diff options
Diffstat (limited to 'plugins/omega/coq_omega.ml')
| -rw-r--r-- | plugins/omega/coq_omega.ml | 622 |
1 files changed, 311 insertions, 311 deletions
diff --git a/plugins/omega/coq_omega.ml b/plugins/omega/coq_omega.ml index 075188f54..e037ee8bf 100644 --- a/plugins/omega/coq_omega.ml +++ b/plugins/omega/coq_omega.ml @@ -58,7 +58,7 @@ let write f x = f:=x open Goptions let _ = - declare_bool_option + declare_bool_option { optsync = false; optname = "Omega system time displaying flag"; optkey = ["Omega";"System"]; @@ -66,7 +66,7 @@ let _ = optwrite = write display_system_flag } let _ = - declare_bool_option + declare_bool_option { optsync = false; optname = "Omega action display flag"; optkey = ["Omega";"Action"]; @@ -74,7 +74,7 @@ let _ = optwrite = write display_action_flag } let _ = - declare_bool_option + declare_bool_option { optsync = false; optname = "Omega old style flag"; optkey = ["Omega";"OldStyle"]; @@ -89,16 +89,16 @@ let elim_time = timing "Elim " let simpl_time = timing "Simpl " let generalize_time = timing "Generalize" -let new_identifier = - let cpt = ref 0 in +let new_identifier = + let cpt = ref 0 in (fun () -> let s = "Omega" ^ string_of_int !cpt in incr cpt; id_of_string s) -let new_identifier_state = - let cpt = ref 0 in +let new_identifier_state = + let cpt = ref 0 in (fun () -> let s = make_ident "State" (Some !cpt) in incr cpt; s) -let new_identifier_var = - let cpt = ref 0 in +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 = @@ -115,17 +115,17 @@ 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 -> + (fun (name : identifier) -> + try Hashtbl.find table name with Not_found -> let idx = !cpt in - Hashtbl.add table name idx; + 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 -> + (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 false (Some 1) 1 (Rawterm.ImplicitBindings [c]) @@ -134,10 +134,10 @@ let generalize_tac t = generalize_time (generalize t) let elim t = elim_time (simplest_elim t) let exact t = exact_time (Tactics.refine t) let unfold s = Tactics.unfold_in_concl [all_occurrences, Lazy.force s] - + let rev_assoc k = let rec loop = function - | [] -> raise Not_found | (v,k')::_ when k = k' -> v | _ :: l -> loop l + | [] -> raise Not_found | (v,k')::_ when k = k' -> v | _ :: l -> loop l in loop @@ -347,15 +347,15 @@ let mk_eq_rel t1 t2 = mkApp (build_coq_eq (), let mk_inj t = mkApp (Lazy.force coq_Z_of_nat, [| t |]) let mk_integer n = - let rec loop n = - if n =? one then Lazy.force coq_xH else + let rec loop n = + 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 =? zero then Lazy.force coq_Z0 + 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 | Zsucc | Zopp | Plus | Mult | Minus | Pred | S | O @@ -371,7 +371,7 @@ type omega_proposition = | Keq of constr * constr * constr | Kn -type result = +type result = | Kvar of identifier | Kapp of omega_constant * constr list | Kimp of constr * constr @@ -442,18 +442,18 @@ let recognize_number t = | 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" + | _ -> failwith "not a number" in - match decompose_app t with + match decompose_app t with | 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 = | P_APP of int (* Abstraction and product *) - | P_BODY + | P_BODY | P_TYPE (* Case *) | P_BRANCH of int @@ -461,8 +461,8 @@ type constr_path = | P_ARG let context operation path (t : constr) = - let rec loop i p0 t = - match (p0,kind_of_term t) with + let rec loop i p0 t = + match (p0,kind_of_term t) with | (p, Cast (c,k,t)) -> mkCast (loop i p c,k,t) | ([], _) -> operation i t | ((P_APP n :: p), App (f,v)) -> @@ -493,9 +493,9 @@ let context operation path (t : constr) = (mkLambda (n,loop i p t,c)) | ((P_TYPE :: p), LetIn (n,b,t,c)) -> (mkLetIn (n,b,loop i p t,c)) - | (p, _) -> + | (p, _) -> ppnl (Printer.pr_lconstr t); - failwith ("abstract_path " ^ string_of_int(List.length p)) + failwith ("abstract_path " ^ string_of_int(List.length p)) in loop 1 path t @@ -514,9 +514,9 @@ let occurence path (t : constr) = | ((P_TYPE :: p), Prod (n,term,c)) -> loop p term | ((P_TYPE :: p), Lambda (n,term,c)) -> loop p term | ((P_TYPE :: p), LetIn (n,b,term,c)) -> loop p term - | (p, _) -> + | (p, _) -> ppnl (Printer.pr_lconstr t); - failwith ("occurence " ^ string_of_int(List.length p)) + failwith ("occurence " ^ string_of_int(List.length p)) in loop path t @@ -539,13 +539,13 @@ type oformula = | Oz of bigint | Oufo of constr -let rec oprint = function - | Oplus(t1,t2) -> - print_string "("; oprint t1; print_string "+"; +let rec oprint = function + | Oplus(t1,t2) -> + print_string "("; oprint t1; print_string "+"; oprint t2; print_string ")" | Oinv t -> print_string "~"; oprint t - | Otimes (t1,t2) -> - print_string "("; oprint t1; print_string "*"; + | Otimes (t1,t2) -> + print_string "("; oprint t1; print_string "*"; oprint t2; print_string ")" | Oatom s -> print_string (string_of_id s) | Oz i -> print_string (string_of_bigint i) @@ -567,92 +567,92 @@ let rec val_of = function | Oplus(t1,t2) -> mkApp (Lazy.force coq_Zplus, [| val_of t1; val_of t2 |]) | Oufo c -> c -let compile name kind = +let compile name kind = let rec loop accu = function | Oplus(Otimes(Oatom v,Oz n),r) -> loop ({v=intern_id v; c=n} :: accu) r | Oz n -> let id = new_id () in tag_hypothesis name id; {kind = kind; body = List.rev accu; constant = n; id = id} - | _ -> anomaly "compile_equation" + | _ -> anomaly "compile_equation" in loop [] -let rec decompile af = +let rec decompile af = let rec loop = function - | ({v=v; c=n}::r) -> Oplus(Otimes(Oatom (unintern_id v),Oz n),loop r) - | [] -> Oz af.constant + | ({v=v; c=n}::r) -> Oplus(Otimes(Oatom (unintern_id v),Oz n),loop r) + | [] -> Oz af.constant in loop af.body let mkNewMeta () = mkMeta (Evarutil.new_meta()) -let clever_rewrite_base_poly typ p result theorem gl = +let clever_rewrite_base_poly typ p result theorem gl = let full = pf_concl gl in let (abstracted,occ) = abstract_path typ (List.rev p) full in - let t = + let t = applist (mkLambda - (Name (id_of_string "P"), + (Name (id_of_string "P"), mkArrow typ mkProp, mkLambda (Name (id_of_string "H"), applist (mkRel 1,[result]), - mkApp (Lazy.force coq_eq_ind_r, + mkApp (Lazy.force coq_eq_ind_r, [| typ; result; mkRel 2; mkRel 1; occ; theorem |]))), - [abstracted]) + [abstracted]) in exact (applist(t,[mkNewMeta()])) gl -let clever_rewrite_base p result theorem gl = +let clever_rewrite_base p result theorem gl = clever_rewrite_base_poly (Lazy.force coq_Z) p result theorem gl -let clever_rewrite_base_nat p result theorem gl = +let clever_rewrite_base_nat p result theorem gl = clever_rewrite_base_poly (Lazy.force coq_nat) p result theorem gl -let clever_rewrite_gen p result (t,args) = - let theorem = applist(t, args) in +let clever_rewrite_gen p result (t,args) = + let theorem = applist(t, args) in clever_rewrite_base p result theorem -let clever_rewrite_gen_nat p result (t,args) = - let theorem = applist(t, args) in +let clever_rewrite_gen_nat p result (t,args) = + let theorem = applist(t, args) in clever_rewrite_base_nat p result theorem -let clever_rewrite p vpath t gl = +let clever_rewrite p vpath t gl = let full = pf_concl gl in let (abstracted,occ) = abstract_path (Lazy.force coq_Z) (List.rev p) full in 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) = +let rec shuffle p (t1,t2) = match t1,t2 with | Oplus(l1,r1), Oplus(l2,r2) -> - if weight l1 > weight l2 then + if weight l1 > weight l2 then let (tac,t') = shuffle (P_APP 2 :: p) (r1,t2) in - (clever_rewrite p [[P_APP 1;P_APP 1]; + (clever_rewrite p [[P_APP 1;P_APP 1]; [P_APP 1; P_APP 2];[P_APP 2]] (Lazy.force coq_fast_Zplus_assoc_reverse) :: tac, Oplus(l1,t')) - else + else let (tac,t') = shuffle (P_APP 2 :: p) (t1,r2) in (clever_rewrite p [[P_APP 1];[P_APP 2;P_APP 1];[P_APP 2;P_APP 2]] (Lazy.force coq_fast_Zplus_permute) :: tac, Oplus(l2,t')) - | Oplus(l1,r1), t2 -> + | Oplus(l1,r1), 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_reverse) - :: tac, + :: tac, Oplus(l1, t') - else - [clever_rewrite p [[P_APP 1];[P_APP 2]] + else + [clever_rewrite p [[P_APP 1];[P_APP 2]] (Lazy.force coq_fast_Zplus_comm)], Oplus(t2,t1) - | t1,Oplus(l2,r2) -> + | t1,Oplus(l2,r2) -> if weight l2 > weight t1 then let (tac,t') = shuffle (P_APP 2 :: p) (t1,r2) in clever_rewrite p [[P_APP 1];[P_APP 2;P_APP 1];[P_APP 2;P_APP 2]] @@ -664,11 +664,11 @@ let rec shuffle p (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]] + [clever_rewrite p [[P_APP 1];[P_APP 2]] (Lazy.force coq_fast_Zplus_comm)], Oplus(t2,t1) else [],Oplus(t1,t2) - + let rec shuffle_mult p_init k1 e1 k2 e2 = let rec loop p = function | (({c=c1;v=v1}::l1) as l1'),(({c=c2;v=v2}::l2) as l2') -> @@ -681,13 +681,13 @@ let rec shuffle_mult p_init k1 e1 k2 e2 = [P_APP 2; P_APP 1; P_APP 2]; [P_APP 1; P_APP 2]; [P_APP 2; P_APP 2]] - (Lazy.force coq_fast_OMEGA10) + (Lazy.force coq_fast_OMEGA10) in - if Bigint.add (Bigint.mult k1 c1) (Bigint.mult k2 c2) =? zero then - let tac' = + 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 - tac :: focused_simpl (P_APP 1::P_APP 2:: p) :: tac' :: + tac :: focused_simpl (P_APP 1::P_APP 2:: p) :: tac' :: loop p (l1,l2) else tac :: loop (P_APP 2 :: p) (l1,l2) else if v1 > v2 then @@ -706,7 +706,7 @@ let rec shuffle_mult p_init k1 e1 k2 e2 = [P_APP 2; P_APP 2]] (Lazy.force coq_fast_OMEGA12) :: loop (P_APP 2 :: p) (l1',l2) - | ({c=c1;v=v1}::l1), [] -> + | ({c=c1;v=v1}::l1), [] -> clever_rewrite p [[P_APP 1; P_APP 1; P_APP 1; P_APP 1]; [P_APP 1; P_APP 1; P_APP 1; P_APP 2]; [P_APP 1; P_APP 1; P_APP 2]; @@ -714,7 +714,7 @@ let rec shuffle_mult p_init k1 e1 k2 e2 = [P_APP 1; P_APP 2]] (Lazy.force coq_fast_OMEGA11) :: loop (P_APP 2 :: p) (l1,[]) - | [],({c=c2;v=v2}::l2) -> + | [],({c=c2;v=v2}::l2) -> clever_rewrite p [[P_APP 2; P_APP 1; P_APP 1; P_APP 1]; [P_APP 2; P_APP 1; P_APP 1; P_APP 2]; [P_APP 1]; @@ -722,10 +722,10 @@ let rec shuffle_mult p_init k1 e1 k2 e2 = [P_APP 2; P_APP 2]] (Lazy.force coq_fast_OMEGA12) :: loop (P_APP 2 :: p) ([],l2) - | [],[] -> [focused_simpl p_init] + | [],[] -> [focused_simpl p_init] in loop p_init (e1,e2) - + let rec shuffle_mult_right p_init e1 k2 e2 = let rec loop p = function | (({c=c1;v=v1}::l1) as l1'),(({c=c2;v=v2}::l2) as l2') -> @@ -738,14 +738,14 @@ let rec shuffle_mult_right p_init e1 k2 e2 = [P_APP 1; P_APP 2]; [P_APP 2; P_APP 1; P_APP 2]; [P_APP 2; P_APP 2]] - (Lazy.force coq_fast_OMEGA15) + (Lazy.force coq_fast_OMEGA15) in - if Bigint.add c1 (Bigint.mult k2 c2) =? zero then - let tac' = + 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) + (Lazy.force coq_fast_Zred_factor5) in - tac :: focused_simpl (P_APP 1::P_APP 2:: p) :: tac' :: + tac :: focused_simpl (P_APP 1::P_APP 2:: p) :: tac' :: loop p (l1,l2) else tac :: loop (P_APP 2 :: p) (l1,l2) else if v1 > v2 then @@ -760,11 +760,11 @@ let rec shuffle_mult_right p_init e1 k2 e2 = [P_APP 2; P_APP 2]] (Lazy.force coq_fast_OMEGA12) :: loop (P_APP 2 :: p) (l1',l2) - | ({c=c1;v=v1}::l1), [] -> + | ({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_reverse) :: loop (P_APP 2 :: p) (l1,[]) - | [],({c=c2;v=v2}::l2) -> + | [],({c=c2;v=v2}::l2) -> clever_rewrite p [[P_APP 2; P_APP 1; P_APP 1; P_APP 1]; [P_APP 2; P_APP 1; P_APP 1; P_APP 2]; [P_APP 1]; @@ -772,89 +772,89 @@ let rec shuffle_mult_right p_init e1 k2 e2 = [P_APP 2; P_APP 2]] (Lazy.force coq_fast_OMEGA12) :: loop (P_APP 2 :: p) ([],l2) - | [],[] -> [focused_simpl p_init] + | [],[] -> [focused_simpl p_init] in loop p_init (e1,e2) -let rec shuffle_cancel p = function +let rec shuffle_cancel p = function | [] -> [focused_simpl p] | ({c=c1}::l1) -> - let tac = + let tac = 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 2; P_APP 2]; [P_APP 1; P_APP 1; P_APP 2; P_APP 1]] - (if c1 >? zero then - (Lazy.force coq_fast_OMEGA13) - else - (Lazy.force coq_fast_OMEGA14)) + (if c1 >? zero then + (Lazy.force coq_fast_OMEGA13) + else + (Lazy.force coq_fast_OMEGA14)) in tac :: shuffle_cancel p l1 - + let rec scalar p n = function - | Oplus(t1,t2) -> - let tac1,t1' = scalar (P_APP 1 :: p) n t1 and + | Oplus(t1,t2) -> + 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_l) :: + (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]] + [clever_rewrite p [[P_APP 1;P_APP 1];[P_APP 2]] (Lazy.force coq_fast_Zmult_opp_comm); focused_simpl (P_APP 2 :: p)], Otimes(t,Oz(neg n)) - | Otimes(t1,Oz x) -> + | 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_reverse); - focused_simpl (P_APP 2 :: p)], + 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" | (Oatom _ as t) -> [], Otimes(t,Oz n) | Oz i -> [focused_simpl p],Oz(n*i) | Oufo c -> [], Oufo (mkApp (Lazy.force coq_Zmult, [| mk_integer n; c |])) - -let rec scalar_norm p_init = + +let rec scalar_norm p_init = let rec loop p = function | [] -> [focused_simpl p_init] - | (_::l) -> + | (_::l) -> clever_rewrite p [[P_APP 1; P_APP 1; P_APP 1];[P_APP 1; P_APP 1; P_APP 2]; [P_APP 1; P_APP 2];[P_APP 2]] - (Lazy.force coq_fast_OMEGA16) :: loop (P_APP 2 :: p) l + (Lazy.force coq_fast_OMEGA16) :: loop (P_APP 2 :: p) l in loop p_init let rec norm_add p_init = let rec loop p = function | [] -> [focused_simpl p_init] - | _:: l -> + | _:: 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_reverse) :: - loop (P_APP 2 :: p) l + loop (P_APP 2 :: p) l in loop p_init let rec scalar_norm_add p_init = let rec loop p = function | [] -> [focused_simpl p_init] - | _ :: l -> + | _ :: l -> clever_rewrite p [[P_APP 1; P_APP 1; P_APP 1; P_APP 1]; [P_APP 1; P_APP 1; P_APP 1; P_APP 2]; [P_APP 1; P_APP 1; P_APP 2]; [P_APP 2]; [P_APP 1; P_APP 2]] - (Lazy.force coq_fast_OMEGA11) :: loop (P_APP 2 :: p) l + (Lazy.force coq_fast_OMEGA11) :: loop (P_APP 2 :: p) l in loop p_init let rec negate p = function - | Oplus(t1,t2) -> - let tac1,t1' = negate (P_APP 1 :: p) t1 and + | Oplus(t1,t2) -> + 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_plus_distr) :: + (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_involutive)], t - | Otimes(t1,Oz x) -> + | Otimes(t1,Oz x) -> [clever_rewrite p [[P_APP 1;P_APP 1];[P_APP 1;P_APP 2]] (Lazy.force coq_fast_Zopp_mult_distr_r); focused_simpl (P_APP 2 :: p)], Otimes(t1,Oz (neg x)) @@ -864,13 +864,13 @@ let rec negate p = function [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 rec transform p t = let default isnat t' = - try + try let v,th,_ = find_constr t' in [clever_rewrite_base p (mkVar v) (mkVar th)], Oatom v - with _ -> + with _ -> let v = new_identifier_var () and th = new_identifier () in hide_constr t' v th isnat; @@ -878,12 +878,12 @@ let rec transform p t = in try match destructurate_term t with | Kapp(Zplus,[t1;t2]) -> - let tac1,t1' = transform (P_APP 1 :: p) t1 + let tac1,t1' = transform (P_APP 1 :: p) t1 and tac2,t2' = transform (P_APP 2 :: p) t2 in let tac,t' = shuffle p (t1',t2') in tac1 @ tac2 @ tac, t' | Kapp(Zminus,[t1;t2]) -> - let tac,t = + let tac,t = transform p (mkApp (Lazy.force coq_Zplus, [| t1; (mkApp (Lazy.force coq_Zopp, [| t2 |])) |])) in @@ -893,18 +893,18 @@ let rec transform p t = [| t1; mk_integer one |])) in unfold sp_Zsucc :: tac,t | Kapp(Zmult,[t1;t2]) -> - let tac1,t1' = transform (P_APP 1 :: p) t1 + let tac1,t1' = transform (P_APP 1 :: p) t1 and tac2,t2' = transform (P_APP 2 :: p) t2 in begin match t1',t2' with | (_,Oz n) -> let