author | skalberg |
Sun, 13 Feb 2005 17:15:14 +0100 | |
changeset 15531 | 08c8dad8e399 |
parent 15457 | 1fbd4aba46e3 |
child 15570 | 8d8c70b41bab |
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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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 -> DatatypeAux.descr 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 = |
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if PureThy.get_name thy = "Datatype" then thy |
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else theory "Datatype"; |
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val node_name = "Datatype_Universe.node"; |
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val In0_name = "Datatype_Universe.In0"; |
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val In1_name = "Datatype_Universe.In1"; |
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val Scons_name = "Datatype_Universe.Scons"; |
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val Leaf_name = "Datatype_Universe.Leaf"; |
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val Numb_name = "Datatype_Universe.Numb"; |
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val Lim_name = "Datatype_Universe.Lim"; |
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val Suml_name = "Datatype.Suml"; |
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val Sumr_name = "Datatype.Sumr"; |
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val [In0_inject, In1_inject, Scons_inject, Leaf_inject, |
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In0_eq, In1_eq, In0_not_In1, In1_not_In0, |
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Lim_inject, Suml_inject, Sumr_inject] = map (get_thm Datatype_thy o rpair NONE) |
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["In0_inject", "In1_inject", "Scons_inject", "Leaf_inject", |
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"In0_eq", "In1_eq", "In0_not_In1", "In1_not_In0", |
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"Lim_inject", "Suml_inject", "Sumr_inject"]; |
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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 arities = get_arities descr' \ 0; |
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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 ("Sum_Type.Inl", T1 --> T) $ (mk_inj' T1 n2 i) |
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else |
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Const ("Sum_Type.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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fun mkT U = (U --> Univ_elT) --> T --> Univ_elT |
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in |
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if i <= n2 then Const (Suml_name, mkT T1) $ mk_inj T1 n2 i |
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else Const (Sumr_name, mkT T2) $ 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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val mk_lim = foldr (fn (T, t) => Lim $ mk_fun_inj T (Abs ("x", T, t))); |
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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 (dt, (j, prems, ts)) = (case strip_dtyp dt of |
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(dts, DtRec k) => |
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let |
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val Ts = map (typ_of_dtyp descr' sorts) dts; |
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val free_t = |
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app_bnds (mk_Free "x" (Ts ---> Univ_elT) j) (length Ts) |
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in (j + 1, list_all (map (pair "x") Ts, |
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HOLogic.mk_Trueprop (HOLogic.mk_mem (free_t, |
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Const (nth_elem (k, rep_set_names), UnivT)))) :: prems, |
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mk_lim (Ts, free_t) :: ts) |
