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-(*************************************************************************
-
- PROJET RNRT Calife - 2001
- Author: Pierre Crégut - France Télécom R&D
- Licence : LGPL version 2.1
-
- *************************************************************************)
-
-let module_refl_name = "ReflOmegaCore"
-let module_refl_path = ["Coq"; "romega"; module_refl_name]
-
-type result =
- Kvar of string
- | Kapp of string * Term.constr list
- | Kimp of Term.constr * Term.constr
- | Kufo;;
-
-let destructurate t =
- let c, args = Term.decompose_app t in
- match Term.kind_of_term c, args with
- | Term.Const sp, args ->
- Kapp (Names.string_of_id
- (Nametab.id_of_global (Libnames.ConstRef sp)),
- args)
- | Term.Construct csp , args ->
- Kapp (Names.string_of_id
- (Nametab.id_of_global (Libnames.ConstructRef csp)),
- args)
- | Term.Ind isp, args ->
- Kapp (Names.string_of_id
- (Nametab.id_of_global (Libnames.IndRef isp)),
- args)
- | Term.Var id,[] -> Kvar(Names.string_of_id id)
- | Term.Prod (Names.Anonymous,typ,body), [] -> Kimp(typ,body)
- | Term.Prod (Names.Name _,_,_),[] ->
- Util.error "Omega: Not a quantifier-free goal"
- | _ -> Kufo
-
-exception Destruct
-
-let dest_const_apply t =
- let f,args = Term.decompose_app t in
- let ref =
- match Term.kind_of_term f with
- | Term.Const sp -> Libnames.ConstRef sp
- | Term.Construct csp -> Libnames.ConstructRef csp
- | Term.Ind isp -> Libnames.IndRef isp
- | _ -> raise Destruct
- in Nametab.id_of_global ref, args
-
-let logic_dir = ["Coq";"Logic";"Decidable"]
-
-let coq_modules =
- Coqlib.init_modules @ [logic_dir] @ Coqlib.arith_modules @ Coqlib.zarith_base_modules
- @ [["Coq"; "Lists"; "List"]]
- @ [module_refl_path]
- @ [module_refl_path@["ZOmega"]]
-
-let constant = Coqlib.gen_constant_in_modules "Omega" coq_modules
-
-(* Logic *)
-let coq_eq = lazy(constant "eq")
-let coq_refl_equal = lazy(constant "refl_equal")
-let coq_and = lazy(constant "and")
-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_I = lazy(constant "I")
-
-(* ReflOmegaCore/ZOmega *)
-
-let coq_h_step = lazy (constant "h_step")
-let coq_pair_step = lazy (constant "pair_step")
-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_t_int = lazy (constant "Tint")
-let coq_t_plus = lazy (constant "Tplus")
-let coq_t_mult = lazy (constant "Tmult")
-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")
-let coq_p_lt = lazy (constant "LtTerm")
-let coq_p_gt = lazy (constant "GtTerm")
-let coq_p_neq = lazy (constant "NeqTerm")
-let coq_p_true = lazy (constant "TrueTerm")
-let coq_p_false = lazy (constant "FalseTerm")
-let coq_p_not = lazy (constant "Tnot")
-let coq_p_or = lazy (constant "Tor")
-let coq_p_and = lazy (constant "Tand")
-let coq_p_imp = lazy (constant "Timp")
-let coq_p_prop = lazy (constant "Tprop")
-
-(* Constructors for shuffle tactic *)
-let coq_t_fusion = lazy (constant "t_fusion")
-let coq_f_equal = lazy (constant "F_equal")
-let coq_f_cancel = lazy (constant "F_cancel")
-let coq_f_left = lazy (constant "F_left")
-let coq_f_right = lazy (constant "F_right")
-
-(* Constructors for reordering tactics *)
-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")