tac,t' = scalar p n t1' in tac1 @ tac2 @ tac,t' | (Oz n,_) -> - let sym = - clever_rewrite p [[P_APP 1];[P_APP 2]] + let sym = + clever_rewrite p [[P_APP 1];[P_APP 2]] (Lazy.force coq_fast_Zmult_comm) in let tac,t' = scalar p n t2' in tac1 @ tac2 @ (sym :: tac),t' | _ -> default false t end - | Kapp((Zpos|Zneg|Z0),_) -> + | Kapp((Zpos|Zneg|Z0),_) -> (try ([],Oz(recognize_number t)) with _ -> default false t) | Kvar s -> [],Oatom s | Kapp(Zopp,[t]) -> @@ -914,28 +914,28 @@ let rec transform p t = | 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 _ -> + | Oatom v,Oatom _ -> 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) -> + | Oatom v, Otimes(_,c2) -> let r = Otimes(Oatom v,Oplus(c2,Oz one)) in - clever_rewrite p [[P_APP 1];[P_APP 2;P_APP 2]] + clever_rewrite p [[P_APP 1];[P_APP 2;P_APP 2]] (Lazy.force coq_fast_Zred_factor2), r - | Otimes (v1,c1),Oatom v -> + | Otimes (v1,c1),Oatom v -> 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) -> let r = Otimes(Oatom v,Oplus(c1,c2)) in - clever_rewrite p + clever_rewrite p [[P_APP 1;P_APP 1];[P_APP 1;P_APP 2];[P_APP 2;P_APP 2]] (Lazy.force coq_fast_Zred_factor4),r - | t1,t2 -> - begin - oprint t1; print_newline (); oprint t2; print_newline (); + | t1,t2 -> + begin + oprint t1; print_newline (); oprint t2; print_newline (); flush Pervasives.stdout; error "shrink.1" end @@ -948,7 +948,7 @@ let reduce_factor p = function let rec compute = function | Oz n -> n | Oplus(t1,t2) -> Bigint.add (compute t1) (compute t2) - | _ -> error "condense.1" + | _ -> error "condense.1" in [focused_simpl (P_APP 2 :: p)], Otimes(Oatom v,Oz(compute c)) | t -> oprint t; error "reduce_factor.1" @@ -957,31 +957,31 @@ let rec condense p = function | Oplus(f1,(Oplus(f2,r) as t)) -> if weight f1 = weight f2 then begin let shrink_tac,t = shrink_pair (P_APP 1 :: p) f1 f2 in - let assoc_tac = - clever_rewrite p + 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) in let tac_list,t' = condense p (Oplus(t,r)) in (assoc_tac :: shrink_tac :: tac_list), t' end else begin let tac,f = reduce_factor (P_APP 1 :: p) f1 in - let tac',t' = condense (P_APP 2 :: p) t in - (tac @ tac'), Oplus(f,t') + let tac',t' = condense (P_APP 2 :: p) t in + (tac @ tac'), Oplus(f,t') end - | Oplus(f1,Oz n) -> + | Oplus(f1,Oz n) -> let tac,f1' = reduce_factor (P_APP 1 :: p) f1 in tac,Oplus(f1',Oz n) - | Oplus(f1,f2) -> + | Oplus(f1,f2) -> if weight f1 = weight f2 then begin let tac_shrink,t = shrink_pair p f1 f2 in let tac,t' = condense p t in tac_shrink :: tac,t' end else begin let tac,f = reduce_factor (P_APP 1 :: p) f1 in - let tac',t' = condense (P_APP 2 :: p) f2 in - (tac @ tac'),Oplus(f,t') + let tac',t' = condense (P_APP 2 :: p) f2 in + (tac @ tac'),Oplus(f,t') end | Oz _ as t -> [],t - | t -> + | t -> let tac,t' = reduce_factor p t in let final = Oplus(t',Oz zero) in let tac' = clever_rewrite p [[]] (Lazy.force coq_fast_Zred_factor6) in @@ -990,99 +990,99 @@ let rec condense p = function let rec clear_zero p = function | Oplus(Otimes(Oatom v,Oz n),r) when n =? zero -> let tac = - clever_rewrite p [[P_APP 1;P_APP 1];[P_APP 2]] + clever_rewrite p [[P_APP 1;P_APP 1];[P_APP 2]] (Lazy.force coq_fast_Zred_factor5) in let tac',t = clear_zero p r in tac :: tac',t - | Oplus(f,r) -> + | Oplus(f,r) -> let tac,t = clear_zero (P_APP 2 :: p) r in tac,Oplus(f,t) | t -> [],t -let replay_history tactic_normalisation = +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 izero = mk_integer zero in let rec loop t = match t with - | HYP e :: l -> - begin - try - tclTHEN - (List.assoc (hyp_of_tag e.id) tactic_normalisation) + | HYP e :: l -> + begin + try + tclTHEN + (List.assoc (hyp_of_tag e.id) tactic_normalisation) (loop l) with Not_found -> loop l end | NEGATE_CONTRADICT (e2,e1,b) :: l -> - let eq1 = decompile e1 - and eq2 = decompile e2 in - let id1 = hyp_of_tag e1.id + let eq1 = decompile e1 + 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 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 [ - (generalize_tac - [mkApp (Lazy.force coq_OMEGA17, [| + (generalize_tac + [mkApp (Lazy.force coq_OMEGA17, [| val_of eq1; val_of eq2; - mk_integer k; + mk_integer k; mkVar id1; mkVar id2 |])]); (mk_then tac); (intros_using [aux]); (resolve_id aux); reflexivity ] - | CONTRADICTION (e1,e2) :: l -> - let eq1 = decompile e1 - and eq2 = decompile e2 in + | CONTRADICTION (e1,e2) :: l -> + let eq1 = decompile e1 + and eq2 = decompile e2 in let p_initial = [P_APP 2;P_TYPE] in let tac = shuffle_cancel p_initial e1.body in let solve_le = - let not_sup_sup = mkApp (build_coq_eq (), [| - Lazy.force coq_comparison; + let not_sup_sup = mkApp (build_coq_eq (), [| + Lazy.force coq_comparison; Lazy.force coq_Gt; Lazy.force coq_Gt |]) in - tclTHENS + tclTHENS (tclTHENLIST [ (unfold sp_Zle); (simpl_in_concl); intro; (absurd not_sup_sup) ]) - [ assumption ; reflexivity ] + [ assumption ; reflexivity ] in let theorem = - mkApp (Lazy.force coq_OMEGA2, [| - val_of eq1; val_of eq2; + mkApp (Lazy.force coq_OMEGA2, [| + val_of eq1; val_of eq2; mkVar (hyp_of_tag e1.id); mkVar (hyp_of_tag