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end |
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| _ => |
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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 (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) []) 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 false (SOME name') (name, tvs, mx) c NONE |
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(rtac exI 1 THEN |
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QUIET_BREADTH_FIRST (has_fewer_prems 1) |
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(resolve_tac rep_intrs 1))) thy |> #1) |
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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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201 |
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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 (strip_dtyp dt, strip_type T) of |
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((_, DtRec m), (Us, U)) => (j + 1, free_t :: l_args, mk_lim (Us, |
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Const (nth_elem (m, all_rep_names), U --> Univ_elT) $ |
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app_bnds free_t (length Us)) :: r_args) |
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| _ => (j + 1, free_t::l_args, (Leaf $ mk_inj T free_t)::r_args)) |
217 |
end; |
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218 |
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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); |
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val rhs = mk_univ_inj r_args n i; |
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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)] |> |
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(PureThy.add_defs_i false o map Thm.no_attributes) [(def_name, def)]; |
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8436 | 233 |
in (thy', defs @ [def_thm], eqns @ [eqn], i + 1) end; |
5177 | 234 |
|
235 |
(* constructor definitions for datatype *) |
|
236 |
||
237 |
fun dt_constr_defs ((thy, defs, eqns, rep_congs, dist_lemmas), |
|
238 |
((((_, (_, _, constrs)), tname), T), constr_syntax)) = |
|
239 |
let |
|
240 |
val _ $ (_ $ (cong_f $ _) $ _) = concl_of arg_cong; |
|
6394 | 241 |
val sg = Theory.sign_of thy; |
5177 | 242 |
val rep_const = cterm_of sg |
243 |
(Const (Sign.intern_const sg ("Rep_" ^ tname), T --> Univ_elT)); |
|
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244 |
val cong' = standard (cterm_instantiate [(cterm_of sg cong_f, rep_const)] arg_cong); |
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245 |
val dist = standard (cterm_instantiate [(cterm_of sg distinct_f, rep_const)] distinct_lemma); |
5177 | 246 |
val (thy', defs', eqns', _) = foldl ((make_constr_def tname T) (length constrs)) |
5661 | 247 |
((add_path flat_names tname thy, defs, [], 1), constrs ~~ constr_syntax) |
5177 | 248 |
in |
5661 | 249 |
(parent_path flat_names thy', defs', eqns @ [eqns'], |
5177 | 250 |
rep_congs @ [cong'], dist_lemmas @ [dist]) |
251 |
end; |
|
252 |
||
253 |
val (thy4, constr_defs, constr_rep_eqns, rep_congs, dist_lemmas) = foldl dt_constr_defs |
|
5661 | 254 |
((thy3 |> Theory.add_consts_i iso_decls |> parent_path flat_names, [], [], [], []), |
5177 | 255 |
hd descr ~~ new_type_names ~~ newTs ~~ constr_syntax); |
256 |
||
257 |
(*********** isomorphisms for new types (introduced by typedef) ***********) |
|
258 |
||
6427 | 259 |
val _ = message "Proving isomorphism properties ..."; |
5177 | 260 |
|
261 |
(* get axioms from theory *) |
|
262 |
||
263 |
val newT_iso_axms = map (fn s => |
|
15531 | 264 |
(get_thm thy4 ("Abs_" ^ s ^ "_inverse", NONE), |
265 |
get_thm thy4 ("Rep_" ^ s ^ "_inverse", NONE), |
|
266 |
get_thm thy4 ("Rep_" ^ s, NONE))) new_type_names; |
|
5177 | 267 |
|
268 |
(*------------------------------------------------*) |
|
269 |
(* prove additional theorems: *) |
|
270 |
(* inj_on dt_Abs_i rep_set_i and inj dt_Rep_i *) |
|
271 |
(*------------------------------------------------*) |
