src/HOL/Codatatype/Tools/bnf_wrap.ML
author blanchet
Tue Sep 04 13:02:25 2012 +0200 (2012-09-04)
changeset 49111 9d511132394e
parent 49075 ed769978dc8d
child 49113 ef3eea7ae251
permissions -rw-r--r--
export "wrap" function
     1 (*  Title:      HOL/Codatatype/Tools/bnf_wrap.ML
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Copyright   2012
     4 
     5 Wrapping existing datatypes.
     6 *)
     7 
     8 signature BNF_WRAP =
     9 sig
    10   val wrap: ({prems: thm list, context: Proof.context} -> tactic) list list ->
    11     (term list * term) * (binding list * binding list list) -> Proof.context -> local_theory
    12 end;
    13 
    14 structure BNF_Wrap : BNF_WRAP =
    15 struct
    16 
    17 open BNF_Util
    18 open BNF_Wrap_Tactics
    19 
    20 val is_N = "is_";
    21 val un_N = "un_";
    22 fun mk_un_N 1 1 suf = un_N ^ suf
    23   | mk_un_N _ l suf = un_N ^ suf ^ string_of_int l;
    24 
    25 val case_congN = "case_cong";
    26 val case_discsN = "case_discs";
    27 val casesN = "cases";
    28 val ctr_selsN = "ctr_sels";
    29 val disc_exclusN = "disc_exclus";
    30 val disc_exhaustN = "disc_exhaust";
    31 val discsN = "discs";
    32 val distinctN = "distinct";
    33 val exhaustN = "exhaust";
    34 val injectN = "inject";
    35 val nchotomyN = "nchotomy";
    36 val selsN = "sels";
    37 val splitN = "split";
    38 val split_asmN = "split_asm";
    39 val weak_case_cong_thmsN = "weak_case_cong";
    40 
    41 val default_name = @{binding _};
    42 
    43 fun pad_list x n xs = xs @ replicate (n - length xs) x;
    44 
    45 fun mk_half_pairss' _ [] = []
    46   | mk_half_pairss' indent (y :: ys) =
    47     indent @ fold_rev (cons o single o pair y) ys (mk_half_pairss' ([] :: indent) ys);
    48 
    49 fun mk_half_pairss ys = mk_half_pairss' [[]] ys;
    50 
    51 val mk_Trueprop_eq = HOLogic.mk_Trueprop o HOLogic.mk_eq;
    52 
    53 fun mk_undef T Ts = Const (@{const_name undefined}, Ts ---> T);
    54 
    55 fun eta_expand_caseof_arg xs f_xs = fold_rev Term.lambda xs f_xs;
    56 
    57 fun name_of_ctr t =
    58   case head_of t of
    59     Const (s, _) => s
    60   | Free (s, _) => s
    61   | _ => error "Cannot extract name of constructor";
    62 
    63 fun prepare_wrap prep_term ((raw_ctrs, raw_caseof), (raw_disc_names, raw_sel_namess))
    64   no_defs_lthy =
    65   let
    66     (* TODO: sanity checks on arguments *)
    67 
    68     (* TODO: normalize types of constructors w.r.t. each other *)
    69 
    70     val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
    71     val caseof0 = prep_term no_defs_lthy raw_caseof;
    72 
    73     val n = length ctrs0;
    74     val ks = 1 upto n;
    75 
    76     val (T_name, As0) = dest_Type (body_type (fastype_of (hd ctrs0)));
    77     val b = Binding.qualified_name T_name;
    78 
    79     val (As, B) =
    80       no_defs_lthy
    81       |> mk_TFrees (length As0)
    82       ||> the_single o fst o mk_TFrees 1;
    83 
    84     fun mk_ctr Ts ctr =
    85       let val Ts0 = snd (dest_Type (body_type (fastype_of ctr))) in
    86         Term.subst_atomic_types (Ts0 ~~ Ts) ctr
    87       end;
    88 
    89     val T = Type (T_name, As);
    90     val ctrs = map (mk_ctr As) ctrs0;
    91     val ctr_Tss = map (binder_types o fastype_of) ctrs;
    92 
    93     val ms = map length ctr_Tss;
    94 
    95     val disc_names =
    96       pad_list default_name n raw_disc_names
    97       |> map2 (fn ctr => fn disc =>
    98         if Binding.eq_name (disc, default_name) then
    99           Binding.name (prefix is_N (Long_Name.base_name (name_of_ctr ctr)))
   100         else
   101           disc) ctrs0;
   102 
   103     val sel_namess =
   104       pad_list [] n raw_sel_namess
   105       |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
   106         if Binding.eq_name (sel, default_name) then