e2.id) |]) in tclTHEN (tclTHEN (generalize_tac [theorem]) (mk_then tac)) (solve_le) | DIVIDE_AND_APPROX (e1,e2,k,d) :: l -> let id = hyp_of_tag e1.id in - let eq1 = val_of(decompile e1) + let eq1 = val_of(decompile e1) and eq2 = val_of(decompile e2) in - let kk = mk_integer k + let kk = mk_integer k and dd = mk_integer d in let rhs = mk_plus (mk_times eq2 kk) dd in let state_eg = mk_eq eq1 rhs in let tac = scalar_norm_add [P_APP 3] e2.body in - tclTHENS - (cut state_eg) + tclTHENS + (cut state_eg) [ tclTHENS (tclTHENLIST [ (intros_using [aux]); - (generalize_tac + (generalize_tac [mkApp (Lazy.force coq_OMEGA1, [| eq1; rhs; mkVar aux; mkVar id |])]); (clear [aux;id]); (intros_using [id]); (cut (mk_gt kk dd)) ]) - [ tclTHENS - (cut (mk_gt kk izero)) + [ tclTHENS + (cut (mk_gt kk izero)) [ tclTHENLIST [ (intros_using [aux1; aux2]); - (generalize_tac + (generalize_tac [mkApp (Lazy.force coq_Zmult_le_approx, [| kk;eq2;dd;mkVar aux1;mkVar aux2; mkVar id |])]); (clear [aux1;aux2;id]); @@ -1095,23 +1095,23 @@ let replay_history tactic_normalisation = tclTHENLIST [ (unfold sp_Zgt); simpl_in_concl; reflexivity ] ]; tclTHEN (mk_then tac) reflexivity ] - + | NOT_EXACT_DIVIDE (e1,k) :: l -> let c = floor_div e1.constant k in let d = Bigint.sub e1.constant (Bigint.mult c k) in - let e2 = {id=e1.id; kind=EQUA;constant = c; + let e2 = {id=e1.id; kind=EQUA;constant = c; body = map_eq_linear (fun c -> c / k) e1.body } in let eq2 = val_of(decompile e2) in - let kk = mk_integer k + let kk = mk_integer k and dd = mk_integer d in let tac = scalar_norm_add [P_APP 2] e2.body in - tclTHENS - (cut (mk_gt dd izero)) - [ tclTHENS (cut (mk_gt kk dd)) + tclTHENS + (cut (mk_gt dd izero)) + [ tclTHENS (cut (mk_gt kk dd)) [tclTHENLIST [ (intros_using [aux2;aux1]); - (generalize_tac - [mkApp (Lazy.force coq_OMEGA4, + (generalize_tac + [mkApp (Lazy.force coq_OMEGA4, [| dd;kk;eq2;mkVar aux1; mkVar aux2 |])]); (clear [aux1;aux2]); (unfold sp_not); @@ -1121,7 +1121,7 @@ let replay_history tactic_normalisation = assumption ] ; tclTHENLIST [ (unfold sp_Zgt); - simpl_in_concl; + simpl_in_concl; reflexivity ] ]; tclTHENLIST [ (unfold sp_Zgt); @@ -1130,18 +1130,18 @@ let replay_history tactic_normalisation = | EXACT_DIVIDE (e1,k) :: l -> let id = hyp_of_tag e1.id in let e2 = map_eq_afine (fun c -> c / k) e1 in - let eq1 = val_of(decompile e1) + let eq1 = val_of(decompile e1) and eq2 = val_of(decompile e2) in let kk = mk_integer k in let state_eq = mk_eq eq1 (mk_times eq2 kk) in if e1.kind = DISE then let tac = scalar_norm [P_APP 3] e2.body in - tclTHENS - (cut state_eq) + tclTHENS + (cut state_eq) [tclTHENLIST [ (intros_using [aux1]); - (generalize_tac - [mkApp (Lazy.force coq_OMEGA18, + (generalize_tac + [mkApp (Lazy.force coq_OMEGA18, [| eq1;eq2;kk;mkVar aux1; mkVar id |])]); (clear [aux1;id]); (intros_using [id]); @@ -1149,14 +1149,14 @@ let replay_history tactic_normalisation = tclTHEN (mk_then tac) reflexivity ] else let tac = scalar_norm [P_APP 3] e2.body in - tclTHENS (cut state_eq) + tclTHENS (cut state_eq) [ - tclTHENS - (cut (mk_gt kk izero)) + tclTHENS + (cut (mk_gt kk izero)) [tclTHENLIST [ (intros_using [aux2;aux1]); - (generalize_tac - [mkApp (Lazy.force coq_OMEGA3, + (generalize_tac + [mkApp (Lazy.force coq_OMEGA3, [| eq1; eq2; kk; mkVar aux2; mkVar aux1;mkVar id|])]); (clear [aux1;aux2;id]); (intros_using [id]); @@ -1169,35 +1169,35 @@ let replay_history tactic_normalisation = | (MERGE_EQ(e3,e1,e2)) :: l -> let id = new_identifier () in tag_hypothesis id e3; - let id1 = hyp_of_tag e1.id + let id1 = hyp_of_tag e1.id and id2 = hyp_of_tag e2 in - let eq1 = val_of(decompile e1) + let eq1 = val_of(decompile e1) and eq2 = val_of (decompile (negate_eq e1)) in - let tac = - clever_rewrite [P_APP 3] [[P_APP 1]] + let tac = + clever_rewrite [P_APP 3] [[P_APP 1]] (Lazy.force coq_fast_Zopp_eq_mult_neg_1) :: - scalar_norm [P_APP 3] e1.body + scalar_norm [P_APP 3] e1.body in - tclTHENS - (cut (mk_eq eq1 (mk_inv eq2))) + tclTHENS + (cut (mk_eq eq1 (mk_inv eq2))) [tclTHENLIST [ (intros_using [aux]); - (generalize_tac [mkApp (Lazy.force coq_OMEGA8, + (generalize_tac [mkApp (Lazy.force coq_OMEGA8, [| eq1;eq2;mkVar id1;mkVar id2; mkVar aux|])]); (clear [id1;id2;aux]); (intros_using [id]); (loop l) ]; tclTHEN (mk_then tac) reflexivity] - + | STATE {st_new_eq=e;st_def=def;st_orig=orig;st_coef=m;st_var=v} :: l -> - let id = new_identifier () + let id = new_identifier () and id2 = hyp_of_tag orig.id in tag_hypothesis id e.id; - let eq1 = val_of(decompile def) + let eq1 = val_of(decompile def) and eq2 = val_of(decompile orig) in let vid = unintern_id v in let theorem = - mkApp (build_coq_ex (), [| + mkApp (build_coq_ex (), [| Lazy.force coq_Z; mkLambda (Name vid, @@ -1206,20 +1206,20 @@ let replay_history tactic_normalisation = in let mm = mk_integer m in let p_initial = [P_APP 2;P_TYPE] in - let tac = - clever_rewrite (P_APP 1 :: P_APP 1 :: P_APP 2 :: p_initial) + let tac = + clever_rewrite (P_APP 1 :: P_APP 1 :: P_APP 2 :: p_initial) [[P_APP 1]] (Lazy.force coq_fast_Zopp_eq_mult_neg_1) :: shuffle_mult_right p_initial