|
272 |
||
273 |
fun prove_newT_iso_inj_thm (((s, (thm1, thm2, _)), T), rep_set_name) = |
|
274 |
let |
|
6394 | 275 |
val sg = Theory.sign_of thy4; |
5177 | 276 |
val RepT = T --> Univ_elT; |
277 |
val Rep_name = Sign.intern_const sg ("Rep_" ^ s); |
|
278 |
val AbsT = Univ_elT --> T; |
|
279 |
val Abs_name = Sign.intern_const sg ("Abs_" ^ s); |
|
280 |
||
6171 | 281 |
val inj_Abs_thm = |
282 |
prove_goalw_cterm [] |
|
283 |
(cterm_of sg |
|
284 |
(HOLogic.mk_Trueprop |
|
11435 | 285 |
(Const ("Fun.inj_on", [AbsT, UnivT] ---> HOLogic.boolT) $ |
6171 | 286 |
Const (Abs_name, AbsT) $ Const (rep_set_name, UnivT)))) |
5177 | 287 |
(fn _ => [rtac inj_on_inverseI 1, etac thm1 1]); |
288 |
||
6171 | 289 |
val setT = HOLogic.mk_setT T |
290 |
||
291 |
val inj_Rep_thm = |
|
292 |
prove_goalw_cterm [] |
|
293 |
(cterm_of sg |
|
294 |
(HOLogic.mk_Trueprop |
|
11435 | 295 |
(Const ("Fun.inj_on", [RepT, setT] ---> HOLogic.boolT) $ |
296 |
Const (Rep_name, RepT) $ Const ("UNIV", setT)))) |
|
5177 | 297 |
(fn _ => [rtac inj_inverseI 1, rtac thm2 1]) |
298 |
||
6171 | 299 |
in (inj_Abs_thm, inj_Rep_thm) end; |
5177 | 300 |
|
301 |
val newT_iso_inj_thms = map prove_newT_iso_inj_thm |
|
302 |
(new_type_names ~~ newT_iso_axms ~~ newTs ~~ |
|
303 |
take (length newTs, rep_set_names)); |
|
304 |
||
305 |
(********* isomorphisms between existing types and "unfolded" types *******) |
|
306 |
||
307 |
(*---------------------------------------------------------------------*) |
|
308 |
(* isomorphisms are defined using primrec-combinators: *) |
|
309 |
(* generate appropriate functions for instantiating primrec-combinator *) |
|
310 |
(* *) |
|
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311 |
(* e.g. dt_Rep_i = list_rec ... (%h t y. In1 (Scons (Leaf h) y)) *) |
5177 | 312 |
(* *) |
313 |
(* also generate characteristic equations for isomorphisms *) |
|
314 |
(* *) |
|
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|
315 |
(* e.g. dt_Rep_i (cons h t) = In1 (Scons (dt_Rep_j h) (dt_Rep_i t)) *) |
5177 | 316 |
(*---------------------------------------------------------------------*) |
317 |
||
318 |
fun make_iso_def k ks n ((fs, eqns, i), (cname, cargs)) = |
|
319 |
let |
|
320 |
val argTs = map (typ_of_dtyp descr' sorts) cargs; |
|
321 |
val T = nth_elem (k, recTs); |
|
322 |
val rep_name = nth_elem (k, all_rep_names); |
|
323 |
val rep_const = Const (rep_name, T --> Univ_elT); |
|
324 |
val constr = Const (cname, argTs ---> T); |
|
325 |
||
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|
326 |
fun process_arg ks' ((i2, i2', ts, Ts), dt) = |
13641
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|
327 |
let |
63d1790a43ed
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|
328 |
val T' = typ_of_dtyp descr' sorts dt; |
63d1790a43ed
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|
329 |
val (Us, U) = strip_type T' |
63d1790a43ed
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|
330 |
in (case strip_dtyp dt of |
63d1790a43ed
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changeset
|
331 |
(_, DtRec j) => if j mem ks' then |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
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|
332 |
(i2 + 1, i2' + 1, ts @ [mk_lim (Us, app_bnds |
63d1790a43ed
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changeset
|
333 |
(mk_Free "y" (Us ---> Univ_elT) i2') (length Us))], |
63d1790a43ed
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changeset
|
334 |
Ts @ [Us ---> Univ_elT]) |
5177 | 335 |
else |
13641
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|
336 |
(i2 + 1, i2', ts @ [mk_lim (Us, |
63d1790a43ed
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|
337 |
Const (nth_elem (j, all_rep_names), U --> Univ_elT) $ |
63d1790a43ed
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|
338 |
app_bnds (mk_Free "x" T' i2) (length Us))], Ts) |
7015
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- Datatype package now also supports arbitrarily branching datatypes
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6522