   107           Binding.name (mk_un_N m l (Long_Name.base_name (name_of_ctr ctr)))
   108         else
   109           sel) (1 upto m) o pad_list default_name m) ctrs0 ms;
   110 
   111     fun mk_caseof Ts T =
   112       let val (binders, body) = strip_type (fastype_of caseof0) in
   113         Term.subst_atomic_types ((body, T) :: (snd (dest_Type (List.last binders)) ~~ Ts)) caseof0
   114       end;
   115 
   116     val caseofB = mk_caseof As B;
   117     val caseofB_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
   118 
   119     fun mk_caseofB_term eta_fs = Term.list_comb (caseofB, eta_fs);
   120 
   121     val (((((((xss, yss), fs), gs), (v, v')), w), (p, p')), names_lthy) = no_defs_lthy |>
   122       mk_Freess "x" ctr_Tss
   123       ||>> mk_Freess "y" ctr_Tss
   124       ||>> mk_Frees "f" caseofB_Ts
   125       ||>> mk_Frees "g" caseofB_Ts
   126       ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "v") T
   127       ||>> yield_singleton (mk_Frees "w") T
   128       ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
   129 
   130     val q = Free (fst p', B --> HOLogic.boolT);
   131 
   132     val xctrs = map2 (curry Term.list_comb) ctrs xss;
   133     val yctrs = map2 (curry Term.list_comb) ctrs yss;
   134 
   135     val xfs = map2 (curry Term.list_comb) fs xss;
   136     val xgs = map2 (curry Term.list_comb) gs xss;
   137 
   138     val eta_fs = map2 eta_expand_caseof_arg xss xfs;
   139     val eta_gs = map2 eta_expand_caseof_arg xss xgs;
   140 
   141     val caseofB_fs = Term.list_comb (caseofB, eta_fs);
   142 
   143     val exist_xs_v_eq_ctrs =
   144       map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (v, xctr))) xctrs xss;
   145 
   146     fun mk_sel_caseof_args k xs x T =
   147       map2 (fn Ts => fn i => if i = k then fold_rev Term.lambda xs x else mk_undef T Ts) ctr_Tss ks;
   148 
   149     fun disc_spec b exist_xs_v_eq_ctr =
   150       mk_Trueprop_eq (Free (Binding.name_of b, T --> HOLogic.boolT) $ v, exist_xs_v_eq_ctr);
   151 
   152     fun sel_spec b x xs k =
   153       let val T' = fastype_of x in
   154         mk_Trueprop_eq (Free (Binding.name_of b, T --> T') $ v,
   155           Term.list_comb (mk_caseof As T', mk_sel_caseof_args k xs x T') $ v)
   156       end;
   157 
   158     val (((raw_discs, (_, raw_disc_defs)), (raw_selss, (_, raw_sel_defss))), (lthy', lthy)) =
   159       no_defs_lthy
   160       |> apfst (apsnd split_list o split_list) o fold_map2 (fn b => fn exist_xs_v_eq_ctr =>
   161         Specification.definition (SOME (b, NONE, NoSyn),
   162           ((Thm.def_binding b, []), disc_spec b exist_xs_v_eq_ctr))) disc_names exist_xs_v_eq_ctrs
   163       ||>> apfst (apsnd split_list o split_list) o fold_map3 (fn bs => fn xs => fn k =>
   164         apfst (apsnd split_list o split_list) o fold_map2 (fn b => fn x =>
   165           Specification.definition (SOME (b, NONE, NoSyn),
   166             ((Thm.def_binding b, []), sel_spec b x xs k))) bs xs) sel_namess xss ks
   167       ||> `Local_Theory.restore;
   168 
   169     (*transforms defined frees into consts (and more)*)
   170     val phi = Proof_Context.export_morphism lthy lthy';
   171 
   172     val disc_defs = map (Morphism.thm phi) raw_disc_defs;
   173     val sel_defss = map (map (Morphism.thm phi)) raw_sel_defss;
   174 
   175     val discs0 = map (Morphism.term phi) raw_discs;
   176     val selss0 = map (map (Morphism.term phi)) raw_selss;
   177 
   178     fun mk_disc_or_sel Ts t =
   179       Term.subst_atomic_types (snd (dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
   180 
   181     val discs = map (mk_disc_or_sel As) discs0;
   182     val selss = map (map (mk_disc_or_sel As)) selss0;
   183 
   184     fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
   185 
   186     val goal_exhaust =
