rename Result->ResultNode
[sbp.git] / src / edu / berkeley / sbp / Parser.java
index 0b5f7c1..56ee0ca 100644 (file)
-// Copyright 2006 all rights reserved; see LICENSE file for BSD-style license
+// Copyright 2006-2007 all rights reserved; see LICENSE file for BSD-style license
 
 package edu.berkeley.sbp;
-import edu.berkeley.sbp.*;
 import edu.berkeley.sbp.util.*;
-import edu.berkeley.sbp.Sequence.Position;
+import edu.berkeley.sbp.Sequence.Pos;
+import edu.berkeley.sbp.Sequence.Pos;
 import java.io.*;
 import java.util.*;
 
 /** a parser which translates an Input<Token> into a Forest<NodeType> */
-public abstract class Parser<Token, NodeType> {
+public abstract class Parser<Token, NodeType> implements Serializable {
 
-    protected final Table<Token> pt;
+    final Table pt;
 
     /** create a parser to parse the grammar with start symbol <tt>u</tt> */
-    public Parser(Union u, Topology<Token> top)  { this.pt = new Table<Token>(u, top); }
+    public Parser(Union u)  { this.pt = new Table(u); }
 
     /** implement this method to create the output forest corresponding to a lone shifted input token */
-    public abstract Forest<NodeType> shiftToken(Token t, Input.Location newloc);
+    public abstract Forest<NodeType> shiftToken(Token t, Input.Region region);
 
-    public String toString() { return pt.toString(); }
+    public abstract Topology<Token> emptyTopology();
 
-    private boolean verbose = false;;
-    private static final char[] spin = new char[] { '-', '\\', '|', '/' };
-    private int spinpos = 0;
-    private long last = 0;
-    void spin() {
-        if (verbose) {
-            long now = System.currentTimeMillis();
-            if (now-last < 70) return;
-            last = now;
-            System.err.print("\r  " + spin[spinpos++ % (spin.length)]+"\r");
-        }
-    }
+    public String toString() { return pt.toString(); }
 
