src/ZF/Tools/inductive_package.ML
author wenzelm
Wed Apr 13 18:34:22 2005 +0200 (2005-04-13)
changeset 15703 727ef1b8b3ee
parent 15574 b1d1b5bfc464
child 15705 b5edb9dcec9a
permissions -rw-r--r--
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(*  Title:      ZF/Tools/inductive_package.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1994  University of Cambridge
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Fixedpoint definition module -- for Inductive/Coinductive Definitions
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The functor will be instantiated for normal sums/products (inductive defs)
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                         and non-standard sums/products (coinductive defs)
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Sums are used only for mutual recursion;
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Products are used only to derive "streamlined" induction rules for relations
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*)
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type inductive_result =
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   {defs       : thm list,             (*definitions made in thy*)
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    bnd_mono   : thm,                  (*monotonicity for the lfp definition*)
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    dom_subset : thm,                  (*inclusion of recursive set in dom*)
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    intrs      : thm list,             (*introduction rules*)
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    elim       : thm,                  (*case analysis theorem*)
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    mk_cases   : string -> thm,        (*generates case theorems*)
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    induct     : thm,                  (*main induction rule*)
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    mutual_induct : thm};              (*mutual induction rule*)
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(*Functor's result signature*)
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signature INDUCTIVE_PACKAGE =
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sig
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  (*Insert definitions for the recursive sets, which
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     must *already* be declared as constants in parent theory!*)
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  val add_inductive_i: bool -> term list * term ->
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    ((bstring * term) * theory attribute list) list ->
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    thm list * thm list * thm list * thm list -> theory -> theory * inductive_result
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  val add_inductive_x: string list * string -> ((bstring * string) * theory attribute list) list
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    -> thm list * thm list * thm list * thm list -> theory -> theory * inductive_result
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  val add_inductive: string list * string ->
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    ((bstring * string) * Attrib.src list) list ->
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    (thmref * Attrib.src list) list * (thmref * Attrib.src list) list *
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    (thmref * Attrib.src list) list * (thmref * Attrib.src list) list ->
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    theory -> theory * inductive_result
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end;
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(*Declares functions to add fixedpoint/constructor defs to a theory.
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  Recursive sets must *already* be declared as constants.*)
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functor Add_inductive_def_Fun
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    (structure Fp: FP and Pr : PR and CP: CARTPROD and Su : SU val coind: bool)
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 : INDUCTIVE_PACKAGE =
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struct
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open Logic Ind_Syntax;
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val co_prefix = if coind then "co" else "";
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(* utils *)
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(*make distinct individual variables a1, a2, a3, ..., an. *)
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fun mk_frees a [] = []
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  | mk_frees a (T::Ts) = Free(a,T) :: mk_frees (Symbol.bump_string a) Ts;
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(* add_inductive(_i) *)
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(*internal version, accepting terms*)
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fun add_inductive_i verbose (rec_tms, dom_sum)
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  intr_specs (monos, con_defs, type_intrs, type_elims) thy =
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let
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  val _ = Theory.requires thy "Inductive" "(co)inductive definitions";
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  val sign = sign_of thy;
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  val (intr_names, intr_tms) = split_list (map fst intr_specs);
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  val case_names = RuleCases.case_names intr_names;
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  (*recT and rec_params should agree for all mutually recursive components*)
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  val rec_hds = map head_of rec_tms;
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  val dummy = assert_all is_Const rec_hds
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          (fn t => "Recursive set not previously declared as constant: " ^
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                   Sign.string_of_term sign t);
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  (*Now we know they are all Consts, so get their names, type and params*)
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  val rec_names = map (#1 o dest_Const) rec_hds
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  and (Const(_,recT),rec_params) = strip_comb (hd rec_tms);
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  val rec_base_names = map Sign.base_name rec_names;
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  val dummy = assert_all Syntax.is_identifier rec_base_names
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    (fn a => "Base name of recursive set not an identifier: " ^ a);
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  local (*Checking the introduction rules*)
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    val intr_sets = map (#2 o rule_concl_msg sign) intr_tms;
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    fun intr_ok set =
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        case head_of set of Const(a,recT) => a mem rec_names | _ => false;
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  in
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    val dummy =  assert_all intr_ok intr_sets
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       (fn t => "Conclusion of rule does not name a recursive set: " ^
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                Sign.string_of_term sign t);
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  end;
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  val dummy = assert_all is_Free rec_params
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      (fn t => "Param in recursion term not a free variable: " ^
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               Sign.string_of_term sign t);
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  (*** Construct the fixedpoint definition ***)
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  val mk_variant = variant (foldr add_term_names [] intr_tms);
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  val z' = mk_variant"z" and X' = mk_variant"X" and w' = mk_variant"w";
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  fun dest_tprop (Const("Trueprop",_) $ P) = P
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    | dest_tprop Q = error ("Ill-formed premise of introduction rule: " ^
