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(* Title: HOL/Tools/datatype_abs_proofs.ML
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ID: $Id$
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Author: Stefan Berghofer, TU Muenchen
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Proofs and defintions independent of concrete representation
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of datatypes (i.e. requiring only abstract properties such as
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injectivity / distinctness of constructors and induction)
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- case distinction (exhaustion) theorems
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- characteristic equations for primrec combinators
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- characteristic equations for case combinators
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- equations for splitting "P (case ...)" expressions
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- datatype size function
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- "nchotomy" and "case_cong" theorems for TFL
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*)
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signature DATATYPE_ABS_PROOFS =
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sig
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val prove_casedist_thms : string list ->
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DatatypeAux.descr list -> (string * sort) list -> thm ->
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attribute list -> theory -> thm list * theory
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val prove_primrec_thms : bool -> string list ->
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DatatypeAux.descr list -> (string * sort) list ->
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DatatypeAux.datatype_info Symtab.table -> thm list list -> thm list list ->
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simpset -> thm -> theory -> (string list * thm list) * theory
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val prove_case_thms : bool -> string list ->
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DatatypeAux.descr list -> (string * sort) list ->
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string list -> thm list -> theory -> (thm list list * string list) * theory
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val prove_split_thms : string list ->
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DatatypeAux.descr list -> (string * sort) list ->
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thm list list -> thm list list -> thm list -> thm list list -> theory ->
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(thm * thm) list * theory
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val prove_size_thms : bool -> string list ->
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DatatypeAux.descr list -> (string * sort) list ->
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string list -> thm list -> theory -> thm list * theory
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val prove_nchotomys : string list -> DatatypeAux.descr list ->
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(string * sort) list -> thm list -> theory -> thm list * theory
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val prove_weak_case_congs : string list -> DatatypeAux.descr list ->
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(string * sort) list -> theory -> thm list * theory
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val prove_case_congs : string list ->
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DatatypeAux.descr list -> (string * sort) list ->
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thm list -> thm list list -> theory -> thm list * theory
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end;
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structure DatatypeAbsProofs: DATATYPE_ABS_PROOFS =
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struct
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open DatatypeAux;
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(************************ case distinction theorems ***************************)
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fun prove_casedist_thms new_type_names descr sorts induct case_names_exhausts thy =
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let
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val _ = message "Proving case distinction theorems ...";
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val descr' = List.concat descr;
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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 {maxidx, ...} = rep_thm induct;
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val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