     /** parse <tt>input</tt>, and return the shared packed parse forest (or throw an exception) */
     public Forest<NodeType> parse(Input<Token> input) throws IOException, ParseFailed {
+        long start = System.currentTimeMillis();
         verbose = System.getProperty("sbp.verbose", null) != null;
         spinpos = 0;
+        GSS gss = new GSS(input, this);
+        int idmax = 0;
+        int[][] count = new int[1024*1024][];
+        HashMap<Pos,Integer> ids = new HashMap<Pos,Integer>();
         try {
-            GSS gss = new GSS(input, this);
             for(GSS.Phase current = gss.new Phase<Token>(pt.start); ;) {
-                
-                if (verbose) {
-                    String s;
-                    s = "  " + spin[spinpos++ % (spin.length)]+" parsing ";
-                    s += input.getName();
-                    s += " "+input.getLocation();
-                    while(s.indexOf(':') != -1 && s.indexOf(':') < 8) s = " " + s;
-                    String y = "@"+gss.viewPos+" ";
-                    while(y.length() < 9) y = " " + y;
-                    s += y;
-                    //s += "   doom="+Node.doomedNodes;
-                    //while(s.length() < 40) s = s + " ";
-                    s += "   nodes="+gss.numOldNodes;
-                    while(s.length() < 50) s = s + " ";
-                    s += " shifted="+gss.numNewNodes;
-                    while(s.length() < 60) s = s + " ";
-                    s += " reductions="+gss.numReductions;
-                    System.err.print("\r"+s+ANSI.clreol()+"\r");
-                }
-                
-                // FIXME: make sure all the locations line up properly in here
+                if (verbose) debug(current.token, gss, input);
                 if (current.isDone()) return (Forest<NodeType>)current.finalResult;
-                Forest forest = shiftToken((Token)current.token, input.getLocation());
+                Input.Region region = current.getLocation().createRegion(current.getNextLocation());
+                Forest forest = shiftToken((Token)current.token, region);
+                /*
+                int maxid = 0;
+                for(Reduction r : gss.finishedReductions)
+                    if (ids.get(r.reduction())==null)
+                        ids.put(r.reduction(), idmax++);
+                count[current.pos] = new int[idmax];
+                for(Reduction r : gss.finishedReductions)
+                    count[current.pos][ids.get(r.reduction())]++;
+                */
                 current = gss.new Phase<Token>(current, forest);
             }
         } finally {
-            if (verbose)
-                System.err.print("\r                                                                                \r");
+            if (verbose) {
+                long time = System.currentTimeMillis() - start;
+                System.err.println("\r parse time: " + time +"ms "+ ANSI.clreol());
+                debug(null, gss, input);
+            }
+            /*
+            PrintWriter pw = new PrintWriter(new OutputStreamWriter(new FileOutputStream("out.plot")));
+            boolean[] use = new boolean[idmax];
+            for(int i=0; i<count.length; i++)
+                if (count[i]!=null)
+                for(int j=0; j<count[i].length; j++)
+                    if (count[i][j]>20)
+                        use[j] = true;
+            for(int i=0; i<count.length; i++)
+                if (count[i]!=null) {
+                    int row = 0;
+                    for(int j=0; j<use.length; j++)
+                        if (use[j]) {
+                            row++;
+                            pw.println(i+", "+row+", "+(j>=count[i].length ? 0 : count[i][j]));
+                        }
+                    pw.println();
+                }
+            pw.close();
+            pw = new PrintWriter(new OutputStreamWriter(new FileOutputStream("test.plot")));
+            pw.println("set terminal postscript enhanced color");
+            pw.println("set output \"out.ps\"");
+            pw.println("set pm3d map");
+            pw.println("set autoscale");
+            pw.println("set view 0,0");
+            pw.println("set ytics (\\");
+            int q = -1;
+            for(int j=0; j<use.length; j++)
+                if (use[j]) {
+                    q++;
+                    for(Pos p : ids.keySet())
+                        if (ids.get(p) == j) {
+                            String title = p.toString();
+                            System.out.println(q + " " + title);
+                            pw.println("\""+q+"\"  "+(((double)q)+0.5)+",\\");
+                            break;
+                        }
+                }
+            pw.println("\".\"  "+(q+1)+")");
+            pw.println("set size square");
+            pw.println("splot \"out.plot\"");
+            pw.close();
+            */
         }
     }
 
+    // Spinner //////////////////////////////////////////////////////////////////////////////
+
+    private boolean verbose = false;
+    private static final char[] spin = new char[] { '-', '\\', '|', '/' };
+    private int spinpos = 0;
+    private long last = 0;
+    void spin() {
+        if (!verbose) return;
+        long now = System.currentTimeMillis();
+        if (now-last < 70) return;
+        last = now;
+        System.err.print("\r  " + spin[spinpos++ % (spin.length)]+"\r");
+    }
+
+    private int _last = -1;
+    private String buf = "";
+    private void debug(Object t, GSS gss, Input input) {
+        //FIXME
+        int c = t==null ? -1 : ((t+"").charAt(0));
+        int last = _last;
+        _last = c;
+        switch(c) {
+            case edu.berkeley.sbp.chr.CharAtom.left:
+                buf += "\033[31m>\033[0m";
+                break;
+            case edu.berkeley.sbp.chr.CharAtom.right:
+                buf += "\033[31m<\033[0m";
+                break;
+            case -1: // FIXME 
+            case '\n':
+                if (verbose) {
+                    if (last==' ') buf += ANSI.blue("\\n");
+                    System.err.println("\r"+ANSI.clreol()+"\r"+buf);
+                    buf = "";
+                }
+                break;
+            default:
+                buf += ANSI.cyan(""+((char)c));
+                break;
+        }
+        if (t==null) return;
+
+        // FIXME: clean this up
+        String s;
+        s = "  " + spin[spinpos++ % (spin.length)]+" parsing ";
+        s += input.getName();
+        s += " "+input.getLocation();
+        while(s.indexOf(':') != -1 && s.indexOf(':') < 8) s = " " + s;
+        String y = "@"+gss.viewPos+" ";
+        while(y.length() < 9) y = " " + y;
+        s += y;
+        s += "   nodes="+gss.numOldNodes;
+        while(s.length() < 50) s = s + " ";
+        s += " shifted="+gss.numNewNodes;
+        while(s.length() < 60) s = s + " ";
+        s += " reductions="+gss.numReductions;
+        while(s.length() < 78) s = s + " ";
+        System.err.print("\r"+ANSI.invert(s+ANSI.clreol())+"\r");
+    }
 