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                            Sign.string_of_term sign Q);
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  (*Makes a disjunct from an introduction rule*)
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  fun fp_part intr = (*quantify over rule's free vars except parameters*)
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    let val prems = map dest_tprop (strip_imp_prems intr)
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        val dummy = List.app (fn rec_hd => List.app (chk_prem rec_hd) prems) rec_hds
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        val exfrees = term_frees intr \\ rec_params
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        val zeq = FOLogic.mk_eq (Free(z',iT), #1 (rule_concl intr))
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    in foldr FOLogic.mk_exists
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             (fold_bal FOLogic.mk_conj (zeq::prems)) exfrees
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    end;
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  (*The Part(A,h) terms -- compose injections to make h*)
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  fun mk_Part (Bound 0) = Free(X',iT) (*no mutual rec, no Part needed*)
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    | mk_Part h         = Part_const $ Free(X',iT) $ Abs(w',iT,h);
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  (*Access to balanced disjoint sums via injections*)
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  val parts =
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      map mk_Part (accesses_bal (fn t => Su.inl $ t, fn t => Su.inr $ t, Bound 0)
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                                (length rec_tms));
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  (*replace each set by the corresponding Part(A,h)*)
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  val part_intrs = map (subst_free (rec_tms ~~ parts) o fp_part) intr_tms;
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  val fp_abs = absfree(X', iT,
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                   mk_Collect(z', dom_sum,
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                              fold_bal FOLogic.mk_disj part_intrs));
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  val fp_rhs = Fp.oper $ dom_sum $ fp_abs
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  val dummy = List.app (fn rec_hd => deny (rec_hd occs fp_rhs)
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                             "Illegal occurrence of recursion operator")
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           rec_hds;
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  (*** Make the new theory ***)
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  (*A key definition:
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    If no mutual recursion then it equals the one recursive set.
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    If mutual recursion then it differs from all the recursive sets. *)
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  val big_rec_base_name = space_implode "_" rec_base_names;
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  val big_rec_name = Sign.intern_const sign big_rec_base_name;
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  val dummy = conditional verbose (fn () =>
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    writeln ((if coind then "Coind" else "Ind") ^ "uctive definition " ^ quote big_rec_name));
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  (*Forbid the inductive definition structure from clashing with a theory
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    name.  This restriction may become obsolete as ML is de-emphasized.*)
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  val dummy = deny (big_rec_base_name mem (Sign.stamp_names_of sign))
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               ("Definition " ^ big_rec_base_name ^
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                " would clash with the theory of the same name!");
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  (*Big_rec... is the union of the mutually recursive sets*)
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  val big_rec_tm = list_comb(Const(big_rec_name,recT), rec_params);
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  (*The individual sets must already be declared*)
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  val axpairs = map Logic.mk_defpair
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        ((big_rec_tm, fp_rhs) ::
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         (case parts of
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             [_] => []                        (*no mutual recursion*)
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           | _ => rec_tms ~~          (*define the sets as Parts*)
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                  map (subst_atomic [(Free(X',iT),big_rec_tm)]) parts));
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  (*tracing: print the fixedpoint definition*)
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  val dummy = if !Ind_Syntax.trace then
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              List.app (writeln o Sign.string_of_term sign o #2) axpairs
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          else ()
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  (*add definitions of the inductive sets*)
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  val thy1 = thy |> Theory.add_path big_rec_base_name
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                 |> (#1 o PureThy.add_defs_i false (map Thm.no_attributes axpairs))
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  (*fetch fp definitions from the theory*)
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  val big_rec_def::part_rec_defs =
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    map (get_def thy1)
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        (case rec_names of [_] => rec_names
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                         | _   => big_rec_base_name::rec_names);
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  val sign1 = sign_of thy1;
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  (********)
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  val dummy = writeln "  Proving monotonicity...";
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  val bnd_mono =
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      prove_goalw_cterm []
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        (cterm_of sign1
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                  (FOLogic.mk_Trueprop (Fp.bnd_mono $ dom_sum $ fp_abs)))
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        (fn _ =>
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         [rtac (Collect_subset RS bnd_monoI) 1,
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          REPEAT (ares_tac (basic_monos @ monos) 1)]);
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  val dom_subset = standard (big_rec_def RS Fp.subs);
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  val unfold = standard ([big_rec_def, bnd_mono] MRS Fp.Tarski);
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  (********)
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  val dummy = writeln "  Proving the introduction rules...";
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  (*Mutual recursion?  Helps to derive subset rules for the
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    individual sets.*)
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  val Part_trans =
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      case rec_names of
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           [_] => asm_rl
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         | _   => standard (Part_subset RS subset_trans);
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  (*To type-check recursive occurrences of the inductive sets, possibly
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    enclosed in some monotonic operator M.*)
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  val rec_typechecks =
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     [dom_subset] RL (asm_rl :: ([Part_trans] RL monos))
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     RL [subsetD];
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  (*Type-checking is hardest aspect of proof;