   187       let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (v, xctr)]) in
   188         mk_imp_p (map2 mk_prem xctrs xss)
   189       end;
   190 
   191     val goal_injectss =
   192       let
   193         fun mk_goal _ _ [] [] = []
   194           | mk_goal xctr yctr xs ys =
   195             [mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
   196               Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys))];
   197       in
   198         map4 mk_goal xctrs yctrs xss yss
   199       end;
   200 
   201     val goal_half_distinctss =
   202       map (map (HOLogic.mk_Trueprop o HOLogic.mk_not o HOLogic.mk_eq)) (mk_half_pairss xctrs);
   203 
   204     val goal_cases = map2 (fn xctr => fn xf => mk_Trueprop_eq (caseofB_fs $ xctr, xf)) xctrs xfs;
   205 
   206     val goals = [goal_exhaust] :: goal_injectss @ goal_half_distinctss @ [goal_cases];
   207 
   208     fun after_qed thmss lthy =
   209       let
   210         val ([exhaust_thm], (inject_thmss, (half_distinct_thmss, [case_thms]))) =
   211           (hd thmss, apsnd (chop (n * n)) (chop n (tl thmss)));
   212 
   213         val exhaust_thm' =
   214           let val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As) in
   215             Drule.instantiate' [] [SOME (certify lthy v)]
   216               (Thm.instantiate (Tinst, []) (Drule.zero_var_indexes exhaust_thm))
   217           end;
   218 
   219         val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
   220 
   221         val (distinct_thmsss', distinct_thmsss) =
   222           map2 (map2 append) (Library.chop_groups n half_distinct_thmss)
   223             (transpose (Library.chop_groups n other_half_distinct_thmss))
   224           |> `transpose;
   225         val distinct_thms = interleave (flat half_distinct_thmss) (flat other_half_distinct_thmss);
   226 
   227         val nchotomy_thm =
   228           let
   229             val goal =
   230               HOLogic.mk_Trueprop (HOLogic.mk_all (fst v', snd v',
   231                 Library.foldr1 HOLogic.mk_disj exist_xs_v_eq_ctrs));
   232           in
   233             Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
   234           end;
   235 
   236         val sel_thmss =
   237           let
   238             fun mk_thm k xs goal_case case_thm x sel_def =
   239               let
   240                 val T = fastype_of x;
   241                 val cTs =
   242                   map ((fn T' => certifyT lthy (if T' = B then T else T')) o TFree)
   243                     (rev (Term.add_tfrees goal_case []));
   244                 val cxs = map (certify lthy) (mk_sel_caseof_args k xs x T);
   245               in
   246                 Local_Defs.fold lthy [sel_def]
   247                   (Drule.instantiate' (map SOME cTs) (map SOME cxs) case_thm)
   248               end;
   249             fun mk_thms k xs goal_case case_thm sel_defs =
   250               map2 (mk_thm k xs goal_case case_thm) xs sel_defs;
   251           in
   252             map5 mk_thms ks xss goal_cases case_thms sel_defss
   253           end;
   254 
   255         val discD_thms = map (fn def => def RS iffD1) disc_defs;
   256         val discI_thms =
   257           map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms disc_defs;
   258         val not_disc_thms =
   259           map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
   260                   (Local_Defs.unfold lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
   261             ms disc_defs;
   262 
   263         val (disc_thmss', disc_thmss) =
   264           let
   265             fun mk_thm discI _ [] = refl RS discI
   266               | mk_thm _ not_disc [distinct] = distinct RS not_disc;
   267             fun mk_thms discI not_disc distinctss = map (mk_thm discI not_disc) distinctss;
   268           in
