author | haftmann |
Mon, 06 Jul 2009 14:19:13 +0200 | |
changeset 31949 | 3f933687fae9 |
parent 31775 | 2b04504fcb69 |
child 31986 | a68f88d264f7 |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/datatype_rep_proofs.ML |
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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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include DATATYPE_COMMON |
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val distinctness_limit : int Config.T |
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val distinctness_limit_setup : theory -> theory |
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val representation_proofs : config -> info Symtab.table -> |
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string list -> descr list -> (string * sort) list -> |
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(binding * mixfix) list -> (binding * mixfix) list list -> attribute |
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-> theory -> (thm list list * thm list list * thm list list * |
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DatatypeAux.simproc_dist list * thm) * theory |
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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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(*the kind of distinctiveness axioms depends on number of constructors*) |
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val (distinctness_limit, distinctness_limit_setup) = |
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Attrib.config_int "datatype_distinctness_limit" 7; |
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val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma); |
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val collect_simp = rewrite_rule [mk_meta_eq mem_Collect_eq]; |
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(** theory context references **) |
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fun exh_thm_of (dt_info : 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 (config : config) (dt_info : 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 = ThyInfo.the_theory "Datatype" thy; |
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val node_name = "Datatype.node"; |
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val In0_name = "Datatype.In0"; |
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val In1_name = "Datatype.In1"; |
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val Scons_name = "Datatype.Scons"; |
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val Leaf_name = "Datatype.Leaf"; |
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val Numb_name = "Datatype.Numb"; |
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val Lim_name = "Datatype.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 (PureThy.get_thm Datatype_thy) |
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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 config) big_name thy; |
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val big_rec_name = big_name ^ "_rep_set"; |
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val rep_set_names' = |
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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 rep_set_names = map (Sign.full_bname thy1) rep_set_names'; |
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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 BalancedTree.make (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 \\ List.foldr OldTerm.add_typ_tfree_names [] (leafTs' @ branchTs); |
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val leafTs = leafTs' @ (map (fn n => TFree (n, (the o AList.lookup (op =) sorts) n)) unneeded_vars); |
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val recTs = get_rec_types descr' sorts; |
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val newTs = Library.take (length (hd descr), recTs); |
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val oldTs = Library.drop (length (hd descr), recTs); |
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val sumT = if null leafTs then HOLogic.unitT |
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else BalancedTree.make (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 UnivT' = Univ_elT --> HOLogic.boolT; |
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val Collect = Const ("Collect", UnivT' --> UnivT); |
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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 = BalancedTree.access |
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{left = fn t => In0 $ t, |
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right = fn t => In1 $ t, |