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    disjIn selects the correct disjunct after unfolding*)
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  fun intro_tacsf disjIn prems =
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    [(*insert prems and underlying sets*)
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     cut_facts_tac prems 1,
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     DETERM (stac unfold 1),
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     REPEAT (resolve_tac [Part_eqI,CollectI] 1),
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     (*Now 2-3 subgoals: typechecking, the disjunction, perhaps equality.*)
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     rtac disjIn 2,
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     (*Not ares_tac, since refl must be tried before equality assumptions;
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       backtracking may occur if the premises have extra variables!*)
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     DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 2 APPEND assume_tac 2),
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     (*Now solve the equations like Tcons(a,f) = Inl(?b4)*)
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     rewrite_goals_tac con_defs,
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     REPEAT (rtac refl 2),
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     (*Typechecking; this can fail*)
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     if !Ind_Syntax.trace then print_tac "The type-checking subgoal:"
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     else all_tac,
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     REPEAT (FIRSTGOAL (        dresolve_tac rec_typechecks
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                        ORELSE' eresolve_tac (asm_rl::PartE::SigmaE2::
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                                              type_elims)
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                        ORELSE' hyp_subst_tac)),
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     if !Ind_Syntax.trace then print_tac "The subgoal after monos, type_elims:"
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     else all_tac,
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     DEPTH_SOLVE (swap_res_tac (SigmaI::subsetI::type_intrs) 1)];
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  (*combines disjI1 and disjI2 to get the corresponding nested disjunct...*)
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  val mk_disj_rls =
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      let fun f rl = rl RS disjI1
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          and g rl = rl RS disjI2
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      in  accesses_bal(f, g, asm_rl)  end;
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  fun prove_intr (ct, tacsf) = prove_goalw_cterm part_rec_defs ct tacsf;
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  val intrs = ListPair.map prove_intr
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                (map (cterm_of sign1) intr_tms,
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                 map intro_tacsf (mk_disj_rls(length intr_tms)))
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               handle MetaSimplifier.SIMPLIFIER (msg,thm) => (print_thm thm; error msg);
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  (********)
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  val dummy = writeln "  Proving the elimination rule...";
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  (*Breaks down logical connectives in the monotonic function*)
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  val basic_elim_tac =
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      REPEAT (SOMEGOAL (eresolve_tac (Ind_Syntax.elim_rls @ Su.free_SEs)
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                ORELSE' bound_hyp_subst_tac))
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      THEN prune_params_tac
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          (*Mutual recursion: collapse references to Part(D,h)*)
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      THEN fold_tac part_rec_defs;
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  (*Elimination*)
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  val elim = rule_by_tactic basic_elim_tac
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                 (unfold RS Ind_Syntax.equals_CollectD)
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  (*Applies freeness of the given constructors, which *must* be unfolded by
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      the given defs.  Cannot simply use the local con_defs because
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      con_defs=[] for inference systems.
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    Proposition A should have the form t:Si where Si is an inductive set*)
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  fun make_cases ss A =
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    rule_by_tactic
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      (basic_elim_tac THEN ALLGOALS (asm_full_simp_tac ss) THEN basic_elim_tac)
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      (Thm.assume A RS elim)
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      |> Drule.standard';
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  fun mk_cases a = make_cases (*delayed evaluation of body!*)
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    (simpset ()) (read_cterm (Thm.sign_of_thm elim) (a, propT));
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  fun induction_rules raw_induct thy =
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   let
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     val dummy = writeln "  Proving the induction rule...";
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     (*** Prove the main induction rule ***)
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     val pred_name = "P";            (*name for predicate variables*)
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     (*Used to make induction rules;
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        ind_alist = [(rec_tm1,pred1),...] associates predicates with rec ops
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        prem is a premise of an intr rule*)
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     fun add_induct_prem ind_alist (prem as Const("Trueprop",_) $
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                      (Const("op :",_)$t$X), iprems) =
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          (case gen_assoc (op aconv) (ind_alist, X) of
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               SOME pred => prem :: FOLogic.mk_Trueprop (pred $ t) :: iprems
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             | NONE => (*possibly membership in M(rec_tm), for M monotone*)
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                 let fun mk_sb (rec_tm,pred) =
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                             (rec_tm, Ind_Syntax.Collect_const$rec_tm$pred)
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                 in  subst_free (map mk_sb ind_alist) prem :: iprems  end)
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       | add_induct_prem ind_alist (prem,iprems) = prem :: iprems;
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     (*Make a premise of the induction rule.*)
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     fun induct_prem ind_alist intr =
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       let val quantfrees = map dest_Free (term_frees intr \\ rec_params)
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           val iprems = foldr (add_induct_prem ind_alist) []
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                              (Logic.strip_imp_prems intr)
wenzelm@12132
   316
           val (t,X) = Ind_Syntax.rule_concl intr
skalberg@15531
   317
           val (SOME pred) = gen_assoc (op aconv) (ind_alist, X)
wenzelm@12132
   318
           val concl = FOLogic.mk_Trueprop (pred $ t)
paulson@6051
   319
       in list_all_free (quantfrees, Logic.list_implies (iprems,concl)) end
paulson@6051
   320
       handle Bind => error"Recursion term not found in conclusion";
paulson@6051
   321
paulson@6051
   322
     (*Minimizes backtracking by delivering the correct premise to each goal.
