berghofe@5177: (*  Title:      HOL/Tools/datatype_abs_proofs.ML
wenzelm@11539:     Author:     Stefan Berghofer, TU Muenchen
berghofe@5177: 
berghofe@5177: Proofs and defintions independent of concrete representation
berghofe@5177: of datatypes  (i.e. requiring only abstract properties such as
berghofe@5177: injectivity / distinctness of constructors and induction)
berghofe@5177: 
berghofe@5177:  - case distinction (exhaustion) theorems
berghofe@5177:  - characteristic equations for primrec combinators
berghofe@5177:  - characteristic equations for case combinators
berghofe@5177:  - equations for splitting "P (case ...)" expressions
wenzelm@29264:  - "nchotomy" and "case_cong" theorems for TFL
berghofe@5177: *)
berghofe@5177: 
berghofe@5177: signature DATATYPE_ABS_PROOFS =
berghofe@5177: sig
haftmann@31737:   include DATATYPE_COMMON
haftmann@31737:   val prove_casedist_thms : config -> string list ->
haftmann@31668:     descr list -> (string * sort) list -> thm ->
wenzelm@18728:     attribute list -> theory -> thm list * theory
haftmann@31737:   val prove_primrec_thms : config -> string list ->
haftmann@31668:     descr list -> (string * sort) list ->
haftmann@32915:       (string -> thm list) -> thm list list -> thm list list * thm list list ->
haftmann@32915:         thm -> theory -> (string list * thm list) * theory
haftmann@31737:   val prove_case_thms : config -> string list ->
haftmann@31668:     descr list -> (string * sort) list ->
haftmann@18314:       string list -> thm list -> theory -> (thm list list * string list) * theory
haftmann@31737:   val prove_split_thms : config -> string list ->
haftmann@31668:     descr list -> (string * sort) list ->
berghofe@5177:       thm list list -> thm list list -> thm list -> thm list list -> theory ->
haftmann@18314:         (thm * thm) list * theory
haftmann@31737:   val prove_nchotomys : config -> string list -> descr list ->
haftmann@18314:     (string * sort) list -> thm list -> theory -> thm list * theory
haftmann@31668:   val prove_weak_case_congs : string list -> descr list ->
haftmann@18314:     (string * sort) list -> theory -> thm list * theory
berghofe@13641:   val prove_case_congs : string list ->
haftmann@31668:     descr list -> (string * sort) list ->
haftmann@18314:       thm list -> thm list list -> theory -> thm list * theory
berghofe@5177: end;
berghofe@5177: 
wenzelm@8436: structure DatatypeAbsProofs: DATATYPE_ABS_PROOFS =
berghofe@5177: struct
berghofe@5177: 
berghofe@5177: open DatatypeAux;
berghofe@5177: 
berghofe@5177: (************************ case distinction theorems ***************************)
berghofe@5177: 
haftmann@31737: fun prove_casedist_thms (config : config) new_type_names descr sorts induct case_names_exhausts thy =
berghofe@5177:   let
haftmann@31668:     val _ = message config "Proving case distinction theorems ...";
berghofe@5177: 
wenzelm@32952:     val descr' = flat descr;
berghofe@5177:     val recTs = get_rec_types descr' sorts;
haftmann@33955:     val newTs = (uncurry take) (length (hd descr), recTs);
berghofe@5177: 
berghofe@8477:     val {maxidx, ...} = rep_thm induct;
wenzelm@8305:     val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
berghofe@5177: 
haftmann@33063:     fun prove_casedist_thm (i, (T, t)) =
berghofe@5177:       let
berghofe@5177:         val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) =>
berghofe@5177:           Abs ("z", T', Const ("True", T''))) induct_Ps;
berghofe@8477:         val P = Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx+1), T), Bound 0) $
berghofe@5177:           Var (("P", 0), HOLogic.boolT))