   269             map3 mk_thms discI_thms not_disc_thms distinct_thmsss'
   270             |> `transpose
   271           end;
   272 
   273         val disc_exclus_thms =
   274           let
   275             fun mk_goal ((_, disc), (_, disc')) =
   276               Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (disc $ v),
   277                 HOLogic.mk_Trueprop (HOLogic.mk_not (disc' $ v))));
   278             fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac);
   279 
   280             val bundles = ms ~~ discD_thms ~~ discs;
   281             val half_pairss = mk_half_pairss bundles;
   282 
   283             val goal_halvess = map (map mk_goal) half_pairss;
   284             val half_thmss =
   285               map3 (fn [] => K (K [])
   286                      | [(((m, discD), _), _)] => fn disc_thm => fn [goal] =>
   287                 [prove (mk_half_disc_exclus_tac m discD disc_thm) goal])
   288               half_pairss (flat disc_thmss') goal_halvess;
   289 
   290             val goal_other_halvess = map (map (mk_goal o swap)) half_pairss;
   291             val other_half_thmss =
   292               map2 (map2 (prove o mk_other_half_disc_exclus_tac)) half_thmss goal_other_halvess;
   293           in
   294             interleave (flat half_thmss) (flat other_half_thmss)
   295           end;
   296 
   297         val disc_exhaust_thm =
   298           let
   299             fun mk_prem disc = mk_imp_p [HOLogic.mk_Trueprop (disc $ v)];
   300             val goal = fold Logic.all [p, v] (mk_imp_p (map mk_prem discs));
   301           in
   302             Skip_Proof.prove lthy [] [] goal (fn _ => mk_disc_exhaust_tac n exhaust_thm discI_thms)
   303           end;
   304 
   305         val ctr_sel_thms =
   306           let
   307             fun mk_goal ctr disc sels =
   308               Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (disc $ v),
   309                 mk_Trueprop_eq ((null sels ? swap)
   310                   (Term.list_comb (ctr, map (fn sel => sel $ v) sels), v))));
   311             val goals = map3 mk_goal ctrs discs selss;
   312           in
   313             map4 (fn goal => fn m => fn discD => fn sel_thms =>
   314               Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
   315                 mk_ctr_sel_tac ctxt m discD sel_thms))
   316               goals ms discD_thms sel_thmss
   317           end;
   318 
   319         val case_disc_thm =
   320           let
   321             fun mk_core f sels = Term.list_comb (f, map (fn sel => sel $ v) sels);
   322             fun mk_rhs _ [f] [sels] = mk_core f sels
   323               | mk_rhs (disc :: discs) (f :: fs) (sels :: selss) =
   324                 Const (@{const_name If}, HOLogic.boolT --> B --> B --> B) $
   325                   (disc $ v) $ mk_core f sels $ mk_rhs discs fs selss;
   326             val goal = mk_Trueprop_eq (caseofB_fs $ v, mk_rhs discs fs selss);
   327           in
   328             Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
   329               mk_case_disc_tac ctxt exhaust_thm' case_thms disc_thmss' sel_thmss)
   330             |> singleton (Proof_Context.export names_lthy lthy)
   331           end;
   332 
   333         val (case_cong_thm, weak_case_cong_thm) =
   334           let
   335             fun mk_prem xctr xs f g =
   336               fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (w, xctr),
   337                 mk_Trueprop_eq (f, g)));
   338 
   339             val v_eq_w = mk_Trueprop_eq (v, w);
   340             val caseof_fs = mk_caseofB_term eta_fs;
   341             val caseof_gs = mk_caseofB_term eta_gs;
   342 
   343             val goal =
   344               Logic.list_implies (v_eq_w :: map4 mk_prem xctrs xss fs gs,
   345                  mk_Trueprop_eq (caseof_fs $ v, caseof_gs $ w));
   346             val goal_weak =