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fun prove_casedist_thm ((i, t), T) =
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let
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val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) =>
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Abs ("z", T', Const ("True", T''))) induct_Ps;
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val P = Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx+1), T), Bound 0) $
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Var (("P", 0), HOLogic.boolT))
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val insts = Library.take (i, dummyPs) @ (P::(Library.drop (i + 1, dummyPs)));
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val cert = cterm_of thy;
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val insts' = (map cert induct_Ps) ~~ (map cert insts);
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val induct' = refl RS ((List.nth
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(split_conj_thm (cterm_instantiate insts' induct), i)) RSN (2, rev_mp))
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in
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standard (Goal.prove thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
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(fn prems => EVERY
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[rtac induct' 1,
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REPEAT (rtac TrueI 1),
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REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
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REPEAT (rtac TrueI 1)]))
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end;
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val casedist_thms = map prove_casedist_thm ((0 upto (length newTs - 1)) ~~
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(DatatypeProp.make_casedists descr sorts) ~~ newTs)
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in
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thy
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|> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms
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end;
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(*************************** primrec combinators ******************************)
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fun prove_primrec_thms flat_names new_type_names descr sorts
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(dt_info : datatype_info Symtab.table) constr_inject dist_rewrites dist_ss induct thy =
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let
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val _ = message "Constructing primrec combinators ...";
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val big_name = space_implode "_" new_type_names;
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val thy0 = add_path flat_names big_name thy;
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val descr' = List.concat descr;
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val recTs = get_rec_types descr' sorts;
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val used = foldr add_typ_tfree_names [] recTs;
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val newTs = Library.take (length (hd descr), recTs);
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val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
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val big_rec_name' = big_name ^ "_rec_set";
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val rec_set_names = map (Sign.full_name (Theory.sign_of thy0))
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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 (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
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val rec_set_Ts = map (fn (T1, T2) => reccomb_fn_Ts ---> HOLogic.mk_setT
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(HOLogic.mk_prodT (T1, T2))) (recTs ~~ rec_result_Ts);
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val rec_fns = map (uncurry (mk_Free "f"))
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(reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
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val rec_sets = map (fn c => list_comb (Const c, rec_fns))
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(rec_set_names ~~ rec_set_Ts);
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(* introduction rules for graph of primrec function *)
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fun make_rec_intr T set_name ((rec_intr_ts, l), (cname, cargs)) =
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let
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fun mk_prem ((dt, U), (j, k, prems, t1s, t2s)) =