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init = |
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if ts = [] then Const (@{const_name undefined}, Univ_elT) |
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else 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 = List.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 config "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 |
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(Free (nth rep_set_names' k, UnivT') $ free_t)) :: prems, |
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mk_lim free_t Ts :: ts) |
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end |
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| _ => |
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let val T = typ_of_dtyp descr' sorts dt |
166 |
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) = List.foldr mk_prem (1, [], []) cargs; |
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val concl = HOLogic.mk_Trueprop |
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(Free (s, UnivT') $ mk_univ_inj ts n i) |
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in Logic.list_implies (prems, concl) |
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end; |
174 |
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val intr_ts = maps (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 ({raw_induct = rep_induct, intrs = rep_intrs, ...}, thy2) = |
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Inductive.add_inductive_global (serial_string ()) |
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{quiet_mode = #quiet config, verbose = false, kind = Thm.internalK, |
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alt_name = Binding.name big_rec_name, coind = false, no_elim = true, no_ind = false, |
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skip_mono = true, fork_mono = false} |
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(map (fn s => ((Binding.name s, UnivT'), NoSyn)) rep_set_names') [] |
185 |
(map (fn x => (Attrib.empty_binding, x)) intr_ts) [] thy1; |
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(********************************* typedef ********************************) |
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val (typedefs, thy3) = thy2 |> |
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parent_path (#flat_names config) |> |
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fold_map (fn ((((name, mx), tvs), c), name') => |
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Typedef.add_typedef false (SOME (Binding.name name')) (name, tvs, mx) |
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(Collect $ Const (c, UnivT')) NONE |
194 |
(rtac exI 1 THEN rtac CollectI 1 THEN |
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195 |
QUIET_BREADTH_FIRST (has_fewer_prems 1) |
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196 |
(resolve_tac rep_intrs 1))) |
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(types_syntax ~~ tyvars ~~ |
198 |
(Library.take (length newTs, rep_set_names)) ~~ new_type_names) ||> |
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199 |
add_path (#flat_names config) big_name; |
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201 |
(*********************** definition of constructors ***********************) |
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202 |
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203 |
val big_rep_name = (space_implode "_" new_type_names) ^ "_Rep_"; |
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204 |
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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206 |
(1 upto (length (flat (tl descr)))); |
22578 | 207 |
val all_rep_names = map (Sign.intern_const thy3) rep_names @ |
28965 | 208 |
map (Sign.full_bname thy3) rep_names'; |
5177 | 209 |
|
210 |
(* isomorphism declarations *) |
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||
30345 | 212 |
val iso_decls = map (fn (T, s) => (Binding.name s, T --> Univ_elT, NoSyn)) |
5177 | 213 |
(oldTs ~~ rep_names'); |
214 |
||
215 |
(* constructor definitions *) |
|
216 |
||
217 |
fun make_constr_def tname T n ((thy, defs, eqns, i), ((cname, cargs), (cname', mx))) = |
|
218 |
let |
|
219 |
fun constr_arg (dt, (j, l_args, r_args)) = |
|
220 |
let val T = typ_of_dtyp descr' sorts dt; |
|
221 |
val free_t = mk_Free "x" T j |
|
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222 |
in (case (strip_dtyp dt, strip_type T) of |
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|
223 |
((_, DtRec m), (Us, U)) => (j + 1, free_t :: l_args, mk_lim |
31949 | 224 |
(Const (nth all_rep_names m, U --> Univ_elT) $ |
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|
