg _ -> Mc.PEc Mc.Z0 | _ -> Mc.PEpow(expr, Mc.Z.to_N exp)) zop_spec - let parse_qexpr = parse_expr - qconstant + let parse_qexpr sigma = parse_expr sigma + (qconstant sigma) (fun expr x -> - let exp = parse_z x in + let exp = parse_z sigma x in match exp with | Mc.Zneg _ -> begin @@ -1139,21 +1143,22 @@ struct Mc.PEpow(expr,exp)) qop_spec - let parse_rexpr = parse_expr - rconstant + let parse_rexpr sigma = parse_expr sigma + (rconstant sigma) (fun expr x -> - let exp = Mc.N.of_nat (parse_nat x) in + let exp = Mc.N.of_nat (parse_nat sigma x) in Mc.PEpow(expr,exp)) rop_spec let parse_arith parse_op parse_expr env cstr gl = + let sigma = gl.sigma in if debug - then Feedback.msg_debug (Pp.str "parse_arith: " ++ Printer.prterm cstr ++ fnl ()); - match kind_of_term cstr with + then Feedback.msg_debug (Pp.str "parse_arith: " ++ Printer.pr_leconstr cstr ++ fnl ()); + match EConstr.kind sigma cstr with | App(op,args) -> let (op,lhs,rhs) = parse_op gl (op,args) in - let (e1,env) = parse_expr env lhs in - let (e2,env) = parse_expr env rhs in + let (e1,env) = parse_expr sigma env lhs in + let (e2,env) = parse_expr sigma env rhs in ({Mc.flhs = e1; Mc.fop = op;Mc.frhs = e2},env) | _ -> failwith "error : parse_arith(2)" @@ -1191,6 +1196,7 @@ struct *) let parse_formula gl parse_atom env tg term = + let sigma = gl.sigma in let parse_atom env tg t = try @@ -1199,34 +1205,34 @@ struct with e when CErrors.noncritical e -> (X(t),env,tg) in let is_prop term = - let sort = Retyping.get_sort_of (Tacmach.pf_env gl) (Tacmach.project gl) term in - Term.is_prop_sort sort in + let sort = Retyping.get_sort_of gl.env gl.sigma term in + Sorts.is_prop sort in let rec xparse_formula env tg term = - match kind_of_term term with + match EConstr.kind sigma term with | App(l,rst) -> (match rst with - | [|a;b|] when eq_constr l (Lazy.force coq_and) -> + | [|a;b|] when eq_constr sigma l (Lazy.force coq_and) -> let f,env,tg = xparse_formula env tg a in let g,env, tg = xparse_formula env tg b in mkformula_binary mkC term f g,env,tg - | [|a;b|] when eq_constr l (Lazy.force coq_or) -> + | [|a;b|] when eq_constr sigma l (Lazy.force coq_or) -> let f,env,tg = xparse_formula env tg a in let g,env,tg = xparse_formula env tg b in mkformula_binary mkD term f g,env,tg - | [|a|] when eq_constr l (Lazy.force coq_not) -> + | [|a|] when eq_constr sigma l (Lazy.force coq_not) -> let (f,env,tg) = xparse_formula env tg a in (N(f), env,tg) - | [|a;b|] when eq_constr l (Lazy.force coq_iff) -> + | [|a;b|] when eq_constr sigma l (Lazy.force coq_iff) -> let f,env,tg = xparse_formula env tg a in let g,env,tg = xparse_formula env tg b in mkformula_binary mkIff term f g,env,tg | _ -> parse_atom env tg term) - | Prod(typ,a,b) when not (Termops.dependent (mkRel 1) b)-> + | Prod(typ,a,b) when Vars.noccurn sigma 1 b -> let f,env,tg = xparse_formula env tg a in let g,env,tg = xparse_formula env tg b in mkformula_binary mkI term f g,env,tg - | _ when eq_constr term (Lazy.force coq_True) -> (TT,env,tg) - | _ when eq_constr term (Lazy.force coq_False) -> (FF,env,tg) + | _ when eq_constr sigma term (Lazy.force coq_True) -> (TT,env,tg) + | _ when eq_constr sigma term (Lazy.force coq_False) -> (FF,env,tg) | _ when is_prop term -> X(term),env,tg | _ -> raise ParseError in @@ -1246,10 +1252,10 @@ struct xdump f - let prop_env_of_formula form = + let prop_env_of_formula sigma form = let rec doit env = function | TT | FF | A(_,_,_) -> env - | X t -> fst (Env.compute_rank_add env t) + | X t -> fst (Env.compute_rank_add env sigma t) | C(f1,f2) | D(f1,f2) | I(f1,_,f2) -> doit (doit env f1) f2 | N f -> doit env f in @@ -1380,14 +1386,22 @@ let dump_rexpr = lazy *) -let rec make_goal_of_formula dexpr form = +let prodn n env b = + let rec prodrec = function + | (0, env, b) -> b + | (n, ((v,t)::l), b) -> prodrec (n-1, l, mkProd (v,t,b)) + | _ -> assert false + in + prodrec (n,env,b) + +let make_goal_of_formula sigma dexpr form = let vars_idx = List.mapi (fun i v -> (v, i+1)) (ISet.elements (var_env_of_formula form)) in (* List.iter (fun (v,i) -> Printf.fprintf stdout "var %i has index %i\n" v i) vars_idx ;*) - let props = prop_env_of_formula form in + let props = prop_env_of_formula sigma form in let vars_n = List.map (fun (_,i) -> (Names.id_of_string (Printf.sprintf "__x%i" i)) , dexpr.interp_typ) vars_idx in let props_n = List.mapi (fun i _ -> (Names.id_of_string (Printf.sprintf "__p%i" (i+1))) , Term.mkProp) props in @@ -1428,7 +1442,7 @@ let rec make_goal_of_formula dexpr form = | I(x,_,y) -> mkArrow (xdump pi xi x) (xdump (pi+1) (xi+1) y) | N(x) -> mkArrow (xdump pi xi x) (Lazy.force coq_False) | A(x,_,_) -> dump_cstr xi x - | X(t) -> let idx = Env.get_rank props t in + | X(t) -> let idx = Env.get_rank props sigma t in mkRel (pi+idx) in let nb_vars = List.length vars_n in @@ -1437,13 +1451,13 @@ let rec make_goal_of_formula dexpr form = (* Printf.fprintf stdout "NBProps : %i\n" nb_props ;*) let subst_prop p = - let idx = Env.get_rank props p in + let idx = Env.get_rank props sigma p in mkVar (Names.id_of_string (Printf.sprintf "__p%i" idx)) in let form' = map_prop subst_prop form in - (Term.prodn nb_props (List.map (fun (x,y) -> Names.Name x,y) props_n) - (Term.prodn nb_vars (List.map (fun (x,y) -> Names.Name x,y) vars_n) + (prodn nb_props (List.map (fun (x,y) -> Names.Name x,y) props_n) + (prodn nb_vars (List.map (fun (x,y) -> Names.Name x,y) vars_n) (xdump (List.length vars_n) 0 form)), List.rev props_n, List.rev var_name_pos,form') @@ -1517,19 +1531,19 @@ let rec apply_ids t ids = | [] -> t | i::ids -> apply_ids (Term.mkApp(t,[| Term.mkVar i |])) ids -let coq_Node = lazy - (Coqlib.gen_constant_in_modules "VarMap" - [["Coq" ; "micromega" ; "VarMap"];["VarMap"]] "Node") -let coq_Leaf = lazy - (Coqlib.gen_constant_in_modules "VarMap" - [["Coq" ; "micromega" ; "VarMap"];["VarMap"]] "Leaf") -let coq_Empty = lazy - (Coqlib.gen_constant_in_modules "VarMap" - [["Coq" ; "micromega" ;"VarMap"];["VarMap"]] "Empty") - -let coq_VarMap = lazy - (Coqlib.gen_constant_in_modules "VarMap" - [["Coq" ; "micromega" ; "VarMap"] ; ["VarMap"]] "t") +let coq_Node = + lazy (EConstr.of_constr (Coqlib.gen_constant_in_modules "VarMap" + [["Coq" ; "micromega" ; "VarMap"];["VarMap"]] "Node")) +let coq_Leaf = + lazy (EConstr.of_constr (Coqlib.gen_constant_in_modules "VarMap" + [["Coq" ; "micromega" ; "VarMap"];["VarMap"]] "Leaf")) +let coq_Empty = + lazy (EConstr.of_constr (Coqlib.gen_constant_in_modules "VarMap" + [["Coq" ; "micromega" ;"VarMap"];["VarMap"]] "Empty")) + +let coq_VarMap = + lazy (EConstr.of_constr (Coqlib.gen_constant_in_modules "VarMap" + [["Coq" ; "micromega" ; "VarMap"] ; ["VarMap"]] "t")) let rec dump_varmap typ m = @@ -1687,7 +1701,8 @@ let rec mk_topo_order le l = | (Some v,l') -> v :: (mk_topo_order le l') -let topo_sort_constr l = mk_topo_order Termops.dependent l +let topo_sort_constr l = + mk_topo_order (fun c t -> Termops.dependent Evd.empty (** FIXME *) (EConstr.of_constr c) (EConstr.of_constr t)) l (** @@ -1702,7 +1717,6 @@ let micromega_order_change spec cert cert_typ env ff (*: unit Proofview.tactic* let vm = dump_varmap (spec.typ) (vm_of_list