     // Table //////////////////////////////////////////////////////////////////////////////
 
     /** an SLR(1) parse table which may contain conflicts */
-    static class Table<Token> extends Cache {
+    class Table implements Serializable {
 
         /** the start state */
-        public  final State<Token>   start;
+        final State<Token>   start;
 
-        /** the state from which no reductions can be done */
+        /** a dummy state from which no reductions can be performed */
         private final State<Token>   dead_state;
 
         /** used to generate unique values for State.idx */
         private int master_state_idx = 0;
-        HashSet<State<Token>>   all_states    = new HashSet<State<Token>>();
-        HashMap<HashSet<Position>,State<Token>>   doomed_states    = new HashMap<HashSet<Position>,State<Token>>();
-        HashMap<HashSet<Position>,State<Token>>   normal_states    = new HashMap<HashSet<Position>,State<Token>>();
+
+        /** all the states for this table */
+        private transient HashSet<State<Token>>                all_states       = new HashSet<State<Token>>();
+
+        /** all the doomed states in this table */
+        private transient HashMap<HashSet<Pos>,State<Token>>   doomed_states    = new HashMap<HashSet<Pos>,State<Token>>();
+
+        /** all the non-doomed states in this table */
+        private transient HashMap<HashSet<Pos>,State<Token>>   normal_states    = new HashMap<HashSet<Pos>,State<Token>>();
 
         /** construct a parse table for the given grammar */
-        public Table(Topology top) { this("s", top); }
-        public Table(String startSymbol, Topology top) { this(new Union(startSymbol), top); }
-        public Table(Union ux, Topology top) {
-            super(ux, top);
-            Union start0 = new Union("0");
-            Sequence seq0 = new Sequence.Singleton(ux);
-            start0.add(seq0);
-            buildFollowSet(seq0, top, true);
-
-            // construct the set of states
-            HashSet<Position> hp = new HashSet<Position>();
-            reachable(start0, hp);
-
-            this.dead_state = new State<Token>(new HashSet<Position>(), true);
-            this.start = new State<Token>(hp);
+        Table(Union ux) {
+            Union rootUnion = new Union("0", Sequence.create(ux), true);
+            Grammar<Token> grammar = new Grammar<Token>(rootUnion) {
+                public Topology<Token> emptyTopology() { return Parser.this.emptyTopology(); }
+            };
+
+            // create the "dead state"
+            this.dead_state = new State<Token>(new HashSet<Pos>(), true, grammar);
 
+            // construct the start state; this will recursively create *all* the states
+            this.start = new State<Token>(reachable(rootUnion), false, grammar);
+
+            buildReductions(grammar);
+            sortReductions(grammar);
+        }
+
+        /** fill in the reductions table */
+        private void buildReductions(Grammar<Token> grammar) {
             // for each state, fill in the corresponding "row" of the parse table
             for(State<Token> state : all_states)
-                for(Position p : state.hs) {
-
-                    // the Grammar's designated "last position" is the only accepting state
-                    if (start0.contains(p.owner()) && p.next()==null && !state.doomed)
-                        state.accept = true;
-
-                    if (isRightNullable(p)) {
-                        Topology<Token> follow = (Topology<Token>)follow(p.owner());
-                        for(Position p2 = p; p2 != null && p2.element() != null; p2 = p2.next()) {
-                            if (!(p2.element() instanceof Union)) throw new Error("impossible");
-                            Union u = (Union)p2.element();
-                            Atom set = new edu.berkeley.sbp.chr.CharAtom(new edu.berkeley.sbp.chr.CharTopology((Topology<Character>)epsilonFollowSet(u)));
-                            Element p2e = p2.element();
-                            if (p2e instanceof Union)
-                                for(Sequence p2es : ((Union)p2e))
-                                    follow = follow.intersect(follow(p2es));
-                            if (set != null) follow = follow.intersect(set.getTokenTopology());
-                        }
-                        state.reductions.put(follow, p);
-                        if (followEof.contains(p.owner())) state.eofReductions.add(p);
-                    }
+                for(Pos p : state.hs) {
 