paulson@6051
   323
       Intro rules with extra Vars in premises still cause some backtracking *)
paulson@6051
   324
     fun ind_tac [] 0 = all_tac
wenzelm@12132
   325
       | ind_tac(prem::prems) i =
paulson@13747
   326
             DEPTH_SOLVE_1 (ares_tac [prem, refl] i) THEN ind_tac prems (i-1);
paulson@6051
   327
paulson@6051
   328
     val pred = Free(pred_name, Ind_Syntax.iT --> FOLogic.oT);
paulson@6051
   329
wenzelm@12132
   330
     val ind_prems = map (induct_prem (map (rpair pred) rec_tms))
wenzelm@12132
   331
                         intr_tms;
paulson@6051
   332
wenzelm@12132
   333
     val dummy = if !Ind_Syntax.trace then
wenzelm@12132
   334
                 (writeln "ind_prems = ";
skalberg@15570
   335
                  List.app (writeln o Sign.string_of_term sign1) ind_prems;
wenzelm@12132
   336
                  writeln "raw_induct = "; print_thm raw_induct)
wenzelm@12132
   337
             else ();
paulson@6051
   338
paulson@6051
   339
wenzelm@12132
   340
     (*We use a MINIMAL simpset. Even FOL_ss contains too many simpules.
paulson@6051
   341
       If the premises get simplified, then the proofs could fail.*)
paulson@6051
   342
     val min_ss = empty_ss
wenzelm@12725
   343
           setmksimps (map mk_eq o ZF_atomize o gen_all)
wenzelm@12132
   344
           setSolver (mk_solver "minimal"
wenzelm@12132
   345
                      (fn prems => resolve_tac (triv_rls@prems)
wenzelm@12132
   346
                                   ORELSE' assume_tac
wenzelm@12132
   347
                                   ORELSE' etac FalseE));
paulson@6051
   348
wenzelm@12132
   349
     val quant_induct =
wenzelm@12132
   350
         prove_goalw_cterm part_rec_defs
wenzelm@12132
   351
           (cterm_of sign1
wenzelm@12132
   352
            (Logic.list_implies
wenzelm@12132
   353
             (ind_prems,
wenzelm@12132
   354
              FOLogic.mk_Trueprop (Ind_Syntax.mk_all_imp(big_rec_tm,pred)))))
wenzelm@12132
   355
           (fn prems =>
wenzelm@12132
   356
            [rtac (impI RS allI) 1,
wenzelm@12132
   357
             DETERM (etac raw_induct 1),
wenzelm@12132
   358
             (*Push Part inside Collect*)
wenzelm@12132
   359
             full_simp_tac (min_ss addsimps [Part_Collect]) 1,
wenzelm@12132
   360
             (*This CollectE and disjE separates out the introduction rules*)
wenzelm@12132
   361
             REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE])),
wenzelm@12132
   362
             (*Now break down the individual cases.  No disjE here in case
wenzelm@12132
   363
               some premise involves disjunction.*)
paulson@13747
   364
             REPEAT (FIRSTGOAL (eresolve_tac [CollectE, exE, conjE]
paulson@13747
   365
	                        ORELSE' bound_hyp_subst_tac)),
wenzelm@12132
   366
             ind_tac (rev prems) (length prems) ]);
paulson@6051
   367
wenzelm@12132
   368
     val dummy = if !Ind_Syntax.trace then
wenzelm@12132
   369
                 (writeln "quant_induct = "; print_thm quant_induct)
wenzelm@12132
   370
             else ();
paulson@6051
   371
paulson@6051
   372
paulson@6051
   373
     (*** Prove the simultaneous induction rule ***)
paulson@6051
   374
paulson@6051
   375
     (*Make distinct predicates for each inductive set*)
paulson@6051
   376
paulson@6051
   377
     (*The components of the element type, several if it is a product*)
paulson@6051
   378
     val elem_type = CP.pseudo_type dom_sum;
paulson@6051
   379
     val elem_factors = CP.factors elem_type;
paulson@6051
   380
     val elem_frees = mk_frees "za" elem_factors;
paulson@6051
   381
     val elem_tuple = CP.mk_tuple Pr.pair elem_type elem_frees;
paulson@6051
   382
paulson@6051
   383
     (*Given a recursive set and its domain, return the "fsplit" predicate
paulson@6051
   384
       and a conclusion for the simultaneous induction rule.
