src/Pure/Syntax/parser.ML
author wenzelm
Mon Jul 09 11:44:20 2007 +0200 (2007-07-09)
changeset 23660 18765718cf62
parent 22573 2ac646ab2f6c
child 23909 6e4fba2ea7d0
permissions -rw-r--r--
type output = string indicates raw system output;
     1 (*  Title:      Pure/Syntax/parser.ML
     2     ID:         $Id$
     3     Author:     Carsten Clasohm, Sonia Mahjoub, and Markus Wenzel, TU Muenchen
     4 
     5 General context-free parser for the inner syntax of terms, types, etc.
     6 *)
     7 
     8 signature PARSER =
     9 sig
    10   type gram
    11   val empty_gram: gram
    12   val extend_gram: gram -> SynExt.xprod list -> gram
    13   val make_gram: SynExt.xprod list -> gram
    14   val merge_grams: gram -> gram -> gram
    15   val pretty_gram: gram -> Pretty.T list
    16   datatype parsetree =
    17     Node of string * parsetree list |
    18     Tip of Lexicon.token
    19   val parse: gram -> string -> Lexicon.token list -> parsetree list
    20   val branching_level: int ref
    21 end;
    22 
    23 structure Parser: PARSER =
    24 struct
    25 
    26 open Lexicon SynExt;
    27 
    28 
    29 (** datatype gram **)
    30 
    31 type nt_tag = int;              (*production for the NTs are stored in an array
    32                                   so we can identify NTs by their index*)
    33 
    34 datatype symb = Terminal of token
    35               | Nonterminal of nt_tag * int;              (*(tag, precedence)*)
    36 
    37 type nt_gram = ((nt_tag list * token list) *
    38                 (token option * (symb list * string * int) list) list);
    39                                      (*(([dependent_nts], [start_tokens]),
    40                                         [(start_token, [(rhs, name, prio)])])*)
    41                               (*depent_nts is a list of all NTs whose lookahead
    42                                 depends on this NT's lookahead*)
    43 
    44 datatype gram =
    45   Gram of {nt_count: int, prod_count: int,
    46            tags: nt_tag Symtab.table,
    47            chains: (nt_tag * nt_tag list) list,              (*[(to, [from])]*)
    48            lambdas: nt_tag list,
    49            prods: nt_gram Array.array};
    50                        (*"tags" is used to map NT names (i.e. strings) to tags;
    51                          chain productions are not stored as normal productions
    52                          but instead as an entry in "chains";
    53                          lambda productions are stored as normal productions
    54                          and also as an entry in "lambdas"*)
    55 
    56 val UnknownStart = EndToken;       (*productions for which no starting token is
    57                                      known yet are associated with this token*)
    58 
    59 (* get all NTs that are connected with a list of NTs
    60    (used for expanding chain list)*)
    61 fun connected_with _ [] relatives = relatives
    62   | connected_with chains (root :: roots) relatives =
    63     let val branches = subtract (op =) relatives (these (AList.lookup (op =) chains root));
    64     in connected_with chains (branches @ roots) (branches @ relatives) end;
    65 
    66 (* convert productions to grammar;
    67    N.B. that the chains parameter has the form [(from, [to])];
    68    prod_count is of type "int option" and is only updated if it is <> NONE*)
    69 fun add_prods _ chains lambdas prod_count [] = (chains, lambdas, prod_count)
    70   | add_prods prods chains lambdas prod_count
    71               ((lhs, new_prod as (rhs, name, pri)) :: ps) =
    72     let
    73       val chain_from = case (pri, rhs) of (~1, [Nonterminal (id, ~1)]) => SOME id | _ => NONE;
    74 
    75       (*store chain if it does not already exist*)
    76       val (new_chain, chains') = case chain_from of NONE => (NONE, chains) | SOME from_ =>
    77         let val old_tos = these (AList.lookup (op =) chains from_) in
    78           if member (op =) old_tos lhs then (NONE, chains)
    79           else (SOME from_, AList.update (op =) (from_, insert (op =) lhs old_tos) chains)
    80         end;
    81 
    82       (*propagate new chain in lookahead and lambda lists;
    83         added_starts is used later to associate existing
    84         productions with new starting tokens*)
    85       val (added_starts, lambdas') =
    86         if is_none new_chain then ([], lambdas) else
    87         let (*lookahead of chain's source*)
    88             val ((from_nts, from_tks), _) = Array.sub (prods, the new_chain);
    89 
    90             (*copy from's lookahead to chain's destinations*)
    91             fun copy_lookahead [] added = added
    92               | copy_lookahead (to :: tos) added =
    93                 let
    94                   val ((to_nts, to_tks), ps) = Array.sub (prods, to);
    95 
    96                   val new_tks = subtract (op =) to_tks from_tks;  (*added lookahead tokens*)
    97                 in Array.update (prods, to, ((to_nts, to_tks @ new_tks), ps));
    98                    copy_lookahead tos (if null new_tks then added
    99                                        else (to, new_tks) :: added)
   100                 end;
   101 
   102             val tos = connected_with chains' [lhs] [lhs];
   103         in (copy_lookahead tos [],
   104             (if member (op =) lambdas lhs then tos else []) union lambdas)
   105         end;
   106 
   107       (*test if new production can produce lambda