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changeset
|
339 |
| _ => (i2 + 1, i2', ts @ [Leaf $ mk_inj T' (mk_Free "x" T' i2)], Ts)) |
5177 | 340 |
end; |
341 |
||
7015
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6522
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changeset
|
342 |
val (i2, i2', ts, Ts) = foldl (process_arg ks) ((1, 1, [], []), cargs); |
5177 | 343 |
val xs = map (uncurry (mk_Free "x")) (argTs ~~ (1 upto (i2 - 1))); |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
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parents:
6522
diff
changeset
|
344 |
val ys = map (uncurry (mk_Free "y")) (Ts ~~ (1 upto (i2' - 1))); |
5177 | 345 |
val f = list_abs_free (map dest_Free (xs @ ys), mk_univ_inj ts n i); |
346 |
||
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
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6522
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changeset
|
347 |
val (_, _, ts', _) = foldl (process_arg []) ((1, 1, [], []), cargs); |
5177 | 348 |
val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq |
349 |
(rep_const $ list_comb (constr, xs), mk_univ_inj ts' n i)) |
|
350 |
||
351 |
in (fs @ [f], eqns @ [eqn], i + 1) end; |
|
352 |
||
353 |
(* define isomorphisms for all mutually recursive datatypes in list ds *) |
|
354 |
||
355 |
fun make_iso_defs (ds, (thy, char_thms)) = |
|
356 |
let |
|
357 |
val ks = map fst ds; |
|
358 |
val (_, (tname, _, _)) = hd ds; |
|
359 |
val {rec_rewrites, rec_names, ...} = the (Symtab.lookup (dt_info, tname)); |
|
360 |
||
361 |
fun process_dt ((fs, eqns, isos), (k, (tname, _, constrs))) = |
|
362 |
let |
|
363 |
val (fs', eqns', _) = foldl (make_iso_def k ks (length constrs)) |
|
364 |
((fs, eqns, 1), constrs); |
|
365 |
val iso = (nth_elem (k, recTs), nth_elem (k, all_rep_names)) |
|
366 |
in (fs', eqns', isos @ [iso]) end; |
|
367 |
||
368 |
val (fs, eqns, isos) = foldl process_dt (([], [], []), ds); |
|
369 |
val fTs = map fastype_of fs; |
|
370 |
val defs = map (fn (rec_name, (T, iso_name)) => ((Sign.base_name iso_name) ^ "_def", |
|
371 |
equals (T --> Univ_elT) $ Const (iso_name, T --> Univ_elT) $ |
|
372 |
list_comb (Const (rec_name, fTs @ [T] ---> Univ_elT), fs))) (rec_names ~~ isos); |
|
9315 | 373 |
val (thy', def_thms) = (PureThy.add_defs_i false o map Thm.no_attributes) defs thy; |
5177 | 374 |
|
375 |
(* prove characteristic equations *) |
|
376 |
||
5553 | 377 |
val rewrites = def_thms @ (map mk_meta_eq rec_rewrites); |
5177 | 378 |
val char_thms' = map (fn eqn => prove_goalw_cterm rewrites |
6394 | 379 |
(cterm_of (Theory.sign_of thy') eqn) (fn _ => [rtac refl 1])) eqns; |
5177 | 380 |
|
381 |
in (thy', char_thms' @ char_thms) end; |
|
382 |
||
5661 | 383 |
val (thy5, iso_char_thms) = foldr make_iso_defs |
384 |
(tl descr, (add_path flat_names big_name thy4, [])); |
|
5177 | 385 |
|
386 |
(* prove isomorphism properties *) |
|
387 |
||
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
388 |
fun mk_funs_inv thm = |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
389 |
let |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
390 |
val {sign, prop, ...} = rep_thm thm; |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
391 |
val (_ $ (_ $ (Const (_, Type (_, [U, _])) $ _ $ S)) $ |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
392 |
(_ $ (_ $ (r $ (a $ _)) $ _)), _) = Type.freeze_thaw prop; |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
393 |
val used = add_term_tfree_names (a, []); |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
394 |
|
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
395 |
fun mk_thm i = |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
396 |
let |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
397 |
val Ts = map (TFree o rpair HOLogic.typeS) |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
398 |
(variantlist (replicate i "'t", used)); |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
399 |
val f = Free ("f", Ts ---> U) |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
400 |
