src/HOL/Tools/BNF/bnf_fp_def_sugar_tactics.ML
author wenzelm
Fri Mar 21 20:33:56 2014 +0100 (2014-03-21)
changeset 56245 84fc7dfa3cd4
parent 55966 972f0aa7091b
child 56765 644f0d4820a1
permissions -rw-r--r--
more qualified names;
     1 (*  Title:      HOL/Tools/BNF/bnf_fp_def_sugar_tactics.ML
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Copyright   2012
     4 
     5 Tactics for datatype and codatatype sugar.
     6 *)
     7 
     8 signature BNF_FP_DEF_SUGAR_TACTICS =
     9 sig
    10   val sumprod_thms_map: thm list
    11   val sumprod_thms_set: thm list
    12   val sumprod_thms_rel: thm list
    13 
    14   val mk_coinduct_tac: Proof.context -> thm list -> int -> int list -> thm -> thm list ->
    15     thm list -> thm list -> thm list -> thm list -> thm list list -> thm list list list ->
    16     thm list list list -> tactic
    17   val mk_corec_tac: thm list -> thm list -> thm -> thm -> thm -> thm -> Proof.context -> tactic
    18   val mk_ctor_iff_dtor_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm ->
    19     tactic
    20   val mk_disc_corec_iff_tac: thm list -> thm list -> thm list -> Proof.context -> tactic
    21   val mk_exhaust_tac: Proof.context -> int -> thm list -> thm -> thm -> tactic
    22   val mk_half_distinct_tac: Proof.context -> thm -> thm -> thm list -> tactic
    23   val mk_induct_tac: Proof.context -> int -> int list -> int list list -> int list list list ->
    24     thm list -> thm -> thm list -> thm list -> thm list -> thm list list -> tactic
    25   val mk_inject_tac: Proof.context -> thm -> thm -> thm -> tactic
    26   val mk_rec_tac: thm list -> thm list -> thm list -> thm -> thm -> thm -> thm -> Proof.context ->
    27     tactic
    28 end;
    29 
    30 structure BNF_FP_Def_Sugar_Tactics : BNF_FP_DEF_SUGAR_TACTICS =
    31 struct
    32 
    33 open BNF_Tactics
    34 open BNF_Util
    35 open BNF_FP_Util
    36 
    37 val basic_simp_thms = @{thms simp_thms(7,8,12,14,22,24)};
    38 val more_simp_thms = basic_simp_thms @ @{thms simp_thms(11,15,16,21)};
    39 
    40 val sumprod_thms_map = @{thms id_apply map_prod_simp prod.case sum.case map_sum.simps};
    41 val sumprod_thms_set =
    42   @{thms UN_empty UN_insert Un_empty_left Un_empty_right Un_iff UN_simps(10) UN_iff
    43       Union_Un_distrib image_iff o_apply map_prod_simp
    44       mem_Collect_eq prod_set_simps map_sum.simps sum_set_simps};
    45 val sumprod_thms_rel = @{thms rel_prod_apply rel_sum_simps id_apply};
    46 
    47 fun hhf_concl_conv cv ctxt ct =
    48   (case Thm.term_of ct of
    49     Const (@{const_name Pure.all}, _) $ Abs _ =>
    50     Conv.arg_conv (Conv.abs_conv (hhf_concl_conv cv o snd) ctxt) ct
    51   | _ => Conv.concl_conv ~1 cv ct);
    52 
    53 fun co_induct_inst_as_projs ctxt k thm =
    54   let
    55     val fs = Term.add_vars (prop_of thm) []
    56       |> filter (fn (_, Type (@{type_name fun}, [_, T'])) => T' <> HOLogic.boolT | _ => false);
    57     fun mk_cfp (f as (_, T)) =
    58       (certify ctxt (Var f), certify ctxt (mk_proj T (num_binder_types T) k));
    59     val cfps = map mk_cfp fs;
    60   in
    61     Drule.cterm_instantiate cfps thm
    62   end;
    63 
    64 val co_induct_inst_as_projs_tac = PRIMITIVE oo co_induct_inst_as_projs;
    65 
    66 fun mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor sumEN' =
    67   unfold_thms_tac ctxt (ctor_iff_dtor :: ctr_defs) THEN HEADGOAL (rtac sumEN') THEN
    68   HEADGOAL (EVERY' (maps (fn k => [select_prem_tac n (rotate_tac 1) k,