   108         (rhs must either be empty or only consist of lambda NTs)*)
   109       val (new_lambda, lambdas') =
   110         if forall (fn (Nonterminal (id, _)) => member (op =) lambdas' id
   111                     | (Terminal _) => false) rhs then
   112           (true, lambdas' union (connected_with chains' [lhs] [lhs]))
   113         else
   114           (false, lambdas');
   115 
   116       (*list optional terminal and all nonterminals on which the lookahead
   117         of a production depends*)
   118       fun lookahead_dependency _ [] nts = (NONE, nts)
   119         | lookahead_dependency _ ((Terminal tk) :: _) nts = (SOME tk, nts)
   120         | lookahead_dependency lambdas ((Nonterminal (nt, _)) :: symbs) nts =
   121             if member (op =) lambdas nt then
   122               lookahead_dependency lambdas symbs (nt :: nts)
   123             else (NONE, nt :: nts);
   124 
   125       (*get all known starting tokens for a nonterminal*)
   126       fun starts_for_nt nt = snd (fst (Array.sub (prods, nt)));
   127 
   128       val token_union = gen_union matching_tokens;
   129 
   130       (*update prods, lookaheads, and lambdas according to new lambda NTs*)
   131       val (added_starts', lambdas') =
   132         let
   133           (*propagate added lambda NT*)
   134           fun propagate_lambda [] added_starts lambdas= (added_starts, lambdas)
   135             | propagate_lambda (l :: ls) added_starts lambdas =
   136               let
   137                 (*get lookahead for lambda NT*)
   138                 val ((dependent, l_starts), _) = Array.sub (prods, l);
   139 
   140                 (*check productions whose lookahead may depend on lambda NT*)
   141                 fun examine_prods [] add_lambda nt_dependencies added_tks
   142                                   nt_prods =
   143                       (add_lambda, nt_dependencies, added_tks, nt_prods)
   144                   | examine_prods ((p as (rhs, _, _)) :: ps) add_lambda
   145                       nt_dependencies added_tks nt_prods =
   146                     let val (tk, nts) = lookahead_dependency lambdas rhs [];
   147                     in
   148                       if member (op =) nts l then       (*update production's lookahead*)
   149                       let
   150                         val new_lambda = is_none tk andalso nts subset lambdas;
   151 
   152                         val new_tks = subtract (op =) l_starts
   153                           ((if is_some tk then [the tk] else []) @
   154                             Library.foldl token_union ([], map starts_for_nt nts));
   155 
   156                         val added_tks' = token_union (new_tks, added_tks);
   157 
   158                         val nt_dependencies' = nts union nt_dependencies;
   159 
   160                         (*associate production with new starting tokens*)
   161                         fun copy [] nt_prods = nt_prods
   162                           | copy (tk :: tks) nt_prods =
   163                             let val old_prods = these (AList.lookup (op =) nt_prods tk);
   164 
   165                                 val prods' = p :: old_prods;
   166                             in nt_prods
   167                                |> AList.update (op =) (tk, prods')
   168                                |> copy tks
   169                             end;
   170 
   171                         val nt_prods' =
   172                           let val new_opt_tks = map SOME new_tks;
   173                           in copy ((if new_lambda then [NONE] else []) @
   174                                    new_opt_tks) nt_prods
   175                           end;
   176                       in examine_prods ps (add_lambda orelse new_lambda)
   177                            nt_dependencies' added_tks' nt_prods'
   178                       end
   179                       else                                  (*skip production*)
   180                         examine_prods ps add_lambda nt_dependencies
   181                                       added_tks nt_prods
   182                     end;
   183 
   184                 (*check each NT whose lookahead depends on new lambda NT*)
   185                 fun process_nts [] added_lambdas added_starts =
   186                       (added_lambdas, added_starts)
   187                   | process_nts (nt :: nts) added_lambdas added_starts =
   188                     let
   189                       val (lookahead as (old_nts, old_tks), nt_prods) =
   190                         Array.sub (prods, nt);
   191 
   192                       (*existing productions whose lookahead may depend on l*)
   193                       val tk_prods =
   194                         (these o AList.lookup (op =) nt_prods)
   195                                (SOME (hd l_starts  handle Empty => UnknownStart));
   196 
   197                       (*add_lambda is true if an existing production of the nt
   198                         produces lambda due to the new lambda NT l*)
   199                       val (add_lambda, nt_dependencies, added_tks, nt_prods') =
   200                         examine_prods tk_prods false [] [] nt_prods;
   201 
   202                       val added_nts = subtract (op =) old_nts nt_dependencies;
   203 
   204                       val added_lambdas' =
   205                         if add_lambda then nt :: added_lambdas
   206                         else added_lambdas;