paulson@6051
   385
       NOTE.  This will not work for mutually recursive predicates.  Previously
paulson@6051
   386
       a summand 'domt' was also an argument, but this required the domain of
paulson@6051
   387
       mutual recursion to invariably be a disjoint sum.*)
wenzelm@12132
   388
     fun mk_predpair rec_tm =
paulson@6051
   389
       let val rec_name = (#1 o dest_Const o head_of) rec_tm
wenzelm@12132
   390
           val pfree = Free(pred_name ^ "_" ^ Sign.base_name rec_name,
wenzelm@12132
   391
                            elem_factors ---> FOLogic.oT)
wenzelm@12132
   392
           val qconcl =
skalberg@15574
   393
             foldr FOLogic.mk_all
skalberg@15574
   394
               (FOLogic.imp $
wenzelm@12132
   395
                (Ind_Syntax.mem_const $ elem_tuple $ rec_tm)
skalberg@15574
   396
                      $ (list_comb (pfree, elem_frees))) elem_frees
wenzelm@12132
   397
       in  (CP.ap_split elem_type FOLogic.oT pfree,
wenzelm@12132
   398
            qconcl)
paulson@6051
   399
       end;
paulson@6051
   400
paulson@6051
   401
     val (preds,qconcls) = split_list (map mk_predpair rec_tms);
paulson@6051
   402
paulson@6051
   403
     (*Used to form simultaneous induction lemma*)
wenzelm@12132
   404
     fun mk_rec_imp (rec_tm,pred) =
wenzelm@12132
   405
         FOLogic.imp $ (Ind_Syntax.mem_const $ Bound 0 $ rec_tm) $
wenzelm@12132
   406
                          (pred $ Bound 0);
paulson@6051
   407
paulson@6051
   408
     (*To instantiate the main induction rule*)
wenzelm@12132
   409
     val induct_concl =
wenzelm@12132
   410
         FOLogic.mk_Trueprop
wenzelm@12132
   411
           (Ind_Syntax.mk_all_imp
wenzelm@12132
   412
            (big_rec_tm,
wenzelm@12132
   413
             Abs("z", Ind_Syntax.iT,
wenzelm@12132
   414
                 fold_bal FOLogic.mk_conj
wenzelm@12132
   415
                 (ListPair.map mk_rec_imp (rec_tms, preds)))))
paulson@6051
   416
     and mutual_induct_concl =
wenzelm@7695
   417
      FOLogic.mk_Trueprop(fold_bal FOLogic.mk_conj qconcls);
paulson@6051
   418
wenzelm@12132
   419
     val dummy = if !Ind_Syntax.trace then
wenzelm@12132
   420
                 (writeln ("induct_concl = " ^
wenzelm@12132
   421
                           Sign.string_of_term sign1 induct_concl);
wenzelm@12132
   422
                  writeln ("mutual_induct_concl = " ^
wenzelm@12132
   423
                           Sign.string_of_term sign1 mutual_induct_concl))
wenzelm@12132
   424
             else ();
paulson@6051
   425
paulson@6051
   426
paulson@6051
   427
     val lemma_tac = FIRST' [eresolve_tac [asm_rl, conjE, PartE, mp],
wenzelm@12132
   428
                             resolve_tac [allI, impI, conjI, Part_eqI],
wenzelm@12132
   429
                             dresolve_tac [spec, mp, Pr.fsplitD]];
paulson@6051
   430
paulson@6051
   431
     val need_mutual = length rec_names > 1;
paulson@6051
   432
paulson@6051
   433
     val lemma = (*makes the link between the two induction rules*)
paulson@6051
   434
       if need_mutual then
wenzelm@12132
   435
          (writeln "  Proving the mutual induction rule...";
wenzelm@12132
   436
           prove_goalw_cterm part_rec_defs
wenzelm@12132
   437
                 (cterm_of sign1 (Logic.mk_implies (induct_concl,
wenzelm@12132
   438
                                                   mutual_induct_concl)))
wenzelm@12132
   439
                 (fn prems =>
wenzelm@12132
   440
                  [cut_facts_tac prems 1,
wenzelm@12132
   441
                   REPEAT (rewrite_goals_tac [Pr.split_eq] THEN
wenzelm@12132
   442
                           lemma_tac 1)]))
paulson@6051
   443
       else (writeln "  [ No mutual induction rule needed ]";
wenzelm@12132
   444
             TrueI);
paulson@6051
   445
wenzelm@12132
   446
     val dummy = if !Ind_Syntax.trace then
wenzelm@12132
   447
                 (writeln "lemma = "; print_thm lemma)
wenzelm@12132
   448
             else ();
