diff options
Diffstat (limited to 'contrib/romega/const_omega.ml')
-rw-r--r-- | contrib/romega/const_omega.ml | 260 |
1 files changed, 148 insertions, 112 deletions
diff --git a/contrib/romega/const_omega.ml b/contrib/romega/const_omega.ml index 69b4b2de..bdec6bf4 100644 --- a/contrib/romega/const_omega.ml +++ b/contrib/romega/const_omega.ml @@ -48,64 +48,16 @@ let dest_const_apply t = | _ -> raise Destruct in Nametab.id_of_global ref, args -let recognize_number t = - let rec loop t = - let f,l = dest_const_apply t in - match Names.string_of_id f,l with - "xI",[t] -> Bigint.add Bigint.one (Bigint.mult Bigint.two (loop t)) - | "xO",[t] -> Bigint.mult Bigint.two (loop t) - | "xH",[] -> Bigint.one - | _ -> failwith "not a number" in - let f,l = dest_const_apply t in - match Names.string_of_id f,l with - "Zpos",[t] -> loop t - | "Zneg",[t] -> Bigint.neg (loop t) - | "Z0",[] -> Bigint.zero - | _ -> failwith "not a number";; - - let logic_dir = ["Coq";"Logic";"Decidable"] let coq_modules = Coqlib.init_modules @ [logic_dir] @ Coqlib.arith_modules @ Coqlib.zarith_base_modules - @ [["Coq"; "omega"; "OmegaLemmas"]] @ [["Coq"; "Lists"; "List"]] @ [module_refl_path] - + @ [module_refl_path@["ZOmega"]] let constant = Coqlib.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_Z0 = lazy (constant "Z0") -let coq_Zpos = lazy (constant "Zpos") -let coq_Zneg = lazy (constant "Zneg") -let coq_Z = lazy (constant "Z") -let coq_comparison = lazy (constant "comparison") -let coq_Gt = lazy (constant "Gt") -let coq_Lt = 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_Zsucc = lazy (constant "Zsucc") -let coq_Zgt = lazy (constant "Zgt") -let coq_Zle = lazy (constant "Zle") -let coq_Z_of_nat = lazy (constant "Z_of_nat") - -(* Peano *) -let coq_le = lazy(constant "le") -let coq_gt = lazy(constant "gt") - -(* Integers *) -let coq_nat = lazy(constant "nat") -let coq_S = lazy(constant "S") -let coq_O = lazy(constant "O") -let coq_minus = lazy(constant "minus") - (* Logic *) let coq_eq = lazy(constant "eq") let coq_refl_equal = lazy(constant "refl_equal") @@ -114,15 +66,9 @@ let coq_not = lazy(constant "not") let coq_or = lazy(constant "or") let coq_True = lazy(constant "True") let coq_False = lazy(constant "False") -let coq_ex = lazy(constant "ex") let coq_I = lazy(constant "I") -(* Lists *) -let coq_cons = lazy (constant "cons") -let coq_nil = lazy (constant "nil") - -let coq_pcons = lazy (constant "Pcons") -let coq_pnil = lazy (constant "Pnil") +(* ReflOmegaCore/ZOmega *) let coq_h_step = lazy (constant "h_step") let coq_pair_step = lazy (constant "pair_step") @@ -130,8 +76,6 @@ let coq_p_left = lazy (constant "P_LEFT") let coq_p_right = lazy (constant "P_RIGHT") let coq_p_invert = lazy (constant "P_INVERT") let coq_p_step = lazy (constant "P_STEP") -let coq_p_nop = lazy (constant "P_NOP") - let coq_t_int = lazy (constant "Tint") let