   207                     in Array.update (prods, nt,
   208                                    ((added_nts @ old_nts, old_tks @ added_tks),
   209                                     nt_prods'));
   210                                           (*N.B. that because the tks component
   211                                             is used to access existing
   212                                             productions we have to add new
   213                                             tokens at the _end_ of the list*)
   214 
   215                        if null added_tks then
   216                          process_nts nts added_lambdas' added_starts
   217                        else
   218                          process_nts nts added_lambdas'
   219                                       ((nt, added_tks) :: added_starts)
   220                     end;
   221 
   222                 val (added_lambdas, added_starts') =
   223                   process_nts dependent [] added_starts;
   224 
   225                 val added_lambdas' = subtract (op =) lambdas added_lambdas;
   226               in propagate_lambda (ls @ added_lambdas') added_starts'
   227                                   (added_lambdas' @ lambdas)
   228               end;
   229         in propagate_lambda (subtract (op =) lambdas lambdas') added_starts lambdas' end;
   230 
   231       (*insert production into grammar*)
   232       val (added_starts', prod_count') =
   233         if is_some chain_from then (added_starts', prod_count)  (*don't store chain production*)
   234         else let
   235           (*lookahead tokens of new production and on which
   236             NTs lookahead depends*)
   237           val (start_tk, start_nts) = lookahead_dependency lambdas' rhs [];
   238 
   239           val start_tks = Library.foldl token_union
   240                           (if is_some start_tk then [the start_tk] else [],
   241                            map starts_for_nt start_nts);
   242 
   243           val opt_starts = (if new_lambda then [NONE]
   244                             else if null start_tks then [SOME UnknownStart]
   245                             else []) @ (map SOME start_tks);
   246 
   247           (*add lhs NT to list of dependent NTs in lookahead*)
   248           fun add_nts [] = ()
   249             | add_nts (nt :: nts) =
   250               let val ((old_nts, old_tks), ps) = Array.sub (prods, nt);
   251               in if member (op =) old_nts lhs then ()
   252                  else Array.update (prods, nt, ((lhs :: old_nts, old_tks), ps))
   253               end;
   254 
   255           (*add new start tokens to chained NTs' lookahead list;
   256             also store new production for lhs NT*)
   257           fun add_tks [] added prod_count = (added, prod_count)
   258             | add_tks (nt :: nts) added prod_count =
   259               let
   260                 val ((old_nts, old_tks), nt_prods) = Array.sub (prods, nt);
   261 
   262                 val new_tks = subtract matching_tokens old_tks start_tks;
   263 
   264                 (*store new production*)
   265                 fun store [] prods is_new =
   266                       (prods, if is_some prod_count andalso is_new then
   267                                 Option.map (fn x => x+1) prod_count
   268                               else prod_count, is_new)
   269                   | store (tk :: tks) prods is_new =
   270                     let val tk_prods = (these o AList.lookup (op =) prods) tk;
   271 
   272                         (*if prod_count = NONE then we can assume that
   273                           grammar does not contain new production already*)
   274                         val (tk_prods', is_new') =
   275                           if is_some prod_count then
   276                             if member (op =) tk_prods new_prod then (tk_prods, false)
   277                             else (new_prod :: tk_prods, true)
   278                           else (new_prod :: tk_prods, true);
   279 
   280                         val prods' = prods
   281                                      |> is_new' ? AList.update (op =) (tk, tk_prods');
   282                     in store tks prods' (is_new orelse is_new') end;
   283 
   284                 val (nt_prods', prod_count', changed) =
   285                   if nt = lhs then store opt_starts nt_prods false
   286                               else (nt_prods, prod_count, false);
   287               in if not changed andalso null new_tks then ()
   288                  else Array.update (prods, nt, ((old_nts, old_tks @ new_tks),
   289                                                 nt_prods'));
   290                  add_tks nts (if null new_tks then added
   291                               else (nt, new_tks) :: added) prod_count'
   292               end;
   293         in add_nts start_nts;
   294            add_tks (connected_with chains' [lhs] [lhs]) [] prod_count
   295         end;
   296 
   297       (*associate productions with new lookaheads*)
   298       val dummy =
   299         let
   300           (*propagate added start tokens*)
   301           fun add_starts [] = ()
   302             | add_starts ((changed_nt, new_tks) :: starts) =
   303               let
   304                 (*token under which old productions which
   305                   depend on changed_nt could be stored*)
   306                 val key =
