author | wenzelm |
Fri, 28 Sep 2001 19:19:26 +0200 | |
changeset 11628 | e57a6e51715e |
parent 11539 | 0f17da240450 |
child 11806 | e1fd22a657ae |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/datatype_rep_proofs.ML |
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ID: $Id$ |
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Author: Stefan Berghofer, TU Muenchen |
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License: GPL (GNU GENERAL PUBLIC LICENSE) |
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Definitional introduction of datatypes |
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Proof of characteristic theorems: |
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- injectivity of constructors |
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- distinctness of constructors |
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- induction theorem |
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*) |
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signature DATATYPE_REP_PROOFS = |
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sig |
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val representation_proofs : bool -> DatatypeAux.datatype_info Symtab.table -> |
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string list -> (int * (string * DatatypeAux.dtyp list * |
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(string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list -> |
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(string * mixfix) list -> (string * mixfix) list list -> theory attribute |
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-> theory -> theory * thm list list * thm list list * thm list list * |
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DatatypeAux.simproc_dist list * thm |
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end; |
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structure DatatypeRepProofs : DATATYPE_REP_PROOFS = |
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struct |
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open DatatypeAux; |
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val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma); |
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(** theory context references **) |
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val f_myinv_f = thm "f_myinv_f"; |
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val myinv_f_f = thm "myinv_f_f"; |
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fun exh_thm_of (dt_info : datatype_info Symtab.table) tname = |
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#exhaustion (the (Symtab.lookup (dt_info, tname))); |
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(******************************************************************************) |
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fun representation_proofs flat_names (dt_info : datatype_info Symtab.table) |
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new_type_names descr sorts types_syntax constr_syntax case_names_induct thy = |
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let |
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val Datatype_thy = theory "Datatype"; |
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val node_name = Sign.intern_tycon (Theory.sign_of Datatype_thy) "node"; |
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val [In0_name, In1_name, Scons_name, Leaf_name, Numb_name, Lim_name, |
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Funs_name, o_name, sum_case_name] = |
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map (Sign.intern_const (Theory.sign_of Datatype_thy)) |
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["In0", "In1", "Scons", "Leaf", "Numb", "Lim", "Funs", "op o", "sum_case"]; |
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val [In0_inject, In1_inject, Scons_inject, Leaf_inject, In0_eq, In1_eq, |
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In0_not_In1, In1_not_In0, Funs_mono, FunsI, Lim_inject, |
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Funs_inv, FunsD, Funs_rangeE, Funs_nonempty, sum_case_inject] = map (get_thm Datatype_thy) |
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["In0_inject", "In1_inject", "Scons_inject", "Leaf_inject", "In0_eq", "In1_eq", |
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"In0_not_In1", "In1_not_In0", "Funs_mono", "FunsI", "Lim_inject", |
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"Funs_inv", "FunsD", "Funs_rangeE", "Funs_nonempty", "sum_case_inject"]; |
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val Funs_IntE = (Int_lower2 RS Funs_mono RS |
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(Int_lower1 RS Funs_mono RS Int_greatest) RS subsetD) RS IntE; |
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val descr' = flat descr; |
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val big_name = space_implode "_" new_type_names; |
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val thy1 = add_path flat_names big_name thy; |
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val big_rec_name = big_name ^ "_rep_set"; |
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val rep_set_names = map (Sign.full_name (Theory.sign_of thy1)) |
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(if length descr' = 1 then [big_rec_name] else |
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(map ((curry (op ^) (big_rec_name ^ "_")) o string_of_int) |
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(1 upto (length descr')))); |
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val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr); |
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val leafTs' = get_nonrec_types descr' sorts; |
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val branchTs = get_branching_types descr' sorts; |