                     // if the element following this position is an atom, copy the corresponding
                     // set of rows out of the "master" goto table and into this state's shift table
                     if (p.element() != null && p.element() instanceof Atom)
                         state.shifts.addAll(state.gotoSetTerminals.subset(((Atom)p.element()).getTokenTopology()));
+
+                    // RNGLR: we can potentially reduce from any "right-nullable" position -- that is,
+                    // any position for which all Elements after it in the Sequence are capable of
+                    // matching the empty string.
+                    if (!grammar.isRightNullable(p)) continue;
+                    Topology<Token> follow = grammar.follow(p.owner());
+                    for(Pos p2 = p; p2 != null && p2.element() != null; p2 = p2.next()) {
+                        if (!(p2.element() instanceof Union))
+                            throw new Error("impossible -- only Unions can be nullable");
+                        
+                        // interesting RNGLR-followRestriction interaction: we must intersect
+                        // not just the follow-set of the last non-nullable element, but the
+                        // follow-sets of the nulled elements as well.
+                        for(Sequence s : ((Union)p2.element()))
+                            follow = follow.intersect(grammar.follow(s));
+                        Topology<Token> set = grammar.epsilonFollowSet((Union)p2.element());
+                        if (set != null) follow = follow.intersect(set);
+                    }
+                    
+                    // indicate that when the next token is in the set "follow", nodes in this
+                    // state should reduce according to Pos "p"
+                    state.reductions.put(follow, p);
+                    if (grammar.followEof.contains(p.owner())) state.eofReductions.add(p);
                 }
 
-            if (top instanceof IntegerTopology)
+            // optimize the reductions table
+            if (emptyTopology() instanceof IntegerTopology)
                 for(State<Token> state : all_states) {
-                    state.oreductions = state.reductions.optimize(((IntegerTopology)top).functor());
-                    state.oshifts = state.shifts.optimize(((IntegerTopology)top).functor());
+                    // FIXME: this is pretty ugly
+                    state.oreductions = state.reductions.optimize(((IntegerTopology)emptyTopology()).functor());
+                    state.oshifts     = state.shifts.optimize(((IntegerTopology)emptyTopology()).functor());
                 }
+        }
 
+        // FIXME: this method needs to be cleaned up and documented
+        private void sortReductions(Grammar<Token> grammar) {
             // crude algorithm to assing an ordinal ordering to every position
             // al will be sorted in DECREASING order (al[0] >= al[1])
-            ArrayList<Sequence.Position> al = new ArrayList<Sequence.Position>();
+            ArrayList<Sequence.Pos> al = new ArrayList<Sequence.Pos>();
             for(State s : all_states) {
-                for(Object po : s) {
-                    Sequence.Position p = (Sequence.Position)po;
+                for(Object po : s.positions()) {
+                    Sequence.Pos p = (Sequence.Pos)po;
                     if (al.contains(p)) continue;
                     int i=0;
                     for(; i<al.size(); i++) {
-                        if (comparePositions(p, al.get(i)) < 0)
+                        if (grammar.comparePositions(p, al.get(i)) < 0)
                             break;
                     }
                     al.add(i, p);
@@ -162,8 +266,8 @@ public abstract class Parser<Token, NodeType> {
             OUTER: while(true) {
                 for(int i=0; i<al.size(); i++)
                     for(int j=i+1; j<al.size(); j++)
-                        if (comparePositions(al.get(i), al.get(j)) > 0) {
-                            Sequence.Position p = al.remove(j);
+                        if (grammar.comparePositions(al.get(i), al.get(j)) > 0) {
+                            Sequence.Pos p = al.remove(j);
                             al.add(i, p);
                             continue OUTER;
                         }
@@ -175,7 +279,7 @@ public abstract class Parser<Token, NodeType> {
             for(int i=0; i<al.size(); i++) {
                 boolean inc = false;
                 for(int k=pk; k<i; k++) {
-                    if (comparePositions(al.get(k), al.get(i)) > 0)
+                    if (grammar.comparePositions(al.get(k), al.get(i)) > 0)
                         { inc = true; break; }
                 }
                 inc = true;
@@ -185,56 +289,81 @@ public abstract class Parser<Token, NodeType> {
                 }
                 al.get(i).ord = j;
             }
-
-            /*
-            for(int i=0; i<al.size(); i++)
-                if (isRightNullable(al.get(i)))
-                    System.out.println(al.get(i).ord + "   " + al.get(i));
-            */
-            //mastercache = this;
         }
 
