diff options
Diffstat (limited to 'contrib/omega/coq_omega.ml')
| -rw-r--r-- | contrib/omega/coq_omega.ml | 344 |
1 files changed, 172 insertions, 172 deletions
diff --git a/contrib/omega/coq_omega.ml b/contrib/omega/coq_omega.ml index 7a20aeb6..ee3301d7 100644 --- a/contrib/omega/coq_omega.ml +++ b/contrib/omega/coq_omega.ml @@ -13,13 +13,12 @@ (* *) (**************************************************************************) -(* $Id: coq_omega.ml,v 1.59.2.3 2004/07/16 19:30:12 herbelin Exp $ *) +(* $Id: coq_omega.ml 7837 2006-01-11 09:47:32Z herbelin $ *) open Util open Pp open Reduction open Proof_type -open Ast open Names open Nameops open Term @@ -36,9 +35,11 @@ open Clenv open Logic open Libnames open Nametab -open Omega open Contradiction +module OmegaSolver = Omega.MakeOmegaSolver (Bigint) +open OmegaSolver + (* Added by JCF, 09/03/98 *) let elim_id id gl = simplest_elim (pf_global gl id) gl @@ -56,16 +57,6 @@ let write f x = f:=x open Goptions -(* Obsolete, subsumed by Time Omega -let _ = - declare_bool_option - { optsync = false; - optname = "Omega time displaying flag"; - optkey = SecondaryTable ("Omega","Time"); - optread = read display_time_flag; - optwrite = write display_time_flag } -*) - let _ = declare_bool_option { optsync = false; @@ -110,6 +101,31 @@ let new_identifier_var = let cpt = ref 0 in (fun () -> let s = "Zvar" ^ string_of_int !cpt in incr cpt; id_of_string s) +let new_id = + let cpt = ref 0 in fun () -> incr cpt; !cpt + +let new_var_num = + let cpt = ref 1000 in (fun () -> incr cpt; !cpt) + +let new_var = + let cpt = ref 0 in fun () -> incr cpt; Nameops.make_ident "WW" (Some !cpt) + +let display_var i = Printf.sprintf "X%d" i + +let intern_id,unintern_id = + let cpt = ref 0 in + let table = Hashtbl.create 7 and co_table = Hashtbl.create 7 in + (fun (name : identifier) -> + try Hashtbl.find table name with Not_found -> + let idx = !cpt in + Hashtbl.add table name idx; + Hashtbl.add co_table idx name; + incr cpt; idx), + (fun idx -> + try Hashtbl.find co_table idx with Not_found -> + let v = new_var () in + Hashtbl.add table v idx; Hashtbl.add co_table idx v; v) + let mk_then = tclTHENLIST let exists_tac c = constructor_tac (Some 1) 1 (Rawterm.ImplicitBindings [c]) @@ -156,22 +172,22 @@ let constant = gen_constant_in_modules "Omega" coq_modules let coq_xH = lazy (constant "xH") let coq_xO = lazy (constant "xO") let coq_xI = lazy (constant "xI") -let coq_ZERO = lazy (constant (if !Options.v7 then "ZERO" else "Z0")) -let coq_POS = lazy (constant (if !Options.v7 then "POS" else "Zpos")) -let coq_NEG = lazy (constant (if !Options.v7 then "NEG" else "Zneg")) +let coq_Z0 = lazy (constant "Z0") +let coq_Zpos = lazy (constant "Zpos") +let coq_Zneg = lazy (constant "Zneg") let coq_Z = lazy (constant "Z") -let coq_relation = lazy (constant (if !Options.v7 then "relation" else "comparison")) -let coq_SUPERIEUR = lazy (constant "SUPERIEUR") -let coq_INFEEIEUR = lazy (constant "INFERIEUR") -let coq_EGAL = lazy (constant "EGAL") +let coq_comparison = lazy (constant "comparison") +let coq_Gt = lazy (constant "Gt") +let coq_INFEEIEUR = lazy (constant "Lt") +let coq_Eq = lazy (constant "Eq") let coq_Zplus = lazy (constant "Zplus") let coq_Zmult = lazy (constant "Zmult") let coq_Zopp = lazy (constant "Zopp") let coq_Zminus = lazy (constant "Zminus") -let coq_Zs = lazy (constant "Zs") +let coq_Zsucc = lazy (constant "Zsucc") let coq_Zgt = lazy (constant "Zgt") let coq_Zle = lazy (constant "Zle") -let coq_inject_nat = lazy (constant "inject_nat") +let coq_Z_of_nat = lazy (constant "Z_of_nat") let coq_inj_plus = lazy (constant "inj_plus") let coq_inj_mult = lazy (constant "inj_mult") let coq_inj_minus1 = lazy (constant "inj_minus1") @@ -183,12 +199,12 @@ let coq_inj_ge = lazy (constant "inj_ge") let coq_inj_gt = lazy (constant "inj_gt") let coq_inj_neq = lazy (constant "inj_neq") let coq_inj_eq = lazy (constant "inj_eq") -let coq_fast_Zplus_assoc_r = lazy (constant "fast_Zplus_assoc_r") -let coq_fast_Zplus_assoc_l = lazy (constant "fast_Zplus_assoc_l") -let coq_fast_Zmult_assoc_r = lazy (constant "fast_Zmult_assoc_r") +let coq_fast_Zplus_assoc_reverse = lazy (constant "fast_Zplus_assoc_reverse") +let coq_fast_Zplus_assoc = lazy (constant "fast_Zplus_assoc") +let coq_fast_Zmult_assoc_reverse = lazy (constant "fast_Zmult_assoc_reverse") let coq_fast_Zplus_permute = lazy (constant "fast_Zplus_permute") -let coq_fast_Zplus_sym = lazy (constant "fast_Zplus_sym") -let coq_fast_Zmult_sym = lazy (constant "fast_Zmult_sym") +let coq_fast_Zplus_comm = lazy (constant "fast_Zplus_comm") +let coq_fast_Zmult_comm = lazy (constant "fast_Zmult_comm") let coq_Zmult_le_approx = lazy (constant "Zmult_le_approx") let coq_OMEGA1 = lazy (constant "OMEGA1") let coq_OMEGA2 = lazy (constant "OMEGA2") @@ -217,12 +233,12 @@ let coq_fast_Zred_factor3 = lazy (constant "fast_Zred_factor3") let coq_fast_Zred_factor4 = lazy (constant "fast_Zred_factor4") let coq_fast_Zred_factor5 = lazy (constant "fast_Zred_factor5") let coq_fast_Zred_factor6 = lazy (constant "fast_Zred_factor6") -let coq_fast_Zmult_plus_distr = lazy (constant "fast_Zmult_plus_distr") -let coq_fast_Zmult_Zopp_left = lazy (constant "fast_Zmult_Zopp_left") -let coq_fast_Zopp_Zplus = lazy (constant "fast_Zopp_Zplus") -let coq_fast_Zopp_Zmult_r = lazy (constant "fast_Zopp_Zmult_r") -let coq_fast_Zopp_one = lazy (constant "fast_Zopp_one") -let coq_fast_Zopp_Zopp = lazy (constant "fast_Zopp_Zopp") +let coq_fast_Zmult_plus_distr_l = lazy (constant "fast_Zmult_plus_distr_l") +let coq_fast_Zmult_opp_comm = lazy (constant "fast_Zmult_opp_comm") +let coq_fast_Zopp_plus_distr = lazy (constant "fast_Zopp_plus_distr") +let coq_fast_Zopp_mult_distr_r = lazy (constant "fast_Zopp_mult_distr_r") +let coq_fast_Zopp_eq_mult_neg_1 = lazy (constant "fast_Zopp_eq_mult_neg_1") +let coq_fast_Zopp_involutive = lazy (constant "fast_Zopp_involutive") let coq_Zegal_left = lazy (constant "Zegal_left") let coq_Zne_left = lazy (constant "Zne_left") let coq_Zlt_left = lazy (constant "Zlt_left") @@ -240,10 +256,10 @@ let coq_dec_Zgt = lazy (constant "dec_Zgt") let coq_dec_Zge = lazy (constant "dec_Zge") let coq_not_Zeq = lazy (constant "not_Zeq") -let coq_not_Zle = lazy (constant "not_Zle") -let coq_not_Zlt = lazy (constant "not_Zlt") -let coq_not_Zge = lazy (constant "not_Zge") -let coq_not_Zgt = lazy (constant "not_Zgt") +let coq_Znot_le_gt = lazy (constant "Znot_le_gt") +let coq_Znot_lt_ge = lazy (constant "Znot_lt_ge") +let coq_Znot_ge_lt = lazy (constant "Znot_ge_lt") +let coq_Znot_gt_le = lazy (constant "Znot_gt_le") let coq_neq = lazy (constant "neq") let coq_Zne = lazy (constant "Zne") let coq_Zle = lazy (constant "Zle") @@ -304,7 +320,7 @@ let evaluable_ref_of_constr s c = match kind_of_term (Lazy.force c) with EvalConstRef kn | _ -> anomaly ("Coq_omega: "^s^" is not an evaluable constant") -let sp_Zs = lazy (evaluable_ref_of_constr "Zs" coq_Zs) +let sp_Zsucc = lazy (evaluable_ref_of_constr "Zsucc" coq_Zsucc) let sp_Zminus = lazy (evaluable_ref_of_constr "Zminus" coq_Zminus) let sp_Zle = lazy (evaluable_ref_of_constr "Zle" coq_Zle) let sp_Zgt = lazy (evaluable_ref_of_constr "Zgt" coq_Zgt) @@ -324,23 +340,23 @@ let mk_and t1 t2 = mkApp (build_coq_and (), [| t1; t2 |]) let mk_or t1 t2 = mkApp (build_coq_or (), [| t1; t2 |]) let mk_not t = mkApp (build_coq_not (), [| t |]) let mk_eq_rel t1 t2 = mkApp (build_coq_eq (), - [| Lazy.force coq_relation; t1; t2 |]) -let mk_inj t = mkApp (Lazy.force coq_inject_nat, [| t |]) + [| Lazy.force coq_comparison; t1; t2 |]) +let mk_inj t = mkApp (Lazy.force coq_Z_of_nat, [| t |]) let mk_integer n = let rec loop n = - if n=1 then Lazy.force coq_xH else - mkApp ((if n mod 2 = 0 then Lazy.force coq_xO else Lazy.force coq_xI), - [| loop (n/2) |]) + if n =? one then Lazy.force coq_xH else + mkApp((if n mod two =? zero then Lazy.force coq_xO else Lazy.force coq_xI), + [| loop (n/two) |]) in - if n = 0 then Lazy.force coq_ZERO - else mkApp ((if n > 0 then Lazy.force coq_POS else Lazy.force coq_NEG), + if n =? zero then Lazy.force coq_Z0 + else mkApp ((if n >? zero then Lazy.force coq_Zpos else Lazy.force coq_Zneg), [| loop (abs n) |]) type omega_constant = - | Zplus | Zmult | Zminus | Zs | Zopp + | Zplus | Zmult | Zminus | Zsucc | Zopp | Plus | Mult | Minus | Pred | S | O - | POS | NEG | ZERO | Inject_nat + | Zpos | Zneg | Z0 | Z_of_nat | Eq | Neq | Zne | Zle | Zlt | Zge | Zgt | Z | Nat @@ -401,7 +417,7 @@ let destructurate_term t = | _, [_;_] when c = Lazy.force coq_Zplus -> Kapp (Zplus,args) | _, [_;_] when c = Lazy.force coq_Zmult -> Kapp (Zmult,args) | _, [_;_] when c = Lazy.force coq_Zminus -> Kapp (Zminus,args) - | _, [_] when c = Lazy.force coq_Zs -> Kapp (Zs,args) + | _, [_] when c = Lazy.force coq_Zsucc -> Kapp (Zsucc,args) | _, [_] when c = Lazy.force coq_Zopp -> Kapp (Zopp,args) | _, [_;_] when c = Lazy.force coq_plus -> Kapp (Plus,args) | _, [_;_] when c = Lazy.force coq_mult -> Kapp (Mult,args) @@ -409,25 +425,25 @@ let destructurate_term t = | _, [_] when c = Lazy.force coq_pred -> Kapp (Pred,args) | _, [_] when c = Lazy.force coq_S -> Kapp (S,args) | _, [] when c = Lazy.force coq_O -> Kapp (O,args) - | _, [_] when c = Lazy.force coq_POS -> Kapp (NEG,args) - | _, [_] when c = Lazy.force coq_NEG -> Kapp (POS,args) - | _, [] when c = Lazy.force coq_ZERO -> Kapp (ZERO,args) - | _, [_] when c = Lazy.force coq_inject_nat -> Kapp (Inject_nat,args) + | _, [_] when c = Lazy.force coq_Zpos -> Kapp (Zneg,args) + | _, [_] when c = Lazy.force coq_Zneg -> Kapp (Zpos,args) + | _, [] when c = Lazy.force coq_Z0 -> Kapp (Z0,args) + | _, [_] when c = Lazy.force coq_Z_of_nat -> Kapp (Z_of_nat,args) | Var id,[] -> Kvar id | _ -> Kufo let recognize_number t = let rec loop t = match decompose_app t with - | f, [t] when f = Lazy.force coq_xI -> 1 + 2 * loop t - | f, [t] when f = Lazy.force coq_xO -> 2 * loop t - | f, [] when f = Lazy.force coq_xH -> 1 + | f, [t] when f = Lazy.force coq_xI -> one + two * loop t + | f, [t] when f = Lazy.force coq_xO -> two * loop t + | f, [] when f = Lazy.force coq_xH -> one | _ -> failwith "not a number" in match decompose_app t with - | f, [t] when f = Lazy.force coq_POS -> loop t - | f, [t] when f = Lazy.force coq_NEG -> - (loop t) - | f, [] when f = Lazy.force coq_ZERO -> 0 + | f, [t] when f = Lazy.force coq_Zpos -> loop t + | f, [t] when f = Lazy.force coq_Zneg -> neg (loop t) + | f, [] when f = Lazy.force coq_Z0 -> zero | _ -> failwith "not a number" type constr_path = @@ -443,13 +459,11 @@ type constr_path = let context operation path (t : constr) = let rec loop i p0 t = match (p0,kind_of_term t) with - | (p, Cast (c,t)) -> mkCast (loop i p c,t) + | (p, Cast (c,k,t)) -> mkCast (loop i p c,k,t) | ([], _) -> operation i t | ((P_APP n :: p), App (f,v)) -> -(* let f,l = get_applist t in NECESSAIRE ?? - let v' = Array.of_list (f::l) in *) let v' = Array.copy v in - v'.(n-1) <- loop i p v'.(n-1); mkApp (f, v') + v'.(pred n) <- loop i p v'.(pred n); mkApp (f, v') | ((P_BRANCH n :: p), Case (ci,q,c,v)) -> (* avant, y avait mkApp... anyway, BRANCH seems nowhere used *) let v' = Array.copy v in @@ -462,13 +476,13 @@ let context operation path (t : constr) = | (p, Fix ((_,n as ln),(tys,lna,v))) -> let l = Array.length v in let v' = Array.copy v in - v'.(n) <- loop (i+l) p v.(n); (mkFix (ln,(tys,lna,v'))) + v'.(n)<- loop (Pervasives.(+) i l) p v.(n); (mkFix (ln,(tys,lna,v'))) | ((P_BODY :: p), Prod (n,t,c)) -> - (mkProd (n,t,loop (i+1) p c)) + (mkProd (n,t,loop (succ i) p c)) | ((P_BODY :: p), Lambda (n,t,c)) -> - (mkLambda (n,t,loop (i+1) p c)) + (mkLambda (n,t,loop (succ i) p c)) | ((P_BODY :: p), LetIn (n,b,t,c)) -> - (mkLetIn (n,b,t,loop (i+1) p c)) + (mkLetIn (n,b,t,loop (succ i) p c)) | ((P_TYPE :: p), Prod (n,t,c)) -> (mkProd (n,loop i p t,c)) | ((P_TYPE :: p), Lambda (n,t,c)) -> @@ -476,16 +490,16 @@ let context operation path (t : constr) = | ((P_TYPE :: p), LetIn (n,b,t,c)) -> (mkLetIn (n,b,loop i p t,c)) | (p, _) -> - ppnl (Printer.prterm t); + ppnl (Printer.pr_lconstr t); failwith ("abstract_path " ^ string_of_int(List.length p)) in loop 1 path t let occurence path (t : constr) = let rec loop p0 t = match (p0,kind_of_term t) with - | (p, Cast (c,t)) -> loop p c + | (p, Cast (c,_,_)) -> loop p c | ([], _) -> t - | ((P_APP n :: p), App (f,v)) -> loop p v.