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val branchT = if null branchTs then HOLogic.unitT |
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else fold_bal (fn (T, U) => Type ("+", [T, U])) branchTs; |
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val unneeded_vars = hd tyvars \\ foldr add_typ_tfree_names (leafTs' @ branchTs, []); |
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val leafTs = leafTs' @ (map (fn n => TFree (n, the (assoc (sorts, n)))) unneeded_vars); |
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val recTs = get_rec_types descr' sorts; |
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val newTs = take (length (hd descr), recTs); |
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val oldTs = drop (length (hd descr), recTs); |
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val sumT = if null leafTs then HOLogic.unitT |
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else fold_bal (fn (T, U) => Type ("+", [T, U])) leafTs; |
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val Univ_elT = HOLogic.mk_setT (Type (node_name, [sumT, branchT])); |
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val UnivT = HOLogic.mk_setT Univ_elT; |
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val In0 = Const (In0_name, Univ_elT --> Univ_elT); |
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val In1 = Const (In1_name, Univ_elT --> Univ_elT); |
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val Leaf = Const (Leaf_name, sumT --> Univ_elT); |
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val Lim = Const (Lim_name, (branchT --> Univ_elT) --> Univ_elT); |
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(* make injections needed for embedding types in leaves *) |
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fun mk_inj T' x = |
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let |
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fun mk_inj' T n i = |
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if n = 1 then x else |
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let val n2 = n div 2; |
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val Type (_, [T1, T2]) = T |
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in |
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if i <= n2 then |
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Const ("Inl", T1 --> T) $ (mk_inj' T1 n2 i) |
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else |
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Const ("Inr", T2 --> T) $ (mk_inj' T2 (n - n2) (i - n2)) |
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end |
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in mk_inj' sumT (length leafTs) (1 + find_index_eq T' leafTs) |
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end; |
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(* make injections for constructors *) |
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fun mk_univ_inj ts = access_bal (fn t => In0 $ t, fn t => In1 $ t, if ts = [] then |
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Const ("arbitrary", Univ_elT) |
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else |
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foldr1 (HOLogic.mk_binop Scons_name) ts); |
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(* function spaces *) |
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fun mk_fun_inj T' x = |
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let |
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fun mk_inj T n i = |
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if n = 1 then x else |
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let |
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val n2 = n div 2; |
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val Type (_, [T1, T2]) = T; |
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val sum_case = Const (sum_case_name, [T1 --> Univ_elT, T2 --> Univ_elT, T] ---> Univ_elT) |
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in |
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if i <= n2 then |
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sum_case $ (mk_inj T1 n2 i) $ Const ("arbitrary", T2 --> Univ_elT) |
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else |
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sum_case $ Const ("arbitrary", T1 --> Univ_elT) $ mk_inj T2 (n - n2) (i - n2) |
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end |
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in mk_inj branchT (length branchTs) (1 + find_index_eq T' branchTs) |
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end; |
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(************** generate introduction rules for representing set **********) |
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val _ = message "Constructing representing sets ..."; |
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(* make introduction rule for a single constructor *) |
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fun make_intr s n (i, (_, cargs)) = |
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let |
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fun mk_prem (DtRec k, (j, prems, ts)) = |
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let val free_t = mk_Free "x" Univ_elT j |
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in (j + 1, (HOLogic.mk_mem (free_t, |
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Const (nth_elem (k, rep_set_names), UnivT)))::prems, free_t::ts) |
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end |
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| mk_prem (DtType ("fun", [T, DtRec k]), (j, prems, ts)) = |
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let val T' = typ_of_dtyp descr' sorts T; |