   307                  case find_first (not o member (op =) new_tks)
   308                                  (starts_for_nt changed_nt) of
   309                       NONE => SOME UnknownStart
   310                     | t => t;
   311 
   312                 (*copy productions whose lookahead depends on changed_nt;
   313                   if key = SOME UnknownToken then tk_prods is used to hold
   314                   the productions not copied*)
   315                 fun update_prods [] result = result
   316                   | update_prods ((p as (rhs, _, _)) :: ps)
   317                       (tk_prods, nt_prods) =
   318                     let
   319                       (*lookahead dependency for production*)
   320                       val (tk, depends) = lookahead_dependency lambdas' rhs [];
   321 
   322                       (*test if this production has to be copied*)
   323                       val update = member (op =) depends changed_nt;
   324 
   325                       (*test if production could already be associated with
   326                         a member of new_tks*)
   327                       val lambda = length depends > 1 orelse
   328                                    not (null depends) andalso is_some tk
   329                                    andalso member (op =) new_tks (the tk);
   330 
   331                       (*associate production with new starting tokens*)
   332                       fun copy [] nt_prods = nt_prods
   333                         | copy (tk :: tks) nt_prods =
   334                           let
   335                             val tk_prods = (these o AList.lookup (op =) nt_prods) (SOME tk);
   336 
   337                             val tk_prods' =
   338                               if not lambda then p :: tk_prods
   339                               else insert (op =) p tk_prods;
   340                                       (*if production depends on lambda NT we
   341                                         have to look for duplicates*)
   342                          in
   343                            nt_prods
   344                            |> AList.update (op =) (SOME tk, tk_prods')
   345                            |> copy tks
   346                          end;
   347                       val result =
   348                         if update then
   349                           (tk_prods, copy new_tks nt_prods)
   350                         else if key = SOME UnknownStart then
   351                           (p :: tk_prods, nt_prods)
   352                         else (tk_prods, nt_prods);
   353                     in update_prods ps result end;
   354 
   355                 (*copy existing productions for new starting tokens*)
   356                 fun process_nts [] added = added
   357                   | process_nts (nt :: nts) added =
   358                     let
   359                       val (lookahead as (old_nts, old_tks), nt_prods) =
   360                         Array.sub (prods, nt);
   361 
   362                       val tk_prods = (these o AList.lookup (op =) nt_prods) key;
   363 
   364                       (*associate productions with new lookahead tokens*)
   365                       val (tk_prods', nt_prods') =
   366                         update_prods tk_prods ([], nt_prods);
   367 
   368                       val nt_prods' =
   369                         nt_prods'
   370                         |> (key = SOME UnknownStart) ? AList.update (op =) (key, tk_prods')
   371 
   372                       val added_tks =
   373                         subtract matching_tokens old_tks new_tks;
   374                     in if null added_tks then
   375                          (Array.update (prods, nt, (lookahead, nt_prods'));
   376                           process_nts nts added)
   377                        else
   378                          (Array.update (prods, nt,
   379                             ((old_nts, added_tks @ old_tks), nt_prods'));
   380                           process_nts nts ((nt, added_tks) :: added))
   381                     end;
   382 
   383                 val ((dependent, _), _) = Array.sub (prods, changed_nt);
   384               in add_starts (starts @ (process_nts dependent [])) end;
   385         in add_starts added_starts' end;
   386   in add_prods prods chains' lambdas' prod_count ps end;
   387 
   388 
   389 (* pretty_gram *)
   390 
   391 fun pretty_gram (Gram {tags, prods, chains, ...}) =
   392   let
   393     fun pretty_name name = [Pretty.str (name ^ " =")];
   394 
   395     val taglist = Symtab.dest tags;
   396 
   397     fun pretty_symb (Terminal (Token s)) = Pretty.quote (Pretty.str s)
   398       | pretty_symb (Terminal tok) = Pretty.str (str_of_token tok)
   399       | pretty_symb (Nonterminal (tag, p)) =
   400         let val name = fst (the (find_first (fn (n, t) => t = tag) taglist));
   401         in Pretty.str (name ^ "[" ^ string_of_int p ^ "]") end;
   402 
   403     fun pretty_const "" = []
   404       | pretty_const c = [Pretty.str ("=> " ^ Library.quote c)];
   405 
   406     fun pretty_pri p = [Pretty.str ("(" ^ string_of_int p ^ ")")];
   407 
   408     fun pretty_prod name (symbs, const, pri) =
   409       Pretty.block (Pretty.breaks (pretty_name name @
   410         map pretty_symb symbs @ pretty_const const @ pretty_pri pri));
   411 
   412     fun pretty_nt (name, tag) =
   413       let
   414         fun prod_of_chain from_ = ([Nonterminal (from_, ~1)], "", ~1);