225 |
app_bnds free_t (length Us)) Us :: r_args) |
5177 | 226 |
| _ => (j + 1, free_t::l_args, (Leaf $ mk_inj T free_t)::r_args)) |
227 |
end; |
|
228 |
||
30190 | 229 |
val (_, l_args, r_args) = List.foldr constr_arg (1, [], []) cargs; |
5177 | 230 |
val constrT = (map (typ_of_dtyp descr' sorts) cargs) ---> T; |
22578 | 231 |
val abs_name = Sign.intern_const thy ("Abs_" ^ tname); |
232 |
val rep_name = Sign.intern_const thy ("Rep_" ^ tname); |
|
5177 | 233 |
val lhs = list_comb (Const (cname, constrT), l_args); |
234 |
val rhs = mk_univ_inj r_args n i; |
|
27330 | 235 |
val def = Logic.mk_equals (lhs, Const (abs_name, Univ_elT --> T) $ rhs); |
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|
236 |
val def_name = Long_Name.base_name cname ^ "_def"; |
5177 | 237 |
val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq |
238 |
(Const (rep_name, T --> Univ_elT) $ lhs, rhs)); |
|
18377 | 239 |
val ([def_thm], thy') = |
240 |
thy |
|
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|
241 |
|> Sign.add_consts_i [(cname', constrT, mx)] |
29579 | 242 |
|> (PureThy.add_defs false o map Thm.no_attributes) [(Binding.name def_name, def)]; |
5177 | 243 |
|
8436 | 244 |
in (thy', defs @ [def_thm], eqns @ [eqn], i + 1) end; |
5177 | 245 |
|
246 |
(* constructor definitions for datatype *) |
|
247 |
||
248 |
fun dt_constr_defs ((thy, defs, eqns, rep_congs, dist_lemmas), |
|
249 |
((((_, (_, _, constrs)), tname), T), constr_syntax)) = |
|
250 |
let |
|
251 |
val _ $ (_ $ (cong_f $ _) $ _) = concl_of arg_cong; |
|
22578 | 252 |
val rep_const = cterm_of thy |
253 |
(Const (Sign.intern_const thy ("Rep_" ^ tname), T --> Univ_elT)); |
|
254 |
val cong' = standard (cterm_instantiate [(cterm_of thy cong_f, rep_const)] arg_cong); |
|
255 |
val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma); |
|
15570 | 256 |
val (thy', defs', eqns', _) = Library.foldl ((make_constr_def tname T) (length constrs)) |
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|
257 |
((add_path (#flat_names config) tname thy, defs, [], 1), constrs ~~ constr_syntax) |
5177 | 258 |
in |
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|
259 |
(parent_path (#flat_names config) thy', defs', eqns @ [eqns'], |
5177 | 260 |
rep_congs @ [cong'], dist_lemmas @ [dist]) |
261 |
end; |
|
262 |
||
15570 | 263 |
val (thy4, constr_defs, constr_rep_eqns, rep_congs, dist_lemmas) = Library.foldl dt_constr_defs |
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|
264 |
((thy3 |> Sign.add_consts_i iso_decls |> parent_path (#flat_names config), [], [], [], []), |
5177 | 265 |
hd descr ~~ new_type_names ~~ newTs ~~ constr_syntax); |
266 |
||
267 |
(*********** isomorphisms for new types (introduced by typedef) ***********) |
|
268 |
||
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|
269 |
val _ = message config "Proving isomorphism properties ..."; |
5177 | 270 |
|
21021 | 271 |
val newT_iso_axms = map (fn (_, td) => |
272 |
(collect_simp (#Abs_inverse td), #Rep_inverse td, |
|
273 |
collect_simp (#Rep td))) typedefs; |
|
5177 | 274 |
|
21021 | 275 |
val newT_iso_inj_thms = map (fn (_, td) => |
276 |
(collect_simp (#Abs_inject td) RS iffD1, #Rep_inject td RS iffD1)) typedefs; |
|
5177 | 277 |
|
278 |
(********* isomorphisms between existing types and "unfolded" types *******) |
|
279 |
||
280 |
(*---------------------------------------------------------------------*) |
|
281 |
(* isomorphisms are defined using primrec-combinators: *) |
|
282 |
(* generate appropriate functions for instantiating primrec-combinator *) |
|
283 |
(* *) |
|
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|
284 |
(* e.g. dt_Rep_i = list_rec ... (%h t y. In1 (Scons (Leaf h) y)) *) |
5177 | 285 |
(* *) |
286 |
(* also generate characteristic equations for isomorphisms *) |
|
287 |
(* *) |
|
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|
288 |
(* e.g. dt_Rep_i (cons h t) = In1 (Scons (dt_Rep_j h) (dt_Rep_i t)) *) |
5177 | 289 |
(*---------------------------------------------------------------------*) |
290 |
||
291 |
fun make_iso_def k ks n ((fs, eqns, i), (cname, cargs)) = |
|
292 |
let |
|
293 |
val argTs = map (typ_of_dtyp descr' sorts) cargs; |
|
31949 | 294 |
val T = nth recTs k; |
295 |
val rep_name = nth all_rep_names k; |
|
5177 | 296 |
val rep_const = Const (rep_name, T --> Univ_elT); |
297 |
val constr = Const (cname, argTs ---> T); |
|
298 |
||
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changeset
|
299 |
fun process_arg ks' ((i2, i2', ts, Ts), dt) = |
13641
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berghofe
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changeset
|
300 |
let |
63d1790a43ed
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diff
changeset
|
301 |
