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Diffstat (limited to 'contrib/romega/const_omega.ml')
| -rw-r--r-- | contrib/romega/const_omega.ml | 488 |
1 files changed, 488 insertions, 0 deletions
diff --git a/contrib/romega/const_omega.ml b/contrib/romega/const_omega.ml new file mode 100644 index 00000000..3b2a7d31 --- /dev/null +++ b/contrib/romega/const_omega.ml @@ -0,0 +1,488 @@ +(************************************************************************* + + 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 + let env = Global.env() 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 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] -> 1 + 2 * loop t + | "xO",[t] -> 2 * loop t + | "xH",[] -> 1 + | _ -> 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] -> - (loop t) | "Z0",[] -> 0 + | _ -> 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"; (if !Options.v7 then "PolyList" else "List")]] + @ [module_refl_path] + + +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_ZERO = lazy (constant "Z0") +let coq_POS = lazy (constant "Zpos") +let coq_NEG = lazy (constant "Zneg") +let coq_Z = lazy (constant "Z") +let coq_relation = lazy (constant "comparison") +let coq_SUPERIEUR = lazy (constant "SUPERIEUR") +let coq_INFEEIEUR = lazy (constant "INFERIEUR") +let coq_EGAL = lazy (constant "EGAL") +let coq_Zplus = lazy (constant "Zplus") +let coq_Zmult = lazy (constant "Zmult") +let coq_Zopp = lazy (constant "Zopp") + +let coq_Zminus = lazy (constant "Zminus") +let coq_Zs = lazy (constant "Zs") +let coq_Zgt = lazy (constant "Zgt") +let coq_Zle = lazy (constant "Zle") +let coq_inject_nat = lazy (constant "inject_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") +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_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") + +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_p_nop = lazy (constant "P_NOP") + + +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_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") + +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") +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_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") +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_sym = lazy (constant "C_PLUS_SYM") +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_sym = lazy (constant "C_MULT_SYM") + +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_decompose_solve_valid = + lazy (constant "decompose_solve_valid") +let coq_do_reduce_lhyps = lazy (constant "do_reduce_lhyps") +let coq_do_omega = lazy (constant "do_omega") + +(** +let constant dir s = + try + Libnames.constr_of_reference + (Nametab.absolute_reference + (Libnames.make_path + (Names.make_dirpath (List.map Names.id_of_string (List.rev dir))) + (Names.id_of_string s))) + with e -> print_endline (String.concat "." dir); print_endline s; + raise e + +let path_fast_integer = ["Coq"; "ZArith"; "fast_integer"] +let path_zarith_aux = ["Coq"; "ZArith"; "zarith_aux"] +let path_logic = ["Coq"; "Init";"Logic"] +let path_datatypes = ["Coq"; "Init";"Datatypes"] +let path_peano = ["Coq"; "Init"; "Peano"] +let path_list = ["Coq"; "Lists"; "PolyList"] + +let coq_xH = lazy (constant path_fast_integer "xH") +let coq_xO = lazy (constant path_fast_integer "xO") +let coq_xI = lazy (constant path_fast_integer "xI") +let coq_ZERO = lazy (constant path_fast_integer "ZERO") +let coq_POS = lazy (constant path_fast_integer "POS") +let coq_NEG = lazy (constant path_fast_integer "NEG") +let coq_Z = lazy (constant path_fast_integer "Z") +let coq_relation = lazy (constant path_fast_integer "relation") +let coq_SUPERIEUR = lazy (constant path_fast_integer "SUPERIEUR") +let coq_INFEEIEUR = lazy (constant path_fast_integer "INFERIEUR") +let coq_EGAL = lazy (constant path_fast_integer "EGAL") +let coq_Zplus = lazy (constant path_fast_integer "Zplus") +let coq_Zmult = lazy (constant path_fast_integer "Zmult") +let coq_Zopp = lazy (constant path_fast_integer "Zopp") + +(* auxiliaires zarith *) +let coq_Zminus = lazy (constant path_zarith_aux "Zminus") +let coq_Zs = lazy (constant path_zarith_aux "Zs") +let coq_Zgt = lazy (constant path_zarith_aux "Zgt") +let coq_Zle = lazy (constant path_zarith_aux "Zle") +let coq_inject_nat = lazy (constant path_zarith_aux "inject_nat") + +(* Peano *) +let coq_le = lazy(constant path_peano "le") +let coq_gt = lazy(constant path_peano "gt") + +(* Integers *) +let coq_nat = lazy(constant path_datatypes "nat") +let coq_S = lazy(constant path_datatypes "S") +let coq_O = lazy(constant path_datatypes "O") + +(* Minus *) +let coq_minus = lazy(constant ["Arith"; "Minus"] "minus") + +(* Logic *) +let coq_eq = lazy(constant path_logic "eq") +let coq_refl_equal = lazy(constant path_logic "refl_equal") +let coq_and = lazy(constant path_logic "and") +let coq_not = lazy(constant path_logic "not") +let coq_or = lazy(constant path_logic "or") +let coq_true = lazy(constant path_logic "true") +let coq_false = lazy(constant path_logic "false") +let coq_ex = lazy(constant path_logic "ex") +let coq_I = lazy(constant path_logic "I") + +(* Lists *) +let coq_cons = lazy (constant path_list "cons") +let coq_nil = lazy (constant path_list "nil") + +let coq_pcons = lazy (constant module_refl_path "Pcons") +let coq_pnil = lazy (constant module_refl_path "Pnil") + +let coq_h_step = lazy (constant module_refl_path "h_step") +let coq_pair_step = lazy (constant module_refl_path "pair_step") +let coq_p_left = lazy (constant module_refl_path "P_LEFT") +let coq_p_right = lazy (constant module_refl_path "P_RIGHT") +let coq_p_invert = lazy (constant module_refl_path "P_INVERT") +let coq_p_step = lazy (constant module_refl_path "P_STEP") +let coq_p_nop = lazy (constant module_refl_path "P_NOP") + + +let coq_t_int = lazy (constant module_refl_path "Tint") +let coq_t_plus = lazy (constant module_refl_path "Tplus") +let coq_t_mult = lazy (constant module_refl_path "Tmult") +let coq_t_opp = lazy (constant module_refl_path "Topp") +let coq_t_minus = lazy (constant module_refl_path "Tminus") +let coq_t_var = lazy (constant module_refl_path "Tvar") + +let coq_p_eq = lazy (constant module_refl_path "EqTerm") +let coq_p_leq = lazy (constant module_refl_path "LeqTerm") +let coq_p_geq = lazy (constant module_refl_path "GeqTerm") +let coq_p_lt = lazy (constant module_refl_path "LtTerm") +let coq_p_gt = lazy (constant module_refl_path "GtTerm") +let coq_p_neq = lazy (constant module_refl_path "NeqTerm") +let coq_p_true = lazy (constant module_refl_path "TrueTerm") +let coq_p_false = lazy (constant module_refl_path "FalseTerm") +let coq_p_not = lazy (constant module_refl_path "Tnot") +let coq_p_or = lazy (constant module_refl_path "Tor") +let coq_p_and = lazy (constant module_refl_path "Tand") +let coq_p_imp = lazy (constant module_refl_path "Timp") +let coq_p_prop = lazy (constant module_refl_path "Tprop") + +let coq_proposition = lazy (constant module_refl_path "proposition") +let coq_interp_sequent = lazy (constant module_refl_path "interp_goal_concl") +let coq_normalize_sequent = lazy (constant module_refl_path "normalize_goal") +let coq_execute_sequent = lazy (constant module_refl_path "execute_goal") +let coq_do_concl_to_hyp = lazy (constant module_refl_path "do_concl_to_hyp") +let coq_sequent_to_hyps = lazy (constant module_refl_path "goal_to_hyps") +let coq_normalize_hyps_goal = + lazy (constant module_refl_path "normalize_hyps_goal") + +(* Constructors for shuffle tactic *) +let coq_t_fusion = lazy (constant module_refl_path "t_fusion") +let coq_f_equal = lazy (constant module_refl_path "F_equal") +let coq_f_cancel = lazy (constant module_refl_path "F_cancel") +let coq_f_left = lazy (constant module_refl_path "F_left") +let coq_f_right = lazy (constant module_refl_path "F_right") + +(* Constructors for reordering tactics *) +let coq_step = lazy (constant module_refl_path "step") +let coq_c_do_both = lazy (constant module_refl_path "C_DO_BOTH") +let coq_c_do_left = lazy (constant module_refl_path "C_LEFT") +let coq_c_do_right = lazy (constant module_refl_path "C_RIGHT") +let coq_c_do_seq = lazy (constant module_refl_path "C_SEQ") +let coq_c_nop = lazy (constant module_refl_path "C_NOP") +let coq_c_opp_plus = lazy (constant module_refl_path "C_OPP_PLUS") +let coq_c_opp_opp = lazy (constant