   347               Logic.mk_implies (v_eq_w, mk_Trueprop_eq (caseof_fs $ v, caseof_fs $ w));
   348           in
   349             (Skip_Proof.prove lthy [] [] goal (fn _ => mk_case_cong_tac exhaust_thm' case_thms),
   350              Skip_Proof.prove lthy [] [] goal_weak (K (etac arg_cong 1)))
   351             |> pairself (singleton (Proof_Context.export names_lthy lthy))
   352           end;
   353 
   354         val (split_thm, split_asm_thm) =
   355           let
   356             fun mk_conjunct xctr xs f_xs =
   357               list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (v, xctr), q $ f_xs));
   358             fun mk_disjunct xctr xs f_xs =
   359               list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (v, xctr),
   360                 HOLogic.mk_not (q $ f_xs)));
   361 
   362             val lhs = q $ (mk_caseofB_term eta_fs $ v);
   363 
   364             val goal =
   365               mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
   366             val goal_asm =
   367               mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
   368                 (map3 mk_disjunct xctrs xss xfs)));
   369 
   370             val split_thm =
   371               Skip_Proof.prove lthy [] [] goal
   372                 (fn _ => mk_split_tac exhaust_thm' case_thms inject_thmss distinct_thmsss)
   373               |> singleton (Proof_Context.export names_lthy lthy)
   374             val split_asm_thm =
   375               Skip_Proof.prove lthy [] [] goal_asm (fn {context = ctxt, ...} =>
   376                 mk_split_asm_tac ctxt split_thm)
   377               |> singleton (Proof_Context.export names_lthy lthy)
   378           in
   379             (split_thm, split_asm_thm)
   380           end;
   381 
   382         (* TODO: case syntax *)
   383         (* TODO: attributes (simp, case_names, etc.) *)
   384 
   385         val notes =
   386           [(case_congN, [case_cong_thm]),
   387            (case_discsN, [case_disc_thm]),
   388            (casesN, case_thms),
   389            (ctr_selsN, ctr_sel_thms),
   390            (discsN, (flat disc_thmss)),
   391            (disc_exclusN, disc_exclus_thms),
   392            (disc_exhaustN, [disc_exhaust_thm]),
   393            (distinctN, distinct_thms),
   394            (exhaustN, [exhaust_thm]),
   395            (injectN, (flat inject_thmss)),
   396            (nchotomyN, [nchotomy_thm]),
   397            (selsN, (flat sel_thmss)),
   398            (splitN, [split_thm]),
   399            (split_asmN, [split_asm_thm]),
   400            (weak_case_cong_thmsN, [weak_case_cong_thm])]
   401           |> map (fn (thmN, thms) =>
   402             ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]));
   403       in
   404         lthy |> Local_Theory.notes notes |> snd
   405       end;
   406   in
   407     (goals, after_qed, lthy')
   408   end;
   409 
   410 fun wrap tacss = (fn (goalss, after_qed, lthy) =>
   411   map2 (map2 (Skip_Proof.prove lthy [] [])) goalss tacss
   412   |> (fn thms => after_qed thms lthy)) oo
   413   prepare_wrap (singleton o Type_Infer_Context.infer_types)
   414 
   415 val parse_bindings = Parse.$$$ "[" |--  Parse.list Parse.binding --| Parse.$$$ "]";
   416 
   417 val parse_bindingss = Parse.$$$ "[" |-- Parse.list parse_bindings --| Parse.$$$ "]";
   418 
   419 val wrap_data_cmd = (fn (goalss, after_qed, lthy) =>
   420   Proof.theorem NONE after_qed (map (map (rpair [])) goalss) lthy) oo
   421   prepare_wrap Syntax.read_term;
   422 
   423 val _ =
   424   Outer_Syntax.local_theory_to_proof @{command_spec "wrap_data"} "wraps an existing datatype"
   425     (((Parse.$$$ "[" |-- Parse.list Parse.term --| Parse.$$$ "]") -- Parse.term --
   426       Scan.optional (parse_bindings -- Scan.optional parse_bindingss []) ([], []))
   427      >> wrap_data_cmd);
   428 
   429 end;