val T' = typ_of_dtyp descr' sorts dt; |
63d1790a43ed
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changeset
|
302 |
val (Us, U) = strip_type T' |
63d1790a43ed
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berghofe
parents:
13585
diff
changeset
|
303 |
in (case strip_dtyp dt of |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
304 |
(_, DtRec j) => if j mem ks' then |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
305 |
(i2 + 1, i2' + 1, ts @ [mk_lim (app_bnds |
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
306 |
(mk_Free "y" (Us ---> Univ_elT) i2') (length Us)) Us], |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
307 |
Ts @ [Us ---> Univ_elT]) |
5177 | 308 |
else |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
309 |
(i2 + 1, i2', ts @ [mk_lim |
31949 | 310 |
(Const (nth all_rep_names j, U --> Univ_elT) $ |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
311 |
app_bnds (mk_Free "x" T' i2) (length Us)) Us], Ts) |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
312 |
| _ => (i2 + 1, i2', ts @ [Leaf $ mk_inj T' (mk_Free "x" T' i2)], Ts)) |
5177 | 313 |
end; |
314 |
||
15570 | 315 |
val (i2, i2', ts, Ts) = Library.foldl (process_arg ks) ((1, 1, [], []), cargs); |
5177 | 316 |
val xs = map (uncurry (mk_Free "x")) (argTs ~~ (1 upto (i2 - 1))); |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
317 |
val ys = map (uncurry (mk_Free "y")) (Ts ~~ (1 upto (i2' - 1))); |
5177 | 318 |
val f = list_abs_free (map dest_Free (xs @ ys), mk_univ_inj ts n i); |
319 |
||
15570 | 320 |
val (_, _, ts', _) = Library.foldl (process_arg []) ((1, 1, [], []), cargs); |
5177 | 321 |
val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq |
322 |
(rep_const $ list_comb (constr, xs), mk_univ_inj ts' n i)) |
|
323 |
||
324 |
in (fs @ [f], eqns @ [eqn], i + 1) end; |
|
325 |
||
326 |
(* define isomorphisms for all mutually recursive datatypes in list ds *) |
|
327 |
||
328 |
fun make_iso_defs (ds, (thy, char_thms)) = |
|
329 |
let |
|
330 |
val ks = map fst ds; |
|
331 |
val (_, (tname, _, _)) = hd ds; |
|
17412 | 332 |
val {rec_rewrites, rec_names, ...} = the (Symtab.lookup dt_info tname); |
5177 | 333 |
|
334 |
fun process_dt ((fs, eqns, isos), (k, (tname, _, constrs))) = |
|
335 |
let |
|
15570 | 336 |
val (fs', eqns', _) = Library.foldl (make_iso_def k ks (length constrs)) |
5177 | 337 |
((fs, eqns, 1), constrs); |
31949 | 338 |
val iso = (nth recTs k, nth all_rep_names k) |
5177 | 339 |
in (fs', eqns', isos @ [iso]) end; |
340 |
||
15570 | 341 |
val (fs, eqns, isos) = Library.foldl process_dt (([], [], []), ds); |
5177 | 342 |
val fTs = map fastype_of fs; |
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset
|
343 |
val defs = map (fn (rec_name, (T, iso_name)) => (Binding.name (Long_Name.base_name iso_name ^ "_def"), |
27330 | 344 |
Logic.mk_equals (Const (iso_name, T --> Univ_elT), |
345 |
list_comb (Const (rec_name, fTs @ [T] ---> Univ_elT), fs)))) (rec_names ~~ isos); |
|
28362
b0ebac91c8d5
explicit checkpoint for low-level (global) theory operations admits concurrent SkipProof.prove;
wenzelm
parents:
28084
diff
changeset
|
346 |
val (def_thms, thy') = |
b0ebac91c8d5
explicit checkpoint for low-level (global) theory operations admits concurrent SkipProof.prove;
wenzelm
parents:
28084
diff
changeset
|
347 |
apsnd Theory.checkpoint ((PureThy.add_defs false o map Thm.no_attributes) defs thy); |
5177 | 348 |
|
349 |
(* prove characteristic equations *) |
|
350 |
||
5553 | 351 |
val rewrites = def_thms @ (map mk_meta_eq rec_rewrites); |
26531
96e82c7861fa
- use SkipProof.prove_global instead of Goal.prove_global
berghofe
parents:
26475
diff
changeset
|
352 |
val char_thms' = map (fn eqn => SkipProof.prove_global thy' [] [] eqn |
20046 | 353 |
(fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])) eqns; |
5177 | 354 |
|
355 |
in (thy', char_thms' @ char_thms) end; |
|
356 |
||
30190 | 357 |
val (thy5, iso_char_thms) = apfst Theory.checkpoint (List.foldr make_iso_defs |
31668
a616e56a5ec8
datatype packages: record datatype_config for configuration flags; less verbose signatures
haftmann
parents:
31643
diff
changeset
|
358 |
(add_path (#flat_names config) big_name thy4, []) (tl descr)); |
5177 | 359 |
|
360 |
(* prove isomorphism properties *) |
|
361 |
||
28362
b0ebac91c8d5
explicit checkpoint for low-level (global) theory operations admits concurrent SkipProof.prove;
wenzelm
parents:
28084
diff
changeset
|
362 |
fun mk_funs_inv thy thm = |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
363 |
let |
26626
c6231d64d264
rep_cterm/rep_thm: no longer dereference theory_ref;
wenzelm
parents:
26531
diff
changeset
|
364 |
val prop = Thm.prop_of thm; |
21021 | 365 |
val _ $ (_ $ ((S as Const (_, Type (_, [U, _]))) $ _ )) $ |
16287 | 366 |