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val free_t = mk_Free "x" (T' --> Univ_elT) j |
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in (j + 1, (HOLogic.mk_mem (free_t, |
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Const (Funs_name, UnivT --> HOLogic.mk_setT (T' --> Univ_elT)) $ |
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Const (nth_elem (k, rep_set_names), UnivT)))::prems, |
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Lim $ mk_fun_inj T' free_t::ts) |
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end |
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| mk_prem (dt, (j, prems, ts)) = |
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let val T = typ_of_dtyp descr' sorts dt |
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in (j + 1, prems, (Leaf $ mk_inj T (mk_Free "x" T j))::ts) |
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end; |
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val (_, prems, ts) = foldr mk_prem (cargs, (1, [], [])); |
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val concl = HOLogic.mk_Trueprop (HOLogic.mk_mem |
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(mk_univ_inj ts n i, Const (s, UnivT))) |
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in Logic.list_implies (map HOLogic.mk_Trueprop prems, concl) |
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end; |
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val consts = map (fn s => Const (s, UnivT)) rep_set_names; |
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val intr_ts = flat (map (fn ((_, (_, _, constrs)), rep_set_name) => |
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map (make_intr rep_set_name (length constrs)) |
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((1 upto (length constrs)) ~~ constrs)) (descr' ~~ rep_set_names)); |
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val (thy2, {raw_induct = rep_induct, intrs = rep_intrs, ...}) = |
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setmp InductivePackage.quiet_mode (!quiet_mode) |
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(InductivePackage.add_inductive_i false true big_rec_name false true false |
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consts (map (fn x => (("", x), [])) intr_ts) [Funs_mono] []) thy1; |
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(********************************* typedef ********************************) |
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val thy3 = add_path flat_names big_name (foldl (fn (thy, ((((name, mx), tvs), c), name')) => |
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setmp TypedefPackage.quiet_mode true |
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(TypedefPackage.add_typedef_i_no_def name' (name, tvs, mx) c [] [] |
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(Some (QUIET_BREADTH_FIRST (has_fewer_prems 1) |
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(resolve_tac (Funs_nonempty::rep_intrs) 1)))) thy) |
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(parent_path flat_names thy2, types_syntax ~~ tyvars ~~ |
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(take (length newTs, consts)) ~~ new_type_names)); |
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(*********************** definition of constructors ***********************) |
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val big_rep_name = (space_implode "_" new_type_names) ^ "_Rep_"; |
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val rep_names = map (curry op ^ "Rep_") new_type_names; |
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val rep_names' = map (fn i => big_rep_name ^ (string_of_int i)) |
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(1 upto (length (flat (tl descr)))); |
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val all_rep_names = map (Sign.intern_const (Theory.sign_of thy3)) rep_names @ |
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map (Sign.full_name (Theory.sign_of thy3)) rep_names'; |
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(* isomorphism declarations *) |
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val iso_decls = map (fn (T, s) => (s, T --> Univ_elT, NoSyn)) |
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(oldTs ~~ rep_names'); |
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(* constructor definitions *) |
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fun make_constr_def tname T n ((thy, defs, eqns, i), ((cname, cargs), (cname', mx))) = |
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let |
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fun constr_arg (dt, (j, l_args, r_args)) = |
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let val T = typ_of_dtyp descr' sorts dt; |
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val free_t = mk_Free "x" T j |
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in (case dt of |
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DtRec m => (j + 1, free_t::l_args, (Const (nth_elem (m, all_rep_names), |
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T --> Univ_elT) $ free_t)::r_args) |
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| DtType ("fun", [T', DtRec m]) => |
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let val ([T''], T''') = strip_type T |
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in (j + 1, free_t::l_args, (Lim $ mk_fun_inj T'' |
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(Const (o_name, [T''' --> Univ_elT, T, T''] ---> Univ_elT) $ |
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Const (nth_elem (m, all_rep_names), T''' --> Univ_elT) $ free_t))::r_args) |
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end |
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| _ => (j + 1, free_t::l_args, (Leaf $ mk_inj T free_t)::r_args)) |
222 |
end; |