coq_t_plus = lazy (constant "Tplus") @@ -140,6 +84,7 @@ let coq_t_opp = lazy (constant "Topp") let coq_t_minus = lazy (constant "Tminus") let coq_t_var = lazy (constant "Tvar") +let coq_proposition = lazy (constant "proposition") let coq_p_eq = lazy (constant "EqTerm") let coq_p_leq = lazy (constant "LeqTerm") let coq_p_geq = lazy (constant "GeqTerm") @@ -154,14 +99,6 @@ let coq_p_and = lazy (constant "Tand") let coq_p_imp = lazy (constant "Timp") let coq_p_prop = lazy (constant "Tprop") -let coq_proposition = lazy (constant "proposition") -let coq_interp_sequent = lazy (constant "interp_goal_concl") -let coq_normalize_sequent = lazy (constant "normalize_goal") -let coq_execute_sequent = lazy (constant "execute_goal") -let coq_do_concl_to_hyp = lazy (constant "do_concl_to_hyp") -let coq_sequent_to_hyps = lazy (constant "goal_to_hyps") -let coq_normalize_hyps_goal = lazy (constant "normalize_hyps_goal") - (* Constructors for shuffle tactic *) let coq_t_fusion = lazy (constant "t_fusion") let coq_f_equal = lazy (constant "F_equal") @@ -170,7 +107,6 @@ let coq_f_left = lazy (constant "F_left") let coq_f_right = lazy (constant "F_right") (* Constructors for reordering tactics *) -let coq_step = lazy (constant "step") let coq_c_do_both = lazy (constant "C_DO_BOTH") let coq_c_do_left = lazy (constant "C_LEFT") let coq_c_do_right = lazy (constant "C_RIGHT") @@ -196,8 +132,7 @@ let coq_c_red4 = lazy (constant "C_RED4") let coq_c_red5 = lazy (constant "C_RED5") let coq_c_red6 = lazy (constant "C_RED6") let coq_c_mult_opp_left = lazy (constant "C_MULT_OPP_LEFT") -let coq_c_mult_assoc_reduced = - lazy (constant "C_MULT_ASSOC_REDUCED") +let coq_c_mult_assoc_reduced = lazy (constant "C_MULT_ASSOC_REDUCED") let coq_c_minus = lazy (constant "C_MINUS") let coq_c_mult_comm = lazy (constant "C_MULT_COMM") @@ -225,30 +160,11 @@ let coq_e_split = lazy (constant "E_SPLIT") let coq_e_extract = lazy (constant "E_EXTRACT") let coq_e_solve = lazy (constant "E_SOLVE") -let coq_decompose_solve_valid = - lazy (constant "decompose_solve_valid") -let coq_do_reduce_lhyps = lazy (constant "do_reduce_lhyps") +let coq_interp_sequent = lazy (constant "interp_goal_concl") let coq_do_omega = lazy (constant "do_omega") (* \subsection{Construction d'expressions} *) - -let mk_var v = Term.mkVar (Names.id_of_string v) -let mk_plus t1 t2 = Term.mkApp (Lazy.force coq_Zplus,[| t1; t2 |]) -let mk_times t1 t2 = Term.mkApp (Lazy.force coq_Zmult, [| t1; t2 |]) -let mk_minus t1 t2 = Term.mkApp (Lazy.force coq_Zminus, [| t1;t2 |]) -let mk_eq t1 t2 = Term.mkApp (Lazy.force coq_eq, [| Lazy.force coq_Z; t1; t2 |]) -let mk_le t1 t2 = Term.mkApp (Lazy.force coq_Zle, [|t1; t2 |]) -let mk_gt t1 t2 = Term.mkApp (Lazy.force coq_Zgt, [|t1; t2 |]) -let mk_inv t = Term.mkApp (Lazy.force coq_Zopp, [|t |]) -let mk_and t1 t2 = Term.mkApp (Lazy.force coq_and, [|t1; t2 |]) -let