haftmann@33955:         val insts = (uncurry take) (i, dummyPs) @ (P::((uncurry drop) (i + 1, dummyPs)));
wenzelm@17985:         val cert = cterm_of thy;
berghofe@5177:         val insts' = (map cert induct_Ps) ~~ (map cert insts);
haftmann@32905:         val induct' = refl RS ((nth
haftmann@32905:           (split_conj_thm (cterm_instantiate insts' induct)) i) RSN (2, rev_mp))
berghofe@5177: 
wenzelm@17985:       in
wenzelm@32970:         Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
wenzelm@26711:           (fn {prems, ...} => EVERY
wenzelm@17985:             [rtac induct' 1,
wenzelm@17985:              REPEAT (rtac TrueI 1),
wenzelm@17985:              REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
wenzelm@20046:              REPEAT (rtac TrueI 1)])
berghofe@5177:       end;
berghofe@5177: 
haftmann@33063:     val casedist_thms = map_index prove_casedist_thm
haftmann@33063:       (newTs ~~ DatatypeProp.make_casedists descr sorts)
haftmann@18314:   in
haftmann@18314:     thy
haftmann@18314:     |> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms
haftmann@18314:   end;
berghofe@5177: 
berghofe@5177: 
berghofe@5177: (*************************** primrec combinators ******************************)
berghofe@5177: 
haftmann@31737: fun prove_primrec_thms (config : config) new_type_names descr sorts
haftmann@32915:     injects_of constr_inject (dist_rewrites, other_dist_rewrites) induct thy =
berghofe@5177:   let
haftmann@31668:     val _ = message config "Constructing primrec combinators ...";
berghofe@5661: 
berghofe@5661:     val big_name = space_implode "_" new_type_names;
haftmann@32124:     val thy0 = Sign.add_path big_name thy;
berghofe@5177: 
wenzelm@32952:     val descr' = flat descr;
berghofe@5177:     val recTs = get_rec_types descr' sorts;
wenzelm@30190:     val used = List.foldr OldTerm.add_typ_tfree_names [] recTs;
haftmann@33955:     val newTs = (uncurry take) (length (hd descr), recTs);
berghofe@5177: 
wenzelm@8305:     val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
berghofe@5177: 
berghofe@5661:     val big_rec_name' = big_name ^ "_rec_set";
berghofe@21021:     val rec_set_names' =
berghofe@21021:       if length descr' = 1 then [big_rec_name'] else
berghofe@21021:         map ((curry (op ^) (big_rec_name' ^ "_")) o string_of_int)
berghofe@21021:           (1 upto (length descr'));
haftmann@28965:     val rec_set_names = map (Sign.full_bname thy0) rec_set_names';
berghofe@5177: 
berghofe@15459:     val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
berghofe@5177: 
berghofe@21021:     val rec_set_Ts = map (fn (T1, T2) =>
berghofe@21021:       reccomb_fn_Ts @ [T1, T2] ---> HOLogic.boolT) (recTs ~~ rec_result_Ts);
berghofe@5177: 
berghofe@5177:     val rec_fns = map (uncurry (mk_Free "f"))
berghofe@5177:       (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
berghofe@21021:     val rec_sets' = map (fn c => list_comb (Free c, rec_fns))
berghofe@21021:       (rec_set_names' ~~ rec_set_Ts);
berghofe@5177:     val rec_sets = map (fn c => list_comb (Const c, rec_fns))
berghofe@5177:       (rec_set_names ~~ rec_set_Ts);
berghofe@5177: 
berghofe@5177:     (* introduction rules for graph of primrec function *)
berghofe@5177: 
haftmann@32906:     fun make_rec_intr T rec_set (cname, cargs) (rec_intr_ts, l) =
berghofe@5177:       let
wenzelm@33338:         fun mk_prem (dt, U) (j, k, prems, t1s, t2s) =
berghofe@7015:           let val free1 = mk_Free "x" U j
berghofe@13641:           in (case (strip_dtyp dt, strip_type U) of
berghofe@13641:              ((_, DtRec m), (Us, _)) =>
berghofe@13641:                let
