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Diffstat (limited to 'contrib/romega/refl_omega.ml')
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diff --git a/contrib/romega/refl_omega.ml b/contrib/romega/refl_omega.ml deleted file mode 100644 index fc4f7a8f..00000000 --- a/contrib/romega/refl_omega.ml +++ /dev/null @@ -1,1299 +0,0 @@ -(************************************************************************* - - PROJET RNRT Calife - 2001 - Author: Pierre Crégut - France Télécom R&D - Licence : LGPL version 2.1 - - *************************************************************************) - -open Util -open Const_omega -module OmegaSolver = Omega.MakeOmegaSolver (Bigint) -open OmegaSolver - -(* \section{Useful functions and flags} *) -(* Especially useful debugging functions *) -let debug = ref false - -let show_goal gl = - if !debug then Pp.ppnl (Tacmach.pr_gls gl); Tacticals.tclIDTAC gl - -let pp i = print_int i; print_newline (); flush stdout - -(* More readable than the prefix notation *) -let (>>) = Tacticals.tclTHEN - -let mkApp = Term.mkApp - -(* \section{Types} - \subsection{How to walk in a term} - To represent how to get to a proposition. Only choice points are - kept (branch to choose in a disjunction and identifier of the disjunctive - connector) *) -type direction = Left of int | Right of int - -(* Step to find a proposition (operators are at most binary). A list is - a path *) -type occ_step = O_left | O_right | O_mono -type occ_path = occ_step list - -(* chemin identifiant une proposition sous forme du nom de l'hypothèse et - d'une liste de pas à partir de la racine de l'hypothèse *) -type occurence = {o_hyp : Names.identifier; o_path : occ_path} - -(* \subsection{refiable formulas} *) -type oformula = - (* integer *) - | Oint of Bigint.bigint - (* recognized binary and unary operations *) - | Oplus of oformula * oformula - | Omult of oformula * oformula - | Ominus of oformula * oformula - | Oopp of oformula - (* an atome in the environment *) - | Oatom of int - (* weird expression that cannot be translated *) - | Oufo of oformula - -(* Operators for comparison recognized by Omega *) -type comparaison = Eq | Leq | Geq | Gt | Lt | Neq - -(* Type des prédicats réifiés (fragment de calcul propositionnel. Les - * quantifications sont externes au langage) *) -type oproposition = - Pequa of Term.constr * oequation - | Ptrue - | Pfalse - | Pnot of oproposition - | Por of int * oproposition * oproposition - | Pand of int * oproposition * oproposition - | Pimp of int * oproposition * oproposition - | Pprop of Term.constr - -(* Les équations ou proposiitions atomiques utiles du calcul *) -and oequation = { - e_comp: comparaison; (* comparaison *) - e_left: oformula; (* formule brute gauche *) - e_right: oformula; (* formule brute droite *) - e_trace: Term.constr; (* tactique de normalisation *) - e_origin: occurence; (* l'hypothèse dont vient le terme *) - e_negated: bool; (* vrai si apparait en position nié - après normalisation *) - e_depends: direction list; (* liste des points de disjonction dont - dépend l'accès à l'équation avec la - direction (branche) pour y accéder *) - e_omega: afine (* la fonction normalisée *) - } - -(* \subsection{Proof context} - This environment codes - \begin{itemize} - \item the terms and propositions that are given as - parameters of the reified proof (and are represented as variables in the - reified goals) - \item translation functions linking the decision procedure and the Coq proof - \end{itemize} *) - -type environment = { - (* La liste des termes non reifies constituant l'environnement global *) - mutable terms : Term.constr list; - (* La meme chose pour les propositions *) - mutable props : Term.constr list; - (* Les variables introduites par omega *) - mutable om_vars : (oformula * int) list; - (* Traduction des indices utilisés ici en les indices finaux utilisés par - * la tactique Omega après dénombrement des variables utiles *) - real_indices : (int,int) Hashtbl.t; - mutable cnt_connectors : int; - equations : (int,oequation) Hashtbl.t; - constructors : (int, occurence) Hashtbl.t -} - -(* \subsection{Solution tree} - Définition d'une solution trouvée par Omega sous la forme d'un identifiant, - d'un ensemble d'équation dont dépend la solution et d'une trace *) -(* La liste des dépendances est triée et sans redondance *) -type solution = { - s_index : int; - s_equa_deps : int list; - s_trace : action list } - -(* Arbre de solution résolvant complètement un ensemble de systèmes *) -type solution_tree = - Leaf of solution - (* un noeud interne représente un point de branchement correspondant à - l'élimination d'un connecteur générant plusieurs buts - (typ. disjonction). Le premier argument - est l'identifiant du connecteur *) - | Tree of int * solution_tree * solution_tree - -(* Représentation de l'environnement extrait du but initial sous forme de - chemins pour extraire des equations ou d'hypothèses *) - -type context_content = - CCHyp of occurence - | CCEqua of int - -(* \section{Specific utility functions to handle base types} *) -(* Nom arbitraire de l'hypothèse codant la négation du but final *) -let id_concl = Names.id_of_string "__goal__" - -(* Initialisation de l'environnement de réification de la tactique *) -let new_environment () = { - terms = []; props = []; om_vars = []; cnt_connectors = 0; - real_indices = Hashtbl.create 7; - equations = Hashtbl.create 7; - constructors = Hashtbl.create 7; -} - -(* Génération d'un nom d'équation *) -let new_connector_id env = - env.cnt_connectors <- succ env.cnt_connectors; env.cnt_connectors - -(* Calcul de la branche complémentaire *) -let barre = function Left x -> Right x | Right x -> Left x - -(* Identifiant associé à une branche *) -let indice = function Left x | Right x -> x - -(* Affichage de l'environnement de réification (termes et propositions) *) -let