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val (_, l_args, r_args) = foldr constr_arg (cargs, (1, [], [])); |
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val constrT = (map (typ_of_dtyp descr' sorts) cargs) ---> T; |
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val abs_name = Sign.intern_const (Theory.sign_of thy) ("Abs_" ^ tname); |
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val rep_name = Sign.intern_const (Theory.sign_of thy) ("Rep_" ^ tname); |
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val lhs = list_comb (Const (cname, constrT), l_args); |
229 |
val rhs = mk_univ_inj r_args n i; |
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230 |
val def = equals T $ lhs $ (Const (abs_name, Univ_elT --> T) $ rhs); |
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val def_name = (Sign.base_name cname) ^ "_def"; |
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val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq |
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(Const (rep_name, T --> Univ_elT) $ lhs, rhs)); |
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val (thy', [def_thm]) = thy |> |
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Theory.add_consts_i [(cname', constrT, mx)] |> |
9315 | 236 |
(PureThy.add_defs_i false o map Thm.no_attributes) [(def_name, def)]; |
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8436 | 238 |
in (thy', defs @ [def_thm], eqns @ [eqn], i + 1) end; |
5177 | 239 |
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(* constructor definitions for datatype *) |
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241 |
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242 |
fun dt_constr_defs ((thy, defs, eqns, rep_congs, dist_lemmas), |
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243 |
((((_, (_, _, constrs)), tname), T), constr_syntax)) = |
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244 |
let |
|
245 |
val _ $ (_ $ (cong_f $ _) $ _) = concl_of arg_cong; |
|
6394 | 246 |
val sg = Theory.sign_of thy; |
5177 | 247 |
val rep_const = cterm_of sg |
248 |
(Const (Sign.intern_const sg ("Rep_" ^ tname), T --> Univ_elT)); |
|
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val cong' = standard (cterm_instantiate [(cterm_of sg cong_f, rep_const)] arg_cong); |
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250 |
val dist = standard (cterm_instantiate [(cterm_of sg distinct_f, rep_const)] distinct_lemma); |
5177 | 251 |
val (thy', defs', eqns', _) = foldl ((make_constr_def tname T) (length constrs)) |
5661 | 252 |
((add_path flat_names tname thy, defs, [], 1), constrs ~~ constr_syntax) |
5177 | 253 |
in |
5661 | 254 |
(parent_path flat_names thy', defs', eqns @ [eqns'], |
5177 | 255 |
rep_congs @ [cong'], dist_lemmas @ [dist]) |
256 |
end; |
|
257 |
||
258 |
val (thy4, constr_defs, constr_rep_eqns, rep_congs, dist_lemmas) = foldl dt_constr_defs |
|
5661 | 259 |
((thy3 |> Theory.add_consts_i iso_decls |> parent_path flat_names, [], [], [], []), |
5177 | 260 |
hd descr ~~ new_type_names ~~ newTs ~~ constr_syntax); |
261 |
||
262 |
(*********** isomorphisms for new types (introduced by typedef) ***********) |
|
263 |
||
6427 | 264 |
val _ = message "Proving isomorphism properties ..."; |
5177 | 265 |
|
266 |
(* get axioms from theory *) |
|
267 |
||
268 |
val newT_iso_axms = map (fn s => |
|
7904 | 269 |
(get_thm thy4 ("Abs_" ^ s ^ "_inverse"), |
270 |
get_thm thy4 ("Rep_" ^ s ^ "_inverse"), |
|
271 |
get_thm thy4 ("Rep_" ^ s))) new_type_names; |
|
5177 | 272 |
|
273 |
(*------------------------------------------------*) |
|
274 |
(* prove additional theorems: *) |
|
275 |
(* inj_on dt_Abs_i rep_set_i and inj dt_Rep_i *) |
|
276 |
(*------------------------------------------------*) |
|
277 |
||
278 |
fun prove_newT_iso_inj_thm (((s, (thm1, thm2, _)), T), rep_set_name) = |
|
279 |
let |
|
6394 | 280 |
val sg = Theory.sign_of thy4; |
5177 | 281 |
val RepT = T --> Univ_elT; |
282 |
val Rep_name = Sign.intern_const sg ("Rep_" ^ s); |
|
283 |
val AbsT = Univ_elT --> T; |
|
284 |
val Abs_name = Sign.intern_const sg ("Abs_" ^ s); |
|
285 |
||
6171 | 286 |
val inj_Abs_thm = |
287 |
prove_goalw_cterm [] |
|
288 |
(cterm_of sg |
|
289 |
(HOLogic.mk_Trueprop |
|
11435 | 290 |
(Const ("Fun.inj_on", [AbsT, UnivT] ---> HOLogic.boolT) $ |
6171 | 291 |
Const (Abs_name, AbsT) $ Const (rep_set_name, UnivT)))) |
5177 | 292 |
(fn _ => [rtac inj_on_inverseI 1, etac thm1 1]); |
293 |
||
6171 | 294 |
val setT = HOLogic.mk_setT T |
295 |
||
296 |
val inj_Rep_thm = |
|
297 |
prove_goalw_cterm [] |
|
298 |
(cterm_of sg |
|
299 |
(HOLogic.mk_Trueprop |
|
11435 | 300 |
(Const ("Fun.inj_on", [RepT, setT] ---> HOLogic.boolT) $ |
301 |
Const (Rep_name, RepT) $ Const ("UNIV", setT)))) |
|
5177 | 302 |
(fn _ => [rtac inj_inverseI 1, rtac thm2 1]) |
303 |
||
6171 | 304 |
in (inj_Abs_thm, inj_Rep_thm) end; |
5177 | 305 |
|
306 |
val newT_iso_inj_thms = map prove_newT_iso_inj_thm |
|
307 |
(new_type_names ~~ newT_iso_axms ~~ newTs ~~ |
|
308 |
take (length newTs, rep_set_names)); |
|
309 |
||
310 |
(********* isomorphisms between existing types and "unfolded" types *******) |
|
311 |
||
312 |
(*---------------------------------------------------------------------*) |
|
313 |
(* isomorphisms are defined using primrec-combinators: *) |
|
314 |
(* generate appropriate functions for instantiating primrec-combinator *) |
|
315 |
(* *) |
|
316 |
(* e.g. dt_Rep_i = list_rec ... (%h t y. In1 ((Leaf h) $ y)) *) |
|
317 |
(* *) |
|
318 |
(* also generate characteristic equations for isomorphisms *) |
|
319 |
(* *) |
|
320 |
(* e.g. dt_Rep_i (cons h t) = In1 ((dt_Rep_j h) $ (dt_Rep_i t)) *) |
|
321 |
(*---------------------------------------------------------------------*) |
|
322 |
||
323 |
fun make_iso_def k ks n ((fs, eqns, i), (cname, cargs)) = |
|
324 |
let |
|
325 |
val argTs = map (typ_of_dtyp descr' sorts) cargs; |
|
326 |
val T = nth_elem (k, recTs); |