(n-1) + | ((P_APP n :: p), App (f,v)) -> loop p v.(pred n) | ((P_BRANCH n :: p), Case (_,_,_,v)) -> loop p v.(n) | ((P_ARITY :: p), App (f,_)) -> loop p f | ((P_ARG :: p), App (f,v)) -> loop p v.(0) @@ -497,7 +511,7 @@ let occurence path (t : constr) = | ((P_TYPE :: p), Lambda (n,term,c)) -> loop p term | ((P_TYPE :: p), LetIn (n,b,term,c)) -> loop p term | (p, _) -> - ppnl (Printer.prterm t); + ppnl (Printer.pr_lconstr t); failwith ("occurence " ^ string_of_int(List.length p)) in loop path t @@ -509,7 +523,7 @@ let abstract_path typ path t = let focused_simpl path gl = let newc = context (fun i t -> pf_nf gl t) (List.rev path) (pf_concl gl) in - convert_concl_no_check newc gl + convert_concl_no_check newc DEFAULTcast gl let focused_simpl path = simpl_time (focused_simpl path) @@ -518,7 +532,7 @@ type oformula = | Oinv of oformula | Otimes of oformula * oformula | Oatom of identifier - | Oz of int + | Oz of bigint | Oufo of constr let rec oprint = function @@ -530,7 +544,7 @@ let rec oprint = function print_string "("; oprint t1; print_string "*"; oprint t2; print_string ")" | Oatom s -> print_string (string_of_id s) - | Oz i -> print_int i + | Oz i -> print_string (string_of_bigint i) | Oufo f -> print_string "?" let rec weight = function @@ -567,7 +581,7 @@ let rec decompile af = in loop af.body -let mkNewMeta () = mkMeta (Clenv.new_meta()) +let mkNewMeta () = mkMeta (Evarutil.new_meta()) let clever_rewrite_base_poly typ p result theorem gl = let full = pf_concl gl in @@ -606,7 +620,7 @@ let clever_rewrite p vpath t gl = let vargs = List.map (fun p -> occurence p occ) vpath in let t' = applist(t, (vargs @ [abstracted])) in exact (applist(t',[mkNewMeta()])) gl - + let rec shuffle p (t1,t2) = match t1,t2 with | Oplus(l1,r1), Oplus(l2,r2) -> @@ -614,7 +628,7 @@ let rec shuffle p (t1,t2) = let (tac,t') = shuffle (P_APP 2 :: p) (r1,t2) in (clever_rewrite p [[P_APP 1;P_APP 1]; [P_APP 1; P_APP 2];[P_APP 2]] - (Lazy.force coq_fast_Zplus_assoc_r) + (Lazy.force coq_fast_Zplus_assoc_reverse) :: tac, Oplus(l1,t')) else @@ -627,12 +641,12 @@ let rec shuffle p (t1,t2) = if weight l1 > weight t2 then let (tac,t') = shuffle (P_APP 2 :: p) (r1,t2) in clever_rewrite p [[P_APP 1;P_APP 1]; [P_APP 1; P_APP 2];[P_APP 2]] - (Lazy.force coq_fast_Zplus_assoc_r) + (Lazy.force coq_fast_Zplus_assoc_reverse) :: tac, Oplus(l1, t') else [clever_rewrite p [[P_APP 1];[P_APP 2]] - (Lazy.force coq_fast_Zplus_sym)], + (Lazy.force coq_fast_Zplus_comm)], Oplus(t2,t1) | t1,Oplus(l2,r2) -> if weight l2 > weight t1 then @@ -643,11 +657,11 @@ let rec shuffle p (t1,t2) = Oplus(l2,t') else [],Oplus(t1,t2) | Oz t1,Oz t2 -> - [focused_simpl p], Oz(t1+t2) + [focused_simpl p], Oz(Bigint.add t1 t2) | t1,t2 -> if weight t1 < weight t2 then [clever_rewrite p [[P_APP 1];[P_APP 2]] - (Lazy.force coq_fast_Zplus_sym)], + (Lazy.force coq_fast_Zplus_comm)], Oplus(t2,t1) else [],Oplus(t1,t2) @@ -665,7 +679,7 @@ let rec shuffle_mult p_init k1 e1 k2 e2 = [P_APP 2; P_APP 2]] (Lazy.force coq_fast_OMEGA10) in - if k1*c1 + k2 * c2 = 0 then + if Bigint.add (Bigint.mult k1 c1) (Bigint.mult k2 c2) =? zero then let tac' = clever_rewrite p [[P_APP 1;P_APP 1];[P_APP 2]] (Lazy.force coq_fast_Zred_factor5) in @@ -722,7 +736,7 @@ let rec shuffle_mult_right p_init e1 k2 e2 = [P_APP 2; P_APP 2]] (Lazy.force coq_fast_OMEGA15) in - if c1 + k2 * c2 = 0 then + if Bigint.add c1 (Bigint.mult k2 c2) =? zero then let tac' = clever_rewrite p [[P_APP 1;P_APP 1];[P_APP 2]] (Lazy.force coq_fast_Zred_factor5) @@ -732,7 +746,7 @@ let rec shuffle_mult_right p_init e1 k2 e2 = else tac :: loop (P_APP 2 :: p) (l1,l2) else if v1 > v2 then clever_rewrite p [[P_APP 1;P_APP 1]; [P_APP 1; P_APP 2];[P_APP 2]] - (Lazy.force coq_fast_Zplus_assoc_r) :: + (Lazy.force coq_fast_Zplus_assoc_reverse) :: loop (P_APP 2 :: p) (l1,l2') else clever_rewrite p [[P_APP 2; P_APP 1; P_APP 1; P_APP 1]; @@ -744,7 +758,7 @@ let rec shuffle_mult_right p_init e1 k2 e2 = loop (P_APP 2 :: p) (l1',l2) | ({c=c1;v=v1}::l1), [] -> clever_rewrite