   415 
   416         val nt_prods =
   417           Library.foldl (op union) ([], map snd (snd (Array.sub (prods, tag)))) @
   418           map prod_of_chain ((these o AList.lookup (op =) chains) tag);
   419       in map (pretty_prod name) nt_prods end;
   420 
   421   in maps pretty_nt taglist end;
   422 
   423 
   424 (** Operations on gramars **)
   425 
   426 (*The mother of all grammars*)
   427 val empty_gram = Gram {nt_count = 0, prod_count = 0,
   428                        tags = Symtab.empty, chains = [], lambdas = [],
   429                        prods = Array.array (0, (([], []), []))};
   430 
   431 
   432 (*Invert list of chain productions*)
   433 fun inverse_chains [] result = result
   434   | inverse_chains ((root, branches) :: cs) result =
   435     let fun add [] result = result
   436           | add (id :: ids) result =
   437             let val old = (these o AList.lookup (op =) result) id;
   438             in add ids (AList.update (op =) (id, root :: old) result) end;
   439     in inverse_chains cs (add branches result) end;
   440 
   441 
   442 (*Add productions to a grammar*)
   443 fun extend_gram gram [] = gram
   444   | extend_gram (Gram {nt_count, prod_count, tags, chains, lambdas, prods})
   445                 xprods =
   446   let
   447     (*Get tag for existing nonterminal or create a new one*)
   448     fun get_tag nt_count tags nt =
   449       case Symtab.lookup tags nt of
   450         SOME tag => (nt_count, tags, tag)
   451       | NONE => (nt_count+1, Symtab.update_new (nt, nt_count) tags,
   452                  nt_count);
   453 
   454     (*Convert symbols to the form used by the parser;
   455       delimiters and predefined terms are stored as terminals,
   456       nonterminals are converted to integer tags*)
   457     fun symb_of [] nt_count tags result = (nt_count, tags, rev result)
   458       | symb_of ((Delim s) :: ss) nt_count tags result =
   459           symb_of ss nt_count tags ((Terminal (Token s)) :: result)
   460       | symb_of ((Argument (s, p)) :: ss) nt_count tags result =
   461           let
   462             val (nt_count', tags', new_symb) =
   463               case predef_term s of
   464                 NONE =>
   465                   let val (nt_count', tags', s_tag) = get_tag nt_count tags s;
   466                   in (nt_count', tags', Nonterminal (s_tag, p)) end
   467               | SOME tk => (nt_count, tags, Terminal tk);
   468           in symb_of ss nt_count' tags' (new_symb :: result) end
   469       | symb_of (_ :: ss) nt_count tags result =
   470           symb_of ss nt_count tags result;
   471 
   472     (*Convert list of productions by invoking symb_of for each of them*)
   473     fun prod_of [] nt_count prod_count tags result =
   474           (nt_count, prod_count, tags, result)
   475       | prod_of ((XProd (lhs, xsymbs, const, pri)) :: ps)
   476                 nt_count prod_count tags result =
   477         let val (nt_count', tags', lhs_tag) = get_tag nt_count tags lhs;
   478 
   479             val (nt_count'', tags'', prods) =
   480               symb_of xsymbs nt_count' tags' [];
   481         in prod_of ps nt_count'' (prod_count+1) tags''
   482                    ((lhs_tag, (prods, const, pri)) :: result)
   483         end;
   484 
   485     val (nt_count', prod_count', tags', xprods') =
   486       prod_of xprods nt_count prod_count tags [];
   487 
   488     (*Copy array containing productions of old grammar;
   489       this has to be done to preserve the old grammar while being able
   490       to change the array's content*)
   491     val prods' =
   492       let fun get_prod i = if i < nt_count then Array.sub (prods, i)
   493                            else (([], []), []);
   494       in Array.tabulate (nt_count', get_prod) end;
   495 
   496     val fromto_chains = inverse_chains chains [];
   497 
   498     (*Add new productions to old ones*)
   499     val (fromto_chains', lambdas', _) =
   500       add_prods prods' fromto_chains lambdas NONE xprods';
   501 
   502     val chains' = inverse_chains fromto_chains' [];
   503   in Gram {nt_count = nt_count', prod_count = prod_count', tags = tags',
   504            chains = chains', lambdas = lambdas', prods = prods'}
   505   end;
   506 
   507 val make_gram = extend_gram empty_gram;
   508 
   509 
   510 (*Merge two grammars*)
   511 fun merge_grams gram_a gram_b =
   512   let
   513     (*find out which grammar is bigger*)
   514     val (Gram {nt_count = nt_count1, prod_count = prod_count1, tags = tags1,
   515                chains = chains1, lambdas = lambdas1, prods = prods1},
   516          Gram {nt_count = nt_count2, prod_count = prod_count2, tags = tags2,
   517                chains = chains2, lambdas = lambdas2, prods = prods2}) =
   518       let val Gram {prod_count = count_a, ...} = gram_a;
   519           val Gram {prod_count = count_b, ...} = gram_b;
   520       in if count_a > count_b then (gram_a, gram_b)
   521                               else (gram_b, gram_a)
   522       end;
   523 
   524     (*get existing tag from grammar1 or create a new one*)
   525     fun get_tag nt_count tags nt =
   526       case Symtab.lookup tags nt of
   527         SOME tag => (nt_count, tags, tag)
   528       | NONE => (nt_count+1, Symtab.update_new (nt, nt_count) tags,
   529                 nt_count)
   530 
   531     val ((nt_count1', tags1'), tag_table) =
   532       let val tag_list = Symtab.dest tags2;