(_ $ (_ $ (r $ (a $ _)) $ _)) = Type.freeze prop; |
29270
0eade173f77e
moved old add_type_XXX, add_term_XXX etc. to structure OldTerm;
wenzelm
parents:
28965
diff
changeset
|
367 |
val used = OldTerm.add_term_tfree_names (a, []); |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
368 |
|
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
369 |
fun mk_thm i = |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
370 |
let |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
371 |
val Ts = map (TFree o rpair HOLogic.typeS) |
20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset
|
372 |
(Name.variant_list used (replicate i "'t")); |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
373 |
val f = Free ("f", Ts ---> U) |
26531
96e82c7861fa
- use SkipProof.prove_global instead of Goal.prove_global
berghofe
parents:
26475
diff
changeset
|
374 |
in SkipProof.prove_global thy [] [] (Logic.mk_implies |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
375 |
(HOLogic.mk_Trueprop (HOLogic.list_all |
21021 | 376 |
(map (pair "x") Ts, S $ app_bnds f i)), |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
377 |
HOLogic.mk_Trueprop (HOLogic.mk_eq (list_abs (map (pair "x") Ts, |
17985 | 378 |
r $ (a $ app_bnds f i)), f)))) |
26806 | 379 |
(fn _ => EVERY [REPEAT_DETERM_N i (rtac ext 1), |
380 |
REPEAT (etac allE 1), rtac thm 1, atac 1]) |
|
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
381 |
end |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
382 |
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
|
383 |
|
5177 | 384 |
(* prove inj dt_Rep_i and dt_Rep_i x : dt_rep_set_i *) |
385 |
||
26806 | 386 |
val fun_congs = map (fn T => make_elim (Drule.instantiate' |
387 |
[SOME (ctyp_of thy5 T)] [] fun_cong)) branchTs; |
|
388 |
||
5177 | 389 |
fun prove_iso_thms (ds, (inj_thms, elem_thms)) = |
390 |
let |
|
391 |
val (_, (tname, _, _)) = hd ds; |
|
17412 | 392 |
val {induction, ...} = the (Symtab.lookup dt_info tname); |
5177 | 393 |
|
394 |
fun mk_ind_concl (i, _) = |
|
395 |
let |
|
31949 | 396 |
val T = nth recTs i; |
397 |
val Rep_t = Const (nth all_rep_names i, T --> Univ_elT); |
|
398 |
val rep_set_name = nth rep_set_names i |
|
5177 | 399 |
in (HOLogic.all_const T $ Abs ("y", T, HOLogic.imp $ |
400 |
HOLogic.mk_eq (Rep_t $ mk_Free "x" T i, Rep_t $ Bound 0) $ |
|
401 |
HOLogic.mk_eq (mk_Free "x" T i, Bound 0)), |
|
21021 | 402 |
Const (rep_set_name, UnivT') $ (Rep_t $ mk_Free "x" T i)) |
5177 | 403 |
end; |
404 |
||
405 |
val (ind_concl1, ind_concl2) = ListPair.unzip (map mk_ind_concl ds); |
|
406 |
||
5553 | 407 |
val rewrites = map mk_meta_eq iso_char_thms; |
21021 | 408 |
val inj_thms' = map snd newT_iso_inj_thms @ |
26359 | 409 |
map (fn r => r RS @{thm injD}) inj_thms; |
5177 | 410 |
|
26531
96e82c7861fa
- use SkipProof.prove_global instead of Goal.prove_global
berghofe
parents:
26475
diff
changeset
|
411 |
val inj_thm = SkipProof.prove_global thy5 [] [] |
17985 | 412 |
(HOLogic.mk_Trueprop (mk_conj ind_concl1)) (fn _ => EVERY |
25678 | 413 |
[(indtac induction [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1, |
5177 | 414 |
REPEAT (EVERY |
415 |
[rtac allI 1, rtac impI 1, |
|
416 |
exh_tac (exh_thm_of dt_info) 1, |
|
417 |
REPEAT (EVERY |
|
418 |
[hyp_subst_tac 1, |
|
419 |
rewrite_goals_tac rewrites, |
|
420 |
REPEAT (dresolve_tac [In0_inject, In1_inject] 1), |
|
421 |
(eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1) |
|
422 |
ORELSE (EVERY |
|
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
423 |
[REPEAT (eresolve_tac (Scons_inject :: |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
424 |
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
|
425 |
REPEAT (cong_tac 1), rtac refl 1, |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
426 |
REPEAT (atac 1 ORELSE (EVERY |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
427 |
[REPEAT (rtac ext 1), |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
428 |
REPEAT (eresolve_tac (mp :: allE :: |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
429 |
map make_elim (Suml_inject :: Sumr_inject :: |
26806 | 430 |
Lim_inject :: inj_thms') @ fun_congs) 1), |
20046 | 431 |
atac 1]))])])])]); |
5177 | 432 |
|
26359 | 433 |
val inj_thms'' = map (fn r => r RS @{thm datatype_injI}) |
6171 | 434 |
(split_conj_thm inj_thm); |
5177 | 435 |
|
6171 | 436 |
val elem_thm = |
26531
96e82c7861fa
- use SkipProof.prove_global instead of Goal.prove_global
berghofe
parents:
26475
diff
changeset
|
437 |
SkipProof.prove_global thy5 [] [] (HOLogic.mk_Trueprop (mk_conj ind_concl2)) |
20046 | 438 |
(fn _ => |
25678 | 439 |
EVERY [(indtac induction [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1, |
20046 | 440 |
rewrite_goals_tac rewrites, |
441 |
REPEAT ((resolve_tac rep_intrs THEN_ALL_NEW |