haftmann@32905:                  val free2 = mk_Free "y" (Us ---> nth rec_result_Ts m) k;
berghofe@13641:                  val i = length Us
berghofe@13641:                in (j + 1, k + 1, HOLogic.mk_Trueprop (HOLogic.list_all
haftmann@32905:                      (map (pair "x") Us, nth rec_sets' m $
berghofe@21021:                        app_bnds free1 i $ app_bnds free2 i)) :: prems,
berghofe@5177:                    free1::t1s, free2::t2s)
berghofe@5177:                end
berghofe@5177:            | _ => (j + 1, k, prems, free1::t1s, t2s))
berghofe@5177:           end;
berghofe@5177: 
berghofe@5177:         val Ts = map (typ_of_dtyp descr' sorts) cargs;
wenzelm@33338:         val (_, _, prems, t1s, t2s) = fold_rev mk_prem (cargs ~~ Ts) (1, 1, [], [], [])
berghofe@5177: 
berghofe@21021:       in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop
berghofe@21021:         (rec_set $ list_comb (Const (cname, Ts ---> T), t1s) $
haftmann@32905:           list_comb (nth rec_fns l, t1s @ t2s)))], l + 1)
berghofe@5177:       end;
berghofe@5177: 
haftmann@32906:     val (rec_intr_ts, _) = fold (fn ((d, T), set_name) =>
haftmann@32906:       fold (make_rec_intr T set_name) (#3 (snd d)))
haftmann@32906:         (descr' ~~ recTs ~~ rec_sets') ([], 0);
berghofe@5177: 
wenzelm@21365:     val ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) =
wenzelm@33278:       thy0
wenzelm@33278:       |> Sign.map_naming Name_Space.conceal
wenzelm@33726:       |> Inductive.add_inductive_global
wenzelm@33669:           {quiet_mode = #quiet config, verbose = false, alt_name = Binding.name big_rec_name',
wenzelm@33669:             coind = false, no_elim = false, no_ind = true, skip_mono = true, fork_mono = false}
haftmann@28965:           (map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts))
wenzelm@26128:           (map dest_Free rec_fns)
wenzelm@33278:           (map (fn x => (Attrib.empty_binding, x)) rec_intr_ts) []
wenzelm@33278:       ||> Sign.restore_naming thy0
wenzelm@33278:       ||> Theory.checkpoint;
berghofe@5177: 
berghofe@5177:     (* prove uniqueness and termination of primrec combinators *)
berghofe@5177: 
haftmann@31668:     val _ = message config "Proving termination and uniqueness of primrec functions ...";
berghofe@5177: 
haftmann@32906:     fun mk_unique_tac ((((i, (tname, _, constrs)), elim), T), T') (tac, intrs) =
berghofe@5177:       let
berghofe@21021:         val distinct_tac =
berghofe@5177:           (if i < length newTs then
haftmann@32905:              full_simp_tac (HOL_ss addsimps (nth dist_rewrites i)) 1
haftmann@32915:            else full_simp_tac (HOL_ss addsimps (flat other_dist_rewrites)) 1);
berghofe@5177: 
berghofe@5177:         val inject = map (fn r => r RS iffD1)
haftmann@32905:           (if i < length newTs then nth constr_inject i
haftmann@32729:             else injects_of tname);
berghofe@5177: 
haftmann@32906:         fun mk_unique_constr_tac n (cname, cargs) (tac, intr::intrs, j) =
berghofe@5177:           let
haftmann@32729:             val k = length (filter is_rec_type cargs)
berghofe@5177: 
berghofe@5177:           in (EVERY [DETERM tac,
berghofe@5177:                 REPEAT (etac ex1E 1), rtac ex1I 1,
berghofe@5177:                 DEPTH_SOLVE_1 (ares_tac [intr] 1),
berghofe@13641:                 REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1),
berghofe@5177:                 etac elim 1,
berghofe@5177:                 REPEAT_DETERM_N j distinct_tac,
berghofe@21021:                 TRY (dresolve_tac inject 1),
berghofe@5177:                 REPEAT (etac conjE 1), hyp_subst_tac 1,
berghofe@13641:                 REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]),