|
327 |
val rep_name = nth_elem (k, all_rep_names); |
|
328 |
val rep_const = Const (rep_name, T --> Univ_elT); |
|
329 |
val constr = Const (cname, argTs ---> T); |
|
330 |
||
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331 |
fun process_arg ks' ((i2, i2', ts, Ts), dt) = |
5177 | 332 |
let val T' = typ_of_dtyp descr' sorts dt |
333 |
in (case dt of |
|
334 |
DtRec j => if j mem ks' then |
|
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|
335 |
(i2 + 1, i2' + 1, ts @ [mk_Free "y" Univ_elT i2'], Ts @ [Univ_elT]) |
5177 | 336 |
else |
337 |
(i2 + 1, i2', ts @ [Const (nth_elem (j, all_rep_names), |
|
7015
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|
338 |
T' --> Univ_elT) $ mk_Free "x" T' i2], Ts) |
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|
339 |
| (DtType ("fun", [_, DtRec j])) => |
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|
340 |
let val ([T''], T''') = strip_type T' |
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|
341 |
in if j mem ks' then |
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|
342 |
(i2 + 1, i2' + 1, ts @ [Lim $ mk_fun_inj T'' |
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|
343 |
(mk_Free "y" (T'' --> Univ_elT) i2')], Ts @ [T'' --> Univ_elT]) |
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|
344 |
else |
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|
345 |
(i2 + 1, i2', ts @ [Lim $ mk_fun_inj T'' |
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|
346 |
(Const (o_name, [T''' --> Univ_elT, T', T''] ---> Univ_elT) $ |
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|
347 |
Const (nth_elem (j, all_rep_names), T''' --> Univ_elT) $ |
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|
348 |
mk_Free "x" T' i2)], Ts) |
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|
349 |
end |
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|
350 |
| _ => (i2 + 1, i2', ts @ [Leaf $ mk_inj T' (mk_Free "x" T' i2)], Ts)) |
5177 | 351 |
end; |
352 |
||
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|
353 |
val (i2, i2', ts, Ts) = foldl (process_arg ks) ((1, 1, [], []), cargs); |
5177 | 354 |
val xs = map (uncurry (mk_Free "x")) (argTs ~~ (1 upto (i2 - 1))); |
7015
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changeset
|
355 |
val ys = map (uncurry (mk_Free "y")) (Ts ~~ (1 upto (i2' - 1))); |
5177 | 356 |
val f = list_abs_free (map dest_Free (xs @ ys), mk_univ_inj ts n i); |
357 |
||
7015
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changeset
|
358 |
val (_, _, ts', _) = foldl (process_arg []) ((1, 1, [], []), cargs); |
5177 | 359 |
val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq |
360 |
(rep_const $ list_comb (constr, xs), mk_univ_inj ts' n i)) |
|
361 |
||
362 |
in (fs @ [f], eqns @ [eqn], i + 1) end; |
|
363 |
||
364 |
(* define isomorphisms for all mutually recursive datatypes in list ds *) |
|
365 |
||
366 |
fun make_iso_defs (ds, (thy, char_thms)) = |
|
367 |
let |
|
368 |
val ks = map fst ds; |
|
369 |
val (_, (tname, _, _)) = hd ds; |
|
370 |
val {rec_rewrites, rec_names, ...} = the (Symtab.lookup (dt_info, tname)); |
|
371 |
||
372 |
fun process_dt ((fs, eqns, isos), (k, (tname, _, constrs))) = |
|
373 |
let |
|
374 |
val (fs', eqns', _) = foldl (make_iso_def k ks (length constrs)) |
|
375 |
((fs, eqns, 1), constrs); |
|
376 |
val iso = (nth_elem (k, recTs), nth_elem (k, all_rep_names)) |
|
377 |
in (fs', eqns', isos @ [iso]) end; |
|
378 |
||
379 |
val (fs, eqns, isos) = foldl process_dt (([], [], []), ds); |
|
380 |
val fTs = map fastype_of fs; |
|
381 |
val defs = map (fn (rec_name, (T, iso_name)) => ((Sign.base_name iso_name) ^ "_def", |
|
382 |
equals (T --> Univ_elT) $ Const (iso_name, T --> Univ_elT) $ |
|
383 |
list_comb (Const (rec_name, fTs @ [T] ---> Univ_elT), fs))) (rec_names ~~ isos); |
|
9315 | 384 |
val (thy', def_thms) = (PureThy.add_defs_i false o map Thm.no_attributes) defs thy; |
5177 | 385 |
|
386 |
(* prove characteristic equations *) |
|
387 |
||
5553 | 388 |
val rewrites = def_thms @ (map mk_meta_eq rec_rewrites); |
5177 | 389 |
val char_thms' = map (fn eqn => prove_goalw_cterm rewrites |
6394 | 390 |
(cterm_of (Theory.sign_of thy') eqn) (fn _ => [rtac refl 1])) eqns; |
5177 | 391 |
|
392 |
in (thy', char_thms' @ char_thms) end; |
|
393 |
||
5661 | 394 |
val (thy5, iso_char_thms) = foldr make_iso_defs |
395 |
(tl descr, (add_path flat_names big_name thy4, [])); |
|
5177 | 396 |
|
397 |
(* prove isomorphism properties *) |
|
398 |
||
7015
85be09eb136c
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6522
diff
changeset
|
399 |
fun mk_funs_inv thm = |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
400 |
let |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
401 |
val [_, t] = prems_of Funs_inv; |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
402 |
val [_ $ (_ $ _ $ R)] = Logic.strip_assums_hyp t; |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
403 |
val _ $ (_ $ (r $ (a $ _)) $ _) = Logic.strip_assums_concl t; |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
404 |
val [_ $ (_ $ _ $ R')] = prems_of thm; |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
405 |
val _ $ (_ $ (r' $ (a' $ _)) $ _) = concl_of thm; |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
406 |
val inv' = cterm_instantiate (map |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
407 |
((pairself (cterm_of (sign_of_thm thm))) o |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
408 |
(apsnd (map_term_types (incr_tvar 1)))) |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
409 |
[(R, R'), (r, r'), (a, a')]) Funs_inv |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
410 |
in |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
411 |
rule_by_tactic (atac 2) (thm RSN (2, inv')) |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
412 |
end; |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
413 |
|
5177 | 414 |