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let val free1 = mk_Free "x" U j
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in (case (strip_dtyp dt, strip_type U) of
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((_, DtRec m), (Us, _)) =>
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let
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val free2 = mk_Free "y" (Us ---> List.nth (rec_result_Ts, m)) k;
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val i = length Us
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in (j + 1, k + 1, HOLogic.mk_Trueprop (HOLogic.list_all
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(map (pair "x") Us, HOLogic.mk_mem (HOLogic.mk_prod
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(app_bnds free1 i, app_bnds free2 i),
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List.nth (rec_sets, m)))) :: prems,
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free1::t1s, free2::t2s)
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end
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| _ => (j + 1, k, prems, free1::t1s, t2s))
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end;
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val Ts = map (typ_of_dtyp descr' sorts) cargs;
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val (_, _, prems, t1s, t2s) = foldr mk_prem (1, 1, [], [], []) (cargs ~~ Ts)
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in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop (HOLogic.mk_mem
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(HOLogic.mk_prod (list_comb (Const (cname, Ts ---> T), t1s),
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list_comb (List.nth (rec_fns, l), t1s @ t2s)), set_name)))], l + 1)
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end;
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val (rec_intr_ts, _) = Library.foldl (fn (x, ((d, T), set_name)) =>
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Library.foldl (make_rec_intr T set_name) (x, #3 (snd d)))
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(([], 0), descr' ~~ recTs ~~ rec_sets);
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val (thy1, {intrs = rec_intrs, elims = rec_elims, ...}) =
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setmp InductivePackage.quiet_mode (!quiet_mode)
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(InductivePackage.add_inductive_i false true big_rec_name' false false true
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rec_sets (map (fn x => (("", x), [])) rec_intr_ts) []) thy0;
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(* prove uniqueness and termination of primrec combinators *)
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val _ = message "Proving termination and uniqueness of primrec functions ...";
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fun mk_unique_tac ((tac, intrs), ((((i, (tname, _, constrs)), elim), T), T')) =
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let
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val distinct_tac = (etac Pair_inject 1) THEN
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(if i < length newTs then
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full_simp_tac (HOL_ss addsimps (List.nth (dist_rewrites, i))) 1
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else full_simp_tac dist_ss 1);
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val inject = map (fn r => r RS iffD1)
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(if i < length newTs then List.nth (constr_inject, i)
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else #inject (the (Symtab.lookup dt_info tname)));
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fun mk_unique_constr_tac n ((tac, intr::intrs, j), (cname, cargs)) =
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let
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val k = length (List.filter is_rec_type cargs)
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in (EVERY [DETERM tac,
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REPEAT (etac ex1E 1), rtac ex1I 1,
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DEPTH_SOLVE_1 (ares_tac [intr] 1),
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REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1),
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etac elim 1,
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REPEAT_DETERM_N j distinct_tac,
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etac Pair_inject 1, TRY (dresolve_tac inject 1),
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REPEAT (etac conjE 1), hyp_subst_tac 1,
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REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]),
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TRY (hyp_subst_tac 1),
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rtac refl 1,