-let coq_c_do_seq = lazy (constant "C_SEQ")
-let coq_c_nop = lazy (constant "C_NOP")
-let coq_c_opp_plus = lazy (constant "C_OPP_PLUS")
-let coq_c_opp_opp = lazy (constant "C_OPP_OPP")
-let coq_c_opp_mult_r = lazy (constant "C_OPP_MULT_R")
-let coq_c_opp_one = lazy (constant "C_OPP_ONE")
-let coq_c_reduce = lazy (constant "C_REDUCE")
-let coq_c_mult_plus_distr = lazy (constant "C_MULT_PLUS_DISTR")
-let coq_c_opp_left = lazy (constant "C_MULT_OPP_LEFT")
-let coq_c_mult_assoc_r = lazy (constant "C_MULT_ASSOC_R")
-let coq_c_plus_assoc_r = lazy (constant "C_PLUS_ASSOC_R")
-let coq_c_plus_assoc_l = lazy (constant "C_PLUS_ASSOC_L")
-let coq_c_plus_permute = lazy (constant "C_PLUS_PERMUTE")
-let coq_c_plus_comm = lazy (constant "C_PLUS_COMM")
-let coq_c_red0 = lazy (constant "C_RED0")
-let coq_c_red1 = lazy (constant "C_RED1")
-let coq_c_red2 = lazy (constant "C_RED2")
-let coq_c_red3 = lazy (constant "C_RED3")
-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_minus = lazy (constant "C_MINUS")
-let coq_c_mult_comm = lazy (constant "C_MULT_COMM")
-
-let coq_s_constant_not_nul = lazy (constant "O_CONSTANT_NOT_NUL")
-let coq_s_constant_neg = lazy (constant "O_CONSTANT_NEG")
-let coq_s_div_approx = lazy (constant "O_DIV_APPROX")
-let coq_s_not_exact_divide = lazy (constant "O_NOT_EXACT_DIVIDE")
-let coq_s_exact_divide = lazy (constant "O_EXACT_DIVIDE")
-let coq_s_sum = lazy (constant "O_SUM")
-let coq_s_state = lazy (constant "O_STATE")
-let coq_s_contradiction = lazy (constant "O_CONTRADICTION")
-let coq_s_merge_eq = lazy (constant "O_MERGE_EQ")
-let coq_s_split_ineq =lazy (constant "O_SPLIT_INEQ")
-let coq_s_constant_nul =lazy (constant "O_CONSTANT_NUL")
-let coq_s_negate_contradict =lazy (constant "O_NEGATE_CONTRADICT")
-let coq_s_negate_contradict_inv =lazy (constant "O_NEGATE_CONTRADICT_INV")
-
-(* construction for the [extract_hyp] tactic *)
-let coq_direction = lazy (constant "direction")
-let coq_d_left = lazy (constant "D_left")
-let coq_d_right = lazy (constant "D_right")
-let coq_d_mono = lazy (constant "D_mono")
-
-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_interp_sequent = lazy (constant "interp_goal_concl")
-let coq_do_omega = lazy (constant "do_omega")
-
-(* \subsection{Construction d'expressions} *)
-
-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 |] )
-
-let do_right t =
- if t = Lazy.force coq_c_nop then Lazy.force coq_c_nop
- else Term.mkApp (Lazy.force coq_c_do_right, [|t |])
-
-let do_both t1 t2 =
- if t1 = Lazy.force coq_c_nop then do_right t2
- else if t2 = Lazy.force coq_c_nop then do_left t1
- else Term.mkApp (Lazy.force coq_c_do_both , [|t1; t2 |])
-
-let do_seq t1 t2 =
- if t1 = Lazy.force coq_c_nop then t2
- else if t2 = Lazy.force coq_c_nop then t1
- else Term.mkApp (Lazy.force coq_c_do_seq, [|t1; t2 |])
-
-let rec do_list = function
- | [] -> Lazy.force coq_c_nop
- | [x] -> x
- | (x::l) -> do_seq x (do_list l)
-
-(* Nat *)
-
-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
- | [] ->
- Term.mkApp (Lazy.force coq_nil, [|typ|])
- | (step :: l) ->
- Term.mkApp (Lazy.force coq_cons, [|typ; 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
generated by cgit v1.2.3 (git 2.39.1) at 2024-07-04 00:03:32 +0000