mk_or t1 t2 = Term.mkApp (Lazy.force coq_or, [|t1; t2 |]) -let mk_not t = Term.mkApp (Lazy.force coq_not, [|t |]) -let mk_eq_rel t1 t2 = Term.mkApp (Lazy.force coq_eq, [| - Lazy.force coq_comparison; t1; t2 |]) -let mk_inj t = Term.mkApp (Lazy.force coq_Z_of_nat, [|t |]) - - let do_left t = if t = Lazy.force coq_c_nop then Lazy.force coq_c_nop else Term.mkApp (Lazy.force coq_c_do_left, [|t |] ) @@ -272,27 +188,20 @@ let rec do_list = function | [x] -> x | (x::l) -> do_seq x (do_list l) -let mk_integer n = - let rec loop n = - if n=Bigint.one then Lazy.force coq_xH else - let (q,r) = Bigint.euclid n Bigint.two in - Term.mkApp - ((if r = Bigint.zero then Lazy.force coq_xO else Lazy.force coq_xI), - [| loop q |]) in - - if n = Bigint.zero then Lazy.force coq_Z0 - else - if Bigint.is_strictly_pos n then - Term.mkApp (Lazy.force coq_Zpos, [| loop n |]) - else - Term.mkApp (Lazy.force coq_Zneg, [| loop (Bigint.neg n) |]) +(* Nat *) -let mk_Z = mk_integer +let coq_S = lazy(constant "S") +let coq_O = lazy(constant "O") let rec mk_nat = function | 0 -> Lazy.force coq_O | n -> Term.mkApp (Lazy.force coq_S, [| mk_nat (n-1) |]) +(* Lists *) + +let coq_cons = lazy (constant "cons") +let coq_nil = lazy (constant "nil") + let mk_list typ l = let rec loop = function | [] -> @@ -301,14 +210,141 @@ let mk_list typ l = Term.mkApp (Lazy.force coq_cons, [|typ; step; loop l |]) in loop l -let mk_plist l = - let rec loop = function - | [] -> - (Lazy.force coq_pnil) - | (step :: l) -> - Term.mkApp (Lazy.force coq_pcons, [| step; loop l |]) in - loop l - +let mk_plist l = mk_list Term.mkProp l let mk_shuffle_list l = mk_list (Lazy.force coq_t_fusion) l + +type parse_term = + | Tplus of Term.constr * Term.constr + | Tmult of Term.constr * Term.constr + | Tminus of Term.constr * Term.constr + | Topp of Term.constr + | Tsucc of Term.constr + | Tnum of Bigint.bigint + | Tother + +type parse_rel = + | Req of Term.constr * Term.constr + | Rne of Term.constr * Term.constr + | Rlt of Term.constr * Term.constr + | Rle of Term.constr * Term.constr + | Rgt of Term.constr * Term.constr + | Rge of Term.constr * Term.constr + | Rtrue + | Rfalse + | Rnot of Term.constr + | Ror of Term.constr * Term.constr + | Rand of Term.constr * Term.constr + | Rimp of Term.constr * Term.constr + | Riff of Term.constr * Term.constr + | Rother + +let parse_logic_rel c = + try match destructurate c with + | Kapp("True",[]) -> Rtrue + | Kapp("False",[]) -> Rfalse + | Kapp("not",[t]) -> Rnot t + | Kapp("or",[t1;t2]) -> Ror (t1,t2) + | Kapp("and",[t1;t2]) -> Rand (t1,t2) + | Kimp(t1,t2) -> Rimp (t1,t2) + | Kapp("iff",[t1;t2]) -> Riff (t1,t2) + | _ -> Rother + with e when Logic.catchable_exception e -> Rother + + +module type Int = sig + val typ : Term.constr Lazy.t + val plus : Term.constr Lazy.t + val mult : Term.constr Lazy.t + val opp : Term.constr Lazy.t + val minus : Term.constr Lazy.t + + val mk : Bigint.bigint -> Term.constr + val parse_term : Term.constr -> parse_term + val parse_rel : Proof_type.goal Tacmach.sigma -> Term.constr -> parse_rel + (* check whether t is built only with numbers and + * - *) + val is_scalar : Term.constr -> bool +end + +module Z : Int = struct + +let typ = lazy (constant "Z") +let plus = lazy (constant "Zplus") +let mult = lazy (constant "Zmult") +let opp = lazy (constant "Zopp") +let minus = lazy (constant "Zminus") + +let coq_xH = lazy (constant "xH") +let coq_xO = lazy (constant "xO") +let coq_xI = lazy (constant "xI") +let coq_Z0 = lazy (constant "Z0") +let coq_Zpos = lazy (constant "Zpos") +let coq_Zneg = lazy (constant "Zneg") + +let recognize t = + let rec loop t = + let f,l = dest_const_apply t in + match Names.string_of_id f,l with + "xI",[t] -> Bigint.add Bigint.one (Bigint.mult Bigint.two (loop t)) + | "xO",[t] -> Bigint.mult Bigint.two (loop t) + | "xH",[] -> Bigint.one + | _ -> failwith "not a number" in + let f,l = dest_const_apply t in + match Names.string_of_id f,l with + "Zpos",[t] -> loop t + | "Zneg",[t] -> Bigint.neg (loop t) + | "Z0",[] -> Bigint.zero + | _ -> failwith "not a number";; + +let rec mk_positive n = + if n=Bigint.one then Lazy.force coq_xH + else + let (q,r) = Bigint.euclid n Bigint.two in + Term.mkApp + ((if r = Bigint.zero then Lazy.force coq_xO else Lazy.force coq_xI), + [| mk_positive q |]) + +let mk_Z n = + if n = Bigint.zero then Lazy.force coq_Z0 + else if Bigint.is_strictly_pos n then + Term.mkApp (Lazy.force coq_Zpos, [| mk_positive n |]) + else + Term.mkApp (Lazy.force coq_Zneg, [| mk_positive (Bigint.neg n) |]) + +let mk = mk_Z + +let parse_term t = + try match destructurate t with + | Kapp("Zplus",[t1;t2]) -> Tplus (t1,t2) + | Kapp("Zminus",[t1;t2]) -> Tminus (t1,t2) + | Kapp("Zmult",[t1;t2]) -> Tmult (t1,t2) + | Kapp("Zopp",[t]) -> Topp t + | Kapp("Zsucc",[t]) -> Tsucc t + | Kapp("Zpred",[t]) -> Tplus(t, mk_Z (Bigint.neg Bigint.one)) + | Kapp(("Zpos"|"Zneg"|"Z0"),_) -> + (try Tnum (recognize t) with _ -> Tother) + | _ -> Tother + with e when Logic.catchable_exception e -> Tother + +let parse_rel gl t = + try match destructurate t with + | Kapp("eq",[typ;t1;t2]) + when destructurate (Tacmach.pf_nf gl typ) = Kapp("Z",[]) -> Req (t1,t2) + | Kapp("Zne",[t1;t2]) -> Rne (t1,t2) + | Kapp("Zle",[t1;t2]) -> Rle (t1,t2) + | Kapp("Zlt",[t1;t2]) -> Rlt (t1,t2) + | Kapp("Zge",[t1;t2]) -> Rge (t1,t2) + | Kapp("Zgt",[t1;t2]) -> Rgt (t1,t2) + | _ -> parse_logic_rel t + with e when Logic.catchable_exception e -> Rother + +let is_scalar t = + let rec aux t = match destructurate t with + | Kapp(("Zplus"|"Zminus"|"Zmult"),[t1;t2]) -> aux t1 & aux t2 + | Kapp(("Zopp"|"Zsucc"|"Zpred"),[t]) -> aux t + | Kapp(("Zpos"|"Zneg"|"Z0"),_) -> let _ = recognize t in true + | _ -> false in + try aux t with _ -> false + +end |