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REPEAT_DETERM_N (n - j - 1) distinct_tac],
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intrs, j + 1)
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end;
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val (tac', intrs', _) = Library.foldl (mk_unique_constr_tac (length constrs))
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((tac, intrs, 0), constrs);
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in (tac', intrs') end;
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val rec_unique_thms =
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let
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val rec_unique_ts = map (fn (((set_t, T1), T2), i) =>
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Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
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absfree ("y", T2, HOLogic.mk_mem (HOLogic.mk_prod
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(mk_Free "x" T1 i, Free ("y", T2)), set_t)))
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(rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
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val cert = cterm_of thy1
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val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t))
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((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
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val induct' = cterm_instantiate ((map cert induct_Ps) ~~
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(map cert insts)) induct;
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val (tac, _) = Library.foldl mk_unique_tac
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(((rtac induct' THEN_ALL_NEW ObjectLogic.atomize_tac) 1
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THEN rewtac (mk_meta_eq choice_eq), rec_intrs),
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descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts);
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in split_conj_thm (standard (Goal.prove thy1 [] []
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(HOLogic.mk_Trueprop (mk_conj rec_unique_ts)) (K tac)))
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end;
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val rec_total_thms = map (fn r => r RS theI') rec_unique_thms;
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(* define primrec combinators *)
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val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
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val reccomb_names = map (Sign.full_name (Theory.sign_of thy1))
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(if length descr' = 1 then [big_reccomb_name] else
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(map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
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(1 upto (length descr'))));
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val reccombs = map (fn ((name, T), T') => list_comb
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(Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns))
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(reccomb_names ~~ recTs ~~ rec_result_Ts);
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val (reccomb_defs, thy2) =
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thy1
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|> Theory.add_consts_i (map (fn ((name, T), T') =>
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(Sign.base_name name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
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haftmann@18358
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(reccomb_names ~~ recTs ~~ rec_result_Ts))
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|> (PureThy.add_defs_i false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
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((Sign.base_name name) ^ "_def", Logic.mk_equals (comb, absfree ("x", T,
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Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T',
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HOLogic.mk_mem (HOLogic.mk_prod (Free ("x", T), Free ("y", T')), set))))))
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haftmann@18358
|
245 |
(reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts))
|
haftmann@18358
|
246 |
||> parent_path flat_names;
|
berghofe@5177
|
247 |
|
berghofe@5177
|
248 |
|
berghofe@5177
|
249 |
(* prove characteristic equations for primrec combinators *)
|
berghofe@5177
|
250 |
|
wenzelm@6427
|
251 |
val _ = message "Proving characteristic theorems for primrec combinators ..."
|
berghofe@5177
|
252 |
|
wenzelm@17985
|
253 |
val rec_thms = map (fn t => standard (Goal.prove thy2 [] [] t