(* prove inj dt_Rep_i and dt_Rep_i x : dt_rep_set_i *) |
415 |
||
416 |
fun prove_iso_thms (ds, (inj_thms, elem_thms)) = |
|
417 |
let |
|
418 |
val (_, (tname, _, _)) = hd ds; |
|
419 |
val {induction, ...} = the (Symtab.lookup (dt_info, tname)); |
|
420 |
||
421 |
fun mk_ind_concl (i, _) = |
|
422 |
let |
|
423 |
val T = nth_elem (i, recTs); |
|
424 |
val Rep_t = Const (nth_elem (i, all_rep_names), T --> Univ_elT); |
|
425 |
val rep_set_name = nth_elem (i, rep_set_names) |
|
426 |
in (HOLogic.all_const T $ Abs ("y", T, HOLogic.imp $ |
|
427 |
HOLogic.mk_eq (Rep_t $ mk_Free "x" T i, Rep_t $ Bound 0) $ |
|
428 |
HOLogic.mk_eq (mk_Free "x" T i, Bound 0)), |
|
429 |
HOLogic.mk_mem (Rep_t $ mk_Free "x" T i, Const (rep_set_name, UnivT))) |
|
430 |
end; |
|
431 |
||
432 |
val (ind_concl1, ind_concl2) = ListPair.unzip (map mk_ind_concl ds); |
|
433 |
||
5553 | 434 |
val rewrites = map mk_meta_eq iso_char_thms; |
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
435 |
val inj_thms' = flat (map (fn r => [r RS injD, r RS inj_o]) |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
436 |
(map snd newT_iso_inj_thms @ inj_thms)); |
5177 | 437 |
|
6394 | 438 |
val inj_thm = prove_goalw_cterm [] (cterm_of (Theory.sign_of thy5) |
5177 | 439 |
(HOLogic.mk_Trueprop (mk_conj ind_concl1))) (fn _ => |
440 |
[indtac induction 1, |
|
441 |
REPEAT (EVERY |
|
442 |
[rtac allI 1, rtac impI 1, |
|
443 |
exh_tac (exh_thm_of dt_info) 1, |
|
444 |
REPEAT (EVERY |
|
445 |
[hyp_subst_tac 1, |
|
446 |
rewrite_goals_tac rewrites, |
|
447 |
REPEAT (dresolve_tac [In0_inject, In1_inject] 1), |
|
448 |
(eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1) |
|
449 |
ORELSE (EVERY |
|
450 |
[REPEAT (etac Scons_inject 1), |
|
451 |
REPEAT (dresolve_tac |
|
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
452 |
(inj_thms' @ [Leaf_inject, Lim_inject, Inl_inject, Inr_inject]) 1), |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
453 |
REPEAT ((EVERY [etac allE 1, dtac mp 1, atac 1]) ORELSE |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
454 |
(dtac inj_fun_lemma 1 THEN atac 1)), |
5177 | 455 |
TRY (hyp_subst_tac 1), |
456 |
rtac refl 1])])])]); |
|
457 |
||
6171 | 458 |
val inj_thms'' = map (fn r => r RS datatype_injI) |
459 |
(split_conj_thm inj_thm); |
|
5177 | 460 |
|
6171 | 461 |
val elem_thm = |
462 |
prove_goalw_cterm [] |
|
6394 | 463 |
(cterm_of (Theory.sign_of thy5) |
6171 | 464 |
(HOLogic.mk_Trueprop (mk_conj ind_concl2))) |
465 |
(fn _ => |
|
466 |
[indtac induction 1, |
|
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
467 |
rewrite_goals_tac (o_def :: rewrites), |
6171 | 468 |
REPEAT (EVERY |
469 |
[resolve_tac rep_intrs 1, |
|
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
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6522
diff
changeset
|
470 |
REPEAT (FIRST [atac 1, etac spec 1, |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
471 |
resolve_tac (FunsI :: elem_thms) 1])])]); |
5177 | 472 |
|
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
473 |
in (inj_thms'' @ inj_thms, elem_thms @ (split_conj_thm elem_thm)) |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
474 |
end; |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
475 |
|
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
476 |
val (iso_inj_thms_unfolded, iso_elem_thms) = foldr prove_iso_thms |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
477 |
(tl descr, ([], map #3 newT_iso_axms)); |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
478 |
val iso_inj_thms = map snd newT_iso_inj_thms @ iso_inj_thms_unfolded; |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
479 |
|
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
480 |
(* prove x : dt_rep_set_i --> x : range dt_Rep_i *) |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
481 |
|
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
482 |
fun mk_iso_t (((set_name, iso_name), i), T) = |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
483 |
let val isoT = T --> Univ_elT |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
484 |
in HOLogic.imp $ |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
485 |
HOLogic.mk_mem (mk_Free "x" Univ_elT i, Const (set_name, UnivT)) $ |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
486 |
(if i < length newTs then Const ("True", HOLogic.boolT) |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
487 |
else HOLogic.mk_mem (mk_Free "x" Univ_elT i, |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
488 |
Const ("image", [isoT, HOLogic.mk_setT T] ---> UnivT) $ |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
489 |
Const (iso_name, isoT) $ Const ("UNIV", HOLogic.mk_setT T))) |
5177 | 490 |
end; |
491 |
||
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
492 |
val iso_t = HOLogic.mk_Trueprop (mk_conj (map mk_iso_t |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
493 |
(rep_set_names ~~ all_rep_names ~~ (0 upto (length descr' - 1)) ~~ recTs))); |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
494 |
|
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
495 |
(* all the theorems are proved by one single simultaneous induction *) |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
496 |
|
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
497 |
val iso_thms = if length descr = 1 then [] else |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
498 |
drop (length newTs, split_conj_thm |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
499 |
(prove_goalw_cterm [] (cterm_of (Theory.sign_of thy5) iso_t) (fn _ => |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
500 |
[indtac rep_induct 1, |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
501 |
REPEAT (rtac TrueI 1), |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
502 |
REPEAT (EVERY |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
503 |
[rewrite_goals_tac [mk_meta_eq Collect_mem_eq], |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