|
442 |
((REPEAT o etac allE) THEN' ares_tac elem_thms)) 1)]); |
|
5177 | 443 |
|
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
444 |
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
|
445 |
end; |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
446 |
|
30190 | 447 |
val (iso_inj_thms_unfolded, iso_elem_thms) = List.foldr prove_iso_thms |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
448 |
([], map #3 newT_iso_axms) (tl descr); |
21021 | 449 |
val iso_inj_thms = map snd newT_iso_inj_thms @ |
26359 | 450 |
map (fn r => r RS @{thm injD}) iso_inj_thms_unfolded; |
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
451 |
|
21021 | 452 |
(* prove dt_rep_set_i x --> x : range dt_Rep_i *) |
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
453 |
|
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
454 |
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
|
455 |
let val isoT = T --> Univ_elT |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
456 |
in HOLogic.imp $ |
21021 | 457 |
(Const (set_name, UnivT') $ mk_Free "x" Univ_elT i) $ |
31643 | 458 |
(if i < length newTs then HOLogic.true_const |
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
459 |
else HOLogic.mk_mem (mk_Free "x" Univ_elT i, |
31643 | 460 |
Const (@{const_name image}, isoT --> HOLogic.mk_setT T --> UnivT) $ |
30304
d8e4cd2ac2a1
set operations Int, Un, INTER, UNION, Inter, Union, empty, UNIV are now proper qualified constants with authentic syntax
haftmann
parents:
29579
diff
changeset
|
461 |
Const (iso_name, isoT) $ Const (@{const_name UNIV}, HOLogic.mk_setT T))) |
5177 | 462 |
end; |
463 |
||
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
464 |
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
|
465 |
(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
|
466 |
|
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
467 |
(* 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
|
468 |
|
26359 | 469 |
val range_eqs = map (fn r => mk_meta_eq (r RS @{thm range_ex1_eq})) |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
470 |
iso_inj_thms_unfolded; |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
471 |
|
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
472 |
val iso_thms = if length descr = 1 then [] else |
15570 | 473 |
Library.drop (length newTs, split_conj_thm |
26531
96e82c7861fa
- use SkipProof.prove_global instead of Goal.prove_global
berghofe
parents:
26475
diff
changeset
|
474 |
(SkipProof.prove_global thy5 [] [] iso_t (fn _ => EVERY |
25678 | 475 |
[(indtac rep_induct [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1, |
11471
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
476 |
REPEAT (rtac TrueI 1), |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
477 |
rewrite_goals_tac (mk_meta_eq choice_eq :: |
26359 | 478 |
symmetric (mk_meta_eq @{thm expand_fun_eq}) :: range_eqs), |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
479 |
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
|
480 |
REPEAT (EVERY |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
481 |
[REPEAT (eresolve_tac ([rangeE, ex1_implies_ex RS exE] @ |
28362
b0ebac91c8d5
explicit checkpoint for low-level (global) theory operations admits concurrent SkipProof.prove;
wenzelm
parents:
28084
diff
changeset
|
482 |
maps (mk_funs_inv thy5 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
|
483 |
TRY (hyp_subst_tac 1), |
ba2c252b55ad
- Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents:
11435
diff
changeset
|
484 |
rtac (sym RS range_eqI) 1, |
20046 | 485 |
resolve_tac iso_char_thms 1])]))); |
11435 | 486 |
|
487 |
val Abs_inverse_thms' = |
|
488 |
map #1 newT_iso_axms @ |
|
31949 | 489 |
map2 (fn r_inj => fn r => @{thm f_inv_f} OF [r_inj, r RS mp]) |
18330 | 490 |
iso_inj_thms_unfolded iso_thms; |
11435 | 491 |
|
28362
b0ebac91c8d5
explicit checkpoint for low-level (global) theory operations admits concurrent SkipProof.prove;
wenzelm
parents:
28084
diff
changeset
|
492 |
val Abs_inverse_thms = maps (mk_funs_inv thy5) Abs_inverse_thms'; |
5177 | 493 |
|
494 |
(******************* freeness theorems for constructors *******************) |
|
495 |
||
31668
a616e56a5ec8
datatype packages: record datatype_config for configuration flags; less verbose signatures
haftmann
parents:
31643
diff
changeset
|
496 |
val _ = message config "Proving freeness of constructors ..."; |
5177 | 497 |
|
498 |
(* prove theorem Rep_i (Constr_j ...) = Inj_j ... *) |
|
499 |
||
500 |
fun prove_constr_rep_thm eqn = |
|
501 |
let |
|
21021 | 502 |
val inj_thms = map fst newT_iso_inj_thms; |
26359 | 503 |
val rewrites = @{thm o_def} :: constr_defs @ (map (mk_meta_eq o #2) newT_iso_axms) |
26531
96e82c7861fa
- use SkipProof.prove_global instead of Goal.prove_global