   533 
   534           val table = Array.array (nt_count2, ~1);
   535 
   536           fun store_tag nt_count tags ~1 = (nt_count, tags)
   537             | store_tag nt_count tags tag =
   538               let val (nt_count', tags', tag') =
   539                    get_tag nt_count tags
   540                      (fst (the (find_first (fn (n, t) => t = tag) tag_list)));
   541               in Array.update (table, tag, tag');
   542                  store_tag nt_count' tags' (tag-1)
   543               end;
   544       in (store_tag nt_count1 tags1 (nt_count2-1), table) end;
   545 
   546     (*convert grammar2 tag to grammar1 tag*)
   547     fun convert_tag tag = Array.sub (tag_table, tag);
   548 
   549     (*convert chain list to raw productions*)
   550     fun mk_chain_prods [] result = result
   551       | mk_chain_prods ((to, froms) :: cs) result =
   552         let
   553           val to_tag = convert_tag to;
   554 
   555           fun make [] result = result
   556             | make (from_ :: froms) result = make froms ((to_tag,
   557                 ([Nonterminal (convert_tag from_, ~1)], "", ~1)) :: result);
   558         in mk_chain_prods cs (make froms [] @ result) end;
   559 
   560     val chain_prods = mk_chain_prods chains2 [];
   561 
   562     (*convert prods2 array to productions*)
   563     fun process_nt ~1 result = result
   564       | process_nt nt result =
   565         let
   566           val nt_prods = Library.foldl (op union)
   567                              ([], map snd (snd (Array.sub (prods2, nt))));
   568           val lhs_tag = convert_tag nt;
   569 
   570           (*convert tags in rhs*)
   571           fun process_rhs [] result = result
   572             | process_rhs (Terminal tk :: rhs) result =
   573                 process_rhs rhs (result @ [Terminal tk])
   574             | process_rhs (Nonterminal (nt, prec) :: rhs) result =
   575                 process_rhs rhs
   576                             (result @ [Nonterminal (convert_tag nt, prec)]);
   577 
   578           (*convert tags in productions*)
   579           fun process_prods [] result = result
   580             | process_prods ((rhs, id, prec) :: ps) result =
   581                 process_prods ps ((lhs_tag, (process_rhs rhs [], id, prec))
   582                                   :: result);
   583         in process_nt (nt-1) (process_prods nt_prods [] @ result) end;
   584 
   585     val raw_prods = chain_prods @ process_nt (nt_count2-1) [];
   586 
   587     val prods1' =
   588       let fun get_prod i = if i < nt_count1 then Array.sub (prods1, i)
   589                            else (([], []), []);
   590       in Array.tabulate (nt_count1', get_prod) end;
   591 
   592     val fromto_chains = inverse_chains chains1 [];
   593 
   594     val (fromto_chains', lambdas', SOME prod_count1') =
   595       add_prods prods1' fromto_chains lambdas1 (SOME prod_count1) raw_prods;
   596 
   597     val chains' = inverse_chains fromto_chains' [];
   598   in Gram {nt_count = nt_count1', prod_count = prod_count1',
   599            tags = tags1', chains = chains', lambdas = lambdas',
   600            prods = prods1'}
   601   end;
   602 
   603 
   604 (** Parser **)
   605 
   606 datatype parsetree =
   607   Node of string * parsetree list |
   608   Tip of token;
   609 
   610 type state =
   611   nt_tag * int *                (*identification and production precedence*)
   612   parsetree list *              (*already parsed nonterminals on rhs*)
   613   symb list *                   (*rest of rhs*)
   614   string *                      (*name of production*)
   615   int;                          (*index for previous state list*)
   616 
   617 
   618 (*Get all rhss with precedence >= minPrec*)
   619 fun getRHS minPrec = List.filter (fn (_, _, prec:int) => prec >= minPrec);
   620 
   621 (*Get all rhss with precedence >= minPrec and < maxPrec*)
   622 fun getRHS' minPrec maxPrec =
   623   List.filter (fn (_, _, prec:int) => prec >= minPrec andalso prec < maxPrec);
   624 
   625 (*Make states using a list of rhss*)
   626 fun mkStates i minPrec lhsID rhss =
   627   let fun mkState (rhs, id, prodPrec) = (lhsID, prodPrec, [], rhs, id, i);
   628   in map mkState rhss end;
   629 
   630 (*Add parse tree to list and eliminate duplicates
   631   saving the maximum precedence*)
   632 fun conc (t: parsetree list, prec:int) [] = (NONE, [(t, prec)])
   633   | conc (t, prec) ((t', prec') :: ts) =
   634       if t = t' then
   635         (SOME prec', if prec' >= prec then (t', prec') :: ts
   636                      else (t, prec) :: ts)
   637       else
   638         let val (n, ts') = conc (t, prec) ts
   639         in (n, (t', prec') :: ts') end;
   640 
   641 (*Update entry in used*)
   642 fun update_trees ((B: nt_tag, (i, ts)) :: used) (A, t) =
   643   if A = B then
   644     let val (n, ts') = conc t ts
   645     in ((A, (i, ts')) :: used, n) end
   646   else
   647     let val (used', n) = update_trees used (A, t)
   648     in ((B, (i, ts)) :: used', n) end;
   649 
   650 (*Replace entry in used*)
   651 fun update_prec (A: nt_tag, prec) used =
   652   let fun update ((hd as (B, (_, ts))) :: used, used') =
   653         if A = B
   654         then used' @ ((A, (prec, ts)) :: used)
   655         else update (used, hd :: used')
   656   in update (used, []) end;
   657 
   658 fun getS A maxPrec Si =
   659   List.filter
   660     (fn (_, _, _, Nonterminal (B, prec) :: _, _, _)