print_env_reification env = - let rec loop c i = function - [] -> Printf.printf " ===============================\n\n" - | t :: l -> - Printf.printf " (%c%02d) := " c i; - Pp.ppnl (Printer.pr_lconstr t); - Pp.flush_all (); - loop c (succ i) l in - print_newline (); - Printf.printf " ENVIRONMENT OF PROPOSITIONS :\n\n"; loop 'P' 0 env.props; - Printf.printf " ENVIRONMENT OF TERMS :\n\n"; loop 'V' 0 env.terms - - -(* \subsection{Gestion des environnements de variable pour Omega} *) -(* generation d'identifiant d'equation pour Omega *) - -let new_omega_eq, rst_omega_eq = - let cpt = ref 0 in - (function () -> incr cpt; !cpt), - (function () -> cpt:=0) - -(* generation d'identifiant de variable pour Omega *) - -let new_omega_var, rst_omega_var = - let cpt = ref 0 in - (function () -> incr cpt; !cpt), - (function () -> cpt:=0) - -(* Affichage des variables d'un système *) - -let display_omega_var i = Printf.sprintf "OV%d" i - -(* Recherche la variable codant un terme pour Omega et crée la variable dans - l'environnement si il n'existe pas. Cas ou la variable dans Omega représente - le terme d'un monome (le plus souvent un atome) *) - -let intern_omega env t = - begin try List.assoc t env.om_vars - with Not_found -> - let v = new_omega_var () in - env.om_vars <- (t,v) :: env.om_vars; v - end - -(* Ajout forcé d'un lien entre un terme et une variable Cas où la - variable est créée par Omega et où il faut la lier après coup à un atome - réifié introduit de force *) -let intern_omega_force env t v = env.om_vars <- (t,v) :: env.om_vars - -(* Récupère le terme associé à une variable *) -let unintern_omega env id = - let rec loop = function - [] -> failwith "unintern" - | ((t,j)::l) -> if id = j then t else loop l in - loop env.om_vars - -(* \subsection{Gestion des environnements de variable pour la réflexion} - Gestion des environnements de traduction entre termes des constructions - non réifiés et variables des termes reifies. Attention il s'agit de - l'environnement initial contenant tout. Il faudra le réduire après - calcul des variables utiles. *) - -let add_reified_atom t env = - try list_index0 t env.terms - with Not_found -> - let i = List.length env.terms in - env.terms <- env.terms @ [t]; i - -let get_reified_atom env = - try List.nth env.terms with _ -> failwith "get_reified_atom" - -(* \subsection{Gestion de l'environnement de proposition pour Omega} *) -(* ajout d'une proposition *) -let add_prop env t = - try list_index0 t env.props - with Not_found -> - let i = List.length env.props in env.props <- env.props @ [t]; i - -(* accès a une proposition *) -let get_prop v env = try List.nth v env with _ -> failwith "get_prop" - -(* \subsection{Gestion du nommage des équations} *) -(* Ajout d'une equation dans l'environnement de reification *) -let add_equation env e = - let id = e.e_omega.id in - try let _ = Hashtbl.find env.equations id in () - with Not_found -> Hashtbl.add env.equations id e - -(* accès a une equation *) -let get_equation env id = - try Hashtbl.find env.equations id - with e -> Printf.printf "Omega Equation %d non trouvée\n" id; raise e - -(* Affichage des termes réifiés *) -let rec oprint ch = function - | Oint n -> Printf.fprintf ch "%s" (Bigint.to_string n) - | Oplus (t1,t2) -> Printf.fprintf ch "(%a + %a)" oprint t1 oprint t2 - | Omult (t1,t2) -> Printf.fprintf ch "(%a * %a)" oprint t1 oprint t2 - | Ominus(t1,t2) -> Printf.fprintf ch "(%a - %a)" oprint t1 oprint t2 - | Oopp t1 ->Printf.fprintf ch "~ %a" oprint t1 - | Oatom n -> Printf.fprintf ch "V%02d" n - | Oufo x -> Printf.fprintf ch "?" - -let rec pprint ch = function - Pequa (_,{ e_comp=comp; e_left=t1; e_right=t2 }) -> - let connector = - match comp with - Eq -> "=" | Leq -> "<=" | Geq -> ">=" - | Gt -> ">" | Lt -> "<" | Neq -> "!=" in - Printf.fprintf ch "%a %s %a" oprint t1 connector oprint t2 - | Ptrue -> Printf.fprintf ch "TT" - | Pfalse -> Printf.fprintf ch "FF" - | Pnot t -> Printf.fprintf ch "not(%a)" pprint t - | Por (_,t1,t2) -> Printf.fprintf ch "(%a or %a)" pprint t1 pprint t2 - | Pand(_,t1,t2) -> Printf.fprintf ch "(%a and %a)" pprint t1 pprint t2 - | Pimp(_,t1,t2) -> Printf.fprintf ch "(%a => %a)" pprint t1 pprint t2 - | Pprop c -> Printf.fprintf ch "Prop" - -let rec weight env = function - | Oint _ -> -1 - | Oopp c -> weight env c - | Omult(c,_) -> weight env c - | Oplus _ -> failwith "weight" - | Ominus _ -> failwith "weight minus" - | Oufo _ -> -1 - | Oatom _ as c -> (intern_omega env c) - -(* \section{Passage entre oformules et représentation interne de Omega} *) - -(* \subsection{Oformula vers Omega} *) - -let omega_of_oformula env kind = - let rec loop accu = function - | Oplus(Omult(v,Oint n),r) -> - loop ({v=intern_omega env v; c=n} :: accu) r - | Oint n -> - let id = new_omega_eq () in - (*i tag_equation name id; i*) - {kind = kind; body = List.rev accu; - constant = n; id = id} - | t -> print_string "CO"; oprint stdout t; failwith "compile_equation" in - loop [] - -(* \subsection{Omega vers Oformula} *) - -let rec oformula_of_omega env af = - let rec loop = function - | ({v=v; c=n}::r) -> - Oplus(Omult(unintern_omega env v,Oint n),loop r) - | [] -> Oint af.constant in - loop af.body - -let app f v = mkApp(Lazy.force f,v) - -(* \subsection{Oformula vers COQ reel} *) - -let rec coq_of_formula env t = - let rec loop = function - | Oplus (t1,t2) -> app Z.plus [| loop t1; loop t2 |] - | Oopp t -> app Z.opp [| loop t |] - | Omult(t1,t2) -> app Z.mult [| loop t1; loop t2 |] - | Oint v -> Z.mk v - | Oufo t -> loop t - | Oatom var -> - (* attention ne traite pas les nouvelles variables si on ne les - * met pas dans env.term *) - get_reified_atom env var - | Ominus(t1,t2) -> app Z.minus [| loop t1; loop t2 |] in - loop t - -(* \subsection{Oformula vers COQ reifié} *) - -let reified_of_atom env i = - try Hashtbl.find env.real_indices i - with Not_found -> - Printf.printf "Atome %d non trouvé\n" i; - Hashtbl.iter (fun k v -> Printf.printf "%d -> %d\n" k v) env.real_indices; - raise Not_found - -let rec reified_of_formula env = function - | Oplus (t1,t2) -> - app coq_t_plus [| reified_of_formula env t1; reified_of_formula env t2 |] - | Oopp t -> - app coq_t_opp [| reified_of_formula env t |] - | Omult(t1,t2) -> - app coq_t_mult [| reified_of_formula env t1; reified_of_formula env t2 |] - | Oint v -> app coq_t_int [| Z.mk v |] - | Oufo t -> reified_of_formula env t - | Oatom i -> app coq_t_var [| mk_nat (reified_of_atom env i) |] - | Ominus(t1,t2) -> - app coq_t_minus [| reified_of_formula env t1; reified_of_formula env t2 |] - -let reified_of_formula env f = - begin try reified_of_formula env f with e -> oprint stderr f; raise e end - -let rec reified_of_proposition env = function - Pequa (_,{ e_comp=Eq; e_left=t1; e_right=t2 }) -> - app coq_p_eq [| reified_of_formula env t1; reified_of_formula env t2 |] - | Pequa (_,{ e_comp=Leq; e_left=t1; e_right=t2 }) -> - app coq_p_leq [| reified_of_formula env t1; reified_of_formula env t2 |] - | Pequa(_,{ e_comp=Geq; e_left=t1; e_right=t2 }) -> - app coq_p_geq [| reified_of_formula env t1; reified_of_formula env t2 |] - | Pequa(_,{ e_comp=Gt; e_left=t1; e_right=t2 }) -> - app coq_p_gt [| reified_of_formula env t1; reified_of_formula env t2 |] - | Pequa(_,{ e_comp=Lt; e_left=t1; e_right=t2 }) -> - app coq_p_lt [| reified_of_formula env t1; reified_of_formula env t2 |] - | Pequa(_,{ e_comp=Neq; e_left=t1; e_right=t2 }) -> - app coq_p_neq [| reified_of_formula env t1; reified_of_formula env t2 |] - | Ptrue -> Lazy.force coq_p_true - | Pfalse -> Lazy.force coq_p_false - | Pnot t -> - app coq_p_not [| reified_of_proposition env t |] - | Por (_,t1,t2) -> - app coq_p_or - [| reified_of_proposition env t1; reified_of_proposition env t2 |] - | Pand(_,t1,t2) -> - app coq_p_and - [| reified_of_proposition env t1; reified_of_proposition env t2 |] - | Pimp(_,t1,t2) -> - app coq_p_imp - [| reified_of_proposition env t1; reified_of_proposition env t2 |] - | Pprop t -> app coq_p_prop [| mk_nat (add_prop env t) |] - -let reified_of_proposition env f = - begin try reified_of_proposition env f - with e -> pprint stderr f; raise e end - -(* \subsection{Omega vers COQ réifié} *) - -let reified_of_omega env body constant = - let coeff_constant = - app coq_t_int [| Z.mk constant |] in - let mk_coeff {c=c; v=v} t = - let coef = - app coq_t_mult - [| reified_of_formula env (unintern_omega env v); - app coq_t_int [| Z.mk c |] |] in - app coq_t_plus [|coef; t |] in - List.fold_right mk_coeff body coeff_constant - -let reified_of_omega env body c = - begin try - reified_of_omega env body c - with e -> - display_eq display_omega_var (body,c); raise e - end - -(* \section{Opérations sur les équations} -Ces fonctions préparent les traces utilisées par la tactique réfléchie -pour faire des opérations de normalisation sur les équations. *) - -(* \subsection{Extractions des variables d'une équation} *) -(* Extraction des variables d'une équation. *) -(* Chaque fonction retourne une liste triée sans redondance *) - -let (@@) = list_merge_uniq compare - -let rec vars_of_formula = function - | Oint _ -> [] - | Oplus (e1,e2) -> (vars_of_formula e1) @@ (vars_of_formula e2) - | Omult (e1,e2) -> (vars_of_formula e1) @@ (vars_of_formula e2) - | Ominus (e1,e2) -> (vars_of_formula e1) @@ (vars_of_formula e2) - | Oopp e -> vars_of_formula e - | Oatom i -> [i] - | Oufo _ -> [] - -let rec vars_of_equations = function - | [] -> [] - | e::l -> - (vars_of_formula e.e_left) @@ - (vars_of_formula e.e_right) @@ - (vars_of_equations l) - -let rec vars_of_prop = function - | Pequa(_,e) -> vars_of_equations [e] - | Pnot p -> vars_of_prop p - | Por(_,p1,p2) -> (vars_of_prop p1) @@ (vars_of_prop p2) - | Pand(_,p1,p2) -> (vars_of_prop p1) @@ (vars_of_prop p2) - | Pimp(_,p1,p2) -> (vars_of_prop p1) @@ (vars_of_prop p2) - | Pprop _ | Ptrue | Pfalse -> [] - -(* \subsection{Multiplication par un scalaire} *) - -let rec scalar n = function - Oplus(t1,t2) -> - let tac1,t1' = scalar n t1 and - tac2,t2' = scalar n t2 in - do_list [Lazy.force coq_c_mult_plus_distr; do_both tac1 tac2], - Oplus(t1',t2') - | Oopp t -> - do_list [Lazy.force coq_c_mult_opp_left], Omult(t,Oint(Bigint.neg n)) - | Omult(t1,Oint x) -> - do_list [Lazy.force coq_c_mult_assoc_reduced], Omult(t1,Oint (n*x)) - | Omult(t1,t2) -> - Util.error "Omega: Can't solve a goal with non-linear products" - | (Oatom _ as t) -> do_list [], Omult(t,Oint n) - | Oint i -> do_list [Lazy.force coq_c_reduce],Oint(n*i) - | (Oufo _ as t)-> do_list [], Oufo (Omult(t,Oint n)) - | Ominus _ -> failwith "scalar minus" - -(* \subsection{Propagation de l'inversion} *) - -let rec negate = function - Oplus(t1,t2) -> - let tac1,t1' = negate t1 and - tac2,t2' = negate t2 in - do_list [Lazy.force coq_c_opp_plus ; (do_both tac1 tac2)], - Oplus(t1',t2') - | Oopp t -> - do_list [Lazy.force coq_c_opp_opp], t - | Omult(t1,Oint x) -> - do_list [Lazy.force coq_c_opp_mult_r], Omult(t1,Oint (Bigint.neg x)) - | Omult(t1,t2) -> - Util.error "Omega: Can't solve a goal with non-linear products" - | (Oatom _ as t) -> - do_list [Lazy.force coq_c_opp_one], Omult(t,Oint(negone)) - | Oint i -> do_list [Lazy.force coq_c_reduce] ,Oint(Bigint.neg i) - | Oufo c -> do_list [], Oufo (Oopp c) - | Ominus _ -> failwith "negate minus" - -let rec norm l = (List.length l) - -(* \subsection{Mélange (fusion) de deux équations} *) -(* \subsubsection{Version avec coefficients} *) -let rec shuffle_path k1 e1 k2 e2 = - let rec loop = function - (({c=c1;v=v1}::l1) as l1'), - (({c=c2;v=v2}::l2) as l2') -> - if v1 = v2 then - if k1*c1 + k2 * c2 = zero then ( - Lazy.force coq_f_cancel :: loop (l1,l2)) - else ( - Lazy.force coq_f_equal :: loop (l1,l2) ) - else if v1 > v2 then ( - Lazy.force coq_f_left :: loop(l1,l2')) - else ( - Lazy.force coq_f_right :: loop(l1',l2)) - | ({c=c1;v=v1}::l1), [] -> - Lazy.force coq_f_left :: loop(l1,[]) - | [],({c=c2;v=v2}::l2) -> - Lazy.force coq_f_right :: loop([],l2) - | [],[] -> flush stdout; [] in - mk_shuffle_list (loop (e1,e2)) - -(* \subsubsection{Version sans coefficients} *) -let rec shuffle env (t1,t2) = - match t1,t2 with - Oplus(l1,r1), Oplus(l2,r2) -> - if weight env l1 > weight env l2 then - let l_action,t' = shuffle env (r1,t2) in - do_list [Lazy.force coq_c_plus_assoc_r;do_right l_action], Oplus(l1,t') - else - let l_action,t' = shuffle env (t1,r2) in - do_list [Lazy.force coq_c_plus_permute;do_right l_action], Oplus(l2,t') - | Oplus(l1,r1), t2 -> - if weight env l1 > weight env t2 then - let (l_action,t') = shuffle env (r1,t2) in - do_list [Lazy.force coq_c_plus_assoc_r;do_right l_action],Oplus(l1, t') - else do_list [Lazy.force coq_c_plus_comm], Oplus(t2,t1) - | t1,Oplus(l2,r2) -> - if weight env l2 > weight env t1 then - let (l_action,t') = shuffle env (t1,r2) in - do_list [Lazy.force coq_c_plus_permute;do_right l_action], Oplus(l2,t') - else do_list [],Oplus(t1,t2) - | Oint t1,Oint t2 -> - do_list [Lazy.force coq_c_reduce], Oint(t1+t2) - | t1,t2 -> - if weight env t1 < weight env t2 then - do_list [Lazy.force coq_c_plus_comm], Oplus(t2,t1) - else do_list [],Oplus(t1,t2) - -(* \subsection{Fusion avec réduction} *) - -let shrink_pair f1 f2 = - begin match f1,f2 with - Oatom v,Oatom _ -> - Lazy.force coq_c_red1, Omult(Oatom v,Oint two) - | Oatom v, Omult(_,c2) -> - Lazy.force coq_c_red2, Omult(Oatom v,Oplus(c2,Oint one)) - | Omult (v1,c1),Oatom v -> - Lazy.force coq_c_red3, Omult(Oatom v,Oplus(c1,Oint one)) - | Omult (Oatom v,c1),Omult (v2,c2) -> - Lazy.force coq_c_red4, Omult(Oatom v,Oplus(c1,c2)) - | t1,t2 -> - oprint stdout t1; print_newline (); oprint stdout t2; print_newline (); - flush Pervasives.stdout; Util.error "shrink.1" - end - -(* \subsection{Calcul d'une sous formule constante} *) - -let reduce_factor = function - Oatom v -> - let r = Omult(Oatom v,Oint one) in - [Lazy.force coq_c_red0],r - | Omult(Oatom v,Oint n) as f -> [],f - | Omult(Oatom v,c) -> - let rec compute = function - Oint n -> n - | Oplus(t1,t2) -> compute t1 + compute t2 - | _ -> Util.error "condense.1" in - [Lazy.force coq_c_reduce], Omult(Oatom v,Oint(compute c)) - | t -> Util.error "reduce_factor.1" - -(* \subsection{Réordonnancement} *) - -let rec condense env = function - Oplus(f1,(Oplus(f2,r) as t)) -> - if weight env f1 = weight env f2 then begin - let shrink_tac,t = shrink_pair f1 f2 in - let assoc_tac = Lazy.force coq_c_plus_assoc_l in - let tac_list,t' = condense env (Oplus(t,r)) in - assoc_tac :: do_left (do_list [shrink_tac]) :: tac_list, t' - end else begin - let tac,f = reduce_factor f1 in - let tac',t' = condense env t in - [do_both (do_list tac) (do_list tac')], Oplus(f,t') - end - | Oplus(f1,Oint n) -> - let tac,f1' = reduce_factor f1 in - [do_left (do_list tac)],Oplus(f1',Oint n) - | Oplus(f1,f2) -> - if weight env f1 = weight env f2 then begin - let tac_shrink,t = shrink_pair f1 f2 in - let tac,t' = condense env t in - tac_shrink :: tac,t' - end else begin - let tac,f = reduce_factor f1 in - let tac',t' = condense env f2 in - [do_both (do_list tac) (do_list tac')],Oplus(f,t') - end - | (Oint _ as t)-> [],t - | t -> - let tac,t' = reduce_factor t in - let final = Oplus(t',Oint zero) in - tac @ [Lazy.force coq_c_red6], final - -(* \subsection{Elimination des zéros} *) - -let rec clear_zero = function - Oplus(Omult(Oatom v,Oint n),r) when n=zero -> - let tac',t = clear_zero r in - Lazy.force coq_c_red5 :: tac',t - | Oplus(f,r) -> - let tac,t = clear_zero r in - (if tac = [] then [] else [do_right (do_list tac)]),Oplus(f,t) - | t -> [],t;; - -(* \subsection{Transformation des hypothèses} *) - -let rec reduce env = function - Oplus(t1,t2) -> - let t1', trace1 = reduce env t1 in - let t2', trace2 = reduce env t2 in - let trace3,t' = shuffle env (t1',t2') in - t', do_list [do_both trace1 trace2; trace3] - | Ominus(t1,t2) -> - let t,trace = reduce env (Oplus(t1, Oopp t2)) in - t, do_list [Lazy.force coq_c_minus; trace] - | Omult(t1,t2) as t -> - let t1', trace1 = reduce env t1 in - let t2', trace2 = reduce env t2 in - begin match t1',t2' with - | (_, Oint n) -> - let tac,t' = scalar n t1' in - t', do_list [do_both trace1 trace2; tac] - | (Oint n,_) -> - let tac,t' = scalar n t2' in - t', do_list [do_both trace1 trace2; Lazy.force coq_c_mult_comm; tac] - | _ -> Oufo t, Lazy.force coq_c_nop - end - | Oopp t -> - let t',trace = reduce env t in - let trace',t'' = negate t' in - t'', do_list [do_left trace; trace'] - | (Oint _ | Oatom _ | Oufo _) as t -> t, Lazy.force coq_c_nop - -let normalize_linear_term env t = - let t1,trace1 = reduce env t in - let trace2,t2 = condense env t1 in - let trace3,t3 = clear_zero t2 in - do_list [trace1; do_list trace2; do_list trace3], t3 - -(* Cette fonction reproduit très exactement le comportement de [p_invert] *) -let negate_oper = function - Eq -> Neq | Neq -> Eq | Leq -> Gt | Geq -> Lt | Lt -> Geq | Gt -> Leq - -let normalize_equation env (negated,depends,origin,path) (oper,t1,t2) = - let mk_step t1 t2 f kind = - let t = f t1 t2 in - let trace, oterm = normalize_linear_term env t in - let equa = omega_of_oformula env kind oterm in - { e_comp = oper; e_left = t1; e_right = t2; - e_negated = negated; e_depends = depends; - e_origin = { o_hyp = origin; o_path = List.rev path }; - e_trace = trace; e_omega = equa } in - try match (if negated then (negate_oper oper) else oper) with - | Eq -> mk_step t1 t2 (fun o1 o2 -> Oplus (o1,Oopp o2)) EQUA - | Neq -> mk_step t1 t2 (fun o1 o2 -> Oplus (o1,Oopp o2)) DISE - | Leq -> mk_step t1 t2 (fun o1 o2 -> Oplus (o2,Oopp o1)) INEQ - | Geq -> mk_step t1 t2 (fun o1 o2 -> Oplus (o1,Oopp o2)) INEQ - | Lt -> - mk_step t1 t2 (fun o1 o2 -> Oplus (Oplus(o2,Oint negone),Oopp o1)) - INEQ - | Gt -> - mk_step t1 t2 (fun o1 o2 -> Oplus (Oplus(o1,Oint negone),Oopp o2)) - INEQ - with e when Logic.catchable_exception e -> raise e - -(* \section{Compilation des hypothèses} *) - -let rec oformula_of_constr env t = - match Z.parse_term t with - | Tplus (t1,t2) -> binop env (fun x y -> Oplus(x,y)) t1 t2 - | Tminus (t1,t2) -> binop env (fun x y -> Ominus(x,y)) t1 t2 - | Tmult (t1,t2) when Z.is_scalar t1 || Z.is_scalar t2 -> - binop env (fun x y -> Omult(x,y)) t1 t2 - | Topp t -> Oopp(oformula_of_constr env t) - | Tsucc t -> Oplus(oformula_of_constr env t, Oint one) - | Tnum n -> Oint n - | _ -> Oatom (add_reified_atom t env) - -and binop env c t1 t2 = - let t1' = oformula_of_constr env t1 in - let t2' = oformula_of_constr env t2 in - c t1' t2' - -and binprop env (neg2,depends,origin,path) - add_to_depends neg1 gl c t1 t2 = - let i = new_connector_id env in - let depends1 = if add_to_depends then Left i::depends else depends in - let depends2 = if add_to_depends then Right i::depends else depends in - if add_to_depends then - Hashtbl.add env.constructors i {o_hyp = origin; o_path = List.rev path}; - let t1' = - oproposition_of_constr env (neg1,depends1,origin,O_left::path) gl t1 in - let t2' = - oproposition_of_constr env (neg2,depends2,origin,O_right::path) gl t2 in - (* On numérote le connecteur dans l'environnement. *) - c i t1' t2' - -and mk_equation env ctxt c connector t1 t2 = - let t1' = oformula_of_constr env t1 in - let t2' = oformula_of_constr env t2 in - (* On ajoute l'equation dans l'environnement. *) - let omega = normalize_equation env ctxt (connector,t1',t2') in - add_equation env omega; - Pequa (c,omega) - -and oproposition_of_constr env ((negated,depends,origin,path) as ctxt) gl c = - match Z.parse_rel gl c with - | Req (t1,t2) -> mk_equation env ctxt c Eq t1 t2 - | Rne (t1,t2) -> mk_equation env ctxt c Neq t1 t2 - | Rle (t1,t2) -> mk_equation env ctxt c Leq t1 t2 - | Rlt (t1,t2) -> mk_equation env ctxt c Lt t1 t2 - | Rge (t1,t2) -> mk_equation env ctxt c Geq t1 t2 - | Rgt (t1,t2) -> mk_equation env ctxt c Gt t1 t2 - | Rtrue -> Ptrue - | Rfalse -> Pfalse - | Rnot t -> - let t' = - oproposition_of_constr - env (not negated, depends, origin,(O_mono::path)) gl t in - Pnot t' - | Ror (t1,t2) -> - binprop env ctxt (not negated) negated gl (fun i x y -> Por(i,x,y)) t1 t2 - | Rand (t1,t2) -> - binprop env ctxt negated negated gl - (fun i x y -> Pand(i,x,y)) t1 t2 - | Rimp (t1,t2) -> - binprop env ctxt (not negated) (not negated) gl - (fun i x y -> Pimp(i,x,y)) t1 t2 - | Riff (t1,t2) -> - binprop env ctxt negated negated gl - (fun i x y -> Pand(i,x,y)) (Term.mkArrow t1 t2) (Term.mkArrow t2 t1) - | _ -> Pprop c - -(* Destructuration des hypothèses et de la conclusion *) - -let reify_gl env gl = - let concl = Tacmach.pf_concl gl in - let t_concl = - Pnot (oproposition_of_constr env (true,[],id_concl,[O_mono]) gl concl) in - if !debug then begin - Printf.printf "REIFED PROBLEM\n\n"; - Printf.printf " CONCL: "; pprint stdout t_concl; Printf.printf "\n" - end; - let rec loop = function - (i,t) :: lhyps -> - let t' = oproposition_of_constr env (false,[],i,[]) gl t in - if !debug then begin - Printf.printf " %s: " (Names.string_of_id i); - pprint stdout t'; - Printf.printf "\n" - end; - (i,t') :: loop lhyps - | [] -> - if !debug then print_env_reification env; - [] in - let t_lhyps = loop (Tacmach.pf_hyps_types gl) in - (id_concl,t_concl) :: t_lhyps - -let rec destructurate_pos_hyp orig list_equations list_depends = function - | Pequa (_,e) -> [e :: list_equations] - | Ptrue | Pfalse | Pprop _ -> [list_equations] - | Pnot t -> destructurate_neg_hyp orig list_equations list_depends t - | Por (i,t1,t2) -> - let s1 = - destructurate_pos_hyp orig list_equations (i::list_depends) t1 in - let s2 = - destructurate_pos_hyp orig list_equations (i::list_depends) t2 in - s1 @ s2 - | Pand(i,t1,t2) -> - let list_s1 = - destructurate_pos_hyp orig list_equations (list_depends) t1 in - let rec loop = function - le1 :: ll -> destructurate_pos_hyp orig le1 list_depends t2 @ loop ll - | [] -> [] in - loop list_s1 - | Pimp(i,t1,t2) -> - let s1 = - destructurate_neg_hyp orig list_equations (i::list_depends) t1 in - let s2 = - destructurate_pos_hyp orig list_equations (i::list_depends) t2 in - s1 @ s2 - -and destructurate_neg_hyp orig list_equations list_depends = function - | Pequa (_,e) -> [e :: list_equations] - | Ptrue | Pfalse | Pprop _ -> [list_equations] - | Pnot t -> destructurate_pos_hyp orig list_equations list_depends t - | Pand (i,t1,t2) -> - let s1 = - destructurate_neg_hyp orig list_equations (i::list_depends) t1 in - let s2 = - destructurate_neg_hyp orig list_equations (i::list_depends) t2 in - s1 @ s2 - | Por(_,t1,t2) -> - let list_s1 = - destructurate_neg_hyp orig list_equations list_depends t1 in - let rec loop = function - le1 :: ll -> destructurate_neg_hyp orig le1 list_depends t2 @ loop ll - | [] -> [] in - loop list_s1 - | Pimp(_,t1,t2) -> - let list_s1 = - destructurate_pos_hyp orig list_equations list_depends t1 in - let rec loop = function - le1 :: ll -> destructurate_neg_hyp orig le1 list_depends t2 @ loop ll - | [] -> [] in - loop list_s1 - -let destructurate_hyps syst = - let rec loop = function - (i,t) :: l -> - let l_syst1 = destructurate_pos_hyp i [] [] t in - let l_syst2 = loop l in - list_cartesian (@) l_syst1 l_syst2 - | [] -> [[]] in - loop syst - -(* \subsection{Affichage d'un système d'équation} *) - -(* Affichage des dépendances de système *) -let display_depend = function - Left i -> Printf.printf " L%d" i - | Right i -> Printf.printf " R%d" i - -let display_systems syst_list = - let display_omega om_e = - Printf.printf " E%d : %a %s 0\n" - om_e.id - (fun _ -> display_eq display_omega_var) - (om_e.body, om_e.constant) - (operator_of_eq om_e.kind) in - - let display_equation oformula_eq = - pprint stdout (Pequa (Lazy.force coq_c_nop,oformula_eq)); print_newline (); - display_omega oformula_eq.e_omega; - Printf.printf " Depends on:"; - List.iter display_depend oformula_eq.e_depends; - Printf.printf "\n Path: %s" - (String.concat "" - (List.map (function O_left -> "L" | O_right -> "R" | O_mono -> "M") - oformula_eq.e_origin.o_path)); - Printf.printf "\n Origin: %s (negated : %s)\n\n" - (Names.string_of_id oformula_eq.e_origin.o_hyp) - (if oformula_eq.e_negated then "yes" else "no") in - - let display_system syst = - Printf.printf "=SYSTEM===================================\n"; - List.iter display_equation syst in - List.iter display_system syst_list - -(* Extraction des prédicats utilisées dans une trace. Permet ensuite le - calcul des hypothèses *) - -let rec hyps_used_in_trace = function - | act :: l -> - begin match act with - | HYP e -> [e.id] @@ (hyps_used_in_trace l) - | SPLIT_INEQ (_,(_,act1),(_,act2)) -> - hyps_used_in_trace act1 @@ hyps_used_in_trace act2 - | _ -> hyps_used_in_trace l - end - | [] -> [] - -(* Extraction des variables déclarées dans une équation. Permet ensuite - de les déclarer dans l'environnement de la procédure réflexive et - éviter les créations de variable au vol *) - -let rec variable_stated_in_trace = function - | act :: l -> - begin match act with - | STATE action -> - (*i nlle_equa: afine, def: afine, eq_orig: afine, i*) - (*i coef: int, var:int i*) - action :: variable_stated_in_trace l - | SPLIT_INEQ (_,(_,act1),(_,act2)) -> - variable_stated_in_trace act1 @ variable_stated_in_trace act2 - | _ -> variable_stated_in_trace l - end - | [] -> [] -;; - -let add_stated_equations env tree = - (* Il faut trier les variables par ordre d'introduction pour ne pas risquer - de définir dans le mauvais ordre *) - let stated_equations = - let cmpvar x y = Pervasives.(-) x.st_var y.st_var in - let rec loop = function - | Tree(_,t1,t2) -> List.merge cmpvar (loop t1) (loop t2) - | Leaf s -> List.sort cmpvar (variable_stated_in_trace s.s_trace) - in loop tree - in - let add_env st = - (* On retransforme la définition de v en formule reifiée *) - let v_def = oformula_of_omega env st.st_def in - (* Notez que si l'ordre de création des variables n'est pas respecté, - * ca va planter *) - let coq_v = coq_of_formula env v_def in - let v = add_reified_atom coq_v env in - (* Le terme qu'il va falloir introduire *) - let term_to_generalize = app coq_refl_equal [|Lazy.force Z.typ; coq_v|] in - (* sa représentation sous forme d'équation mais non réifié car on n'a pas - * l'environnement pour le faire correctement *) - let term_to_reify = (v_def,Oatom v) in - (* enregistre le lien entre la variable omega et la variable Coq *) - intern_omega_force env (Oatom v) st.st_var; - (v, term_to_generalize,term_to_reify,st.st_def.id) in - List.map add_env stated_equations - -(* Calcule la liste des éclatements à réaliser sur les hypothèses - nécessaires pour extraire une liste d'équations donnée *) - -(* PL: experimentally, the result order of the following function seems - _very_ crucial for efficiency. No idea why. Do not remove the List.rev - or modify the current semantics of Util.list_union (some elements of first - arg, then second arg), unless you know what you're doing. *) - -let rec get_eclatement env = function - i :: r -> - let l = try (get_equation env i).e_depends with Not_found -> [] in - list_union (List.rev l) (get_eclatement env r) - | [] -> [] - -let select_smaller l = - let comp (_,x) (_,y) = Pervasives.(-) (List.length x) (List.length y) in - try List.hd (List.sort comp l) with Failure _ -> failwith "select_smaller" - -let filter_compatible_systems required systems = - let rec select = function - (x::l) -> - if List.mem x required then select l - else if List.mem (barre x) required then failwith "Exit" - else x :: select l - | [] -> [] in - map_succeed (function (sol,splits) -> (sol,select splits)) systems - -let rec equas_of_solution_tree = function - Tree(_,t1,t2) -> (equas_of_solution_tree t1)@@(equas_of_solution_tree t2) - | Leaf s -> s.s_equa_deps - -(* [really_useful_prop] pushes useless props in a new Pprop variable *) -(* Things get shorter, but may also get wrong, since a Prop is considered - to be undecidable in ReflOmegaCore.concl_to_hyp, whereas for instance - Pfalse is decidable. So should not be used on conclusion (??) *) - -let really_useful_prop l_equa c = - let rec real_of = function - Pequa(t,_) -> t - | Ptrue -> app coq_True [||] - | Pfalse -> app coq_False [||] - | Pnot t1 -> app coq_not [|real_of t1|] - | Por(_,t1,t2) -> app coq_or [|real_of t1; real_of t2|] - | Pand(_,t1,t2) -> app coq_and [|real_of t1; real_of t2|] - (* Attention : implications sur le lifting des variables à comprendre ! *) - | Pimp(_,t1,t2) -> Term.mkArrow (real_of t1) (real_of t2) - | Pprop t -> t in - let rec loop c = - match c with - Pequa(_,e) -> - if List.mem e.e_omega.id l_equa then Some c else None - | Ptrue -> None - | Pfalse -> None - | Pnot t1 -> - begin match loop t1 with None -> None | Some t1' -> Some (Pnot t1') end - | Por(i,t1,t2) -> binop (fun (t1,t2) -> Por(i,t1,t2)) t1 t2 - | Pand(i,t1,t2) -> binop (fun (t1,t2) -> Pand(i,t1,t2)) t1 t2 - | Pimp(i,t1,t2) -> binop (fun (t1,t2) -> Pimp(i,t1,t2)) t1 t2 - | Pprop t -> None - and binop f t1 t2 = - begin match loop t1, loop t2 with - None, None -> None - | Some t1',Some t2' -> Some (f(t1',t2')) - | Some t1',None -> Some (f(t1',Pprop (real_of t2))) - | None,Some t2' -> Some (f(Pprop (real_of t1),t2')) - end in - match loop c with - None -> Pprop (real_of c) - | Some t -> t - -let rec display_solution_tree ch = function - Leaf t -> - output_string ch - (Printf.sprintf "%d[%s]" - t.s_index - (String.concat " " (List.map string_of_int t.s_equa_deps))) - | Tree(i,t1,t2) -> - Printf.fprintf ch "S%d(%a,%a)" i - display_solution_tree t1 display_solution_tree t2 - -let rec solve_with_constraints all_solutions path = - let rec build_tree sol buf = function - [] -> Leaf