p [[P_APP 1;P_APP 1]; [P_APP 1; P_APP 2];[P_APP 2]] - (Lazy.force coq_fast_Zplus_assoc_r) :: + (Lazy.force coq_fast_Zplus_assoc_reverse) :: loop (P_APP 2 :: p) (l1,[]) | [],({c=c2;v=v2}::l2) -> clever_rewrite p [[P_APP 2; P_APP 1; P_APP 1; P_APP 1]; @@ -765,7 +779,7 @@ let rec shuffle_cancel p = function clever_rewrite p [[P_APP 1; P_APP 1; P_APP 1];[P_APP 1; P_APP 2]; [P_APP 2; P_APP 2]; [P_APP 1; P_APP 1; P_APP 2; P_APP 1]] - (if c1 > 0 then + (if c1 >? zero then (Lazy.force coq_fast_OMEGA13) else (Lazy.force coq_fast_OMEGA14)) @@ -777,15 +791,15 @@ let rec scalar p n = function let tac1,t1' = scalar (P_APP 1 :: p) n t1 and tac2,t2' = scalar (P_APP 2 :: p) n t2 in clever_rewrite p [[P_APP 1;P_APP 1];[P_APP 1;P_APP 2];[P_APP 2]] - (Lazy.force coq_fast_Zmult_plus_distr) :: + (Lazy.force coq_fast_Zmult_plus_distr_l) :: (tac1 @ tac2), Oplus(t1',t2') | Oinv t -> [clever_rewrite p [[P_APP 1;P_APP 1];[P_APP 2]] - (Lazy.force coq_fast_Zmult_Zopp_left); - focused_simpl (P_APP 2 :: p)], Otimes(t,Oz(-n)) + (Lazy.force coq_fast_Zmult_opp_comm); + focused_simpl (P_APP 2 :: p)], Otimes(t,Oz(neg n)) | Otimes(t1,Oz x) -> [clever_rewrite p [[P_APP 1;P_APP 1];[P_APP 1;P_APP 2];[P_APP 2]] - (Lazy.force coq_fast_Zmult_assoc_r); + (Lazy.force coq_fast_Zmult_assoc_reverse); focused_simpl (P_APP 2 :: p)], Otimes(t1,Oz (n*x)) | Otimes(t1,t2) -> error "Omega: Can't solve a goal with non-linear products" @@ -809,7 +823,7 @@ let rec norm_add p_init = | [] -> [focused_simpl p_init] | _:: l -> clever_rewrite p [[P_APP 1;P_APP 1]; [P_APP 1; P_APP 2];[P_APP 2]] - (Lazy.force coq_fast_Zplus_assoc_r) :: + (Lazy.force coq_fast_Zplus_assoc_reverse) :: loop (P_APP 2 :: p) l in loop p_init @@ -831,31 +845,31 @@ let rec negate p = function let tac1,t1' = negate (P_APP 1 :: p) t1 and tac2,t2' = negate (P_APP 2 :: p) t2 in clever_rewrite p [[P_APP 1;P_APP 1];[P_APP 1;P_APP 2]] - (Lazy.force coq_fast_Zopp_Zplus) :: + (Lazy.force coq_fast_Zopp_plus_distr) :: (tac1 @ tac2), Oplus(t1',t2') | Oinv t -> - [clever_rewrite p [[P_APP 1;P_APP 1]] (Lazy.force coq_fast_Zopp_Zopp)], t + [clever_rewrite p [[P_APP 1;P_APP 1]] (Lazy.force coq_fast_Zopp_involutive)], t | Otimes(t1,Oz x) -> [clever_rewrite p [[P_APP 1;P_APP 1];[P_APP 1;P_APP 2]] - (Lazy.force coq_fast_Zopp_Zmult_r); - focused_simpl (P_APP 2 :: p)], Otimes(t1,Oz (-x)) + (Lazy.force coq_fast_Zopp_mult_distr_r); + focused_simpl (P_APP 2 :: p)], Otimes(t1,Oz (neg x)) | Otimes(t1,t2) -> error "Omega: Can't solve a goal with non-linear products" | (Oatom _ as t) -> - let r = Otimes(t,Oz(-1)) in - [clever_rewrite p [[P_APP 1]] (Lazy.force coq_fast_Zopp_one)], r - | Oz i -> [focused_simpl p],Oz(-i) + let r = Otimes(t,Oz(negone)) in + [clever_rewrite p [[P_APP 1]] (Lazy.force coq_fast_Zopp_eq_mult_neg_1)], r + | Oz i -> [focused_simpl p],Oz(neg i) | Oufo c -> [], Oufo (mkApp (Lazy.force coq_Zopp, [| c |])) let rec transform p t = - let default () = + let default isnat t' = try - let v,th,_ = find_constr t in + let v,th,_ = find_constr t' in [clever_rewrite_base p (mkVar v) (mkVar th)], Oatom v with _ -> let v = new_identifier_var () and th = new_identifier () in - hide_constr t v th false; + hide_constr t' v th isnat; [clever_rewrite_base p (mkVar v) (mkVar th)], Oatom v in try match destructurate_term t with @@ -870,10 +884,10 @@ let rec transform p t = (mkApp (Lazy.force coq_Zplus, [| t1; (mkApp (Lazy.force coq_Zopp, [| t2 |])) |])) in unfold sp_Zminus :: tac,t - | Kapp(Zs,[t1]) -> + | Kapp(Zsucc,[t1]) -> let tac,t = transform p (mkApp (Lazy.force coq_Zplus, - [| t1; mk_integer 1 |])) in - unfold sp_Zs :: tac,t + [| t1; mk_integer one |])) in + unfold sp_Zsucc :: tac,t | Kapp(Zmult,[t1;t2]) -> let tac1,t1' = transform (P_APP 1 :: p) t1 and tac2,t2' = transform (P_APP 2 :: p) t2 in @@ -882,40 +896,32 @@ let rec transform p t = | (Oz n,_) -> let sym = clever_rewrite p [[P_APP 1];[P_APP 2]] - (Lazy.force coq_fast_Zmult_sym) in + (Lazy.force coq_fast_Zmult_comm) in let tac,t' = scalar p n t2' in tac1 @ tac2 @ (sym :: tac),t' - | _ -> default () + | _ -> default false