    69     REPEAT_DETERM o dtac meta_spec, etac meta_mp, atac]) (1 upto n)));
    70 
    71 fun mk_ctor_iff_dtor_tac ctxt cTs cctor cdtor ctor_dtor dtor_ctor =
    72   HEADGOAL (rtac iffI THEN'
    73     EVERY' (map3 (fn cTs => fn cx => fn th =>
    74       dtac (Drule.instantiate' cTs [NONE, NONE, SOME cx] arg_cong) THEN'
    75       SELECT_GOAL (unfold_thms_tac ctxt [th]) THEN'
    76       atac) [rev cTs, cTs] [cdtor, cctor] [dtor_ctor, ctor_dtor]));
    77 
    78 fun mk_half_distinct_tac ctxt ctor_inject abs_inject ctr_defs =
    79   unfold_thms_tac ctxt (ctor_inject :: abs_inject :: @{thms sum.inject} @ ctr_defs) THEN
    80   HEADGOAL (rtac @{thm sum.distinct(1)});
    81 
    82 fun mk_inject_tac ctxt ctr_def ctor_inject abs_inject =
    83   unfold_thms_tac ctxt [ctr_def] THEN
    84   HEADGOAL (rtac (ctor_inject RS ssubst)) THEN
    85   unfold_thms_tac ctxt (abs_inject :: @{thms sum.inject Pair_eq conj_assoc}) THEN
    86   HEADGOAL (rtac refl);
    87 
    88 val rec_unfold_thms =
    89   @{thms comp_def convol_def fst_conv id_def case_prod_Pair_iden snd_conv split_conv
    90       case_unit_Unity} @ sumprod_thms_map;
    91 
    92 fun mk_rec_tac pre_map_defs map_idents rec_defs ctor_rec fp_abs_inverse abs_inverse ctr_def ctxt =
    93   unfold_thms_tac ctxt (ctr_def :: ctor_rec :: fp_abs_inverse :: abs_inverse :: rec_defs @
    94     pre_map_defs @ map_idents @ rec_unfold_thms) THEN HEADGOAL (rtac refl);
    95 
    96 val corec_unfold_thms = @{thms id_def} @ sumprod_thms_map;
    97 
    98 fun mk_corec_tac corec_defs map_idents ctor_dtor_corec pre_map_def abs_inverse ctr_def ctxt =
    99   let
   100     val ss = ss_only (pre_map_def :: abs_inverse :: map_idents @ corec_unfold_thms @
   101       @{thms o_apply vimage2p_def if_True if_False}) ctxt;
   102   in
   103     unfold_thms_tac ctxt (ctr_def :: corec_defs) THEN
   104     HEADGOAL (rtac (ctor_dtor_corec RS trans) THEN' asm_simp_tac ss) THEN_MAYBE
   105     HEADGOAL (rtac refl ORELSE' rtac (@{thm unit_eq} RS arg_cong))
   106   end;
   107 
   108 fun mk_disc_corec_iff_tac case_splits' corecs discs ctxt =
   109   EVERY (map3 (fn case_split_tac => fn corec_thm => fn disc =>
   110       HEADGOAL case_split_tac THEN unfold_thms_tac ctxt [corec_thm] THEN
   111       HEADGOAL (asm_simp_tac (ss_only basic_simp_thms ctxt)) THEN
   112       (if is_refl disc then all_tac else HEADGOAL (rtac disc)))
   113     (map rtac case_splits' @ [K all_tac]) corecs discs);
   114 
   115 fun solve_prem_prem_tac ctxt =
   116   REPEAT o (eresolve_tac @{thms bexE rev_bexI} ORELSE' rtac @{thm rev_bexI[OF UNIV_I]} ORELSE'
   117     hyp_subst_tac ctxt ORELSE' resolve_tac @{thms disjI1 disjI2}) THEN'
   118   (rtac refl ORELSE' atac ORELSE' rtac @{thm singletonI});
   119 
   120 fun mk_induct_leverage_prem_prems_tac ctxt nn kks fp_abs_inverses abs_inverses set_maps
   121     pre_set_defs =
   122   HEADGOAL (EVERY' (maps (fn kk => [select_prem_tac nn (dtac meta_spec) kk, etac meta_mp,
   123     SELECT_GOAL (unfold_thms_tac ctxt (pre_set_defs @ fp_abs_inverses @ abs_inverses @ set_maps @
   124       sumprod_thms_set)),
   125     solve_prem_prem_tac ctxt]) (rev kks)));
   126 
   127 fun mk_induct_discharge_prem_tac ctxt nn n fp_abs_inverses abs_inverses set_maps pre_set_defs m k
   128     kks =
   129   let val r = length kks in
   130     HEADGOAL (EVERY' [select_prem_tac n (rotate_tac 1) k, rotate_tac ~1, hyp_subst_tac ctxt,
   131       REPEAT_DETERM_N m o (dtac meta_spec THEN' rotate_tac ~1)]) THEN
   132     EVERY [REPEAT_DETERM_N r