   661           => A = B andalso prec <= maxPrec
   662       | _ => false) Si;
   663 
   664 fun getS' A maxPrec minPrec Si =
   665   List.filter
   666     (fn (_, _, _, Nonterminal (B, prec) :: _, _, _)
   667           => A = B andalso prec > minPrec andalso prec <= maxPrec
   668       | _ => false) Si;
   669 
   670 fun getStates Estate i ii A maxPrec =
   671   List.filter
   672     (fn (_, _, _, Nonterminal (B, prec) :: _, _, _)
   673           => A = B andalso prec <= maxPrec
   674       | _ => false)
   675     (Array.sub (Estate, ii));
   676 
   677 
   678 fun movedot_term (A, j, ts, Terminal a :: sa, id, i) c =
   679   if valued_token c then
   680     (A, j, ts @ [Tip c], sa, id, i)
   681   else (A, j, ts, sa, id, i);
   682 
   683 fun movedot_nonterm ts (A, j, tss, Nonterminal _ :: sa, id, i) =
   684   (A, j, tss @ ts, sa, id, i);
   685 
   686 fun movedot_lambda _ [] = []
   687   | movedot_lambda (B, j, tss, Nonterminal (A, k) :: sa, id, i) ((t, ki) :: ts) =
   688       if k <= ki then
   689         (B, j, tss @ t, sa, id, i) ::
   690           movedot_lambda (B, j, tss, Nonterminal (A, k) :: sa, id, i) ts
   691       else movedot_lambda (B, j, tss, Nonterminal (A, k) :: sa, id, i) ts;
   692 
   693 
   694 val warned = ref false;                            (*flag for warning message*)
   695 val branching_level = ref 600;                   (*trigger value for warnings*)
   696 
   697 (*get all productions of a NT and NTs chained to it which can
   698   be started by specified token*)
   699 fun prods_for prods chains include_none tk nts =
   700 let
   701     fun token_assoc (list, key) =
   702       let fun assoc [] result = result
   703             | assoc ((keyi, pi) :: pairs) result =
   704                 if is_some keyi andalso matching_tokens (the keyi, key)
   705                    orelse include_none andalso is_none keyi then
   706                   assoc pairs (pi @ result)
   707                 else assoc pairs result;
   708       in assoc list [] end;
   709 
   710     fun get_prods [] result = result
   711       | get_prods (nt :: nts) result =
   712         let val nt_prods = snd (Array.sub (prods, nt));
   713         in get_prods nts ((token_assoc (nt_prods, tk)) @ result) end;
   714 in get_prods (connected_with chains nts nts) [] end;
   715 
   716 
   717 fun PROCESSS prods chains Estate i c states =
   718 let
   719 fun all_prods_for nt = prods_for prods chains true c [nt];
   720 
   721 fun processS used [] (Si, Sii) = (Si, Sii)
   722   | processS used (S :: States) (Si, Sii) =
   723       (case S of
   724         (_, _, _, Nonterminal (nt, minPrec) :: _, _, _) =>
   725           let                                       (*predictor operation*)
   726             val (used', new_states) =
   727               (case AList.lookup (op =) used nt of
   728                 SOME (usedPrec, l) =>       (*nonterminal has been processed*)
   729                   if usedPrec <= minPrec then
   730                                       (*wanted precedence has been processed*)
   731                     (used, movedot_lambda S l)
   732                   else            (*wanted precedence hasn't been parsed yet*)
   733                     let
   734                       val tk_prods = all_prods_for nt;
   735 
   736                       val States' = mkStates i minPrec nt
   737                                       (getRHS' minPrec usedPrec tk_prods);
   738                     in (update_prec (nt, minPrec) used,
   739                         movedot_lambda S l @ States')
   740                     end
   741 
   742               | NONE =>           (*nonterminal is parsed for the first time*)
   743                   let val tk_prods = all_prods_for nt;
   744                       val States' = mkStates i minPrec nt
   745                                       (getRHS minPrec tk_prods);
   746                   in ((nt, (minPrec, [])) :: used, States') end);
   747 
   748             val dummy =
   749               if not (!warned) andalso
   750                  length (new_states @ States) > (!branching_level) then
   751                 (warning "Currently parsed expression could be extremely ambiguous.";
   752                  warned := true)
   753               else ();
   754           in
   755             processS used' (new_states @ States) (S :: Si, Sii)
   756           end
   757       | (_, _, _, Terminal a :: _, _, _) =>               (*scanner operation*)
   758           processS used States
   759             (S :: Si,
   760               if matching_tokens (a, c) then movedot_term S c :: Sii else Sii)
   761       | (A, prec, ts, [], id, j) =>                   (*completer operation*)
   762           let val tt = if id = "" then ts else [Node (id, ts)] in
   763             if j = i then                             (*lambda production?*)
   764               let
   765                 val (used', O) = update_trees used (A, (tt, prec));
   766               in
   767                 case O of
   768                   NONE =>
   769                     let val Slist = getS A prec Si;
   770                         val States' = map (movedot_nonterm tt) Slist;
   771                     in processS used' (States' @ States) (S :: Si, Sii) end
   772                 | SOME n =>
   773                     if n >= prec then processS used' States (S :: Si, Sii)
   774                     else
   775                       let val Slist = getS' A prec n Si;
