src/HOL/Tools/Old_Datatype/old_datatype_aux.ML
author blanchet
Wed Jan 03 11:06:36 2018 +0100 (17 months ago)
changeset 67334 51a7c90fbf19
parent 60781 2da59cdf531c
child 67713 041898537c19
permissions -rw-r--r--
removed dead code
     1 (*  Title:      HOL/Tools/Old_Datatype/old_datatype_aux.ML
     2     Author:     Stefan Berghofer, TU Muenchen
     3 
     4 Datatype package: auxiliary data structures and functions.
     5 *)
     6 
     7 signature OLD_DATATYPE_COMMON =
     8 sig
     9   type config = {strict : bool, quiet : bool}
    10   val default_config : config
    11   datatype dtyp =
    12       DtTFree of string * sort
    13     | DtType of string * dtyp list
    14     | DtRec of int
    15   type descr = (int * (string * dtyp list * (string * dtyp list) list)) list
    16   type info =
    17    {index : int,
    18     descr : descr,
    19     inject : thm list,
    20     distinct : thm list,
    21     induct : thm,
    22     inducts : thm list,
    23     exhaust : thm,
    24     nchotomy : thm,
    25     rec_names : string list,
    26     rec_rewrites : thm list,
    27     case_name : string,
    28     case_rewrites : thm list,
    29     case_cong : thm,
    30     case_cong_weak : thm,
    31     split : thm,
    32     split_asm: thm}
    33   type spec = (binding * (string * sort) list * mixfix) * (binding * typ list * mixfix) list
    34 end
    35 
    36 signature OLD_DATATYPE_AUX =
    37 sig
    38   include OLD_DATATYPE_COMMON
    39 
    40   val message : config -> string -> unit
    41 
    42   val store_thmss_atts : string -> string list -> attribute list list -> thm list list
    43     -> theory -> thm list list * theory
    44   val store_thmss : string -> string list -> thm list list -> theory -> thm list list * theory
    45   val store_thms_atts : string -> string list -> attribute list list -> thm list
    46     -> theory -> thm list * theory
    47   val store_thms : string -> string list -> thm list -> theory -> thm list * theory
    48 
    49   val split_conj_thm : thm -> thm list
    50   val mk_conj : term list -> term
    51   val mk_disj : term list -> term
    52 
    53   val app_bnds : term -> int -> term
    54 
    55   val ind_tac : Proof.context -> thm -> string list -> int -> tactic
    56   val exh_tac : Proof.context -> (string -> thm) -> int -> tactic
    57 
    58   exception Datatype
    59   exception Datatype_Empty of string
    60   val name_of_typ : typ -> string
    61   val dtyp_of_typ : (string * (string * sort) list) list -> typ -> dtyp
    62   val mk_Free : string -> typ -> int -> term
    63   val is_rec_type : dtyp -> bool
    64   val typ_of_dtyp : descr -> dtyp -> typ
    65   val dest_DtTFree : dtyp -> string * sort
    66   val dest_DtRec : dtyp -> int
    67   val strip_dtyp : dtyp -> dtyp list * dtyp
    68   val body_index : dtyp -> int
    69   val mk_fun_dtyp : dtyp list -> dtyp -> dtyp
    70   val get_nonrec_types : descr -> typ list
    71   val get_branching_types : descr -> typ list
    72   val get_arities : descr -> int list
    73   val get_rec_types : descr -> typ list
    74   val interpret_construction : descr -> (string * sort) list ->
    75     {atyp: typ -> 'a, dtyp: typ list -> int * bool -> string * typ list -> 'a} ->
    76     ((string * typ list) * (string * 'a list) list) list
    77   val unfold_datatypes : Proof.context -> descr -> info Symtab.table ->
    78     descr -> int -> descr list * int
    79   val find_shortest_path : descr -> int -> (string * int) option
    80 end;
    81 
    82 structure Old_Datatype_Aux : OLD_DATATYPE_AUX =
    83 struct
    84 
    85 (* datatype option flags *)
    86 
    87 type config = {strict : bool, quiet : bool};
    88 val default_config : config = {strict = true, quiet = false};
    89 
    90 fun message ({quiet = true, ...} : config) s = writeln s
    91   | message _ _ = ();
    92 
    93 
    94 (* store theorems in theory *)
    95 
    96 fun store_thmss_atts name tnames attss thmss =
    97   fold_map (fn ((tname, atts), thms) =>
    98     Global_Theory.note_thmss ""