in prove_goalw_cterm [] (cterm_of sign (Logic.mk_implies |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
401 |
(HOLogic.mk_Trueprop (HOLogic.list_all |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
402 |
(map (pair "x") Ts, HOLogic.mk_mem (app_bnds f i, S))), |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
403 |
HOLogic.mk_Trueprop (HOLogic.mk_eq (list_abs (map (pair "x") Ts, |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
404 |
r $ (a $ app_bnds f i)), f))))) (fn prems => |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
405 |
[cut_facts_tac prems 1, REPEAT (rtac ext 1), |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
406 |
REPEAT (etac allE 1), rtac thm 1, atac 1]) |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
407 |
end |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
408 |
in map (fn r => r RS subst) (thm :: map mk_thm arities) end; |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
409 |
|
5177 | 410 |
(* prove inj dt_Rep_i and dt_Rep_i x : dt_rep_set_i *) |
411 |
||
412 |
fun prove_iso_thms (ds, (inj_thms, elem_thms)) = |
|
413 |
let |
|
414 |
val (_, (tname, _, _)) = hd ds; |
|
415 |
val {induction, ...} = the (Symtab.lookup (dt_info, tname)); |
|
416 |
||
417 |
fun mk_ind_concl (i, _) = |
|
418 |
let |
|
419 |
val T = nth_elem (i, recTs); |
|
420 |
val Rep_t = Const (nth_elem (i, all_rep_names), T --> Univ_elT); |
|
421 |
val rep_set_name = nth_elem (i, rep_set_names) |
|
422 |
in (HOLogic.all_const T $ Abs ("y", T, HOLogic.imp $ |
|
423 |
HOLogic.mk_eq (Rep_t $ mk_Free "x" T i, Rep_t $ Bound 0) $ |
|
424 |
HOLogic.mk_eq (mk_Free "x" T i, Bound 0)), |
|
425 |
HOLogic.mk_mem (Rep_t $ mk_Free "x" T i, Const (rep_set_name, UnivT))) |
|
426 |
end; |
|
427 |
||
428 |
val (ind_concl1, ind_concl2) = ListPair.unzip (map mk_ind_concl ds); |
|
429 |
||
5553 | 430 |
val rewrites = map mk_meta_eq iso_char_thms; |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
431 |
val inj_thms' = map (fn r => r RS injD) |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
432 |
(map snd newT_iso_inj_thms @ inj_thms); |
5177 | 433 |
|
6394 | 434 |
val inj_thm = prove_goalw_cterm [] (cterm_of (Theory.sign_of thy5) |
5177 | 435 |
(HOLogic.mk_Trueprop (mk_conj ind_concl1))) (fn _ => |
11951
381135c295ef
Fixed several bugs concerning arbitrarily branching datatypes.
berghofe
parents:
11827
diff
changeset
|
436 |
[(indtac induction THEN_ALL_NEW ObjectLogic.atomize_tac) 1, |
5177 | 437 |
REPEAT (EVERY |
438 |
[rtac allI 1, rtac impI 1, |
|
439 |
exh_tac (exh_thm_of dt_info) 1, |
|
440 |
REPEAT (EVERY |
|
441 |
[hyp_subst_tac 1, |
|
442 |
rewrite_goals_tac rewrites, |
|
443 |
REPEAT (dresolve_tac [In0_inject, In1_inject] 1), |
|
444 |
(eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1) |
|
445 |
ORELSE (EVERY |
|
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
446 |
[REPEAT (eresolve_tac (Scons_inject :: |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
447 |
map make_elim [Leaf_inject, Inl_inject, Inr_inject]) 1), |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
448 |
REPEAT (cong_tac 1), rtac refl 1, |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
449 |
REPEAT (atac 1 ORELSE (EVERY |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
450 |
[REPEAT (rtac ext 1), |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
451 |
REPEAT (eresolve_tac (mp :: allE :: |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
452 |
map make_elim (Suml_inject :: Sumr_inject :: |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
453 |
Lim_inject :: fun_cong :: inj_thms')) 1), |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
454 |
atac 1]))])])])]); |
5177 | 455 |
|
6171 | 456 |
val inj_thms'' = map (fn r => r RS datatype_injI) |
457 |
(split_conj_thm inj_thm); |
|
5177 | 458 |
|
6171 | 459 |
val elem_thm = |
460 |
prove_goalw_cterm [] |
|
6394 | 461 |
(cterm_of (Theory.sign_of thy5) |
6171 | 462 |
(HOLogic.mk_Trueprop (mk_conj ind_concl2))) |
463 |
(fn _ => |
|
11951
381135c295ef
Fixed several bugs concerning arbitrarily branching datatypes.