-        /** a single state in the LR table and the transitions possible from it */
-        class State<Token> implements IntegerMappable, Iterable<Position> {
+        /**
+         *  A single state in the LR table and the transitions
+         *  possible from it
+         *
+         *  A state corresponds to a set of Sequence.Pos's.  Each
+         *  StateNode in the GSS has a State; the StateNode represents a set of
+         *  possible parses, one for each Pos in the State.
+         *
+         *  Every state is either "doomed" or "normal".  If a Pos
+         *  is part of a Sequence which is a conjunct (that is, it was
+         *  passed to Sequence.{and(),andnot()}), then that Pos
+         *  will appear only in doomed States.  Furthermore, any set
+         *  of Positions reachable from a doomed State also forms a
+         *  doomed State.  Note that in this latter case, a doomed
+         *  state might have exactly the same set of Positions as a
+         *  non-doomed state.
+         *
+         *  Nodes with non-doomed states represent nodes which
+         *  contribute to actual valid parses.  Nodes with doomed
+         *  States exist for no other purpose than to enable/disable
+         *  some future reduction from a non-doomed StateNode.  Because of
+         *  this, we "garbage-collect" Nodes with doomed states if
+         *  there are no more non-doomed Nodes which they could
+         *  affect (see ResultNode, Reduction, and StateNode for details).
+         *
+         *  Without this optimization, many seemingly-innocuous uses
+         *  of positive and negative conjuncts can trigger O(n^2)
+         *  space+time complexity in otherwise simple grammars.  There
+         *  is an example of this in the regression suite.
+         */
+        class State<Token> implements IntegerMappable, Serializable {
         
             public  final     int               idx    = master_state_idx++;
-            private final     HashSet<Position> hs;
-            public HashSet<State<Token>> also = new HashSet<State<Token>>();
+            private final  transient   HashSet<Pos> hs;
+            public HashSet<State<Token>> conjunctStates = new HashSet<State<Token>>();
 
-            public  transient HashMap<Sequence,State<Token>>         gotoSetNonTerminals = new HashMap<Sequence,State<Token>>();
-            private transient TopologicalBag<Token,State<Token>>     gotoSetTerminals    = new TopologicalBag<Token,State<Token>>();
+            HashMap<Pos,State<Token>>      gotoSetNonTerminals = new HashMap<Pos,State<Token>>();
+            private transient TopologicalBag<Token,State<Token>>  gotoSetTerminals    = new TopologicalBag<Token,State<Token>>();
 
-            private           TopologicalBag<Token,Position>      reductions          = new TopologicalBag<Token,Position>();
-            private           HashSet<Position>                   eofReductions       = new HashSet<Position>();
+                       TopologicalBag<Token,Pos>      reductions          = new TopologicalBag<Token,Pos>();
+                       HashSet<Pos>                   eofReductions       = new HashSet<Pos>();
             private           TopologicalBag<Token,State<Token>>  shifts              = new TopologicalBag<Token,State<Token>>();
             private           boolean                             accept              = false;
 
             private VisitableMap<Token,State<Token>> oshifts     = null;
-            private VisitableMap<Token,Position>     oreductions = null;
+            private VisitableMap<Token,Pos>     oreductions = null;
+            public  final boolean doomed;
 