|
wenzelm@17985
|
254 |
(fn _ => EVERY
|
wenzelm@17985
|
255 |
[rewrite_goals_tac reccomb_defs,
|
wenzelm@17985
|
256 |
rtac the1_equality 1,
|
berghofe@5177
|
257 |
resolve_tac rec_unique_thms 1,
|
berghofe@5177
|
258 |
resolve_tac rec_intrs 1,
|
wenzelm@17985
|
259 |
REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)])))
|
berghofe@5177
|
260 |
(DatatypeProp.make_primrecs new_type_names descr sorts thy2)
|
berghofe@5177
|
261 |
|
berghofe@5177
|
262 |
in
|
haftmann@18314
|
263 |
thy2
|
haftmann@18314
|
264 |
|> Theory.add_path (space_implode "_" new_type_names)
|
haftmann@18377
|
265 |
|> PureThy.add_thmss [(("recs", rec_thms), [])]
|
haftmann@18314
|
266 |
||> Theory.parent_path
|
haftmann@18314
|
267 |
|-> (fn thms => pair (reccomb_names, Library.flat thms))
|
berghofe@5177
|
268 |
end;
|
berghofe@5177
|
269 |
|
berghofe@8477
|
270 |
|
berghofe@5177
|
271 |
(***************************** case combinators *******************************)
|
berghofe@5177
|
272 |
|
berghofe@5661
|
273 |
fun prove_case_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
|
berghofe@5177
|
274 |
let
|
wenzelm@6427
|
275 |
val _ = message "Proving characteristic theorems for case combinators ...";
|
berghofe@5661
|
276 |
|
berghofe@5661
|
277 |
val thy1 = add_path flat_names (space_implode "_" new_type_names) thy;
|
berghofe@5177
|
278 |
|
skalberg@15570
|
279 |
val descr' = List.concat descr;
|
berghofe@5177
|
280 |
val recTs = get_rec_types descr' sorts;
|
skalberg@15574
|
281 |
val used = foldr add_typ_tfree_names [] recTs;
|
skalberg@15570
|
282 |
val newTs = Library.take (length (hd descr), recTs);
|
wenzelm@12338
|
283 |
val T' = TFree (variant used "'t", HOLogic.typeS);
|
berghofe@5177
|
284 |
|
berghofe@13641
|
285 |
fun mk_dummyT dt = binder_types (typ_of_dtyp descr' sorts dt) ---> T';
|
berghofe@7015
|
286 |
|
berghofe@5177
|
287 |
val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
|
berghofe@5177
|
288 |
let
|
berghofe@5177
|
289 |
val Ts = map (typ_of_dtyp descr' sorts) cargs;
|
skalberg@15570
|
290 |
val Ts' = map mk_dummyT (List.filter is_rec_type cargs)
|
berghofe@5578
|
291 |
in Const ("arbitrary", Ts @ Ts' ---> T')
|
berghofe@5177
|
292 |
end) constrs) descr';
|
berghofe@5177
|
293 |
|
berghofe@5177
|
294 |
val case_names = map (fn s =>
|
wenzelm@6394
|
295 |
Sign.full_name (Theory.sign_of thy1) (s ^ "_case")) new_type_names;
|
berghofe@5177
|
296 |
|
berghofe@5177
|
297 |
(* define case combinators via primrec combinators *)
|
berghofe@5177
|
298 |
|
skalberg@15570
|
299 |
val (case_defs, thy2) = Library.foldl (fn ((defs, thy),
|
berghofe@5177
|
300 |
((((i, (_, _, constrs)), T), name), recname)) =>
|
berghofe@5177
|
301 |
let
|
berghofe@5177
|
302 |
val (fns1, fns2) = ListPair.unzip (map (fn ((_, cargs), j) =>
|
berghofe@5177
|
303 |
let
|
berghofe@5177
|
304 |
val Ts = map (typ_of_dtyp descr' sorts) cargs;
|
skalberg@15570
|
305 |
val Ts' = Ts @ map mk_dummyT (List.filter is_rec_type cargs);
|
berghofe@5177
|
306 |
val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts'));
|
skalberg@15570
|
307 |
val frees = Library.take (length cargs, frees');
|
berghofe@5177
|
308 |
val free = mk_Free "f" (Ts ---> T') j
|
berghofe@5177
|
309 |
in
|
berghofe@5177
|
310 |
(free, list_abs_free (map dest_Free frees',
|
berghofe@5177
|
311 |
list_comb (free, frees)))
|
berghofe@5177
|
312 |
end) (constrs ~~ (1 upto length constrs)));
|
berghofe@5177
|
313 |
|
berghofe@5177
|
314 |
val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T';
|
skalberg@15570
|
315 |
val fns = (List.concat (Library.take (i, case_dummy_fns))) @
|
skalberg@15570
|
316 |
fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns)));
|
berghofe@5177
|
317 |
val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
|
berghofe@5177
|
318 |
val decl = (Sign.base_name name, caseT, NoSyn);
|
berghofe@5177
|
319 |
val def = ((Sign.base_name name) ^ "_def",
|
berghofe@5177
|
320 |
Logic.mk_equals (list_comb (Const (name, caseT), fns1),
|
skalberg@15570
|
321 |
list_comb (reccomb, (List.concat (Library.take (i, case_dummy_fns))) @
|
skalberg@15570
|
322 |
fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns))) )));
|
haftmann@18358
|
323 |
val ([def_thm], thy') =
|
haftmann@18358
|
324 |
thy
|
haftmann@18358
|
325 |
|> Theory.add_consts_i [decl]
|
haftmann@18358
|
326 |
|> (PureThy.add_defs_i false o map Thm.no_attributes) [def];
|
berghofe@5177
|
327 |
|
wenzelm@8436
|
328 |
in (defs @ [def_thm], thy')
|
berghofe@5661
|
329 |
end) (([], thy1), (hd descr) ~~ newTs ~~ case_names ~~
|
skalberg@15570
|
330 |
(Library.take (length newTs, reccomb_names)));
|
berghofe@5177
|
331 |
|
wenzelm@17985
|
332 |
val case_thms = map (map (fn t => standard (Goal.prove thy2 [] [] t
|
wenzelm@17985
|
333 |
(fn _ => EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1]))))
|
berghofe@8477
|
334 |
(DatatypeProp.make_cases new_type_names descr sorts thy2)
|
berghofe@5177
|
335 |
|
berghofe@8477