env) in (* todo : directly generate the proof term - or generalize before conversion? *) Proofview.Goal.nf_enter { enter = begin fun gl -> - let gl = Tacmach.New.of_old (fun x -> x) gl in Tacticals.New.tclTHENLIST [ Tactics.change_concl @@ -1712,7 +1726,7 @@ let micromega_order_change spec cert cert_typ env ff (*: unit Proofview.tactic* ("__varmap", vm, Term.mkApp(Lazy.force coq_VarMap, [|spec.typ|])); ("__wit", cert, cert_typ) ] - (Tacmach.pf_concl gl)) + (Tacmach.New.pf_concl gl)) ] end } @@ -1903,7 +1917,7 @@ let micromega_tauto negate normalise unsat deduce spec prover env polys1 polys2 let formula_typ = (Term.mkApp(Lazy.force coq_Cstr, [|spec.coeff|])) in let ff = dump_formula formula_typ (dump_cstr spec.typ spec.dump_coeff) ff in - Feedback.msg_notice (Printer.prterm ff); + Feedback.msg_notice (Printer.pr_leconstr ff); Printf.fprintf stdout "cnf : %a\n" (pp_cnf (fun o _ -> ())) cnf_ff end; @@ -1928,7 +1942,7 @@ let micromega_tauto negate normalise unsat deduce spec prover env polys1 polys2 let formula_typ = (Term.mkApp( Lazy.force coq_Cstr,[| spec.coeff|])) in let ff' = dump_formula formula_typ (dump_cstr spec.typ spec.dump_coeff) ff' in - Feedback.msg_notice (Printer.prterm ff'); + Feedback.msg_notice (Printer.pr_leconstr ff'); Printf.fprintf stdout "cnf : %a\n" (pp_cnf (fun o _ -> ())) cnf_ff' end; @@ -1949,11 +1963,13 @@ let micromega_tauto negate normalise unsat deduce spec prover env polys1 polys2 Some (ids,ff',res') - (** * Parse the proof environment, and call micromega_tauto *) +let fresh_id avoid id gl = + Tactics.fresh_id_in_env avoid id (Proofview.Goal.env gl) + let micromega_gen parse_arith (negate:'cst atom -> 'cst mc_cnf) @@ -1961,32 +1977,33 @@ let micromega_gen unsat deduce spec dumpexpr prover tac = Proofview.Goal.nf_enter { enter = begin fun gl -> - let gl = Tacmach.New.of_old (fun x -> x) gl in - let concl = Tacmach.pf_concl gl in - let hyps = Tacmach.pf_hyps_types gl in + let sigma = Tacmach.New.project gl in + let concl = Tacmach.New.pf_concl gl in + let hyps = Tacmach.New.pf_hyps_types gl in try - let (hyps,concl,env) = parse_goal gl parse_arith Env.empty hyps concl in + let gl0 = { env = Tacmach.New.pf_env gl; sigma } in + let (hyps,concl,env) = parse_goal gl0 parse_arith Env.empty hyps concl in let env = Env.elements env in let spec = Lazy.force spec in let dumpexpr = Lazy.force dumpexpr in - match micromega_tauto negate normalise unsat deduce spec prover env hyps concl gl with + match micromega_tauto negate normalise unsat deduce spec prover env hyps concl gl0 with | None -> Tacticals.New.tclFAIL 0 (Pp.str " Cannot find witness") | Some (ids,ff',res') -> - let (arith_goal,props,vars,ff_arith) = make_goal_of_formula dumpexpr ff' in + let (arith_goal,props,vars,ff_arith) = make_goal_of_formula sigma dumpexpr ff' in let intro (id,_) = Tactics.introduction id in let intro_vars = Tacticals.New.tclTHENLIST (List.map intro vars) in let intro_props = Tacticals.New.tclTHENLIST (List.map intro props) in let ipat_of_name id = Some (Loc.ghost, Misctypes.IntroNaming (Misctypes.IntroIdentifier id)) in - let goal_name = Tactics.fresh_id [] (Names.Id.of_string "__arith") gl in + let goal_name = fresh_id [] (Names.Id.of_string "__arith") gl in let env' = List.map (fun (id,i) -> Term.mkVar id,i) vars in let tac_arith = Tacticals.New.tclTHENLIST [ intro_props ; intro_vars ; micromega_order_change spec res' (Term.mkApp(Lazy.force coq_list, [|spec.proof_typ|])) env' ff_arith ] in - let goal_props = List.rev (prop_env_of_formula ff') in + let goal_props = List.rev (prop_env_of_formula sigma ff') in let goal_vars = List.map (fun (_,i) -> List.nth env (i-1)) vars in @@ -2038,7 +2055,6 @@ let micromega_order_changer cert env ff = let ff = dump_formula formula_typ (dump_cstr coeff dump_coeff) ff in let vm = dump_varmap (typ) (vm_of_list env) in Proofview.Goal.nf_enter { enter = begin fun gl -> - let gl = Tacmach.New.of_old (fun x -> x) gl in Tacticals.New.tclTHENLIST [ (Tactics.change_concl @@ -2046,11 +2062,11 @@ let micromega_order_changer cert env ff = [ ("__ff", ff, Term.mkApp(Lazy.force coq_Formula, [|formula_typ |])); ("__varmap", vm, Term.mkApp - (Coqlib.gen_constant_in_modules "VarMap" - [["Coq" ; "micromega" ; "VarMap"] ; ["VarMap"]] "t", [|typ|])); + (EConstr.of_constr (Coqlib.gen_constant_in_modules "VarMap" + [["Coq" ; "micromega" ; "VarMap"] ; ["VarMap"]] "t"), [|typ|])); ("__wit", cert, cert_typ) ] - (Tacmach.pf_concl gl))); + (Tacmach.New.pf_concl gl))); (* Tacticals.New.tclTHENLIST (List.map (fun id -> (Tactics.introduction id)) ids)*) ] end } @@ -2069,38 +2085,39 @@ let micromega_genr prover tac = dump_proof = dump_psatz coq_Q dump_q } in Proofview.Goal.nf_enter { enter = begin fun gl -> - let gl = Tacmach.New.of_old (fun x -> x) gl in - let concl = Tacmach.pf_concl gl in - let hyps = Tacmach.pf_hyps_types gl in + let sigma = Tacmach.New.project gl in + let concl = Tacmach.New.pf_concl gl in + let hyps = Tacmach.New.pf_hyps_types gl in try - let (hyps,concl,env) = parse_goal gl parse_arith Env.empty hyps concl in + let gl0 = { env = Tacmach.New.pf_env gl; sigma } in + let (hyps,concl,env) = parse_goal gl0 parse_arith Env.empty hyps concl in let env = Env.elements env in let spec = Lazy.force spec in let hyps' = List.map (fun (n,f) -> (n, map_atoms (Micromega.map_Formula Micromega.q_of_Rcst) f)) hyps in let concl' = map_atoms (Micromega.map_Formula Micromega.q_of_Rcst) concl in - match micromega_tauto negate normalise unsat deduce spec prover env hyps' concl' gl with + match micromega_tauto negate normalise unsat deduce spec prover env hyps' concl' gl0 with | None -> Tacticals.New.tclFAIL 0 (Pp.str " Cannot find witness") | Some (ids,ff',res') -> let (ff,ids) = formula_hyps_concl (List.filter (fun (n,_) -> List.mem n ids) hyps) concl in let ff' = abstract_wrt_formula ff' ff in - let (arith_goal,props,vars,ff_arith) = make_goal_of_formula (Lazy.force dump_rexpr) ff' in + let (arith_goal,props,vars,ff_arith) = make_goal_of_formula sigma (Lazy.force dump_rexpr) ff' in let intro (id,_) = Tactics.introduction id in let intro_vars = Tacticals.New.tclTHENLIST (List.map intro vars) in let intro_props = Tacticals.New.tclTHENLIST (List.map intro props) in let ipat_of_name id = Some (Loc.ghost, Misctypes.IntroNaming (Misctypes.IntroIdentifier id)) in - let goal_name = Tactics.fresh_id [] (Names.Id.of_string "__arith") gl in + let goal_name = fresh_id [] (Names.Id.of_string "__arith") gl in let env' = List.map (fun (id,i) -> Term.mkVar id,i) vars in let tac_arith = Tacticals.New.tclTHENLIST [ intro_props ; intro_vars ; micromega_order_changer res' env' ff_arith ] in - let goal_props = List.rev (prop_env_of_formula ff') in + let goal_props = List.rev (prop_env_of_formula sigma ff') in let goal_vars = List.map (fun (_,i) -> List.nth env (i-1)) vars in diff --git a/plugins/micromega/g_micromega.ml4 b/plugins/micromega/g_micromega.ml4 index 79020ed03..ccb6daa11 100644 --- a/plugins/micromega/g_micromega.ml4 +++ b/plugins/micromega/g_micromega.ml4 @@ -16,6 +16,7 @@ (*i camlp4deps: "grammar/grammar.cma" i*) +open Ltac_plugin open Stdarg open Tacarg |