t end - | Kapp((POS|NEG|ZERO),_) -> - (try ([],Oz(recognize_number t)) with _ -> default ()) + | Kapp((Zpos|Zneg|Z0),_) -> + (try ([],Oz(recognize_number t)) with _ -> default false t) | Kvar s -> [],Oatom s | Kapp(Zopp,[t]) -> let tac,t' = transform (P_APP 1 :: p) t in let tac',t'' = negate p t' in tac @ tac', t'' - | Kapp(Inject_nat,[t']) -> - begin try - let v,th,_ = find_constr t' in - [clever_rewrite_base p (mkVar v) (mkVar th)],Oatom v - with _ -> - let v = new_identifier_var () and th = new_identifier () in - hide_constr t' v th true; - [clever_rewrite_base p (mkVar v) (mkVar th)], Oatom v - end - | _ -> default () - with e when catchable_exception e -> default () + | Kapp(Z_of_nat,[t']) -> default true t' + | _ -> default false t + with e when catchable_exception e -> default false t let shrink_pair p f1 f2 = match f1,f2 with | Oatom v,Oatom _ -> - let r = Otimes(Oatom v,Oz 2) in + let r = Otimes(Oatom v,Oz two) in clever_rewrite p [[P_APP 1]] (Lazy.force coq_fast_Zred_factor1), r | Oatom v, Otimes(_,c2) -> - let r = Otimes(Oatom v,Oplus(c2,Oz 1)) in + let r = Otimes(Oatom v,Oplus(c2,Oz one)) in clever_rewrite p [[P_APP 1];[P_APP 2;P_APP 2]] (Lazy.force coq_fast_Zred_factor2), r | Otimes (v1,c1),Oatom v -> - let r = Otimes(Oatom v,Oplus(c1,Oz 1)) in + let r = Otimes(Oatom v,Oplus(c1,Oz one)) in clever_rewrite p [[P_APP 2];[P_APP 1;P_APP 2]] (Lazy.force coq_fast_Zred_factor3), r | Otimes (Oatom v,c1),Otimes (v2,c2) -> @@ -931,13 +937,13 @@ let shrink_pair p f1 f2 = let reduce_factor p = function | Oatom v -> - let r = Otimes(Oatom v,Oz 1) in + let r = Otimes(Oatom v,Oz one) in [clever_rewrite p [[]] (Lazy.force coq_fast_Zred_factor0)],r | Otimes(Oatom v,Oz n) as f -> [],f | Otimes(Oatom v,c) -> let rec compute = function | Oz n -> n - | Oplus(t1,t2) -> compute t1 + compute t2 + | Oplus(t1,t2) -> Bigint.add (compute t1) (compute t2) | _ -> error "condense.1" in [focused_simpl (P_APP 2 :: p)], Otimes(Oatom v,Oz(compute c)) @@ -950,7 +956,7 @@ let rec condense p = function let assoc_tac = clever_rewrite p [[P_APP 1];[P_APP 2;P_APP 1];[P_APP 2;P_APP 2]] - (Lazy.force coq_fast_Zplus_assoc_l) in + (Lazy.force coq_fast_Zplus_assoc) in let tac_list,t' = condense p (Oplus(t,r)) in (assoc_tac :: shrink_tac :: tac_list), t' end else begin @@ -958,7 +964,7 @@ let rec condense p = function let tac',t' = condense (P_APP 2 :: p) t in (tac @ tac'), Oplus(f,t') end - | Oplus(f1,Oz n) as t -> + | Oplus(f1,Oz n) -> let tac,f1' = reduce_factor (P_APP 1 :: p) f1 in tac,Oplus(f1',Oz n) | Oplus(f1,f2) -> if weight f1 = weight f2 then begin @@ -973,12 +979,12 @@ let rec condense p = function | Oz _ as t -> [],t | t -> let tac,t' = reduce_factor p t in - let final = Oplus(t',Oz 0) in + let final = Oplus(t',Oz zero) in let tac' = clever_rewrite p [[]] (Lazy.force coq_fast_Zred_factor6) in tac @ [tac'], final let rec clear_zero p = function - | Oplus(Otimes(Oatom v,Oz 0),r) -> + | Oplus(Otimes(Oatom v,Oz n),r) when n =? zero -> let tac = clever_rewrite p [[P_APP 1;P_APP 1];[P_APP 2]] (Lazy.force coq_fast_Zred_factor5) in @@ -992,7 +998,7 @@ let replay_history tactic_normalisation = let aux = id_of_string "auxiliary" in let aux1 = id_of_string "auxiliary_1" in let aux2 = id_of_string "auxiliary_2" in - let zero = mk_integer 0 in + let izero = mk_integer zero in let rec loop t = match t with | HYP e :: l -> @@ -1007,7 +1013,7 @@ let replay_history tactic_normalisation = and eq2 = decompile e2 in let id1 = hyp_of_tag e1.id and id2 = hyp_of_tag e2.id in - let k = if b then (-1) else 1 in + let k = if b then negone else one in let p_initial = [P_APP 1;P_TYPE] in let tac= shuffle_mult_right p_initial e1.body k e2.body in tclTHENLIST [ @@ -1028,11 +1034,10 @@ let replay_history tactic_normalisation = let p_initial = [P_APP 2;P_TYPE] in let tac = shuffle_cancel p_initial e1.body in let solve_le = - let superieur = Lazy.force coq_SUPERIEUR in let not_sup_sup = mkApp (build_coq_eq (), [| - Lazy.force coq_relation; - Lazy.force coq_SUPERIEUR; - Lazy.force coq_SUPERIEUR |]) + Lazy.force coq_comparison; + Lazy.force