orig.body m ({c= negone;v= v}::def.body) in - tclTHENS - (cut theorem) + tclTHENS + (cut theorem) [tclTHENLIST [ (intros_using [aux]); (elim_id aux); (clear [aux]); (intros_using [vid; aux]); (generalize_tac - [mkApp (Lazy.force coq_OMEGA9, + [mkApp (Lazy.force coq_OMEGA9, [| mkVar vid;eq2;eq1;mm; mkVar id2;mkVar aux |])]); (mk_then tac); (clear [aux]); @@ -1227,36 +1227,36 @@ let replay_history tactic_normalisation = (loop l) ]; tclTHEN (exists_tac (inj_open eq1)) reflexivity ] | SPLIT_INEQ(e,(e1,act1),(e2,act2)) :: l -> - let id1 = new_identifier () + let id1 = new_identifier () and id2 = new_identifier () in tag_hypothesis id1 e1; tag_hypothesis id2 e2; let id = hyp_of_tag e.id in let tac1 = norm_add [P_APP 2;P_TYPE] e.body in let tac2 = scalar_norm_add [P_APP 2;P_TYPE] e.body in let eq = val_of(decompile e) in - tclTHENS + tclTHENS (simplest_elim (applist (Lazy.force coq_OMEGA19, [eq; mkVar id]))) [tclTHENLIST [ (mk_then tac1); (intros_using [id1]); (loop act1) ]; tclTHENLIST [ (mk_then tac2); (intros_using [id2]); (loop act2) ]] | SUM(e3,(k1,e1),(k2,e2)) :: l -> let id = new_identifier () in tag_hypothesis id e3; - let id1 = hyp_of_tag e1.id + let id1 = hyp_of_tag e1.id and id2 = hyp_of_tag e2.id in - let eq1 = val_of(decompile e1) + let eq1 = val_of(decompile e1) and eq2 = val_of(decompile e2) in if k1 =? one & e2.kind = EQUA then let tac_thm = match e1.kind with - | EQUA -> Lazy.force coq_OMEGA5 - | INEQ -> Lazy.force coq_OMEGA6 - | DISE -> Lazy.force coq_OMEGA20 + | EQUA -> Lazy.force coq_OMEGA5 + | INEQ -> Lazy.force coq_OMEGA6 + | DISE -> Lazy.force coq_OMEGA20 in let kk = mk_integer k2 in let p_initial = if e1.kind=DISE then [P_APP 1; P_TYPE] else [P_APP 2; P_TYPE] in let tac = shuffle_mult_right p_initial e1.body k2 e2.body in - tclTHENLIST [ + tclTHENLIST [ (generalize_tac [mkApp (tac_thm, [| eq1; eq2; kk; mkVar id1; mkVar id2 |])]); (mk_then tac); @@ -1264,18 +1264,18 @@ let replay_history tactic_normalisation = (loop l) ] else - let kk1 = mk_integer k1 + let kk1 = mk_integer k1 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 izero)) - [tclTHENS - (cut (mk_gt kk2 izero)) + tclTHENS (cut (mk_gt kk1 izero)) + [tclTHENS + (cut (mk_gt kk2 izero)) [tclTHENLIST [ (intros_using [aux2;aux1]); (generalize_tac - [mkApp (Lazy.force coq_OMEGA7, [| - eq1;eq2;kk1;kk2; + [mkApp (Lazy.force coq_OMEGA7, [| + eq1;eq2;kk1;kk2; mkVar aux1;mkVar aux2; mkVar id1;mkVar id2 |])]); (clear [aux1;aux2]); @@ -1288,11 +1288,11 @@ let replay_history tactic_normalisation = reflexivity ] ]; tclTHENLIST [ (unfold sp_Zgt); - simpl_in_concl; + simpl_in_concl; reflexivity ] ] - | CONSTANT_NOT_NUL(e,k) :: l -> + | CONSTANT_NOT_NUL(e,k) :: l -> tclTHEN (generalize_tac [mkVar (hyp_of_tag e)]) Equality.discrConcl - | CONSTANT_NUL(e) :: l -> + | CONSTANT_NUL(e) :: l -> tclTHEN (resolve_id (hyp_of_tag e)) reflexivity | CONSTANT_NEG(e,k) :: l -> tclTHENLIST [ @@ -1302,43 +1302,43 @@ let replay_history tactic_normalisation = (unfold sp_not); (intros_using [aux]); (resolve_id aux); - reflexivity + reflexivity ] - | _ -> tclIDTAC + | _ -> tclIDTAC in loop let normalize p_initial t = let (tac,t') = transform p_initial t in let (tac',t'') = condense p_initial t' in - let (tac'',t''') = clear_zero p_initial t'' in + let (tac'',t''') = clear_zero p_initial t'' in tac @ tac' @ tac'' , t''' - + let normalize_equation id flag theorem pos t t1 t2 (tactic,defs) = let p_initial = [P_APP pos ;P_TYPE] in let (tac,t') = normalize p_initial t in - let shift_left = - tclTHEN + let shift_left = + tclTHEN (generalize_tac [mkApp (theorem, [| t1; t2; mkVar id |]) ]) (tclTRY (clear [id])) in if tac <> [] then - let id' = new_identifier () in + let id' = new_identifier () in ((id',(tclTHENLIST [ (shift_left); (mk_then tac); (intros_using [id']) ])) :: tactic, compile id' flag t' :: defs) - else + else (tactic,defs) - + let destructure_omega gl tac_def (id,c) = - if atompart_of_id id = "State" then + if atompart_of_id id = "State" then tac_def else try match destructurate_prop c with - | Kapp(Eq,[typ;t1;t2]) + | Kapp(Eq,[typ;t1;t2]) when destructurate_type (pf_nf gl typ) = Kapp(Z,[]) -> let t = mk_plus t1 (mk_inv t2) in - normalize_equation + normalize_equation id EQUA (Lazy.force coq_Zegal_left) 2 t t1 t2 tac_def | Kapp(Zne,[t1;t2]) -> let t = mk_plus t1 (mk_inv t2) in @@ -1369,10 +1369,10 @@ let reintroduce id = let coq_omega gl = clear_tables (); - let tactic_normalisation, system = + let tactic_normalisation, system = List.fold_left (destructure_omega gl) ([],[]) (pf_hyps_types gl) in - let prelude,sys = - List.fold_left + let prelude,sys = + List.fold_left (fun (tac,sys) (t,(v,th,b)) -> if b then let id = new_identifier () in @@ -1385,8 +1385,8 @@ let coq_omega gl = (clear [id]); (intros_using [th;id]); tac ]), - {kind = INEQ; - body = [{v=intern_id v; c=one}]; + {kind = INEQ; + body = [{v=intern_id v; c=one}]; constant = zero; id = i} :: sys else (tclTHENLIST [ @@ -1399,17 +1399,17 @@ let coq_omega gl = let system = system @ sys in if !display_system_flag then display_system display_var system; if !old_style_flag then begin - try + try let _ = simplify (new_id,new_var_num,display_var) false system in tclIDTAC gl - with UNSOLVABLE -> + with UNSOLVABLE -> let _,path = depend [] [] (history ()) in if !display_action_flag then display_action display_var path; - (tclTHEN prelude (replay_history tactic_normalisation path)) gl - end else begin + (tclTHEN prelude (replay_history tactic_normalisation path)) gl + end else begin try let path = simplify_strong (new_id,new_var_num,display_var) system in - if !display_action_flag then display_action display_var path; + 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 @@ -1417,10 +1417,10 @@ let coq_omega gl = let coq_omega = solver_time coq_omega let nat_inject gl = - let rec explore p t = + let rec explore p t = try match destructurate_term t with | Kapp(Plus,[t1;t2]) -> - tclTHENLIST [ + tclTHENLIST [ (clever_rewrite_gen p (mk_plus (mk_inj t1) (mk_inj t2)) ((Lazy.force coq_inj_plus),[t1;t2])); (explore (P_APP 1 :: p) t1); @@ -1436,61 +1436,61 @@ let nat_inject gl = | Kapp(Minus,[t1;t2]) -> let id = new_identifier () in tclTHENS - (tclTHEN - (simplest_elim (applist (Lazy.force coq_le_gt_dec, [t2;t1]))) - (intros_using [id])) + (tclTHEN + (simplest_elim (applist (Lazy.force coq_le_gt_dec, [t2;t1]))) + (intros_using [id])) [ tclTHENLIST [ - (clever_rewrite_gen p + (clever_rewrite_gen p (mk_minus (mk_inj t1) (mk_inj t2)) ((Lazy.force coq_inj_minus1),[t1;t2;mkVar id])); (loop [id,mkApp (Lazy.force coq_le, [| t2;t1 |])]); (explore (P_APP 1 :: p) t1); (explore (P_APP 2 :: p) t2) ]; - (tclTHEN + (tclTHEN (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 |])])) ] | Kapp(S,[t']) -> let rec is_number t = - try match destructurate_term t with + try match destructurate_term t with Kapp(S,[t]) -> is_number t | Kapp(O,[]) -> true | _ -> false - with e when catchable_exception e -> false + with e when catchable_exception e -> false in let rec loop p t = - try match destructurate_term t with + try match destructurate_term t with Kapp(S,[t]) -> - (tclTHEN - (clever_rewrite_gen p + (tclTHEN + (clever_rewrite_gen p (mkApp (Lazy.force coq_Zsucc, [| mk_inj t |])) - ((Lazy.force coq_inj_S),[t])) + ((Lazy.force coq_inj_S),[t])) (loop (P_APP 1 :: p) t)) - | _ -> explore p t - with e when catchable_exception e -> explore p t + | _ -> explore p t + with e when catchable_exception e -> explore p t in if is_number t' then focused_simpl p else loop p t | Kapp(Pred,[t]) -> - let t_minus_one = - mkApp (Lazy.force coq_minus, [| t; + let t_minus_one = + mkApp (Lazy.force coq_minus, [| t; mkApp (Lazy.force coq_S, [| Lazy.force coq_O |]) |]) in tclTHEN - (clever_rewrite_gen_nat (P_APP 1 :: p) t_minus_one + (clever_rewrite_gen_nat (P_APP 1 :: p) t_minus_one ((Lazy.force coq_pred_of_minus),[t])) - (explore p t_minus_one) + (explore p t_minus_one) | Kapp(O,[]) -> focused_simpl p - | _ -> tclIDTAC - with e when catchable_exception e -> tclIDTAC - + | _ -> tclIDTAC + with e when catchable_exception e -> tclIDTAC + and loop = function | [] -> tclIDTAC - | (i,t)::lit -> - begin try match destructurate_prop t with + | (i,t)::lit -> + begin try match destructurate_prop t with Kapp(Le,[t1;t2]) -> tclTHENLIST [ - (generalize_tac + (generalize_tac [mkApp (Lazy.force coq_inj_le, [| t1;t2;mkVar i |]) ]); (explore [P_APP 1; P_TYPE] t1); (explore [P_APP 2; P_TYPE] t2); @@ -1499,7 +1499,7 @@ let nat_inject gl = ] | Kapp(Lt,[t1;t2]) -> tclTHENLIST [ - (generalize_tac + (generalize_tac [mkApp (Lazy.force coq_inj_lt, [| t1;t2;mkVar i |]) ]); (explore [P_APP 1; P_TYPE] t1); (explore [P_APP 2; P_TYPE] t2); @@ -1508,7 +1508,7 @@ let nat_inject gl = ] | Kapp(Ge,[t1;t2]) -> tclTHENLIST [ - (generalize_tac + (generalize_tac [mkApp (Lazy.force coq_inj_ge, [| t1;t2;mkVar i |]) ]); (explore [P_APP 1; P_TYPE] t1); (explore [P_APP 2; P_TYPE] t2); @@ -1536,7 +1536,7 @@ let nat_inject gl = | Kapp(Eq,[typ;t1;t2]) -> if pf_conv_x gl typ (Lazy.force coq_nat) then tclTHENLIST [ - (generalize_tac + (generalize_tac [mkApp (Lazy.force coq_inj_eq, [| t1;t2;mkVar i |]) ]); (explore [P_APP 2; P_TYPE] t1); (explore [P_APP 3; P_TYPE] t2); @@ -1545,32 +1545,32 @@ let nat_inject gl = ] else loop lit | _ -> loop lit - with e when catchable_exception e -> loop lit end + with e when catchable_exception e -> loop lit end in loop (List.rev (pf_hyps_types gl)) gl - + let rec decidability gl t = match destructurate_prop t with - | Kapp(Or,[t1;t2]) -> + | Kapp(Or,[t1;t2]) -> mkApp (Lazy.force coq_dec_or, [| t1; t2; decidability gl t1; decidability gl t2 |]) - | Kapp(And,[t1;t2]) -> + | Kapp(And,[t1;t2]) -> mkApp (Lazy.force coq_dec_and, [| t1; t2; decidability gl t1; decidability gl t2 |]) - | Kapp(Iff,[t1;t2]) -> + | Kapp(Iff,[t1;t2]) -> mkApp (Lazy.force coq_dec_iff, [| t1; t2; decidability gl t1; decidability gl t2 |]) - | Kimp(t1,t2) -> + | Kimp(t1,t2) -> mkApp (Lazy.force coq_dec_imp, [| t1; t2; decidability gl t1; decidability gl t2 |]) - | Kapp(Not,[t1]) -> mkApp (Lazy.force coq_dec_not, [| t1; + | Kapp(Not,[t1]) -> mkApp (Lazy.force coq_dec_not, [| t1; decidability gl t1 |]) - | Kapp(Eq,[typ;t1;t2]) -> + | Kapp(Eq,[typ;t1;t2]) -> begin match destructurate_type (pf_nf gl typ) with | Kapp(Z,[]) -> mkApp (Lazy.force coq_dec_eq, [| t1;t2 |]) | Kapp(Nat,[]) -> mkApp (Lazy.force coq_dec_eq_nat, [| t1;t2 |]) - | _ -> errorlabstrm "decidability" - (str "Omega: Can't solve a goal with equality on " ++ + | _ -> errorlabstrm "decidability" + (str "Omega: Can't solve a goal with equality on " ++ Printer.pr_lconstr typ) end | Kapp(Zne,[t1;t2]) -> mkApp (Lazy.force coq_dec_Zne, [| t1;t2 |]) @@ -1584,7 +1584,7 @@ let rec decidability gl t = | Kapp(Gt, [t1;t2]) -> mkApp (Lazy.force coq_dec_gt, [| t1;t2 |]) | Kapp(False,[]) -> Lazy.force coq_dec_False | Kapp(True,[]) -> Lazy.force coq_dec_True - | Kapp(Other t,_::_) -> error + | Kapp(Other t,_::_) -> error ("Omega: Unrecognized predicate or connective: "^t) | Kapp(Other t,[]) -> error ("Omega: Unrecognized atomic proposition: "^t) | Kvar _ -> error "Omega: Can't solve a goal with proposition variables" @@ -1595,7 +1595,7 @@ let onClearedName id tac = (* so renaming may be necessary *) tclTHEN (tclTRY (clear [id])) - (fun gl -> + (fun gl -> let id = fresh_id [] id gl in tclTHEN (introduction id) (tac id) gl) @@ -1607,7 +1607,7 @@ let destructure_hyps gl = | Kapp(False,[]) -> elim_id i | Kapp((Zle|Zge|Zgt|Zlt|Zne),[t1;t2]) -> loop lit | Kapp(Or,[t1;t2]) -> - (tclTHENS + (tclTHENS (elim_id i) [ onClearedName i (fun i -> (loop ((i,None,t1)::lit))); onClearedName i (fun i -> (loop ((i,None,t2)::lit))) ]) @@ -1615,7 +1615,7 @@ let destructure_hyps gl = tclTHENLIST [ (elim_id i); (tclTRY (clear [i])); - (fun gl -> + (fun gl -> let i1 = fresh_id [] (add_suffix i "_left") gl in let i2 = fresh_id [] (add_suffix i "_right") gl in tclTHENLIST [ @@ -1627,7 +1627,7 @@ let destructure_hyps gl = tclTHENLIST [ (elim_id i); (tclTRY (clear [i])); - (fun gl -> + (fun gl -> let i1 = fresh_id [] (add_suffix i "_left") gl in let i2 = fresh_id [] (add_suffix i "_right") gl in tclTHENLIST [ @@ -1661,16 +1661,16 @@ let destructure_hyps gl = ] else loop lit - | Kapp(Not,[t]) -> - begin match destructurate_prop t with - Kapp(Or,[t1;t2]) -> + | Kapp(Not,[t]) -> + begin match destructurate_prop t with + Kapp(Or,[t1;t2]) -> tclTHENLIST [ (generalize_tac [mkApp (Lazy.force coq_not_or,[| t1; t2; mkVar i |])]); (onClearedName i (fun i -> (loop ((i,None,mk_and (mk_not t1) (mk_not t2)):: lit)))) ] - | Kapp(And,[t1;t2]) -> + | Kapp(And,[t1;t2]) -> tclTHENLIST [ (generalize_tac [mkApp (Lazy.force coq_not_and, [| t1; t2; @@ -1690,8 +1690,8 @@ let destructure_hyps gl = ] | Kimp(t1,t2) -> tclTHENLIST [ - (generalize_tac - [mkApp (Lazy.force coq_not_imp, [| t1; t2; + (generalize_tac + [mkApp (Lazy.force coq_not_imp, [| t1; t2; decidability gl t1;mkVar i |])]); (onClearedName i (fun i -> (loop ((i,None,mk_and t1 (mk_not t2)) :: lit)))) @@ -1717,7 +1717,7 @@ let destructure_hyps gl = ] | Kapp(Zlt, [t1;t2]) -> tclTHENLIST [ - (generalize_tac + (generalize_tac [mkApp (Lazy.force coq_Znot_lt_ge, [| t1;t2;mkVar i|])]); (onClearedName i (fun _ -> loop lit)) ] @@ -1752,33 +1752,33 @@ let destructure_hyps gl = (onClearedName i (fun _ -> loop lit)) ] | Kapp(Eq,[typ;t1;t2]) -> - if !old_style_flag then begin + if !old_style_flag then begin match destructurate_type (pf_nf gl typ) with - | Kapp(Nat,_) -> + | Kapp(Nat,_) -> tclTHENLIST [ - (simplest_elim + (simplest_elim (mkApp (Lazy.force coq_not_eq, [|t1;t2;mkVar i|]))); (onClearedName i (fun _ -> loop lit)) ] | Kapp(Z,_) -> tclTHENLIST [ - (simplest_elim + (simplest_elim (mkApp (Lazy.force coq_not_Zeq, [|t1;t2;mkVar i|]))); (onClearedName i (fun _ -> loop lit)) ] | _ -> loop lit - end else begin + end else begin match destructurate_type (pf_nf gl typ) with - | Kapp(Nat,_) -> - (tclTHEN + | Kapp(Nat,_) -> + (tclTHEN (convert_hyp_no_check (i,body, (mkApp (Lazy.force coq_neq, [| t1;t2|])))) (loop lit)) | Kapp(Z,_) -> - (tclTHEN + (tclTHEN (convert_hyp_no_check (i,body, (mkApp (Lazy.force coq_Zne, [| t1;t2|])))) @@ -1786,10 +1786,10 @@ let destructure_hyps gl = | _ -> loop lit end | _ -> loop lit - end - | _ -> loop lit + end + | _ -> loop lit with e when catchable_exception e -> loop lit - end + end in loop (pf_hyps gl) gl @@ -1798,19 +1798,19 @@ let destructure_goal gl = let rec loop t = match destructurate_prop t with | Kapp(Not,[t]) -> - (tclTHEN - (tclTHEN (unfold sp_not) intro) + (tclTHEN + (tclTHEN (unfold sp_not) intro) destructure_hyps) | Kimp(a,b) -> (tclTHEN intro (loop b)) | Kapp(False,[]) -> destructure_hyps | _ -> - (tclTHEN + (tclTHEN (tclTHEN - (Tactics.refine + (Tactics.refine (mkApp (Lazy.force coq_dec_not_not, [| t; decidability gl t; mkNewMeta () |]))) - intro) - (destructure_hyps)) + intro) + (destructure_hyps)) in (loop concl) gl @@ -1818,7 +1818,7 @@ let destructure_goal = all_time (destructure_goal) let omega_solver gl = Coqlib.check_required_library ["Coq";"omega";"Omega"]; - let result = destructure_goal gl in - (* if !display_time_flag then begin text_time (); + let result = destructure_goal gl in + (* if !display_time_flag then begin text_time (); flush Pervasives.stdout end; *) result |