paulson@6051
   449
paulson@6051
   450
paulson@6051
   451
     (*Mutual induction follows by freeness of Inl/Inr.*)
paulson@6051
   452
wenzelm@12132
   453
     (*Simplification largely reduces the mutual induction rule to the
paulson@6051
   454
       standard rule*)
wenzelm@12132
   455
     val mut_ss =
wenzelm@12132
   456
         min_ss addsimps [Su.distinct, Su.distinct', Su.inl_iff, Su.inr_iff];
paulson@6051
   457
paulson@6051
   458
     val all_defs = con_defs @ part_rec_defs;
paulson@6051
   459
paulson@6051
   460
     (*Removes Collects caused by M-operators in the intro rules.  It is very
paulson@6051
   461
       hard to simplify
wenzelm@12132
   462
         list({v: tf. (v : t --> P_t(v)) & (v : f --> P_f(v))})
paulson@6051
   463
       where t==Part(tf,Inl) and f==Part(tf,Inr) to  list({v: tf. P_t(v)}).
paulson@6051
   464
       Instead the following rules extract the relevant conjunct.
paulson@6051
   465
     *)
paulson@6051
   466
     val cmonos = [subset_refl RS Collect_mono] RL monos
wenzelm@12132
   467
                   RLN (2,[rev_subsetD]);
paulson@6051
   468
paulson@6051
   469
     (*Minimizes backtracking by delivering the correct premise to each goal*)
paulson@6051
   470
     fun mutual_ind_tac [] 0 = all_tac
wenzelm@12132
   471
       | mutual_ind_tac(prem::prems) i =
wenzelm@12132
   472
           DETERM
wenzelm@12132
   473
            (SELECT_GOAL
wenzelm@12132
   474
               (
wenzelm@12132
   475
                (*Simplify the assumptions and goal by unfolding Part and
wenzelm@12132
   476
                  using freeness of the Sum constructors; proves all but one
wenzelm@12132
   477
                  conjunct by contradiction*)
wenzelm@12132
   478
                rewrite_goals_tac all_defs  THEN
wenzelm@12132
   479
                simp_tac (mut_ss addsimps [Part_iff]) 1  THEN
wenzelm@12132
   480
                IF_UNSOLVED (*simp_tac may have finished it off!*)
wenzelm@12132
   481
                  ((*simplify assumptions*)
wenzelm@12132
   482
                   (*some risk of excessive simplification here -- might have
wenzelm@12132
   483
                     to identify the bare minimum set of rewrites*)
wenzelm@12132
   484
                   full_simp_tac
wenzelm@12132
   485
                      (mut_ss addsimps conj_simps @ imp_simps @ quant_simps) 1
wenzelm@12132
   486
                   THEN
wenzelm@12132
   487
                   (*unpackage and use "prem" in the corresponding place*)
wenzelm@12132
   488
                   REPEAT (rtac impI 1)  THEN
wenzelm@12132
   489
                   rtac (rewrite_rule all_defs prem) 1  THEN
wenzelm@12132
   490
                   (*prem must not be REPEATed below: could loop!*)
wenzelm@12132
   491
                   DEPTH_SOLVE (FIRSTGOAL (ares_tac [impI] ORELSE'
wenzelm@12132
   492
                                           eresolve_tac (conjE::mp::cmonos))))
wenzelm@12132
   493
               ) i)
wenzelm@12132
   494
            THEN mutual_ind_tac prems (i-1);
paulson@6051
   495
wenzelm@12132
   496
     val mutual_induct_fsplit =
paulson@6051
   497
       if need_mutual then
wenzelm@12132
   498
         prove_goalw_cterm []
wenzelm@12132
   499
               (cterm_of sign1
wenzelm@12132
   500
                (Logic.list_implies
wenzelm@12132
   501
                   (map (induct_prem (rec_tms~~preds)) intr_tms,
wenzelm@12132
   502
                    mutual_induct_concl)))
wenzelm@12132
   503
               (fn prems =>
wenzelm@12132
   504
                [rtac (quant_induct RS lemma) 1,
wenzelm@12132
   505
                 mutual_ind_tac (rev prems) (length prems)])
paulson@6051
   506
       else TrueI;
paulson@6051
   507
paulson@6051
   508
     (** Uncurrying the predicate in the ordinary induction rule **)
paulson@6051
   509
paulson@6051
   510
     (*instantiate the variable to a tuple, if it is non-trivial, in order to
paulson@6051
   511
       allow the predicate to be "opened up".