berghofe
parents:
11827
diff
changeset
|
464 |
[(indtac induction THEN_ALL_NEW ObjectLogic.atomize_tac) 1, |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
465 |
rewrite_goals_tac rewrites, |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
466 |
REPEAT ((resolve_tac rep_intrs THEN_ALL_NEW |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
467 |
((REPEAT o etac allE) THEN' ares_tac elem_thms)) 1)]); |
5177 | 468 |
|
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
469 |
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
|
470 |
end; |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
471 |
|
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
472 |
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
|
473 |
(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
|
474 |
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
|
475 |
|
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
476 |
(* 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
|
477 |
|
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
478 |
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
|
479 |
let val isoT = T --> Univ_elT |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
480 |
in HOLogic.imp $ |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
481 |
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
|
482 |
(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
|
483 |
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
|
484 |
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
|
485 |
Const (iso_name, isoT) $ Const ("UNIV", HOLogic.mk_setT T))) |
5177 | 486 |
end; |
487 |
||
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
488 |
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
|
489 |
(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
|
490 |
|
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
491 |
(* 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
|
492 |
|
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
493 |
val range_eqs = map (fn r => mk_meta_eq (r RS range_ex1_eq)) |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
494 |
iso_inj_thms_unfolded; |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
495 |
|
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
496 |
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
|
497 |
drop (length newTs, split_conj_thm |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
498 |
(prove_goalw_cterm [] (cterm_of (Theory.sign_of thy5) iso_t) (fn _ => |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
499 |
[(indtac rep_induct THEN_ALL_NEW ObjectLogic.atomize_tac) 1, |
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
500 |
REPEAT (rtac TrueI 1), |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
501 |
rewrite_goals_tac (mk_meta_eq choice_eq :: |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
502 |
symmetric (mk_meta_eq expand_fun_eq) :: range_eqs), |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
503 |
rewrite_goals_tac (map symmetric range_eqs), |
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
504 |
REPEAT (EVERY |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
505 |
[REPEAT (eresolve_tac ([rangeE, ex1_implies_ex RS exE] @ |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
506 |
flat (map (mk_funs_inv o #1) newT_iso_axms)) 1), |
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
507 |
TRY (hyp_subst_tac 1), |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
508 |
rtac (sym RS range_eqI) 1, |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
509 |
resolve_tac iso_char_thms 1])]))); |
11435 | 510 |
|
511 |
val Abs_inverse_thms' = |
|
512 |
map #1 newT_iso_axms @ |
|
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
513 |
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
|
514 |
(iso_inj_thms_unfolded, iso_thms); |
11435 | 515 |
|
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
516 |
val Abs_inverse_thms = flat (map mk_funs_inv Abs_inverse_thms'); |
5177 | 517 |
|
518 |
(******************* freeness theorems for constructors *******************) |
|
519 |
||
6427 | 520 |
val _ = message "Proving freeness of constructors ..."; |
5177 | 521 |
|
522 |
(* prove theorem Rep_i (Constr_j ...) = Inj_j ... *) |
|
523 |
||
524 |
fun prove_constr_rep_thm eqn = |