|
336 |
in
|
haftmann@18314
|
337 |
thy2
|
haftmann@18314
|
338 |
|> parent_path flat_names
|
haftmann@18314
|
339 |
|> store_thmss "cases" new_type_names case_thms
|
haftmann@18314
|
340 |
|-> (fn thmss => pair (thmss, case_names))
|
berghofe@8477
|
341 |
end;
|
berghofe@5177
|
342 |
|
berghofe@5177
|
343 |
|
berghofe@5177
|
344 |
(******************************* case splitting *******************************)
|
berghofe@5177
|
345 |
|
berghofe@5177
|
346 |
fun prove_split_thms new_type_names descr sorts constr_inject dist_rewrites
|
berghofe@5177
|
347 |
casedist_thms case_thms thy =
|
berghofe@5177
|
348 |
let
|
wenzelm@6427
|
349 |
val _ = message "Proving equations for case splitting ...";
|
berghofe@5177
|
350 |
|
skalberg@15570
|
351 |
val descr' = List.concat descr;
|
berghofe@5177
|
352 |
val recTs = get_rec_types descr' sorts;
|
skalberg@15570
|
353 |
val newTs = Library.take (length (hd descr), recTs);
|
berghofe@5177
|
354 |
|
berghofe@5177
|
355 |
fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'),
|
berghofe@5177
|
356 |
exhaustion), case_thms'), T) =
|
berghofe@5177
|
357 |
let
|
wenzelm@17985
|
358 |
val cert = cterm_of thy;
|
berghofe@5177
|
359 |
val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
|
berghofe@5177
|
360 |
val exhaustion' = cterm_instantiate
|
berghofe@5177
|
361 |
[(cert lhs, cert (Free ("x", T)))] exhaustion;
|
wenzelm@17985
|
362 |
val tacf = K (EVERY [rtac exhaustion' 1, ALLGOALS (asm_simp_tac
|
wenzelm@17985
|
363 |
(HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))])
|
berghofe@5177
|
364 |
in
|
wenzelm@17985
|
365 |
(standard (Goal.prove thy [] [] t1 tacf),
|
wenzelm@17985
|
366 |
standard (Goal.prove thy [] [] t2 tacf))
|
berghofe@5177
|
367 |
end;
|
berghofe@5177
|
368 |
|
berghofe@5177
|
369 |
val split_thm_pairs = map prove_split_thms
|
berghofe@5177
|
370 |
((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~
|
berghofe@5177
|
371 |
dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
|
berghofe@5177
|
372 |
|
berghofe@5177
|
373 |
val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs
|
berghofe@5177
|
374 |
|
berghofe@5177
|
375 |
in
|
haftmann@18314
|
376 |
thy
|
haftmann@18314
|
377 |
|> store_thms "split" new_type_names split_thms
|
haftmann@18314
|
378 |
||>> store_thms "split_asm" new_type_names split_asm_thms
|
haftmann@18314
|
379 |
|-> (fn (thms1, thms2) => pair (thms1 ~~ thms2))
|
berghofe@5177
|
380 |
end;
|
berghofe@5177
|
381 |
|
berghofe@5177
|
382 |
(******************************* size functions *******************************)
|
berghofe@5177
|
383 |
|
berghofe@5661
|
384 |
fun prove_size_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
|
berghofe@13641
|
385 |
if exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists (fn dt =>
|
berghofe@13641
|
386 |
is_rec_type dt andalso not (null (fst (strip_dtyp dt)))) cargs) constrs)
|
skalberg@15570
|
387 |
(List.concat descr)
|
berghofe@7015
|
388 |
then
|
haftmann@18314
|
389 |
([], thy)
|
berghofe@7015
|
390 |
else
|
berghofe@5177
|
391 |
let
|
wenzelm@6427
|
392 |
val _ = message "Proving equations for size function ...";
|
berghofe@5661
|
393 |
|
berghofe@5661
|
394 |
val big_name = space_implode "_" new_type_names;
|
berghofe@5661
|
395 |
val thy1 = add_path flat_names big_name thy;
|
berghofe@5177
|
396 |
|
skalberg@15570
|
397 |
val descr' = List.concat descr;
|
berghofe@5177
|
398 |
val recTs = get_rec_types descr' sorts;
|
berghofe@5177
|
399 |
|
wenzelm@11957
|
400 |
val size_name = "Nat.size";
|
berghofe@5177
|
401 |
val size_names = replicate (length (hd descr)) size_name @
|
berghofe@9739
|
402 |
map (Sign.full_name (Theory.sign_of thy1)) (DatatypeProp.indexify_names
|
skalberg@15570
|
403 |
(map (fn T => name_of_typ T ^ "_size") (Library.drop (length (hd descr), recTs))));
|
berghofe@9739
|
404 |
val def_names = map (fn s => s ^ "_def") (DatatypeProp.indexify_names
|
berghofe@9739
|
405 |
(map (fn T => name_of_typ T ^ "_size") recTs));
|
berghofe@5177
|
406 |
|
wenzelm@7704
|
407 |
fun plus (t1, t2) = Const ("op +", [HOLogic.natT, HOLogic.natT] ---> HOLogic.natT) $ t1 $ t2;
|
berghofe@5177
|
408 |
|
berghofe@5177
|
409 |
fun make_sizefun (_, cargs) =
|
berghofe@5177
|
410 |
let
|
berghofe@5177
|
411 |
val Ts = map (typ_of_dtyp descr' sorts) cargs;
|
skalberg@15570
|
412 |
val k = length (List.filter is_rec_type cargs);
|
berghofe@5177
|
413 |
val t = if k = 0 then HOLogic.zero else
|
wenzelm@7704
|
414 |
foldl1 plus (map Bound (k - 1 downto 0) @ [HOLogic.mk_nat 1])
|
berghofe@5177
|
415 |
in
|
skalberg@15574
|
416 |
foldr (fn (T, t') => Abs ("x", T, t')) t (Ts @ replicate k HOLogic.natT)
|
berghofe@5177
|
417 |
end;
|
berghofe@5177
|
418 |
|
skalberg@15570
|
419 |
val fs = List.concat (map (fn (_, (_, _, constrs)) => map make_sizefun constrs) descr');
|
berghofe@5177
|
420 |
val fTs = map fastype_of fs;
|
berghofe@5177
|
421 |
|
haftmann@18358
|
422 |
val (size_def_thms, thy') =
|
haftmann@18358
|
423 |
thy1
|