paulson@6051
   512
       The name "x.1" comes from the "RS spec" !*)
wenzelm@12132
   513
     val inst =
wenzelm@12132
   514
         case elem_frees of [_] => I
wenzelm@12132
   515
            | _ => instantiate ([], [(cterm_of sign1 (Var(("x",1), Ind_Syntax.iT)),
wenzelm@12132
   516
                                      cterm_of sign1 elem_tuple)]);
paulson@6051
   517
paulson@6051
   518
     (*strip quantifier and the implication*)
paulson@6051
   519
     val induct0 = inst (quant_induct RS spec RSN (2,rev_mp));
paulson@6051
   520
paulson@6051
   521
     val Const ("Trueprop", _) $ (pred_var $ _) = concl_of induct0
paulson@6051
   522
wenzelm@12132
   523
     val induct = CP.split_rule_var(pred_var, elem_type-->FOLogic.oT, induct0)
wenzelm@12132
   524
                  |> standard
paulson@6051
   525
     and mutual_induct = CP.remove_split mutual_induct_fsplit
wenzelm@8438
   526
wenzelm@12191
   527
     val (thy', [induct', mutual_induct']) = thy |> PureThy.add_thms
wenzelm@12227
   528
      [((co_prefix ^ "induct", induct), [case_names, InductAttrib.induct_set_global big_rec_name]),
wenzelm@12191
   529
       (("mutual_induct", mutual_induct), [case_names])];
wenzelm@12227
   530
    in ((thy', induct'), mutual_induct')
paulson@6051
   531
    end;  (*of induction_rules*)
paulson@6051
   532
paulson@6051
   533
  val raw_induct = standard ([big_rec_def, bnd_mono] MRS Fp.induct)
paulson@6051
   534
wenzelm@12227
   535
  val ((thy2, induct), mutual_induct) =
wenzelm@12227
   536
    if not coind then induction_rules raw_induct thy1
wenzelm@12227
   537
    else (thy1 |> PureThy.add_thms [((co_prefix ^ "induct", raw_induct), [])] |> apsnd hd, TrueI)
paulson@6051
   538
  and defs = big_rec_def :: part_rec_defs
paulson@6051
   539
paulson@6051
   540
wenzelm@8438
   541
  val (thy3, ([bnd_mono', dom_subset', elim'], [defs', intrs'])) =
wenzelm@8438
   542
    thy2
wenzelm@12183
   543
    |> IndCases.declare big_rec_name make_cases
wenzelm@12132
   544
    |> PureThy.add_thms
wenzelm@12132
   545
      [(("bnd_mono", bnd_mono), []),
wenzelm@12132
   546
       (("dom_subset", dom_subset), []),
wenzelm@12191
   547
       (("cases", elim), [case_names, InductAttrib.cases_set_global big_rec_name])]
wenzelm@8438
   548
    |>>> (PureThy.add_thmss o map Thm.no_attributes)
wenzelm@8438
   549
        [("defs", defs),
wenzelm@12175
   550
         ("intros", intrs)];
wenzelm@12132
   551
  val (thy4, intrs'') =
wenzelm@12191
   552
    thy3 |> PureThy.add_thms ((intr_names ~~ intrs') ~~ map #2 intr_specs)
wenzelm@12175
   553
    |>> Theory.parent_path;
wenzelm@8438
   554
  in
wenzelm@12132
   555
    (thy4,
wenzelm@8438
   556
      {defs = defs',
wenzelm@8438
   557
       bnd_mono = bnd_mono',
wenzelm@8438
   558
       dom_subset = dom_subset',
wenzelm@12132
   559
       intrs = intrs'',
wenzelm@8438
   560
       elim = elim',
wenzelm@8438
   561
       mk_cases = mk_cases,
wenzelm@8438
   562
       induct = induct,
wenzelm@8438
   563
       mutual_induct = mutual_induct})
wenzelm@8438
   564
  end;
paulson@6051
   565
paulson@6051
   566
paulson@6051
   567
(*external version, accepting strings*)
wenzelm@12132
   568
fun add_inductive_x (srec_tms, sdom_sum) sintrs (monos, con_defs, type_intrs, type_elims) thy =