coq_Gt; + Lazy.force coq_Gt |]) in tclTHENS (tclTHENLIST [ @@ -1070,7 +1075,7 @@ let replay_history tactic_normalisation = (intros_using [id]); (cut (mk_gt kk dd)) ]) [ tclTHENS - (cut (mk_gt kk zero)) + (cut (mk_gt kk izero)) [ tclTHENLIST [ (intros_using [aux1; aux2]); (generalize_tac @@ -1088,20 +1093,16 @@ let replay_history tactic_normalisation = tclTHEN (mk_then tac) reflexivity ] | NOT_EXACT_DIVIDE (e1,k) :: l -> - let id = hyp_of_tag e1.id in let c = floor_div e1.constant k in - let d = e1.constant - c * k in + let d = Bigint.sub e1.constant (Bigint.mult c k) in let e2 = {id=e1.id; kind=EQUA;constant = c; body = map_eq_linear (fun c -> c / k) e1.body } in - let eq1 = val_of(decompile e1) - and eq2 = val_of(decompile e2) in + let eq2 = val_of(decompile e2) in let kk = mk_integer k and dd = mk_integer d in - let rhs = mk_plus (mk_times eq2 kk) dd in - let state_eq = mk_eq eq1 rhs in let tac = scalar_norm_add [P_APP 2] e2.body in tclTHENS - (cut (mk_gt dd zero)) + (cut (mk_gt dd izero)) [ tclTHENS (cut (mk_gt kk dd)) [tclTHENLIST [ (intros_using [aux2;aux1]); @@ -1147,7 +1148,7 @@ let replay_history tactic_normalisation = tclTHENS (cut state_eq) [ tclTHENS - (cut (mk_gt kk zero)) + (cut (mk_gt kk izero)) [tclTHENLIST [ (intros_using [aux2;aux1]); (generalize_tac @@ -1170,7 +1171,7 @@ let replay_history tactic_normalisation = and eq2 = val_of (decompile (negate_eq e1)) in let tac = clever_rewrite [P_APP 3] [[P_APP 1]] - (Lazy.force coq_fast_Zopp_one) :: + (Lazy.force coq_fast_Zopp_eq_mult_neg_1) :: scalar_norm [P_APP 3] e1.body in tclTHENS @@ -1184,13 +1185,13 @@ let replay_history tactic_normalisation = (loop l) ]; tclTHEN (mk_then tac) reflexivity] - | STATE(new_eq,def,orig,m,sigma) :: l -> + | STATE {st_new_eq=e;st_def=def;st_orig=orig;st_coef=m;st_var=v} :: l -> let id = new_identifier () and id2 = hyp_of_tag orig.id in - tag_hypothesis id new_eq.id; + tag_hypothesis id e.id; let eq1 = val_of(decompile def) and eq2 = val_of(decompile orig) in - let vid = unintern_id sigma in + let vid = unintern_id v in let theorem = mkApp (build_coq_ex (), [| Lazy.force coq_Z; @@ -1201,12 +1202,11 @@ let replay_history tactic_normalisation = in let mm = mk_integer m in let p_initial = [P_APP 2;P_TYPE] in - let r = mk_plus eq2 (mk_times (mk_plus (mk_inv (mkVar vid)) eq1) mm) in let tac = clever_rewrite (P_APP 1 :: P_APP 1 :: P_APP 2 :: p_initial) - [[P_APP 1]] (Lazy.force coq_fast_Zopp_one) :: + [[P_APP 1]] (Lazy.force coq_fast_Zopp_eq_mult_neg_1) :: shuffle_mult_right p_initial - orig.body m ({c= -1;v=sigma}::def.body) in + orig.body m ({c= negone;v= v}::def.body) in tclTHENS (cut theorem) [tclTHENLIST [ @@ -1241,7 +1241,7 @@ let replay_history tactic_normalisation = and id2 = hyp_of_tag e2.id in let eq1 = val_of(decompile e1) and eq2 = val_of(decompile e2) in - if k1 = 1 & e2.kind = EQUA then + if k1 =? one & e2.kind = EQUA then let tac_thm = match e1.kind with | EQUA -> Lazy.force coq_OMEGA5 @@ -1264,9 +1264,9 @@ let replay_history tactic_normalisation = and kk2 = mk_integer k2 in let p_initial = [P_APP 2;P_TYPE] in let tac= shuffle_mult p_initial k1 e1.body k2 e2.body in - tclTHENS (cut (mk_gt kk1 zero)) + tclTHENS (cut (mk_gt kk1 izero)) [tclTHENS - (cut (mk_gt kk2 zero)) + (cut (mk_gt kk2 izero)) [tclTHENLIST [ (intros_using [aux2;aux1]); (generalize_tac @@ -1345,7 +1345,7 @@ let destructure_omega gl tac_def (id,c) = normalize_equation id INEQ (Lazy.force coq_Zle_left) 2 t t1 t2 tac_def | Kapp(Zlt,[t1;t2]) -> - let t = mk_plus (mk_plus t2 (mk_integer (-1))) (mk_inv t1) in + let t = mk_plus (mk_plus t2 (mk_integer negone)) (mk_inv t1) in normalize_equation id INEQ (Lazy.force coq_Zlt_left) 2 t t1 t2 tac_def | Kapp(Zge,[t1;t2]) -> @@ -1353,7 +1353,7 @@ let destructure_omega gl tac_def (id,c) = normalize_equation id INEQ (Lazy.force coq_Zge_left) 2 t t1 t2 tac_def | Kapp(Zgt,[t1;t2]) -> - let t = mk_plus (mk_plus t1 (mk_integer (-1))) (mk_inv t2) in + let t = mk_plus (mk_plus t1 (mk_integer negone)) (mk_inv t2) in normalize_equation id INEQ (Lazy.force coq_Zgt_left) 2 t t1 t2 tac_def | _ -> tac_def @@ -1362,7 +1362,7 @@ let destructure_omega gl tac_def (id,c) = let reintroduce id = (* [id] cannot be cleared if dependent: protect it by a try *) tclTHEN (tclTRY (clear [id])) (intro_using id) - + let coq_omega gl = clear_tables (); let tactic_normalisation, system = @@ -1382,8 +1382,8 @@ let coq_omega gl = (intros_using [th;id]); tac ]), {kind = INEQ; - body = [{v=intern_id v; c=1}]; - constant = 0; id = i} :: sys + body = [{v=intern_id v; c=one}]; + constant = zero; id = i} :: sys else (tclTHENLIST [ (simplest_elim (applist (Lazy.force coq_new_var, [t]))); @@ -1393,17 +1393,19 @@ let coq_omega gl = (tclIDTAC,[]) (dump_tables ()) in let system = system @ sys in - if !display_system_flag then display_system system; + if !display_system_flag then display_system display_var system; if !old_style_flag then begin - try let _ = simplify false system in tclIDTAC gl + try + let _ = simplify (new_id,new_var_num,display_var) false system in + tclIDTAC gl with UNSOLVABLE -> let _,path = depend [] [] (history ()) in - if !display_action_flag then display_action path; + if !display_action_flag then display_action display_var path; (tclTHEN prelude (replay_history tactic_normalisation path)) gl end else begin try - let path = simplify_strong system in - if !display_action_flag then display_action path; + let path = simplify_strong (new_id,new_var_num,display_var) system in + if !display_action_flag then display_action display_var path; (tclTHEN prelude (replay_history tactic_normalisation path)) gl with NO_CONTRADICTION -> error "Omega can't solve this system" end @@ -1411,8 +1413,6 @@ let coq_omega gl = let coq_omega = solver_time coq_omega let nat_inject gl = - let aux = id_of_string "auxiliary" in - let table = Hashtbl.create 7 in let rec explore p t = try match destructurate_term t with | Kapp(Plus,[t1;t2]) -> @@ -1444,7 +1444,7 @@ let nat_inject gl = (explore (P_APP 1 :: p) t1); (explore (P_APP 2 :: p) t2) ]; (tclTHEN - (clever_rewrite_gen p (mk_integer 0) + (clever_rewrite_gen p (mk_integer zero) ((Lazy.force coq_inj_minus2),[t1;t2;mkVar id])) (loop [id,mkApp (Lazy.force coq_gt, [| t2;t1 |])])) ] @@ -1461,7 +1461,7 @@ let nat_inject gl = Kapp(S,[t]) -> (tclTHEN (clever_rewrite_gen p - (mkApp (Lazy.force coq_Zs, [| mk_inj t |])) + (mkApp (Lazy.force coq_Zsucc, [| mk_inj t |])) ((Lazy.force coq_inj_S),[t])) (loop (P_APP 1 :: p) t)) | _ -> explore p t @@ -1564,7 +1564,7 @@ let rec decidability gl t = | Kapp(Nat,[]) -> mkApp (Lazy.force coq_dec_eq_nat, [| t1;t2 |]) | _ -> errorlabstrm "decidability" (str "Omega: Can't solve a goal with equality on " ++ - Printer.prterm typ) + Printer.pr_lconstr typ) end | Kapp(Zne,[t1;t2]) -> mkApp (Lazy.force coq_dec_Zne, [| t1;t2 |]) | Kapp(Zle,[t1;t2]) -> mkApp (Lazy.force coq_dec_Zle, [| t1;t2 |]) @@ -1665,25 +1665,25 @@ let destructure_hyps gl = | Kapp(Zle, [t1;t2]) -> tclTHENLIST [ (generalize_tac - [mkApp (Lazy.force coq_not_Zle, [| t1;t2;mkVar i|])]); + [mkApp (Lazy.force coq_Znot_le_gt, [| t1;t2;mkVar i|])]); (onClearedName i (fun _ -> loop lit)) ] | Kapp(Zge, [t1;t2]) -> tclTHENLIST [ (generalize_tac - [mkApp (Lazy.force coq_not_Zge, [| t1;t2;mkVar i|])]); + [mkApp (Lazy.force coq_Znot_ge_lt, [| t1;t2;mkVar i|])]); (onClearedName i (fun _ -> loop lit)) ] | Kapp(Zlt, [t1;t2]) -> tclTHENLIST [ (generalize_tac - [mkApp (Lazy.force coq_not_Zlt, [| t1;t2;mkVar i|])]); + [mkApp (Lazy.force coq_Znot_lt_ge, [| t1;t2;mkVar i|])]); (onClearedName i (fun _ -> loop lit)) ] | Kapp(Zgt, [t1;t2]) -> tclTHENLIST [ (generalize_tac - [mkApp (Lazy.force coq_not_Zgt, [| t1;t2;mkVar i|])]); + [mkApp (Lazy.force coq_Znot_gt_le, [| t1;t2;mkVar i|])]); (onClearedName i (fun _ -> loop lit)) ] | Kapp(Le, [t1;t2]) -> @@ -1776,7 +1776,7 @@ let destructure_goal gl = let destructure_goal = all_time (destructure_goal) let omega_solver gl = - Library.check_required_library ["Coq";"omega";"Omega"]; + Coqlib.check_required_library ["Coq";"omega";"Omega"]; let result = destructure_goal gl in (* if !display_time_flag then begin text_time (); flush Pervasives.stdout end; *) |