   133         (HEADGOAL (rotate_tac ~1 THEN' dtac meta_mp THEN' rotate_tac 1) THEN prefer_tac 2),
   134       if r > 0 then ALLGOALS (Goal.norm_hhf_tac ctxt) else all_tac, HEADGOAL atac,
   135       mk_induct_leverage_prem_prems_tac ctxt nn kks fp_abs_inverses abs_inverses set_maps
   136         pre_set_defs]
   137   end;
   138 
   139 fun mk_induct_tac ctxt nn ns mss kkss ctr_defs ctor_induct' fp_abs_inverses abs_inverses set_maps
   140     pre_set_defss =
   141   let val n = Integer.sum ns in
   142     unfold_thms_tac ctxt ctr_defs THEN HEADGOAL (rtac ctor_induct') THEN
   143     co_induct_inst_as_projs_tac ctxt 0 THEN
   144     EVERY (map4 (EVERY oooo map3 o
   145         mk_induct_discharge_prem_tac ctxt nn n fp_abs_inverses abs_inverses set_maps)
   146       pre_set_defss mss (unflat mss (1 upto n)) kkss)
   147   end;
   148 
   149 fun mk_coinduct_same_ctr_tac ctxt rel_eqs pre_rel_def fp_abs_inverse abs_inverse dtor_ctor ctr_def
   150     discs sels =
   151   hyp_subst_tac ctxt THEN'
   152   CONVERSION (hhf_concl_conv
   153     (Conv.top_conv (K (Conv.try_conv (Conv.rewr_conv ctr_def))) ctxt) ctxt) THEN'
   154   SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: dtor_ctor :: sels)) THEN'
   155   SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: fp_abs_inverse :: abs_inverse :: dtor_ctor ::
   156     sels @ sumprod_thms_rel @ @{thms o_apply vimage2p_def})) THEN'
   157   (atac ORELSE' REPEAT o etac conjE THEN'
   158      full_simp_tac
   159        (ss_only (@{thm prod.inject} :: no_refl discs @ rel_eqs @ more_simp_thms) ctxt) THEN'
   160      REPEAT o etac conjE THEN_MAYBE' REPEAT o hyp_subst_tac ctxt THEN'
   161      REPEAT o (resolve_tac [refl, conjI] ORELSE' atac));
   162 
   163 fun mk_coinduct_distinct_ctrs_tac ctxt discs discs' =
   164   let
   165     val discs'' = map (perhaps (try (fn th => th RS @{thm notnotD}))) (discs @ discs')
   166       |> distinct Thm.eq_thm_prop;
   167   in
   168     hyp_subst_tac ctxt THEN' REPEAT o etac conjE THEN'
   169     full_simp_tac (ss_only (refl :: no_refl discs'' @ basic_simp_thms) ctxt)
   170   end;
   171 
   172 fun mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn kk n pre_rel_def fp_abs_inverse abs_inverse
   173     dtor_ctor exhaust ctr_defs discss selss =
   174   let val ks = 1 upto n in
   175     EVERY' ([rtac allI, rtac allI, rtac impI, select_prem_tac nn (dtac meta_spec) kk,
   176         dtac meta_spec, dtac meta_mp, atac, rtac exhaust, K (co_induct_inst_as_projs_tac ctxt 0),
   177         hyp_subst_tac ctxt] @
   178       map4 (fn k => fn ctr_def => fn discs => fn sels =>
   179         EVERY' ([rtac exhaust, K (co_induct_inst_as_projs_tac ctxt 1)] @
   180           map2 (fn k' => fn discs' =>
   181             if k' = k then
   182               mk_coinduct_same_ctr_tac ctxt rel_eqs' pre_rel_def fp_abs_inverse abs_inverse
   183                 dtor_ctor ctr_def discs sels
   184             else
   185               mk_coinduct_distinct_ctrs_tac ctxt discs discs') ks discss)) ks ctr_defs discss selss)
   186   end;
   187 
   188 fun mk_coinduct_tac ctxt rel_eqs' nn ns dtor_coinduct' pre_rel_defs fp_abs_inverses abs_inverses
   189     dtor_ctors exhausts ctr_defss discsss selsss =
   190   HEADGOAL (rtac dtor_coinduct' THEN'
   191     EVERY' (map10 (mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn)
   192       (1 upto nn) ns pre_rel_defs fp_abs_inverses abs_inverses dtor_ctors exhausts ctr_defss discsss
   193       selsss));
   194 
   195 end;