    99       [((Binding.qualify true tname (Binding.name name), atts), [(thms, [])])]
   100     #-> (fn [(_, res)] => pair res)) (tnames ~~ attss ~~ thmss);
   101 
   102 fun store_thmss name tnames = store_thmss_atts name tnames (replicate (length tnames) []);
   103 
   104 fun store_thms_atts name tnames attss thms =
   105   fold_map (fn ((tname, atts), thm) =>
   106     Global_Theory.note_thmss ""
   107       [((Binding.qualify true tname (Binding.name name), atts), [([thm], [])])]
   108     #-> (fn [(_, [res])] => pair res)) (tnames ~~ attss ~~ thms);
   109 
   110 fun store_thms name tnames = store_thms_atts name tnames (replicate (length tnames) []);
   111 
   112 
   113 (* split theorem thm_1 & ... & thm_n into n theorems *)
   114 
   115 fun split_conj_thm th =
   116   ((th RS conjunct1) :: split_conj_thm (th RS conjunct2)) handle THM _ => [th];
   117 
   118 val mk_conj = foldr1 (HOLogic.mk_binop @{const_name HOL.conj});
   119 val mk_disj = foldr1 (HOLogic.mk_binop @{const_name HOL.disj});
   120 
   121 fun app_bnds t i = list_comb (t, map Bound (i - 1 downto 0));
   122 
   123 
   124 (* instantiate induction rule *)
   125 
   126 fun ind_tac ctxt indrule indnames = CSUBGOAL (fn (cgoal, i) =>
   127   let
   128     val goal = Thm.term_of cgoal;
   129     val ts = HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of indrule));
   130     val ts' = HOLogic.dest_conj (HOLogic.dest_Trueprop (Logic.strip_imp_concl goal));
   131     val getP =
   132       if can HOLogic.dest_imp (hd ts)
   133       then apfst SOME o HOLogic.dest_imp
   134       else pair NONE;
   135     val flt =
   136       if null indnames then I
   137       else filter (member (op =) indnames o fst);
   138     fun abstr (t1, t2) =
   139       (case t1 of
   140         NONE =>
   141           (case flt (Term.add_frees t2 []) of
   142             [(s, T)] => SOME (absfree (s, T) t2)
   143           | _ => NONE)
   144       | SOME (_ $ t') => SOME (Abs ("x", fastype_of t', abstract_over (t', t2))));
   145     val insts =
   146       (ts ~~ ts') |> map_filter (fn (t, u) =>
   147         (case abstr (getP u) of
   148           NONE => NONE
   149         | SOME u' => SOME (t |> getP |> snd |> head_of |> dest_Var |> #1, Thm.cterm_of ctxt u')));
   150     val indrule' = infer_instantiate ctxt insts indrule;
   151   in resolve_tac ctxt [indrule'] i end);
   152 
   153 
   154 (* perform exhaustive case analysis on last parameter of subgoal i *)
   155 
   156 fun exh_tac ctxt exh_thm_of = CSUBGOAL (fn (cgoal, i) =>
   157   let
   158     val goal = Thm.term_of cgoal;
   159     val params = Logic.strip_params goal;
   160     val (_, Type (tname, _)) = hd (rev params);
   161     val exhaustion = Thm.lift_rule cgoal (exh_thm_of tname);
   162     val prem' = hd (Thm.prems_of exhaustion);
   163     val _ $ (_ $ lhs $ _) = hd (rev (Logic.strip_assums_hyp prem'));
   164     val exhaustion' =
   165       infer_instantiate ctxt
   166         [(#1 (dest_Var (head_of lhs)),
   167           Thm.cterm_of ctxt (fold_rev (fn (_, T) => fn t => Abs ("z", T, t)) params (Bound 0)))]
   168         exhaustion;
   169   in compose_tac ctxt (false, exhaustion', Thm.nprems_of exhaustion) i end);
   170 
   171 
   172 (********************** Internal description of datatypes *********************)
   173 
   174 datatype dtyp =
   175     DtTFree of string * sort
   176   | DtType of string * dtyp list
   177   | DtRec of int;
   178 
   179 (* information about datatypes *)
   180 
   181 (* index, datatype name, type arguments, constructor name, types of constructor's arguments *)
   182 type descr = (int * (string * dtyp list * (string * dtyp list) list)) list;
   183 
   184 type info =
   185   {index : int,
   186    descr : descr,
   187    inject : thm list,
   188    distinct : thm list,
   189    induct : thm,
   190    inducts : thm list,
   191    exhaust : thm,
   192    nchotomy : thm,
   193    rec_names : string list,
   194    rec_rewrites : thm list,
   195    case_name : string,
   196    case_rewrites : thm list,
   197    case_cong : thm,
   198    case_cong_weak : thm,
   199    split : thm,