|
525 |
let |
|
526 |
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
|
527 |
val rewrites = o_def :: constr_defs @ (map (mk_meta_eq o #2) newT_iso_axms) |
6394 | 528 |
in prove_goalw_cterm [] (cterm_of (Theory.sign_of thy5) eqn) (fn _ => |
5177 | 529 |
[resolve_tac inj_thms 1, |
530 |
rewrite_goals_tac rewrites, |
|
531 |
rtac refl 1, |
|
532 |
resolve_tac rep_intrs 2, |
|
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
533 |
REPEAT (resolve_tac iso_elem_thms 1)]) |
5177 | 534 |
end; |
535 |
||
536 |
(*--------------------------------------------------------------*) |
|
537 |
(* 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
|
538 |
(* of constructors. *) |
5177 | 539 |
(*--------------------------------------------------------------*) |
540 |
||
541 |
val constr_rep_thms = map (map prove_constr_rep_thm) constr_rep_eqns; |
|
542 |
||
543 |
val dist_rewrites = map (fn (rep_thms, dist_lemma) => |
|
544 |
dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0])) |
|
545 |
(constr_rep_thms ~~ dist_lemmas); |
|
546 |
||
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
547 |
fun prove_distinct_thms (_, []) = [] |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
548 |
| prove_distinct_thms (dist_rewrites', t::_::ts) = |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
549 |
let |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
550 |
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
|
551 |
[simp_tac (HOL_ss addsimps dist_rewrites') 1]) |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
552 |
in dist_thm::(standard (dist_thm RS not_sym)):: |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
553 |
(prove_distinct_thms (dist_rewrites', ts)) |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
554 |
end; |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
555 |
|
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
556 |
val distinct_thms = map prove_distinct_thms (dist_rewrites ~~ |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
557 |
DatatypeProp.make_distincts new_type_names descr sorts thy5); |
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 simproc_dists = map (fn ((((_, (_, _, constrs)), rep_thms), congr), dists) => |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
560 |
if length constrs < !DatatypeProp.dtK then FewConstrs dists |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
561 |
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
|
562 |
constr_rep_thms ~~ rep_congs ~~ distinct_thms); |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
563 |
|
5177 | 564 |
(* prove injectivity of constructors *) |
565 |
||
566 |
fun prove_constr_inj_thm rep_thms t = |
|
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
567 |
let val inj_thms = Scons_inject :: (map make_elim |
5177 | 568 |
((map (fn r => r RS injD) iso_inj_thms) @ |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
569 |
[In0_inject, In1_inject, Leaf_inject, Inl_inject, Inr_inject, |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
570 |
Lim_inject, Suml_inject, Sumr_inject])) |
6394 | 571 |
in prove_goalw_cterm [] (cterm_of (Theory.sign_of thy5) t) (fn _ => |
5177 | 572 |
[rtac iffI 1, |
573 |
REPEAT (etac conjE 2), hyp_subst_tac 2, rtac refl 2, |
|
574 |
dresolve_tac rep_congs 1, dtac box_equals 1, |
|
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
575 |
REPEAT (resolve_tac rep_thms 1), |
5177 | 576 |
REPEAT (eresolve_tac inj_thms 1), |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
577 |
REPEAT (ares_tac [conjI] 1 ORELSE (EVERY [REPEAT (rtac ext 1), |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
578 |
REPEAT (eresolve_tac (make_elim fun_cong :: inj_thms) 1), |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
579 |
atac 1]))]) |
5177 | 580 |
end; |
581 |
||
582 |
val constr_inject = map (fn (ts, thms) => map (prove_constr_inj_thm thms) ts) |
|
583 |
((DatatypeProp.make_injs descr sorts) ~~ constr_rep_thms); |
|
584 |
||
8479
5d327a46dc61
Now returns theorems with correct names in derivations.
berghofe
parents:
8436
diff
changeset
|
585 |
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
|
586 |
store_thmss "inject" new_type_names constr_inject |>>> |
5d327a46dc61
Now returns theorems with correct names in derivations.