   776                           val States' = map (movedot_nonterm tt) Slist;
   777                       in processS used' (States' @ States) (S :: Si, Sii) end
   778               end
   779             else
   780               let val Slist = getStates Estate i j A prec
   781               in processS used (map (movedot_nonterm tt) Slist @ States)
   782                           (S :: Si, Sii)
   783               end
   784           end)
   785 in processS [] states ([], []) end;
   786 
   787 
   788 fun syntax_error toks allowed =
   789   let
   790     val msg =
   791       if null toks then Pretty.str "Inner syntax error: unexpected end of input"
   792       else
   793         Pretty.block (Pretty.str "Inner syntax error at: \"" ::
   794           Pretty.breaks (map (Pretty.str o str_of_token)
   795                  (rev (tl (rev toks)))) @
   796           [Pretty.str "\""]);
   797     val expected =
   798       Pretty.strs ("Expected tokens: " :: map (quote o str_of_token) allowed);
   799   in
   800     error (Pretty.string_of (Pretty.blk (0, [msg, Pretty.fbrk, expected])))
   801   end;
   802 
   803 fun produce prods chains stateset i indata prev_token =
   804                                       (*prev_token is used for error messages*)
   805   (case Array.sub (stateset, i) of
   806     [] => let fun some_prods_for tk nt = prods_for prods chains false tk [nt];
   807 
   808               (*test if tk is a lookahead for a given minimum precedence*)
   809               fun reduction _ minPrec _ (Terminal _ :: _, _, prec:int) =
   810                     if prec >= minPrec then true
   811                     else false
   812                 | reduction tk minPrec checked
   813                             (Nonterminal (nt, nt_prec) :: _, _, prec) =
   814                   if prec >= minPrec andalso not (member (op =) checked nt) then
   815                     let val chained = connected_with chains [nt] [nt];
   816                     in exists
   817                          (reduction tk nt_prec (chained @ checked))
   818                          (some_prods_for tk nt)
   819                     end
   820                   else false;
   821 
   822               (*compute a list of allowed starting tokens
   823                 for a list of nonterminals considering precedence*)
   824               fun get_starts [] result = result
   825                 | get_starts ((nt, minPrec:int) :: nts) result =
   826                   let fun get [] result = result
   827                         | get ((SOME tk, prods) :: ps) result =
   828                             if not (null prods) andalso
   829                                exists (reduction tk minPrec [nt]) prods
   830                             then get ps (tk :: result)
   831                             else get ps result
   832                         | get ((NONE, _) :: ps) result = get ps result;
   833 
   834                       val (_, nt_prods) = Array.sub (prods, nt);
   835 
   836                       val chained = map (fn nt => (nt, minPrec))
   837                                         ((these o AList.lookup (op =) chains) nt);
   838                   in get_starts (chained @ nts)
   839                                 ((get nt_prods []) union result)
   840                   end;
   841 
   842               val nts =
   843                 map_filter (fn (_, _, _, Nonterminal (a, prec) :: _, _, _) =>
   844                            SOME (a, prec) | _ => NONE)
   845                           (Array.sub (stateset, i-1));
   846               val allowed =
   847                 distinct (op =) (get_starts nts [] @
   848                   (map_filter (fn (_, _, _, Terminal a :: _, _, _) => SOME a
   849                                | _ => NONE)
   850                              (Array.sub (stateset, i-1))));
   851           in syntax_error (if prev_token = EndToken then indata
   852                            else prev_token :: indata) allowed
   853           end
   854   | s =>
   855     (case indata of
   856        [] => Array.sub (stateset, i)
   857      | c :: cs =>
   858        let val (si, sii) = PROCESSS prods chains stateset i c s;
   859        in Array.update (stateset, i, si);
   860           Array.update (stateset, i + 1, sii);
   861           produce prods chains stateset (i + 1) cs c
   862        end));
   863 
   864 
   865 fun get_trees l = map_filter (fn (_, _, [pt], _, _, _) => SOME pt | _ => NONE)
   866                             l;
   867 
   868 fun earley prods tags chains startsymbol indata =
   869   let
   870     val start_tag = case Symtab.lookup tags startsymbol of
   871                        SOME tag => tag
   872                      | NONE   => error ("parse: Unknown startsymbol " ^
   873                                         quote startsymbol);
   874     val S0 = [(~1, 0, [], [Nonterminal (start_tag, 0), Terminal EndToken],
   875                "", 0)];
   876     val s = length indata + 1;
   877     val Estate = Array.array (s, []);
   878   in
   879     Array.update (Estate, 0, S0);
   880     warned := false;
   881     get_trees (produce prods chains Estate 0 indata EndToken)
   882   end;
   883 
   884 
   885 fun parse (Gram {tags, prods, chains, ...}) start toks =
   886 let val r =
   887   (case earley prods tags chains start toks of
   888     [] => sys_error "parse: no parse trees"
   889   | pts => pts);
   890 in r end
   891 
   892 end;