sol - | (Left i :: remainder) -> - Tree(i, - build_tree sol (Left i :: buf) remainder, - solve_with_constraints all_solutions (List.rev(Right i :: buf))) - | (Right i :: remainder) -> - Tree(i, - solve_with_constraints all_solutions (List.rev (Left i :: buf)), - build_tree sol (Right i :: buf) remainder) in - let weighted = filter_compatible_systems path all_solutions in - let (winner_sol,winner_deps) = - try select_smaller weighted - with e -> - Printf.printf "%d - %d\n" - (List.length weighted) (List.length all_solutions); - List.iter display_depend path; raise e in - build_tree winner_sol (List.rev path) winner_deps - -let find_path {o_hyp=id;o_path=p} env = - let rec loop_path = function - ([],l) -> Some l - | (x1::l1,x2::l2) when x1 = x2 -> loop_path (l1,l2) - | _ -> None in - let rec loop_id i = function - CCHyp{o_hyp=id';o_path=p'} :: l when id = id' -> - begin match loop_path (p',p) with - Some r -> i,r - | None -> loop_id (succ i) l - end - | _ :: l -> loop_id (succ i) l - | [] -> failwith "find_path" in - loop_id 0 env - -let mk_direction_list l = - let trans = function - O_left -> coq_d_left | O_right -> coq_d_right | O_mono -> coq_d_mono in - mk_list (Lazy.force coq_direction) (List.map (fun d-> Lazy.force(trans d)) l) - - -(* \section{Rejouer l'historique} *) - -let get_hyp env_hyp i = - try list_index0 (CCEqua i) env_hyp - with Not_found -> failwith (Printf.sprintf "get_hyp %d" i) - -let replay_history env env_hyp = - let rec loop env_hyp t = - match t with - | CONTRADICTION (e1,e2) :: l -> - let trace = mk_nat (List.length e1.body) in - mkApp (Lazy.force coq_s_contradiction, - [| trace ; mk_nat (get_hyp env_hyp e1.id); - mk_nat (get_hyp env_hyp e2.id) |]) - | DIVIDE_AND_APPROX (e1,e2,k,d) :: l -> - mkApp (Lazy.force coq_s_div_approx, - [| Z.mk k; Z.mk d; - reified_of_omega env e2.body e2.constant; - mk_nat (List.length e2.body); - loop env_hyp l; mk_nat (get_hyp env_hyp e1.id) |]) - | NOT_EXACT_DIVIDE (e1,k) :: l -> - let e2_constant = floor_div e1.constant k in - let d = e1.constant - e2_constant * k in - let e2_body = map_eq_linear (fun c -> c / k) e1.body in - mkApp (Lazy.force coq_s_not_exact_divide, - [|Z.mk k; Z.mk d; - reified_of_omega env e2_body e2_constant; - mk_nat (List.length e2_body); - mk_nat (get_hyp env_hyp e1.id)|]) - | EXACT_DIVIDE (e1,k) :: l -> - let e2_body = - map_eq_linear (fun c -> c / k) e1.body in - let e2_constant = floor_div e1.constant k in - mkApp (Lazy.force coq_s_exact_divide, - [|Z.mk k; - reified_of_omega env e2_body e2_constant; - mk_nat (List.length e2_body); - loop env_hyp l; mk_nat (get_hyp env_hyp e1.id)|]) - | (MERGE_EQ(e3,e1,e2)) :: l -> - let n1 = get_hyp env_hyp e1.id and n2 = get_hyp env_hyp e2 in - mkApp (Lazy.force coq_s_merge_eq, - [| mk_nat (List.length e1.body); - mk_nat n1; mk_nat n2; - loop (CCEqua e3:: env_hyp) l |]) - | SUM(e3,(k1,e1),(k2,e2)) :: l -> - let n1 = get_hyp env_hyp e1.id - and n2 = get_hyp env_hyp e2.id in - let trace = shuffle_path k1 e1.body k2 e2.body in - mkApp (Lazy.force coq_s_sum, - [| Z.mk k1; mk_nat n1; Z.mk k2; - mk_nat n2; trace; (loop (CCEqua e3 :: env_hyp) l) |]) - | CONSTANT_NOT_NUL(e,k) :: l -> - mkApp (Lazy.force coq_s_constant_not_nul, - [| mk_nat (get_hyp env_hyp e) |]) - | CONSTANT_NEG(e,k) :: l -> - mkApp (Lazy.force coq_s_constant_neg, - [| mk_nat (get_hyp env_hyp e) |]) - | STATE {st_new_eq=new_eq; st_def =def; - st_orig=orig; st_coef=m; - st_var=sigma } :: l -> - let n1 = get_hyp env_hyp orig.id - and n2 = get_hyp env_hyp def.id in - let v = unintern_omega env sigma in - let o_def = oformula_of_omega env def in - let o_orig = oformula_of_omega env orig in - let body = - Oplus (o_orig,Omult (Oplus (Oopp v,o_def), Oint m)) in - let trace,_ = normalize_linear_term env body in - mkApp (Lazy.force coq_s_state, - [| Z.mk m; trace; mk_nat n1; mk_nat n2; - loop (CCEqua new_eq.id :: env_hyp) l |]) - | HYP _ :: l -> loop env_hyp l - | CONSTANT_NUL e :: l -> - mkApp (Lazy.force coq_s_constant_nul, - [| mk_nat (get_hyp env_hyp e) |]) - | NEGATE_CONTRADICT(e1,e2,true) :: l -> - mkApp (Lazy.force coq_s_negate_contradict, - [| mk_nat (get_hyp env_hyp e1.id); - mk_nat (get_hyp env_hyp e2.id) |]) - | NEGATE_CONTRADICT(e1,e2,false) :: l -> - mkApp (Lazy.force coq_s_negate_contradict_inv, - [| mk_nat (List.length e2.body); - mk_nat (get_hyp env_hyp e1.id); - mk_nat (get_hyp env_hyp e2.id) |]) - | SPLIT_INEQ(e,(e1,l1),(e2,l2)) :: l -> - let i = get_hyp env_hyp e.id in - let r1 = loop (CCEqua e1 :: env_hyp) l1 in - let r2 = loop (CCEqua e2 :: env_hyp) l2 in - mkApp (Lazy.force coq_s_split_ineq, - [| mk_nat (List.length e.body); mk_nat i; r1 ; r2 |]) - | (FORGET_C _ | FORGET _ | FORGET_I _) :: l -> - loop env_hyp l - | (WEAKEN _ ) :: l -> failwith "not_treated" - | [] -> failwith "no contradiction" - in loop env_hyp - -let rec decompose_tree env ctxt = function - Tree(i,left,right) -> - let org = - try Hashtbl.find env.constructors i - with Not_found -> - failwith (Printf.sprintf "Cannot find constructor %d" i) in - let (index,path) = find_path org ctxt in - let left_hyp = CCHyp{o_hyp=org.o_hyp;o_path=org.o_path @ [O_left]} in - let right_hyp = CCHyp{o_hyp=org.o_hyp;o_path=org.o_path @ [O_right]} in - app coq_e_split - [| mk_nat index; - mk_direction_list path; - decompose_tree env (left_hyp::ctxt) left; - decompose_tree env (right_hyp::ctxt) right |] - | Leaf s -> - decompose_tree_hyps s.s_trace env ctxt s.s_equa_deps -and decompose_tree_hyps trace env ctxt = function - [] -> app coq_e_solve [| replay_history env ctxt trace |] - | (i::l) -> - let equation = - try Hashtbl.find env.equations i - with Not_found -> - failwith (Printf.sprintf "Cannot find equation %d" i) in - let (index,path) = find_path equation.e_origin ctxt in - let full_path = if equation.e_negated then path @ [O_mono] else path in - let cont = - decompose_tree_hyps trace env - (CCEqua equation.e_omega.id :: ctxt) l