   200    split_asm: thm};
   201 
   202 type spec = (binding * (string * sort) list * mixfix) * (binding * typ list * mixfix) list;
   203 
   204 fun mk_Free s T i = Free (s ^ string_of_int i, T);
   205 
   206 fun subst_DtTFree _ substs (T as DtTFree a) = the_default T (AList.lookup (op =) substs a)
   207   | subst_DtTFree i substs (DtType (name, ts)) = DtType (name, map (subst_DtTFree i substs) ts)
   208   | subst_DtTFree i _ (DtRec j) = DtRec (i + j);
   209 
   210 exception Datatype;
   211 exception Datatype_Empty of string;
   212 
   213 fun dest_DtTFree (DtTFree a) = a
   214   | dest_DtTFree _ = raise Datatype;
   215 
   216 fun dest_DtRec (DtRec i) = i
   217   | dest_DtRec _ = raise Datatype;
   218 
   219 fun is_rec_type (DtType (_, dts)) = exists is_rec_type dts
   220   | is_rec_type (DtRec _) = true
   221   | is_rec_type _ = false;
   222 
   223 fun strip_dtyp (DtType ("fun", [T, U])) = apfst (cons T) (strip_dtyp U)
   224   | strip_dtyp T = ([], T);
   225 
   226 val body_index = dest_DtRec o snd o strip_dtyp;
   227 
   228 fun mk_fun_dtyp [] U = U
   229   | mk_fun_dtyp (T :: Ts) U = DtType ("fun", [T, mk_fun_dtyp Ts U]);
   230 
   231 fun name_of_typ (Type (s, Ts)) =
   232       let val s' = Long_Name.base_name s in
   233         space_implode "_"
   234           (filter_out (equal "") (map name_of_typ Ts) @
   235             [if Symbol_Pos.is_identifier s' then s' else "x"])
   236       end
   237   | name_of_typ _ = "";
   238 
   239 fun dtyp_of_typ _ (TFree a) = DtTFree a
   240   | dtyp_of_typ _ (TVar _) = error "Illegal schematic type variable(s)"
   241   | dtyp_of_typ new_dts (Type (tname, Ts)) =
   242       (case AList.lookup (op =) new_dts tname of
   243         NONE => DtType (tname, map (dtyp_of_typ new_dts) Ts)
   244       | SOME vs =>
   245           if map (try dest_TFree) Ts = map SOME vs then
   246             DtRec (find_index (curry op = tname o fst) new_dts)
   247           else error ("Illegal occurrence of recursive type " ^ quote tname));
   248 
   249 fun typ_of_dtyp descr (DtTFree a) = TFree a
   250   | typ_of_dtyp descr (DtRec i) =
   251       let val (s, ds, _) = the (AList.lookup (op =) descr i)
   252       in Type (s, map (typ_of_dtyp descr) ds) end
   253   | typ_of_dtyp descr (DtType (s, ds)) = Type (s, map (typ_of_dtyp descr) ds);
   254 
   255 (* find all non-recursive types in datatype description *)
   256 
   257 fun get_nonrec_types descr =
   258   map (typ_of_dtyp descr) (fold (fn (_, (_, _, constrs)) =>
   259     fold (fn (_, cargs) => union (op =) (filter_out is_rec_type cargs)) constrs) descr []);
   260 
   261 (* get all recursive types in datatype description *)
   262 
   263 fun get_rec_types descr = map (fn (_ , (s, ds, _)) =>
   264   Type (s, map (typ_of_dtyp descr) ds)) descr;
   265 
   266 (* get all branching types *)
   267 
   268 fun get_branching_types descr =
   269   map (typ_of_dtyp descr)
   270     (fold
   271       (fn (_, (_, _, constrs)) =>
   272         fold (fn (_, cargs) => fold (strip_dtyp #> fst #> fold (insert op =)) cargs) constrs)
   273       descr []);
   274 
   275 fun get_arities descr =
   276   fold
   277     (fn (_, (_, _, constrs)) =>
   278       fold (fn (_, cargs) =>
   279         fold (insert op =) (map (length o fst o strip_dtyp) (filter is_rec_type cargs))) constrs)
   280     descr [];
   281 
   282 (* interpret construction of datatype *)
   283 
   284 fun interpret_construction descr vs {atyp, dtyp} =
   285   let
   286     val typ_of =
   287       typ_of_dtyp descr #>
   288       map_atyps (fn TFree (a, _) => TFree (a, the (AList.lookup (op =) vs a)) | T => T);
   289     fun interpT dT =
   290       (case strip_dtyp dT of
   291         (dTs, DtRec l) =>
   292           let
   293             val (tyco, dTs', _) = the (AList.lookup (op =) descr l);
   294             val Ts = map typ_of dTs;
   295             val Ts' = map typ_of dTs';
   296             val is_proper = forall (can dest_TFree) Ts';
   297           in dtyp Ts (l, is_proper) (tyco, Ts') end
   298       | _ => atyp (typ_of dT));