berghofe@5177:                 TRY (hyp_subst_tac 1),
berghofe@5177:                 rtac refl 1,
berghofe@5177:                 REPEAT_DETERM_N (n - j - 1) distinct_tac],
berghofe@5177:               intrs, j + 1)
berghofe@5177:           end;
berghofe@5177: 
haftmann@32906:         val (tac', intrs', _) = fold (mk_unique_constr_tac (length constrs))
haftmann@32906:           constrs (tac, intrs, 0);
berghofe@5177: 
berghofe@5177:       in (tac', intrs') end;
berghofe@5177: 
berghofe@5177:     val rec_unique_thms =
berghofe@5177:       let
berghofe@5177:         val rec_unique_ts = map (fn (((set_t, T1), T2), i) =>
berghofe@5177:           Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
berghofe@21021:             absfree ("y", T2, set_t $ mk_Free "x" T1 i $ Free ("y", T2)))
berghofe@21021:               (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
wenzelm@17985:         val cert = cterm_of thy1
berghofe@5177:         val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t))
berghofe@5177:           ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
berghofe@5177:         val induct' = cterm_instantiate ((map cert induct_Ps) ~~
berghofe@5177:           (map cert insts)) induct;
haftmann@32906:         val (tac, _) = fold mk_unique_tac (descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts)
haftmann@32906:            (((rtac induct' THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1
haftmann@32906:               THEN rewrite_goals_tac [mk_meta_eq choice_eq], rec_intrs));
berghofe@5177: 
wenzelm@32970:       in split_conj_thm (Skip_Proof.prove_global thy1 [] []
wenzelm@20046:         (HOLogic.mk_Trueprop (mk_conj rec_unique_ts)) (K tac))
berghofe@5177:       end;
berghofe@5177: 
wenzelm@11435:     val rec_total_thms = map (fn r => r RS theI') rec_unique_thms;
berghofe@5177: 
berghofe@5177:     (* define primrec combinators *)
berghofe@5177: 
berghofe@5177:     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
haftmann@28965:     val reccomb_names = map (Sign.full_bname thy1)
berghofe@5177:       (if length descr' = 1 then [big_reccomb_name] else
berghofe@5177:         (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
berghofe@5177:           (1 upto (length descr'))));
berghofe@5177:     val reccombs = map (fn ((name, T), T') => list_comb
berghofe@5177:       (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns))
berghofe@5177:         (reccomb_names ~~ recTs ~~ rec_result_Ts);
berghofe@5177: 
haftmann@18358:     val (reccomb_defs, thy2) =
haftmann@18358:       thy1
wenzelm@24712:       |> Sign.add_consts_i (map (fn ((name, T), T') =>
wenzelm@30364:           (Binding.name (Long_Name.base_name name), reccomb_fn_Ts @ [T] ---> T', NoSyn))
haftmann@18358:           (reccomb_names ~~ recTs ~~ rec_result_Ts))
haftmann@27691:       |> (PureThy.add_defs false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
wenzelm@30364:           (Binding.name (Long_Name.base_name name ^ "_def"), Logic.mk_equals (comb, absfree ("x", T,
wenzelm@11435:            Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T',
berghofe@21021:              set $ Free ("x", T) $ Free ("y", T'))))))
haftmann@18358:                (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts))
haftmann@32124:       ||> Sign.parent_path
wenzelm@28361:       ||> Theory.checkpoint;
berghofe@5177: 
berghofe@5177: 
berghofe@5177:     (* prove characteristic equations for primrec combinators *)
berghofe@5177: 
haftmann@31668:     val _ = message config "Proving characteristic theorems for primrec combinators ..."