             // Interface Methods //////////////////////////////////////////////////////////////////////////////
 
+            public boolean doomed() { return doomed; }
             boolean                    isAccepting()           { return accept; }
-            public Iterator<Position>  iterator()              { return hs.iterator(); }
+
+            Iterable<Pos>  positions()             { return hs; }
+
             boolean                    canShift(Token t)       { return oshifts!=null && oshifts.contains(t); }
-            void                       invokeShifts(Token t, GSS.Phase phase, Result r) { oshifts.invoke(t, phase, r); }
+            void                       invokeShifts(Token t, GSS.Phase phase, StateNode pred, Forest f) { oshifts.invoke(t, phase, pred, f); }
             boolean                    canReduce(Token t)        {
                 return oreductions != null && (t==null ? eofReductions.size()>0 : oreductions.contains(t)); }
-            void          invokeEpsilonReductions(Token t, Node node) {
-                if (t==null) for(Position r : eofReductions) node.invoke(r, null);
-                else         oreductions.invoke(t, node, null);
+            void          invokeEpsilonReductions(Token t, StateNode node) {
+                if (t==null) for(Pos r : eofReductions) node.invoke(r, null, null);
+                else         oreductions.invoke(t, node, null, null);
             }
-            void          invokeReductions(Token t, Node node, Result b) {
-                //System.err.println("\rinvokage:  " + this);
-                if (t==null) for(Position r : eofReductions) node.invoke(r, b);
-                else         oreductions.invoke(t, node, b);
+            void          invokeReductions(Token t, StateNode node, ResultNode b) {
+                if (t==null) for(Pos r : eofReductions) node.invoke(r, b, null);
+                else         oreductions.invoke(t, node, b, null);
             }
 
             // Constructor //////////////////////////////////////////////////////////////////////////////
 
             /**
-             *  create a new state consisting of all the <tt>Position</tt>s in <tt>hs</tt>
-             *  @param hs           the set of <tt>Position</tt>s comprising this <tt>State</tt>
+             *  create a new state consisting of all the <tt>Pos</tt>s in <tt>hs</tt>
+             *  @param hs           the set of <tt>Pos</tt>s comprising this <tt>State</tt>
              *  @param all the set of all elements (Atom instances need not be included)
              *  
              *   In principle these two steps could be merged, but they
@@ -253,152 +382,130 @@ public abstract class Parser<Token, NodeType> {
              *      for non-Atom Elements.
              *  </ul>
              */
-            public State(HashSet<Position> hs) { this(hs, false); }
-            public boolean doomed;
-            public State(HashSet<Position> hs, boolean doomed) {
+            public State(HashSet<Pos> hs, boolean doomed, Grammar<Token> grammar) {
                 this.hs = hs;
                 this.doomed = doomed;
 
-                // register ourselves in the all_states hash so that no
-                // two states are ever created with an identical position set
+                // register ourselves so that no two states are ever
+                // created with an identical position set (termination depends on this)
                 ((HashMap)(doomed ? doomed_states : normal_states)).put(hs, this);
                 ((HashSet)all_states).add(this);
-                
-                for(Position p : hs) {
+
+                for(Pos p : hs) {
+                    // Step 1a: take note if we are an accepting state
+                    //          (last position of the root Union's sequence)
+                    if (p.next()==null && !doomed && grammar.rootUnion.contains(p.owner()))
+                        accept = true;
+
+                    // Step 1b: If any Pos in the set is the first position of its sequence, then this
+                    //          state is responsible for spawning the "doomed" states for each of the
+                    //          Sequence's conjuncts.  This obligation is recorded by adding the to-be-spawned
+                    //          states to conjunctStates.
                     if (!p.isFirst()) continue;
-                    for(Sequence s : p.owner().needs()) {
-                        if (hs.contains(s.firstp())) continue;
-                        HashSet<Position> h2 = new HashSet<Position>();
-                        reachable(s, h2);
-                        also.add(mkstate(h2, true));
-                    }
-                    for(Sequence s : p.owner().hates()) {
-                        if (hs.contains(s.firstp())) continue;
-                        HashSet<Position> h2 = new HashSet<Position>();
-                        reachable(s, h2);
-                        also.add(mkstate(h2, true));
-                    }
+                    for(Sequence s : p.owner().needs())
+                        if (!hs.contains(s.firstp()))
+                            conjunctStates.add(mkstate(reachable(s.firstp()), true, grammar));
+                    for(Sequence s : p.owner().hates())
+                        if (!hs.contains(s.firstp()))
+                            conjunctStates.add(mkstate(reachable(s.firstp()), true, grammar));
                 }
 