   299     fun interpC (c, dTs) = (c, map interpT dTs);
   300     fun interpD (_, (tyco, dTs, cs)) = ((tyco, map typ_of dTs), map interpC cs);
   301   in map interpD descr end;
   302 
   303 (* unfold a list of mutually recursive datatype specifications *)
   304 (* all types of the form DtType (dt_name, [..., DtRec _, ...]) *)
   305 (* need to be unfolded                                         *)
   306 
   307 fun unfold_datatypes ctxt orig_descr (dt_info : info Symtab.table) descr i =
   308   let
   309     fun typ_error T msg =
   310       error ("Non-admissible type expression\n" ^
   311         Syntax.string_of_typ ctxt (typ_of_dtyp (orig_descr @ descr) T) ^ "\n" ^ msg);
   312 
   313     fun get_dt_descr T i tname dts =
   314       (case Symtab.lookup dt_info tname of
   315         NONE =>
   316           typ_error T (quote tname ^ " is not registered as an old-style datatype and hence cannot \
   317             \be used in nested recursion")
   318       | SOME {index, descr, ...} =>
   319           let
   320             val (_, vars, _) = the (AList.lookup (op =) descr index);
   321             val subst = map dest_DtTFree vars ~~ dts
   322               handle ListPair.UnequalLengths =>
   323                 typ_error T ("Type constructor " ^ quote tname ^
   324                   " used with wrong number of arguments");
   325           in
   326             (i + index,
   327               map (fn (j, (tn, args, cs)) =>
   328                 (i + j, (tn, map (subst_DtTFree i subst) args,
   329                   map (apsnd (map (subst_DtTFree i subst))) cs))) descr)
   330           end);
   331 
   332     (* unfold a single constructor argument *)
   333 
   334     fun unfold_arg T (i, Ts, descrs) =
   335       if is_rec_type T then
   336         let val (Us, U) = strip_dtyp T in
   337           if exists is_rec_type Us then
   338             typ_error T "Non-strictly positive recursive occurrence of type"
   339           else
   340             (case U of
   341               DtType (tname, dts) =>
   342                 let
   343                   val (index, descr) = get_dt_descr T i tname dts;
   344                   val (descr', i') =
   345                     unfold_datatypes ctxt orig_descr dt_info descr (i + length descr);
   346                 in (i', Ts @ [mk_fun_dtyp Us (DtRec index)], descrs @ descr') end
   347             | _ => (i, Ts @ [T], descrs))
   348         end
   349       else (i, Ts @ [T], descrs);
   350 
   351     (* unfold a constructor *)
   352 
   353     fun unfold_constr (cname, cargs) (i, constrs, descrs) =
   354       let val (i', cargs', descrs') = fold unfold_arg cargs (i, [], descrs)
   355       in (i', constrs @ [(cname, cargs')], descrs') end;
   356 
   357     (* unfold a single datatype *)
   358 
   359     fun unfold_datatype (j, (tname, tvars, constrs)) (i, dtypes, descrs) =
   360       let val (i', constrs', descrs') = fold unfold_constr constrs (i, [], descrs)
   361       in (i', dtypes @ [(j, (tname, tvars, constrs'))], descrs') end;
   362 
   363     val (i', descr', descrs) = fold unfold_datatype descr (i, [], []);
   364 
   365   in (descr' :: descrs, i') end;
   366 
   367 (* find shortest path to constructor with no recursive arguments *)
   368 
   369 fun find_nonempty descr is i =
   370   let
   371     fun arg_nonempty (_, DtRec i) =
   372           if member (op =) is i
   373           then NONE
   374           else Option.map (Integer.add 1 o snd) (find_nonempty descr (i :: is) i)
   375       | arg_nonempty _ = SOME 0;
   376     fun max_inf (SOME i) (SOME j) = SOME (Integer.max i j)
   377       | max_inf _ _ = NONE;
   378     fun max xs = fold max_inf xs (SOME 0);
   379     val (_, _, constrs) = the (AList.lookup (op =) descr i);
   380     val xs =
   381       sort (int_ord o apply2 snd)
   382         (map_filter (fn (s, dts) => Option.map (pair s)
   383           (max (map (arg_nonempty o strip_dtyp) dts))) constrs)
   384   in if null xs then NONE else SOME (hd xs) end;
   385 
   386 fun find_shortest_path descr i = find_nonempty descr [i] i;
   387 
   388 end;