haftmann@18358
|
424 |
|> Theory.add_consts_i (map (fn (s, T) =>
|
haftmann@18358
|
425 |
(Sign.base_name s, T --> HOLogic.natT, NoSyn))
|
haftmann@18358
|
426 |
(Library.drop (length (hd descr), size_names ~~ recTs)))
|
haftmann@18358
|
427 |
|> (PureThy.add_defs_i true o map Thm.no_attributes) (map (fn (((s, T), def_name), rec_name) =>
|
haftmann@18358
|
428 |
(def_name, Logic.mk_equals (Const (s, T --> HOLogic.natT),
|
haftmann@18358
|
429 |
list_comb (Const (rec_name, fTs @ [T] ---> HOLogic.natT), fs))))
|
haftmann@18358
|
430 |
(size_names ~~ recTs ~~ def_names ~~ reccomb_names))
|
haftmann@18358
|
431 |
||> parent_path flat_names;
|
berghofe@5177
|
432 |
|
oheimb@5553
|
433 |
val rewrites = size_def_thms @ map mk_meta_eq primrec_thms;
|
berghofe@5177
|
434 |
|
wenzelm@17985
|
435 |
val size_thms = map (fn t => standard (Goal.prove thy' [] [] t
|
wenzelm@17985
|
436 |
(fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])))
|
berghofe@9739
|
437 |
(DatatypeProp.make_size descr sorts thy')
|
berghofe@5177
|
438 |
|
berghofe@5177
|
439 |
in
|
haftmann@18314
|
440 |
thy'
|
haftmann@18314
|
441 |
|> Theory.add_path big_name
|
haftmann@18377
|
442 |
|> PureThy.add_thmss [(("size", size_thms), [])]
|
haftmann@18314
|
443 |
||> Theory.parent_path
|
haftmann@18314
|
444 |
|-> (fn thmss => pair (Library.flat thmss))
|
berghofe@5177
|
445 |
end;
|
berghofe@5177
|
446 |
|
nipkow@8601
|
447 |
fun prove_weak_case_congs new_type_names descr sorts thy =
|
nipkow@8601
|
448 |
let
|
nipkow@8601
|
449 |
fun prove_weak_case_cong t =
|
wenzelm@17985
|
450 |
standard (Goal.prove thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
|
wenzelm@17985
|
451 |
(fn prems => EVERY [rtac ((hd prems) RS arg_cong) 1]))
|
nipkow@8601
|
452 |
|
nipkow@8601
|
453 |
val weak_case_congs = map prove_weak_case_cong (DatatypeProp.make_weak_case_congs
|
nipkow@8601
|
454 |
new_type_names descr sorts thy)
|
nipkow@8601
|
455 |
|
nipkow@8601
|
456 |
in thy |> store_thms "weak_case_cong" new_type_names weak_case_congs end;
|
berghofe@8477
|
457 |
|
berghofe@5177
|
458 |
(************************* additional theorems for TFL ************************)
|
berghofe@5177
|
459 |
|
berghofe@5177
|
460 |
fun prove_nchotomys new_type_names descr sorts casedist_thms thy =
|
berghofe@5177
|
461 |
let
|
wenzelm@6427
|
462 |
val _ = message "Proving additional theorems for TFL ...";
|
berghofe@5177
|
463 |
|
berghofe@5177
|
464 |
fun prove_nchotomy (t, exhaustion) =
|
berghofe@5177
|
465 |
let
|
berghofe@5177
|
466 |
(* For goal i, select the correct disjunct to attack, then prove it *)
|
berghofe@5177
|
467 |
fun tac i 0 = EVERY [TRY (rtac disjI1 i),
|
berghofe@5177
|
468 |
hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
|
berghofe@5177
|
469 |
| tac i n = rtac disjI2 i THEN tac i (n - 1)
|
berghofe@5177
|
470 |
in
|
wenzelm@17985
|
471 |
standard (Goal.prove thy [] [] t (fn _ =>
|
wenzelm@17985
|
472 |
EVERY [rtac allI 1,
|
berghofe@5177
|
473 |
exh_tac (K exhaustion) 1,
|
wenzelm@17985
|
474 |
ALLGOALS (fn i => tac i (i-1))]))
|
berghofe@5177
|
475 |
end;
|
berghofe@5177
|
476 |
|
berghofe@5177
|
477 |
val nchotomys =
|
berghofe@5177
|
478 |
map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms)
|
berghofe@5177
|
479 |
|
wenzelm@8436
|
480 |
in thy |> store_thms "nchotomy" new_type_names nchotomys end;
|
berghofe@5177
|
481 |
|
berghofe@5177
|
482 |
fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy =
|
berghofe@5177
|
483 |
let
|
berghofe@5177
|
484 |
fun prove_case_cong ((t, nchotomy), case_rewrites) =
|
berghofe@5177
|
485 |
let
|
berghofe@5177
|
486 |
val (Const ("==>", _) $ tm $ _) = t;
|
berghofe@5177
|
487 |
val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm;
|
wenzelm@6394
|
488 |
val cert = cterm_of (Theory.sign_of thy);
|
berghofe@5177
|
489 |
val nchotomy' = nchotomy RS spec;
|
berghofe@5177
|
490 |
val nchotomy'' = cterm_instantiate
|
berghofe@5177
|
491 |
[(cert (hd (add_term_vars (concl_of nchotomy', []))), cert Ma)] nchotomy'
|
berghofe@5177
|
492 |
in
|
wenzelm@17985
|
493 |
standard (Goal.prove thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
|
wenzelm@17985
|
494 |
(fn prems =>
|
wenzelm@17985
|
495 |
let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites))
|
wenzelm@17985
|
496 |
in EVERY [simp_tac (HOL_ss addsimps [hd prems]) 1,
|
wenzelm@17985
|
497 |
cut_facts_tac [nchotomy''] 1,
|
wenzelm@17985
|
498 |
REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
|
wenzelm@17985
|
499 |
REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
|
wenzelm@17985
|
500 |
end))
|
berghofe@5177
|
501 |
end;
|
berghofe@5177
|
502 |
|
berghofe@5177
|
503 |
val case_congs = map prove_case_cong (DatatypeProp.make_case_congs
|
berghofe@5177
|
504 |
new_type_names descr sorts thy ~~ nchotomys ~~ case_thms)
|
berghofe@5177
|
505 |
|
wenzelm@8436
|
506 |
in thy |> store_thms "case_cong" new_type_names case_congs end;
|
berghofe@5177
|
507 |
|
berghofe@5177
|
508 |
end;
|