berghofe@5177: 
wenzelm@32970:     val rec_thms = map (fn t => Skip_Proof.prove_global thy2 [] [] t
wenzelm@17985:       (fn _ => EVERY
wenzelm@17985:         [rewrite_goals_tac reccomb_defs,
wenzelm@17985:          rtac the1_equality 1,
berghofe@5177:          resolve_tac rec_unique_thms 1,
berghofe@5177:          resolve_tac rec_intrs 1,
wenzelm@20046:          REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)]))
berghofe@5177:            (DatatypeProp.make_primrecs new_type_names descr sorts thy2)
berghofe@5177: 
berghofe@5177:   in
haftmann@18314:     thy2
wenzelm@24712:     |> Sign.add_path (space_implode "_" new_type_names)
blanchet@33056:     |> PureThy.add_thmss [((Binding.name "recs", rec_thms), [Nitpick_Simps.add])]
wenzelm@24712:     ||> Sign.parent_path
wenzelm@28361:     ||> Theory.checkpoint
haftmann@32906:     |-> (fn thms => pair (reccomb_names, flat thms))
berghofe@5177:   end;
berghofe@5177: 
berghofe@8477: 
berghofe@5177: (***************************** case combinators *******************************)
berghofe@5177: 
haftmann@31737: fun prove_case_thms (config : config) new_type_names descr sorts reccomb_names primrec_thms thy =
berghofe@5177:   let
haftmann@31668:     val _ = message config "Proving characteristic theorems for case combinators ...";
berghofe@5661: 
haftmann@32124:     val thy1 = Sign.add_path (space_implode "_" new_type_names) thy;
berghofe@5177: 
wenzelm@32952:     val descr' = flat descr;
berghofe@5177:     val recTs = get_rec_types descr' sorts;
wenzelm@30190:     val used = List.foldr OldTerm.add_typ_tfree_names [] recTs;
haftmann@33955:     val newTs = (uncurry take) (length (hd descr), recTs);
wenzelm@20071:     val T' = TFree (Name.variant used "'t", HOLogic.typeS);
berghofe@5177: 
berghofe@13641:     fun mk_dummyT dt = binder_types (typ_of_dtyp descr' sorts dt) ---> T';
berghofe@7015: 
berghofe@5177:     val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
berghofe@5177:       let
berghofe@5177:         val Ts = map (typ_of_dtyp descr' sorts) cargs;
wenzelm@33317:         val Ts' = map mk_dummyT (filter is_rec_type cargs)
haftmann@28524:       in Const (@{const_name undefined}, Ts @ Ts' ---> T')
berghofe@5177:       end) constrs) descr';
berghofe@5177: 
haftmann@28965:     val case_names = map (fn s => Sign.full_bname thy1 (s ^ "_case")) new_type_names;
berghofe@5177: 
berghofe@5177:     (* define case combinators via primrec combinators *)
berghofe@5177: 
haftmann@32906:     val (case_defs, thy2) = fold (fn ((((i, (_, _, constrs)), T), name), recname) => fn (defs, thy) =>
berghofe@5177:         let
haftmann@32906:           val (fns1, fns2) = split_list (map (fn ((_, cargs), j) =>
berghofe@5177:             let
berghofe@5177:               val Ts = map (typ_of_dtyp descr' sorts) cargs;
wenzelm@33317:               val Ts' = Ts @ map mk_dummyT (filter is_rec_type cargs);
berghofe@5177:               val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts'));
haftmann@33955:               val frees = (uncurry take) (length cargs, frees');
berghofe@5177:               val free = mk_Free "f" (Ts ---> T') j
berghofe@5177:             in
berghofe@5177:              (free, list_abs_free (map dest_Free frees',
berghofe@5177:                list_comb (free, frees)))
berghofe@5177:             end) (constrs ~~ (1 upto length constrs)));
berghofe@5177: 
berghofe@5177:           val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T';
haftmann@33955:           val fns = flat ((uncurry take) (i, case_dummy_fns)) @