module_refl_path "C_OPP_OPP") +let coq_c_opp_mult_r = lazy (constant module_refl_path "C_OPP_MULT_R") +let coq_c_opp_one = lazy (constant module_refl_path "C_OPP_ONE") +let coq_c_reduce = lazy (constant module_refl_path "C_REDUCE") +let coq_c_mult_plus_distr = lazy (constant module_refl_path "C_MULT_PLUS_DISTR") +let coq_c_opp_left = lazy (constant module_refl_path "C_MULT_OPP_LEFT") +let coq_c_mult_assoc_r = lazy (constant module_refl_path "C_MULT_ASSOC_R") +let coq_c_plus_assoc_r = lazy (constant module_refl_path "C_PLUS_ASSOC_R") +let coq_c_plus_assoc_l = lazy (constant module_refl_path "C_PLUS_ASSOC_L") +let coq_c_plus_permute = lazy (constant module_refl_path "C_PLUS_PERMUTE") +let coq_c_plus_sym = lazy (constant module_refl_path "C_PLUS_SYM") +let coq_c_red0 = lazy (constant module_refl_path "C_RED0") +let coq_c_red1 = lazy (constant module_refl_path "C_RED1") +let coq_c_red2 = lazy (constant module_refl_path "C_RED2") +let coq_c_red3 = lazy (constant module_refl_path "C_RED3") +let coq_c_red4 = lazy (constant module_refl_path "C_RED4") +let coq_c_red5 = lazy (constant module_refl_path "C_RED5") +let coq_c_red6 = lazy (constant module_refl_path "C_RED6") +let coq_c_mult_opp_left = lazy (constant module_refl_path "C_MULT_OPP_LEFT") +let coq_c_mult_assoc_reduced = + lazy (constant module_refl_path "C_MULT_ASSOC_REDUCED") +let coq_c_minus = lazy (constant module_refl_path "C_MINUS") +let coq_c_mult_sym = lazy (constant module_refl_path "C_MULT_SYM") + +let coq_s_constant_not_nul = lazy (constant module_refl_path "O_CONSTANT_NOT_NUL") +let coq_s_constant_neg = lazy (constant module_refl_path "O_CONSTANT_NEG") +let coq_s_div_approx = lazy (constant module_refl_path "O_DIV_APPROX") +let coq_s_not_exact_divide = lazy (constant module_refl_path "O_NOT_EXACT_DIVIDE") +let coq_s_exact_divide = lazy (constant module_refl_path "O_EXACT_DIVIDE") +let coq_s_sum = lazy (constant module_refl_path "O_SUM") +let coq_s_state = lazy (constant module_refl_path "O_STATE") +let coq_s_contradiction = lazy (constant module_refl_path "O_CONTRADICTION") +let coq_s_merge_eq = lazy (constant module_refl_path "O_MERGE_EQ") +let coq_s_split_ineq =lazy (constant module_refl_path "O_SPLIT_INEQ") +let coq_s_constant_nul =lazy (constant module_refl_path "O_CONSTANT_NUL") +let coq_s_negate_contradict =lazy (constant module_refl_path "O_NEGATE_CONTRADICT") +let coq_s_negate_contradict_inv =lazy (constant module_refl_path "O_NEGATE_CONTRADICT_INV") + +(* construction for the [extract_hyp] tactic *) +let coq_direction = lazy (constant module_refl_path "direction") +let coq_d_left = lazy (constant module_refl_path "D_left") +let coq_d_right = lazy (constant module_refl_path "D_right") +let coq_d_mono = lazy (constant module_refl_path "D_mono") + +let coq_e_split = lazy (constant module_refl_path "E_SPLIT") +let coq_e_extract = lazy (constant module_refl_path "E_EXTRACT") +let coq_e_solve = lazy (constant module_refl_path "E_SOLVE") + +let coq_decompose_solve_valid = + lazy (constant module_refl_path "decompose_solve_valid") +let coq_do_reduce_lhyps = lazy (constant module_refl_path "do_reduce_lhyps") +let coq_do_omega = lazy (constant module_refl_path "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_relation; t1; t2 |]) +let mk_inj t = Term.mkApp (Lazy.force coq_inject_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 |] ) + +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) + + +let mk_integer n = + let rec loop n = + if n=1 then Lazy.force coq_xH else + Term.mkApp ((if n mod 2 = 0 then Lazy.force coq_xO else Lazy.force coq_xI), + [| loop (n/2) |]) in + + if n = 0 then Lazy.force coq_ZERO + else Term.mkApp ((if n > 0 then Lazy.force coq_POS else Lazy.force coq_NEG), + [| loop (abs n) |]) + +let mk_Z = mk_integer + +let rec mk_nat = function + | 0 -> Lazy.force coq_O + | n -> Term.mkApp (Lazy.force coq_S, [| mk_nat (n-1) |]) + +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 = + let rec loop = function + | [] -> + (Lazy.force coq_pnil) + | (step :: l) -> + Term.mkApp (Lazy.force coq_pcons, [| step; loop l |]) in + loop l + + +let mk_shuffle_list l = mk_list (Lazy.force coq_t_fusion) l + |