berghofe
parents:
8436
diff
changeset
|
587 |
store_thmss "distinct" new_type_names distinct_thms; |
5177 | 588 |
|
589 |
(*************************** induction theorem ****************************) |
|
590 |
||
6427 | 591 |
val _ = message "Proving induction rule for datatypes ..."; |
5177 | 592 |
|
593 |
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
|
594 |
(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
|
595 |
val Rep_inverse_thms' = map (fn r => r RS myinv_f_f) iso_inj_thms_unfolded; |
5177 | 596 |
|
597 |
fun mk_indrule_lemma ((prems, concls), ((i, _), T)) = |
|
598 |
let |
|
599 |
val Rep_t = Const (nth_elem (i, all_rep_names), T --> Univ_elT) $ |
|
600 |
mk_Free "x" T i; |
|
601 |
||
602 |
val Abs_t = if i < length newTs then |
|
6394 | 603 |
Const (Sign.intern_const (Theory.sign_of thy6) |
5177 | 604 |
("Abs_" ^ (nth_elem (i, new_type_names))), Univ_elT --> T) |
11435 | 605 |
else Const ("Inductive.myinv", [T --> Univ_elT, Univ_elT] ---> T) $ |
5177 | 606 |
Const (nth_elem (i, all_rep_names), T --> Univ_elT) |
607 |
||
608 |
in (prems @ [HOLogic.imp $ HOLogic.mk_mem (Rep_t, |
|
609 |
Const (nth_elem (i, rep_set_names), UnivT)) $ |
|
610 |
(mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))], |
|
611 |
concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i]) |
|
612 |
end; |
|
613 |
||
614 |
val (indrule_lemma_prems, indrule_lemma_concls) = |
|
615 |
foldl mk_indrule_lemma (([], []), (descr' ~~ recTs)); |
|
616 |
||
6394 | 617 |
val cert = cterm_of (Theory.sign_of thy6); |
5177 | 618 |
|
619 |
val indrule_lemma = prove_goalw_cterm [] (cert |
|
620 |
(Logic.mk_implies |
|
621 |
(HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems), |
|
622 |
HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls)))) (fn prems => |
|
623 |
[cut_facts_tac prems 1, REPEAT (etac conjE 1), |
|
624 |
REPEAT (EVERY |
|
625 |
[TRY (rtac conjI 1), resolve_tac Rep_inverse_thms 1, |
|
626 |
etac mp 1, resolve_tac iso_elem_thms 1])]); |
|
627 |
||
8305 | 628 |
val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma))); |
5177 | 629 |
val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else |
630 |
map (Free o apfst fst o dest_Var) Ps; |
|
631 |
val indrule_lemma' = cterm_instantiate (map cert Ps ~~ map cert frees) indrule_lemma; |
|
632 |
||
13340
9b0332344ae2
Simplified proof of induction rule for datatypes involving function types.
berghofe
parents:
12922
diff
changeset
|
633 |
val dt_induct = prove_goalw_cterm [] (cert |
5177 | 634 |
(DatatypeProp.make_ind descr sorts)) (fn prems => |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
635 |
[rtac indrule_lemma' 1, |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
636 |
(indtac rep_induct THEN_ALL_NEW ObjectLogic.atomize_tac) 1, |
5177 | 637 |
EVERY (map (fn (prem, r) => (EVERY |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
638 |
[REPEAT (eresolve_tac Abs_inverse_thms 1), |
5177 | 639 |
simp_tac (HOL_basic_ss addsimps ((symmetric r)::Rep_inverse_thms')) 1, |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
640 |
DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)])) |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
641 |
(prems ~~ (constr_defs @ (map mk_meta_eq iso_char_thms))))]); |
5177 | 642 |
|
8436 | 643 |
val (thy7, [dt_induct']) = thy6 |> |
5661 | 644 |
Theory.add_path big_name |> |
13340
9b0332344ae2
Simplified proof of induction rule for datatypes involving function types.
berghofe
parents:
12922
diff
changeset
|
645 |
PureThy.add_thms [(("induct", dt_induct), [case_names_induct])] |>> |
5661 | 646 |
Theory.parent_path; |
5177 | 647 |
|
8479
5d327a46dc61
Now returns theorems with correct names in derivations.
berghofe
parents:
8436
diff
changeset
|
648 |
in (thy7, constr_inject', distinct_thms', dist_rewrites, simproc_dists, dt_induct') |
5177 | 649 |
end; |
650 |
||
651 |
end; |