wenzelm@8819
   569
  let
wenzelm@8819
   570
    val read = Sign.simple_read_term (Theory.sign_of thy);
wenzelm@12132
   571
    val rec_tms = map (read Ind_Syntax.iT) srec_tms;
wenzelm@12132
   572
    val dom_sum = read Ind_Syntax.iT sdom_sum;
wenzelm@12132
   573
    val intr_tms = map (read propT o snd o fst) sintrs;
wenzelm@12132
   574
    val intr_specs = (map (fst o fst) sintrs ~~ intr_tms) ~~ map snd sintrs;
wenzelm@8819
   575
  in
wenzelm@12132
   576
    add_inductive_i true (rec_tms, dom_sum) intr_specs
wenzelm@12132
   577
      (monos, con_defs, type_intrs, type_elims) thy
wenzelm@8819
   578
  end
paulson@6051
   579
wenzelm@12132
   580
wenzelm@12132
   581
(*source version*)
wenzelm@12132
   582
fun add_inductive (srec_tms, sdom_sum) intr_srcs
wenzelm@12132
   583
    (raw_monos, raw_con_defs, raw_type_intrs, raw_type_elims) thy =
wenzelm@12132
   584
  let
wenzelm@12132
   585
    val intr_atts = map (map (Attrib.global_attribute thy) o snd) intr_srcs;
wenzelm@12132
   586
    val (thy', (((monos, con_defs), type_intrs), type_elims)) = thy
wenzelm@12132
   587
      |> IsarThy.apply_theorems raw_monos
wenzelm@12132
   588
      |>>> IsarThy.apply_theorems raw_con_defs
wenzelm@12132
   589
      |>>> IsarThy.apply_theorems raw_type_intrs
wenzelm@12132
   590
      |>>> IsarThy.apply_theorems raw_type_elims;
wenzelm@12132
   591
  in
wenzelm@12132
   592
    add_inductive_x (srec_tms, sdom_sum) (map fst intr_srcs ~~ intr_atts)
wenzelm@12132
   593
      (monos, con_defs, type_intrs, type_elims) thy'
wenzelm@12132
   594
  end;
wenzelm@12132
   595
wenzelm@12132
   596
wenzelm@12132
   597
(* outer syntax *)
wenzelm@12132
   598
wenzelm@12132
   599
local structure P = OuterParse and K = OuterSyntax.Keyword in
wenzelm@12132
   600
wenzelm@12132
   601
fun mk_ind (((((doms, intrs), monos), con_defs), type_intrs), type_elims) =
wenzelm@12132
   602
  #1 o add_inductive doms (map P.triple_swap intrs) (monos, con_defs, type_intrs, type_elims);
wenzelm@12132
   603
wenzelm@12132
   604
val ind_decl =
wenzelm@12132
   605
  (P.$$$ "domains" |-- P.!!! (P.enum1 "+" P.term --
wenzelm@12876
   606
      ((P.$$$ "\\<subseteq>" || P.$$$ "<=") |-- P.term))) --
wenzelm@12132
   607
  (P.$$$ "intros" |--
wenzelm@12876
   608
    P.!!! (Scan.repeat1 (P.opt_thm_name ":" -- P.prop))) --
wenzelm@12876
   609
  Scan.optional (P.$$$ "monos" |-- P.!!! P.xthms1) [] --
wenzelm@12876
   610
  Scan.optional (P.$$$ "con_defs" |-- P.!!! P.xthms1) [] --
wenzelm@12876
   611
  Scan.optional (P.$$$ "type_intros" |-- P.!!! P.xthms1) [] --
wenzelm@12876
   612
  Scan.optional (P.$$$ "type_elims" |-- P.!!! P.xthms1) []
wenzelm@12132
   613
  >> (Toplevel.theory o mk_ind);
wenzelm@12132
   614
wenzelm@12227
   615
val inductiveP = OuterSyntax.command (co_prefix ^ "inductive")
wenzelm@12227
   616
  ("define " ^ co_prefix ^ "inductive sets") K.thy_decl ind_decl;
wenzelm@12132
   617
wenzelm@12132
   618
val _ = OuterSyntax.add_keywords
wenzelm@12132
   619
  ["domains", "intros", "monos", "con_defs", "type_intros", "type_elims"];
wenzelm@12132
   620
val _ = OuterSyntax.add_parsers [inductiveP];
wenzelm@12132
   621
paulson@6051
   622
end;
wenzelm@12132
   623
wenzelm@12132
   624
end;