berghofe
parents:
26475
diff
changeset
|
504 |
in SkipProof.prove_global thy5 [] [] eqn (fn _ => EVERY |
5177 | 505 |
[resolve_tac inj_thms 1, |
506 |
rewrite_goals_tac rewrites, |
|
21021 | 507 |
rtac refl 3, |
5177 | 508 |
resolve_tac rep_intrs 2, |
20046 | 509 |
REPEAT (resolve_tac iso_elem_thms 1)]) |
5177 | 510 |
end; |
511 |
||
512 |
(*--------------------------------------------------------------*) |
|
513 |
(* 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
|
514 |
(* of constructors. *) |
5177 | 515 |
(*--------------------------------------------------------------*) |
516 |
||
517 |
val constr_rep_thms = map (map prove_constr_rep_thm) constr_rep_eqns; |
|
518 |
||
519 |
val dist_rewrites = map (fn (rep_thms, dist_lemma) => |
|
520 |
dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0])) |
|
521 |
(constr_rep_thms ~~ dist_lemmas); |
|
522 |
||
26969
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26806
diff
changeset
|
523 |
fun prove_distinct_thms _ _ (_, []) = [] |
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26806
diff
changeset
|
524 |
| prove_distinct_thms lim dist_rewrites' (k, ts as _ :: _) = |
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26806
diff
changeset
|
525 |
if k >= lim then [] else let |
27002
215d64dc971e
moved distinctness_limit to datatype_rep_proofs.ML
haftmann
parents:
26969
diff
changeset
|
526 |
(*number of constructors < distinctness_limit : C_i ... ~= C_j ...*) |
26969
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26806
diff
changeset
|
527 |
fun prove [] = [] |
27300
4cb3101d2bf7
DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents:
27002
diff
changeset
|
528 |
| prove (t :: ts) = |
26969
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26806
diff
changeset
|
529 |
let |
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26806
diff
changeset
|
530 |
val dist_thm = SkipProof.prove_global thy5 [] [] t (fn _ => |
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26806
diff
changeset
|
531 |
EVERY [simp_tac (HOL_ss addsimps dist_rewrites') 1]) |
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26806
diff
changeset
|
532 |
in dist_thm :: standard (dist_thm RS not_sym) :: prove ts end; |
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26806
diff
changeset
|
533 |
in prove ts end; |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
534 |
|
27300
4cb3101d2bf7
DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents:
27002
diff
changeset
|
535 |
val distinct_thms = DatatypeProp.make_distincts descr sorts |
4cb3101d2bf7
DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents:
27002
diff
changeset
|
536 |
|> map2 (prove_distinct_thms |
4cb3101d2bf7
DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents:
27002
diff
changeset
|
537 |
(Config.get_thy thy5 distinctness_limit)) dist_rewrites; |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
538 |
|
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
539 |
val simproc_dists = map (fn ((((_, (_, _, constrs)), rep_thms), congr), dists) => |
27002
215d64dc971e
moved distinctness_limit to datatype_rep_proofs.ML
haftmann
parents:
26969
diff
changeset
|
540 |
if length constrs < Config.get_thy thy5 distinctness_limit |
24098
f1eb34ae33af
replaced dtK ref by datatype_distinctness_limit configuration option;
wenzelm
parents:
23590
diff
changeset
|
541 |
then FewConstrs dists |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
542 |
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
|
543 |
constr_rep_thms ~~ rep_congs ~~ distinct_thms); |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
544 |
|
5177 | 545 |
(* prove injectivity of constructors *) |
546 |
||
547 |
fun prove_constr_inj_thm rep_thms t = |
|
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
548 |
let val inj_thms = Scons_inject :: (map make_elim |
21021 | 549 |
(iso_inj_thms @ |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
550 |
[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
|
551 |
Lim_inject, Suml_inject, Sumr_inject])) |
26531
96e82c7861fa
- use SkipProof.prove_global instead of Goal.prove_global
berghofe
parents:
26475
diff
changeset
|
552 |
in SkipProof.prove_global thy5 [] [] t (fn _ => EVERY |
5177 | 553 |
[rtac iffI 1, |
554 |
REPEAT (etac conjE 2), hyp_subst_tac 2, rtac refl 2, |
|
555 |
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
|
556 |
REPEAT (resolve_tac rep_thms 1), |
5177 | 557 |
REPEAT (eresolve_tac inj_thms 1), |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
558 |
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
|
559 |
REPEAT (eresolve_tac (make_elim fun_cong :: inj_thms) 1), |
20046 | 560 |
atac 1]))]) |
5177 | 561 |
end; |
562 |
||
563 |