in - app coq_e_extract [|mk_nat index; - mk_direction_list full_path; - cont |] - -(* \section{La fonction principale} *) - (* Cette fonction construit la -trace pour la procédure de décision réflexive. A partir des résultats -de l'extraction des systèmes, elle lance la résolution par Omega, puis -l'extraction d'un ensemble minimal de solutions permettant la -résolution globale du système et enfin construit la trace qui permet -de faire rejouer cette solution par la tactique réflexive. *) - -let resolution env full_reified_goal systems_list = - let num = ref 0 in - let solve_system list_eq = - let index = !num in - let system = List.map (fun eq -> eq.e_omega) list_eq in - let trace = - simplify_strong - (new_omega_eq,new_omega_var,display_omega_var) - system in - (* calcule les hypotheses utilisées pour la solution *) - let vars = hyps_used_in_trace trace in - let splits = get_eclatement env vars in - if !debug then begin - Printf.printf "SYSTEME %d\n" index; - display_action display_omega_var trace; - print_string "\n Depend :"; - List.iter (fun i -> Printf.printf " %d" i) vars; - print_string "\n Split points :"; - List.iter display_depend splits; - Printf.printf "\n------------------------------------\n" - end; - incr num; - {s_index = index; s_trace = trace; s_equa_deps = vars}, splits in - if !debug then Printf.printf "\n====================================\n"; - let all_solutions = List.map solve_system systems_list in - let solution_tree = solve_with_constraints all_solutions [] in - if !debug then begin - display_solution_tree stdout solution_tree; - print_newline() - end; - (* calcule la liste de toutes les hypothèses utilisées dans l'arbre de solution *) - let useful_equa_id = equas_of_solution_tree solution_tree in - (* recupere explicitement ces equations *) - let equations = List.map (get_equation env) useful_equa_id in - let l_hyps' = list_uniquize (List.map (fun e -> e.e_origin.o_hyp) equations) in - let l_hyps = id_concl :: list_remove id_concl l_hyps' in - let useful_hyps = - List.map (fun id -> List.assoc id full_reified_goal) l_hyps in - let useful_vars = - let really_useful_vars = vars_of_equations equations in - let concl_vars = vars_of_prop (List.assoc id_concl full_reified_goal) in - really_useful_vars @@ concl_vars - in - (* variables a introduire *) - let to_introduce = add_stated_equations env solution_tree in - let stated_vars = List.map (fun (v,_,_,_) -> v) to_introduce in - let l_generalize_arg = List.map (fun (_,t,_,_) -> t) to_introduce in - let hyp_stated_vars = List.map (fun (_,_,_,id) -> CCEqua id) to_introduce in - (* L'environnement de base se construit en deux morceaux : - - les variables des équations utiles (et de la conclusion) - - les nouvelles variables declarées durant les preuves *) - let all_vars_env = useful_vars @ stated_vars in - let basic_env = - let rec loop i = function - var :: l -> - let t = get_reified_atom env var in - Hashtbl.add env.real_indices var i; t :: loop (succ i) l - | [] -> [] in - loop 0 all_vars_env in - let env_terms_reified = mk_list (Lazy.force Z.typ) basic_env in - (* On peut maintenant généraliser le but : env est a jour *) - let l_reified_stated = - List.map (fun (_,_,(l,r),_) -> - app coq_p_eq [| reified_of_formula env l; - reified_of_formula env r |]) - to_introduce in - let reified_concl = - match useful_hyps with - (Pnot p) :: _ -> reified_of_proposition env p - | _ -> reified_of_proposition env Pfalse in - let l_reified_terms = - (List.map - (fun p -> - reified_of_proposition env (really_useful_prop useful_equa_id p)) - (List.tl useful_hyps)) in - let env_props_reified = mk_plist env.props in - let reified_goal = - mk_list (Lazy.force coq_proposition) - (l_reified_stated @ l_reified_terms) in - let reified = - app coq_interp_sequent - [| reified_concl;env_props_reified;env_terms_reified;reified_goal|] in - let normalize_equation e = - let rec loop = function - [] -> app (if e.e_negated then coq_p_invert else coq_p_step) - [| e.e_trace |] - | ((O_left | O_mono) :: l) -> app coq_p_left [| loop l |] - | (O_right :: l) -> app coq_p_right [| loop l |] in - let correct_index = - let i = list_index0 e.e_origin.o_hyp l_hyps in - (* PL: it seems that additionnally introduced hyps are in the way during - normalization, hence this index shifting... *) - if i=0 then 0 else Pervasives.(+) i (List.length to_introduce) - in - app coq_pair_step [| mk_nat correct_index; loop e.e_origin.o_path |] in - let normalization_trace = - mk_list (Lazy.force coq_h_step) (List.map normalize_equation equations) in - - let initial_context = - List.map (fun id -> CCHyp{o_hyp=id;o_path=[]}) (List.tl l_hyps) in - let context = - CCHyp{o_hyp=id_concl;o_path=[]} :: hyp_stated_vars @ initial_context in - let decompose_tactic = decompose_tree env context solution_tree in - - Tactics.generalize - (l_generalize_arg @ List.map Term.mkVar (List.tl l_hyps)) >> - Tactics.change_in_concl None reified >> - Tactics.apply (app coq_do_omega [|decompose_tactic; normalization_trace|]) >> - show_goal >> - Tactics.normalise_vm_in_concl >> - (*i Alternatives to the previous line: - - Normalisation without VM: - Tactics.normalise_in_concl - - Skip the conversion check and rely directly on the QED: - Tacmach.convert_concl_no_check (Lazy.force coq_True) Term.VMcast >> - i*) - Tactics.apply (Lazy.force coq_I) - -let total_reflexive_omega_tactic gl = - Coqlib.check_required_library ["Coq";"romega";"ROmega"]; - rst_omega_eq (); - rst_omega_var (); - try - let env = new_environment () in - let full_reified_goal = reify_gl env gl in - let systems_list = destructurate_hyps full_reified_goal in - if !debug then display_systems systems_list; - resolution env full_reified_goal systems_list gl - with NO_CONTRADICTION -> Util.error "ROmega can't solve this system" - - -(*i let tester = Tacmach.hide_atomic_tactic "TestOmega" test_tactic i*) - - |