-                // Step 1a: examine all Position's in this state and compute the mappings from
+                // Step 2a: examine all Pos's in this state and compute the mappings from
                 //          sets of follow tokens (tokens which could follow this position) to sets
                 //          of _new_ positions (positions after shifting).  These mappings are
                 //          collectively known as the _closure_
 
-                TopologicalBag<Token,Position> bag0 = new TopologicalBag<Token,Position>();
-                for(Position position : hs) {
+                TopologicalBag<Token,Pos> bag0 = new TopologicalBag<Token,Pos>();
+                for(Pos position : hs) {
                     if (position.isLast() || !(position.element() instanceof Atom)) continue;
                     Atom a = (Atom)position.element();
-                    HashSet<Position> hp = new HashSet<Position>();
+                    HashSet<Pos> hp = new HashSet<Pos>();
                     reachable(position.next(), hp);
                     bag0.addAll(a.getTokenTopology(), hp);
                 }
 
-                // Step 1b: for each _minimal, contiguous_ set of characters having an identical next-position
+                // Step 2b: for each _minimal, contiguous_ set of characters having an identical next-position
                 //          set, add that character set to the goto table (with the State corresponding to the
                 //          computed next-position set).
 
                 for(Topology<Token> r : bag0) {
-                    HashSet<Position> h = new HashSet<Position>();
-                    for(Position p : bag0.getAll(r)) h.add(p);
-                    ((TopologicalBag)gotoSetTerminals).put(r, mkstate(h, doomed));
+                    HashSet<Pos> h = new HashSet<Pos>();
+                    for(Pos p : bag0.getAll(r)) h.add(p);
+                    ((TopologicalBag)gotoSetTerminals).put(r, mkstate(h, doomed, grammar));
                 }
 
-                // Step 2: for every Sequence, compute the closure over every position in this set which
+                // Step 3: for every Sequence, compute the closure over every position in this set which
                 //         is followed by a symbol which could yield the Sequence.
                 //
                 //         "yields" [in one or more step] is used instead of "produces" [in exactly one step]
                 //         to avoid having to iteratively construct our set of States as shown in most
                 //         expositions of the algorithm (ie "keep doing XYZ until things stop changing").
 
-                HashMapBag<Sequence,Position> move = new HashMapBag<Sequence,Position>();
-                for(Position p : hs)
+                HashMapBag<Sequence,Pos> move = new HashMapBag<Sequence,Pos>();
+                for(Pos p : hs)
                     if (!p.isLast() && p.element() instanceof Union)
                         for(Sequence s : ((Union)p.element())) {
-                            HashSet<Position> hp = new HashSet<Position>();
+                            HashSet<Pos> hp = new HashSet<Pos>();
                             reachable(p.next(), hp);
                             move.addAll(s, hp);
                         }
                 OUTER: for(Sequence y : move) {
                     // if a reduction is "lame", it should wind up in the dead_state after reducing
-                    HashSet<Position> h = move.getAll(y);
-                    State<Token> s = mkstate(h, doomed);
-                    for(Position p : hs)
+                    HashSet<Pos> h = move.getAll(y);
+                    State<Token> s = mkstate(h, doomed, grammar);
+                    for(Pos p : hs)
                         if (p.element() != null && (p.element() instanceof Union))
                             for(Sequence seq : ((Union)p.element()))
                                 if (seq.needs.contains(y) || seq.hates.contains(y)) {
                                     // FIXME: assumption that no sequence is ever both usefully (non-lamely) matched
                                     //        and also directly lamely matched
-                                    ((HashMap)gotoSetNonTerminals).put(y, dead_state);
+                                    for(Pos pp = y.firstp(); pp != null; pp = pp.next())
+                                        ((HashMap)gotoSetNonTerminals).put(pp, dead_state);
                                     continue OUTER;
                                 }
-                    gotoSetNonTerminals.put(y, s);
+                    for(Pos pp = y.firstp(); pp != null; pp = pp.next())
+                        gotoSetNonTerminals.put(pp, s);
                 }
             }
 