504 |
REPEAT (etac Funs_IntE 1), |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
505 |
REPEAT (eresolve_tac (rangeE :: |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
506 |
map (fn r => r RS Funs_rangeE) iso_inj_thms_unfolded) 1), |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
507 |
REPEAT (eresolve_tac (map (fn (iso, _, _) => iso RS subst) newT_iso_axms @ |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
508 |
map (fn (iso, _, _) => mk_funs_inv iso RS subst) newT_iso_axms) 1), |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
509 |
TRY (hyp_subst_tac 1), |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
510 |
rtac (sym RS range_eqI) 1, |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
511 |
resolve_tac iso_char_thms 1])]))); |
11435 | 512 |
|
513 |
val Abs_inverse_thms' = |
|
514 |
map #1 newT_iso_axms @ |
|
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
515 |
map2 (fn (r_inj, r) => f_myinv_f OF [r_inj, r RS mp]) |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
516 |
(iso_inj_thms_unfolded, iso_thms); |
11435 | 517 |
|
518 |
val Abs_inverse_thms = map (fn r => r RS subst) (Abs_inverse_thms' @ |
|
519 |
map mk_funs_inv Abs_inverse_thms'); |
|
5177 | 520 |
|
521 |
(******************* freeness theorems for constructors *******************) |
|
522 |
||
6427 | 523 |
val _ = message "Proving freeness of constructors ..."; |
5177 | 524 |
|
525 |
(* prove theorem Rep_i (Constr_j ...) = Inj_j ... *) |
|
526 |
||
527 |
fun prove_constr_rep_thm eqn = |
|
528 |
let |
|
529 |
val inj_thms = map (fn (r, _) => r RS inj_onD) newT_iso_inj_thms; |
|
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
530 |
val rewrites = o_def :: constr_defs @ (map (mk_meta_eq o #2) newT_iso_axms) |
6394 | 531 |
in prove_goalw_cterm [] (cterm_of (Theory.sign_of thy5) eqn) (fn _ => |
5177 | 532 |
[resolve_tac inj_thms 1, |
533 |
rewrite_goals_tac rewrites, |
|
534 |
rtac refl 1, |
|
535 |
resolve_tac rep_intrs 2, |
|
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
536 |
REPEAT (resolve_tac (FunsI :: iso_elem_thms) 1)]) |
5177 | 537 |
end; |
538 |
||
539 |
(*--------------------------------------------------------------*) |
|
540 |
(* constr_rep_thms and rep_congs are used to prove distinctness *) |
|
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
541 |
(* of constructors. *) |
5177 | 542 |
(*--------------------------------------------------------------*) |
543 |
||
544 |
val constr_rep_thms = map (map prove_constr_rep_thm) constr_rep_eqns; |
|
545 |
||
546 |
val dist_rewrites = map (fn (rep_thms, dist_lemma) => |
|
547 |
dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0])) |
|
548 |
(constr_rep_thms ~~ dist_lemmas); |
|
549 |
||
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
550 |
fun prove_distinct_thms (_, []) = [] |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
551 |
| prove_distinct_thms (dist_rewrites', t::_::ts) = |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
552 |
let |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
553 |
val dist_thm = prove_goalw_cterm [] (cterm_of (Theory.sign_of thy5) t) (fn _ => |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
554 |
[simp_tac (HOL_ss addsimps dist_rewrites') 1]) |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
555 |
in dist_thm::(standard (dist_thm RS not_sym)):: |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
556 |
(prove_distinct_thms (dist_rewrites', ts)) |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
557 |
end; |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
558 |
|
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
559 |
val distinct_thms = map prove_distinct_thms (dist_rewrites ~~ |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
560 |
DatatypeProp.make_distincts new_type_names descr sorts thy5); |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
561 |
|
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
562 |
val simproc_dists = map (fn ((((_, (_, _, constrs)), rep_thms), congr), dists) => |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
563 |
if length constrs < !DatatypeProp.dtK then FewConstrs dists |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
564 |
else ManyConstrs (congr, HOL_basic_ss addsimps rep_thms)) (hd descr ~~ |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
565 |
constr_rep_thms ~~ rep_congs ~~ distinct_thms); |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
566 |
|
5177 | 567 |
(* prove injectivity of constructors *) |
568 |
||
569 |
fun prove_constr_inj_thm rep_thms t = |
|
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
570 |
let val inj_thms = Scons_inject::sum_case_inject::(map make_elim |
5177 | 571 |
((map (fn r => r RS injD) iso_inj_thms) @ |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
572 |
[In0_inject, In1_inject, Leaf_inject, Inl_inject, Inr_inject, Lim_inject])) |
6394 | 573 |
in prove_goalw_cterm [] (cterm_of (Theory.sign_of thy5) t) (fn _ => |
5177 | 574 |
[rtac iffI 1, |
575 |
REPEAT (etac conjE 2), hyp_subst_tac 2, rtac refl 2, |
|
576 |
dresolve_tac rep_congs 1, dtac box_equals 1, |
|
7499 | 577 |
REPEAT (resolve_tac rep_thms 1), rewtac o_def, |
5177 | 578 |
REPEAT (eresolve_tac inj_thms 1), |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
579 |
REPEAT (ares_tac [conjI] 1 ORELSE (EVERY [rtac ext 1, dtac fun_cong 1, |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
580 |
eresolve_tac inj_thms 1, atac 1]))]) |
5177 | 581 |
end; |
582 |
||
583 |
val constr_inject = map (fn (ts, thms) => map (prove_constr_inj_thm thms) ts) |
|
584 |
((DatatypeProp.make_injs descr sorts) ~~ constr_rep_thms); |
|
585 |
||
8479
5d327a46dc61
Now returns theorems with correct names in derivations.
berghofe
parents:
8436
diff
changeset
|
586 |
val (thy6, (constr_inject', distinct_thms'))= thy5 |> parent_path flat_names |> |
5d327a46dc61
Now returns theorems with correct names in derivations.