val constr_inject = map (fn (ts, thms) => map (prove_constr_inj_thm thms) ts) |
|
564 |
((DatatypeProp.make_injs descr sorts) ~~ constr_rep_thms); |
|
565 |
||
18314 | 566 |
val ((constr_inject', distinct_thms'), thy6) = |
567 |
thy5 |
|
31668
a616e56a5ec8
datatype packages: record datatype_config for configuration flags; less verbose signatures
haftmann
parents:
31643
diff
changeset
|
568 |
|> parent_path (#flat_names config) |
18314 | 569 |
|> store_thmss "inject" new_type_names constr_inject |
570 |
||>> store_thmss "distinct" new_type_names distinct_thms; |
|
5177 | 571 |
|
572 |
(*************************** induction theorem ****************************) |
|
573 |
||
31668
a616e56a5ec8
datatype packages: record datatype_config for configuration flags; less verbose signatures
haftmann
parents:
31643
diff
changeset
|
574 |
val _ = message config "Proving induction rule for datatypes ..."; |
5177 | 575 |
|
576 |
val Rep_inverse_thms = (map (fn (_, iso, _) => iso RS subst) newT_iso_axms) @ |
|
31949 | 577 |
(map (fn r => r RS @{thm inv_f_f} RS subst) iso_inj_thms_unfolded); |
578 |
val Rep_inverse_thms' = map (fn r => r RS @{thm inv_f_f}) iso_inj_thms_unfolded; |
|
5177 | 579 |
|
580 |
fun mk_indrule_lemma ((prems, concls), ((i, _), T)) = |
|
581 |
let |
|
31949 | 582 |
val Rep_t = Const (nth all_rep_names i, T --> Univ_elT) $ |
5177 | 583 |
mk_Free "x" T i; |
584 |
||
585 |
val Abs_t = if i < length newTs then |
|
22578 | 586 |
Const (Sign.intern_const thy6 |
31949 | 587 |
("Abs_" ^ (nth new_type_names i)), Univ_elT --> T) |
588 |
else Const (@{const_name Fun.inv}, [T --> Univ_elT, Univ_elT] ---> T) $ |
|
589 |
Const (nth all_rep_names i, T --> Univ_elT) |
|
5177 | 590 |
|
21021 | 591 |
in (prems @ [HOLogic.imp $ |
31949 | 592 |
(Const (nth rep_set_names i, UnivT') $ Rep_t) $ |
5177 | 593 |
(mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))], |
594 |
concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i]) |
|
595 |
end; |
|
596 |
||
597 |
val (indrule_lemma_prems, indrule_lemma_concls) = |
|
15570 | 598 |
Library.foldl mk_indrule_lemma (([], []), (descr' ~~ recTs)); |
5177 | 599 |
|
22578 | 600 |
val cert = cterm_of thy6; |
5177 | 601 |
|
26531
96e82c7861fa
- use SkipProof.prove_global instead of Goal.prove_global
berghofe
parents:
26475
diff
changeset
|
602 |
val indrule_lemma = SkipProof.prove_global thy6 [] [] |
5177 | 603 |
(Logic.mk_implies |
604 |
(HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems), |
|
17985 | 605 |
HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY |
606 |
[REPEAT (etac conjE 1), |
|
5177 | 607 |
REPEAT (EVERY |
608 |
[TRY (rtac conjI 1), resolve_tac Rep_inverse_thms 1, |
|
20046 | 609 |
etac mp 1, resolve_tac iso_elem_thms 1])]); |
5177 | 610 |
|
8305 | 611 |
val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma))); |
5177 | 612 |
val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else |
613 |
map (Free o apfst fst o dest_Var) Ps; |
|
614 |
val indrule_lemma' = cterm_instantiate (map cert Ps ~~ map cert frees) indrule_lemma; |
|
615 |
||
17985 | 616 |
val dt_induct_prop = DatatypeProp.make_ind descr sorts; |
26531
96e82c7861fa
- use SkipProof.prove_global instead of Goal.prove_global
berghofe
parents:
26475
diff
changeset
|
617 |
val dt_induct = SkipProof.prove_global thy6 [] |
17985 | 618 |
(Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop) |
26711 | 619 |
(fn {prems, ...} => EVERY |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
620 |
[rtac indrule_lemma' 1, |
25678 | 621 |
(indtac rep_induct [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1, |
5177 | 622 |
EVERY (map (fn (prem, r) => (EVERY |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
13585
diff
changeset
|
623 |
[REPEAT (eresolve_tac Abs_inverse_thms 1), |
5177 | 624 |
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
|
625 |
DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)])) |
20046 | 626 |
(prems ~~ (constr_defs @ (map mk_meta_eq iso_char_thms))))]); |
5177 | 627 |
|
18377 | 628 |
val ([dt_induct'], thy7) = |
629 |
thy6 |
|
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24112
diff
changeset
|
630 |
|> Sign.add_path big_name |
29579 | 631 |
|> PureThy.add_thms [((Binding.name "induct", dt_induct), [case_names_induct])] |
28362
b0ebac91c8d5
explicit checkpoint for low-level (global) theory operations admits concurrent SkipProof.prove;
wenzelm
parents:
28084
diff
changeset
|
632 |
||> Sign.parent_path |
b0ebac91c8d5
explicit checkpoint for low-level (global) theory operations admits concurrent SkipProof.prove;
wenzelm
parents:
28084
diff
changeset
|
633 |
||> Theory.checkpoint; |
5177 | 634 |
|
18314 | 635 |
in |
636 |
((constr_inject', distinct_thms', dist_rewrites, simproc_dists, dt_induct'), thy7) |
|
5177 | 637 |
end; |
638 |
||
639 |
end; |