-            private State<Token> mkstate(HashSet<Position> h, boolean b) {
-                if (b) return doomed_states.get(h) == null ? (State)new State<Token>(h,b) : (State)doomed_states.get(h);
-                else   return normal_states.get(h) == null ? (State)new State<Token>(h,b) : (State)normal_states.get(h);
-            }
-
-            public String toStringx() {
-                StringBuffer st = new StringBuffer();
-                for(Position p : this) {
-                    if (st.length() > 0) st.append("\n");
-                    st.append(p);
-                }
-                return st.toString();
+            private State<Token> mkstate(HashSet<Pos> h, boolean b, Grammar<Token> grammar) {
+                State ret = (b?doomed_states:normal_states).get(h);
+                if (ret==null) ret = new State<Token>(h,b, grammar);
+                return ret;
             }
 
+            public int toInt() { return idx; }
             public String toString() {
                 StringBuffer ret = new StringBuffer();
-                ret.append("state["+idx+"]: ");
-                for(Position p : this) ret.append("{"+p+"}  ");
+                for(Pos p : hs)
+                    ret.append(p+"\n");
                 return ret.toString();
             }
-
-            public int toInt() { return idx; }
         }
 
-        public String toString() {
-            StringBuffer sb = new StringBuffer();
-            sb.append("parse table");
-            for(State<Token> state : all_states) {
-                sb.append("  " + state + "\n");
-                for(Topology<Token> t : state.shifts) {
-                    sb.append("      shift  \""+
-                              new edu.berkeley.sbp.chr.CharTopology((IntegerTopology<Character>)t)+"\" => ");
-                    for(State st : state.shifts.getAll(t))
-                        sb.append(st.idx+"  ");
-                    sb.append("\n");
-                }
-                for(Topology<Token> t : state.reductions)
-                    sb.append("      reduce \""+
-                              new edu.berkeley.sbp.chr.CharTopology((IntegerTopology<Character>)t)+"\" => " +
-                              state.reductions.getAll(t) + "\n");
-                for(Sequence s : state.gotoSetNonTerminals.keySet())
-                    sb.append("      goto   "+state.gotoSetNonTerminals.get(s)+" from " + s + "\n");
-            }
-            return sb.toString();
-        }
     }
 
     // Helpers //////////////////////////////////////////////////////////////////////////////
     
-    private static void reachable(Sequence s, HashSet<Position> h) {
-        reachable(s.firstp(), h);
-        //for(Sequence ss : s.needs()) reachable(ss, h);
-        //for(Sequence ss : s.hates()) reachable(ss, h);
+    private static HashSet<Pos> reachable(Element e) {
+        HashSet<Pos> h = new HashSet<Pos>();
+        reachable(e, h);
+        return h;
     }
-    private static void reachable(Element e, HashSet<Position> h) {
+    private static void reachable(Element e, HashSet<Pos> h) {
         if (e instanceof Atom) return;
         for(Sequence s : ((Union)e))
-            reachable(s, h);
+            reachable(s.firstp(), h);
     }
-    private static void reachable(Position p, HashSet<Position> h) {
+    private static void reachable(Pos p, HashSet<Pos> h) {
         if (h.contains(p)) return;
         h.add(p);
         if (p.element() != null) reachable(p.element(), h);
     }
-    //public static Cache mastercache = null;
+    private static HashSet<Pos> reachable(Pos p) {
+        HashSet<Pos> ret = new HashSet<Pos>();
+        reachable(p, ret);
+        return ret;
+    }
+
 }