haftmann@33955:             fns2 @ flat ((uncurry drop) (i + 1, case_dummy_fns));
berghofe@5177:           val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
wenzelm@30364:           val decl = ((Binding.name (Long_Name.base_name name), caseT), NoSyn);
wenzelm@30364:           val def = (Binding.name (Long_Name.base_name name ^ "_def"),
berghofe@5177:             Logic.mk_equals (list_comb (Const (name, caseT), fns1),
haftmann@33955:               list_comb (reccomb, (flat ((uncurry take) (i, case_dummy_fns))) @
haftmann@33955:                 fns2 @ (flat ((uncurry drop) (i + 1, case_dummy_fns))) )));
haftmann@18358:           val ([def_thm], thy') =
haftmann@18358:             thy
wenzelm@33173:             |> Sign.declare_const decl |> snd
haftmann@27691:             |> (PureThy.add_defs false o map Thm.no_attributes) [def];
berghofe@5177: 
wenzelm@8436:         in (defs @ [def_thm], thy')
haftmann@32906:         end) (hd descr ~~ newTs ~~ case_names ~~
haftmann@33955:           (uncurry take) (length newTs, reccomb_names)) ([], thy1)
wenzelm@28361:       ||> Theory.checkpoint;
berghofe@5177: 
wenzelm@32970:     val case_thms = map (map (fn t => Skip_Proof.prove_global thy2 [] [] t
wenzelm@20046:       (fn _ => EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1])))
berghofe@8477:           (DatatypeProp.make_cases new_type_names descr sorts thy2)
berghofe@8477:   in
haftmann@18314:     thy2
wenzelm@33459:     |> Context.theory_map ((fold o fold) Nitpick_Simps.add_thm case_thms)
haftmann@32124:     |> Sign.parent_path
haftmann@18314:     |> store_thmss "cases" new_type_names case_thms
haftmann@18314:     |-> (fn thmss => pair (thmss, case_names))
berghofe@8477:   end;
berghofe@5177: 
berghofe@5177: 
berghofe@5177: (******************************* case splitting *******************************)
berghofe@5177: 
haftmann@31737: fun prove_split_thms (config : config) new_type_names descr sorts constr_inject dist_rewrites
berghofe@5177:     casedist_thms case_thms thy =
berghofe@5177:   let
haftmann@31668:     val _ = message config "Proving equations for case splitting ...";
berghofe@5177: 
haftmann@31668:     val descr' = flat descr;
berghofe@5177:     val recTs = get_rec_types descr' sorts;
haftmann@33955:     val newTs = (uncurry take) (length (hd descr), recTs);
berghofe@5177: 
berghofe@5177:     fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'),
berghofe@5177:         exhaustion), case_thms'), T) =
berghofe@5177:       let
wenzelm@17985:         val cert = cterm_of thy;
berghofe@5177:         val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
berghofe@5177:         val exhaustion' = cterm_instantiate
berghofe@5177:           [(cert lhs, cert (Free ("x", T)))] exhaustion;
wenzelm@17985:         val tacf = K (EVERY [rtac exhaustion' 1, ALLGOALS (asm_simp_tac
wenzelm@17985:           (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))])
berghofe@5177:       in
wenzelm@32970:         (Skip_Proof.prove_global thy [] [] t1 tacf,
wenzelm@32970:          Skip_Proof.prove_global thy [] [] t2 tacf)
berghofe@5177:       end;
berghofe@5177: 
berghofe@5177:     val split_thm_pairs = map prove_split_thms
berghofe@5177:       ((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~
berghofe@5177:         dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
berghofe@5177: 
berghofe@5177:     val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs
berghofe@5177: 
berghofe@5177:   in
haftmann@18314:     thy
haftmann@18314:     |> store_thms "split" new_type_names split_thms