berghofe
parents:
8436
diff
changeset
|
587 |
store_thmss "inject" new_type_names constr_inject |>>> |
5d327a46dc61
Now returns theorems with correct names in derivations.
berghofe
parents:
8436
diff
changeset
|
588 |
store_thmss "distinct" new_type_names distinct_thms; |
5177 | 589 |
|
590 |
(*************************** induction theorem ****************************) |
|
591 |
||
6427 | 592 |
val _ = message "Proving induction rule for datatypes ..."; |
5177 | 593 |
|
594 |
val Rep_inverse_thms = (map (fn (_, iso, _) => iso RS subst) newT_iso_axms) @ |
|
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
595 |
(map (fn r => r RS myinv_f_f RS subst) iso_inj_thms_unfolded); |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
596 |
val Rep_inverse_thms' = map (fn r => r RS myinv_f_f) iso_inj_thms_unfolded; |
5177 | 597 |
|
598 |
fun mk_indrule_lemma ((prems, concls), ((i, _), T)) = |
|
599 |
let |
|
600 |
val Rep_t = Const (nth_elem (i, all_rep_names), T --> Univ_elT) $ |
|
601 |
mk_Free "x" T i; |
|
602 |
||
603 |
val Abs_t = if i < length newTs then |
|
6394 | 604 |
Const (Sign.intern_const (Theory.sign_of thy6) |
5177 | 605 |
("Abs_" ^ (nth_elem (i, new_type_names))), Univ_elT --> T) |
11435 | 606 |
else Const ("Inductive.myinv", [T --> Univ_elT, Univ_elT] ---> T) $ |
5177 | 607 |
Const (nth_elem (i, all_rep_names), T --> Univ_elT) |
608 |
||
609 |
in (prems @ [HOLogic.imp $ HOLogic.mk_mem (Rep_t, |
|
610 |
Const (nth_elem (i, rep_set_names), UnivT)) $ |
|
611 |
(mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))], |
|
612 |
concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i]) |
|
613 |
end; |
|
614 |
||
615 |
val (indrule_lemma_prems, indrule_lemma_concls) = |
|
616 |
foldl mk_indrule_lemma (([], []), (descr' ~~ recTs)); |
|
617 |
||
6394 | 618 |
val cert = cterm_of (Theory.sign_of thy6); |
5177 | 619 |
|
620 |
val indrule_lemma = prove_goalw_cterm [] (cert |
|
621 |
(Logic.mk_implies |
|
622 |
(HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems), |
|
623 |
HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls)))) (fn prems => |
|
624 |
[cut_facts_tac prems 1, REPEAT (etac conjE 1), |
|
625 |
REPEAT (EVERY |
|
626 |
[TRY (rtac conjI 1), resolve_tac Rep_inverse_thms 1, |
|
627 |
etac mp 1, resolve_tac iso_elem_thms 1])]); |
|
628 |
||
8305 | 629 |
val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma))); |
5177 | 630 |
val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else |
631 |
map (Free o apfst fst o dest_Var) Ps; |
|
632 |
val indrule_lemma' = cterm_instantiate (map cert Ps ~~ map cert frees) indrule_lemma; |
|
633 |
||
10911
eb5721204b38
proper induction rule for arbitrarily branching datatype;
wenzelm
parents:
9315
diff
changeset
|
634 |
val dt_induct = prove_goalw_cterm [InductivePackage.inductive_forall_def] (cert |
5177 | 635 |
(DatatypeProp.make_ind descr sorts)) (fn prems => |
636 |
[rtac indrule_lemma' 1, indtac rep_induct 1, |
|
637 |
EVERY (map (fn (prem, r) => (EVERY |
|
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
638 |
[REPEAT (eresolve_tac (Funs_IntE::Abs_inverse_thms) 1), |
5177 | 639 |
simp_tac (HOL_basic_ss addsimps ((symmetric r)::Rep_inverse_thms')) 1, |
7499 | 640 |
DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE (EVERY [rewtac o_def, |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
641 |
rtac allI 1, dtac FunsD 1, etac CollectD 1]))])) |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
642 |
(prems ~~ (constr_defs @ (map mk_meta_eq iso_char_thms))))]); |
5177 | 643 |
|
8436 | 644 |
val (thy7, [dt_induct']) = thy6 |> |
5661 | 645 |
Theory.add_path big_name |> |
10911
eb5721204b38
proper induction rule for arbitrarily branching datatype;
wenzelm
parents:
9315
diff
changeset
|
646 |
PureThy.add_thms [(("induct", dt_induct), |
eb5721204b38
proper induction rule for arbitrarily branching datatype;
wenzelm
parents:
9315
diff
changeset
|
647 |
[Drule.rule_attribute (K InductivePackage.rulify), case_names_induct])] |>> |
5661 | 648 |
Theory.parent_path; |
5177 | 649 |
|
8479
5d327a46dc61
Now returns theorems with correct names in derivations.
berghofe
parents:
8436
diff
changeset
|
650 |
in (thy7, constr_inject', distinct_thms', dist_rewrites, simproc_dists, dt_induct') |
5177 | 651 |
end; |
652 |
||
653 |
end; |