haftmann@18314:     ||>> store_thms "split_asm" new_type_names split_asm_thms
haftmann@18314:     |-> (fn (thms1, thms2) => pair (thms1 ~~ thms2))
berghofe@5177:   end;
berghofe@5177: 
nipkow@8601: fun prove_weak_case_congs new_type_names descr sorts thy =
nipkow@8601:   let
nipkow@8601:     fun prove_weak_case_cong t =
wenzelm@32970:        Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
wenzelm@26711:          (fn {prems, ...} => EVERY [rtac ((hd prems) RS arg_cong) 1])
nipkow@8601: 
nipkow@8601:     val weak_case_congs = map prove_weak_case_cong (DatatypeProp.make_weak_case_congs
nipkow@8601:       new_type_names descr sorts thy)
nipkow@8601: 
nipkow@8601:   in thy |> store_thms "weak_case_cong" new_type_names weak_case_congs end;
berghofe@8477: 
berghofe@5177: (************************* additional theorems for TFL ************************)
berghofe@5177: 
haftmann@31737: fun prove_nchotomys (config : config) new_type_names descr sorts casedist_thms thy =
berghofe@5177:   let
haftmann@31668:     val _ = message config "Proving additional theorems for TFL ...";
berghofe@5177: 
berghofe@5177:     fun prove_nchotomy (t, exhaustion) =
berghofe@5177:       let
berghofe@5177:         (* For goal i, select the correct disjunct to attack, then prove it *)
berghofe@5177:         fun tac i 0 = EVERY [TRY (rtac disjI1 i),
berghofe@5177:               hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
berghofe@5177:           | tac i n = rtac disjI2 i THEN tac i (n - 1)
berghofe@5177:       in 
wenzelm@32970:         Skip_Proof.prove_global thy [] [] t (fn _ =>
wenzelm@17985:           EVERY [rtac allI 1,
berghofe@5177:            exh_tac (K exhaustion) 1,
wenzelm@20046:            ALLGOALS (fn i => tac i (i-1))])
berghofe@5177:       end;
berghofe@5177: 
berghofe@5177:     val nchotomys =
berghofe@5177:       map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms)
berghofe@5177: 
wenzelm@8436:   in thy |> store_thms "nchotomy" new_type_names nchotomys end;
berghofe@5177: 
berghofe@5177: fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy =
berghofe@5177:   let
berghofe@5177:     fun prove_case_cong ((t, nchotomy), case_rewrites) =
berghofe@5177:       let
berghofe@5177:         val (Const ("==>", _) $ tm $ _) = t;
berghofe@5177:         val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm;
wenzelm@22578:         val cert = cterm_of thy;
berghofe@5177:         val nchotomy' = nchotomy RS spec;
wenzelm@29264:         val [v] = Term.add_vars (concl_of nchotomy') [];
wenzelm@29264:         val nchotomy'' = cterm_instantiate [(cert (Var v), cert Ma)] nchotomy'
berghofe@5177:       in
wenzelm@32970:         Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
wenzelm@26711:           (fn {prems, ...} => 
wenzelm@17985:             let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites))
wenzelm@17985:             in EVERY [simp_tac (HOL_ss addsimps [hd prems]) 1,
wenzelm@17985:                 cut_facts_tac [nchotomy''] 1,
wenzelm@17985:                 REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
wenzelm@17985:                 REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
wenzelm@20046:             end)
berghofe@5177:       end;
berghofe@5177: 
berghofe@5177:     val case_congs = map prove_case_cong (DatatypeProp.make_case_congs
berghofe@5177:       new_type_names descr sorts thy ~~ nchotomys ~~ case_thms)
berghofe@5177: 
wenzelm@8436:   in thy |> store_thms "case_cong" new_type_names case_congs end;
berghofe@5177: 
berghofe@5177: end;