!752

static final class Prolog {
  boolean upperCaseVariables = false; // true for SNL, false for NL
  long varCount;
  boolean showStuff;
  new L<Entry> stack;
  Trail sofar = null;
  new L<Clause> program;
  new L<L<Clause>> programByArity;
  long steps;
  new L<Native> natives;
  L<S> log;
  int maxLogSize = 1000; // lines
  int maxLevel = 10000; // max stack size
  int timeLimit = 20; // 20 seconds
  long startTime;
  
  // stats
  int maxLevelSeen; // maximum stack level reached during computation
  long topUnifications, exceptions;

  static interface Native {
    public boolean yo(Prolog p, Lisp term);
  }
  
  static class Var extends Lisp {
    long id;
    Lisp instance;
    
    *(S name) {
      super(name);
      instance = this;
    }
    
    *(long id) {
      super("___");
      this.id = id;
      instance = this;
    }
    
    void reset() { instance = this; }
    
    public String toString() {
      if (instance != this)
        ret instance.toString();
      ret isUserVar() ? getName() : "_" + id;
    }
    
    boolean isUserVar() {
      ret id == 0;
    }
    
    S getName() {
      ret head;
    }
    
    Lisp getValue() {
      Lisp l = instance;
      while (l instanceof Var) {
        Var v = cast l;
        if (v.instance == v)
          ret v;
        l = v.instance;
      }
      ret l;
    }
  }
  
  class Clause {
    Lisp head;
    
    // Either body or nat will be set (or none)
    Native nat;
    Goal body;
    
    *(Lisp *head, Native *nat) {}
    *(Lisp *head, Goal *body) {}
    *(Lisp *head, Goal *body, Native *nat) {}
    *(Lisp *head) {}
    
    Clause copy() {
      ret new Clause(Prolog.this.copy(head), body == null ? null : body.copy(), nat);
    }
    
    public String toString() {
      //ret head + " :- " + (body == null ? "true" : body);
      ret nat != null ? head + " :- native" :
        (body == null ? head.toString() : head + " :- " + body);
    }
  }
  
  class Trail {
    Var tcar;
    Trail tcdr;
    
    *(Var *tcar, Trail *tcdr) {}
  }
  
  Trail Trail_Note() { return sofar; }
  void Trail_Push(Var x) { sofar = new Trail(x, sofar); }
  void Trail_Undo(Trail whereto) {
    for (; sofar != whereto; sofar = sofar.tcdr)
      sofar.tcar.reset();
  }
  
  static class TermVarMapping {
    new L<Var> vars;
    
    *(L<Var> *vars) {}
    *(Var... vars) { this.vars.addAll(asList(vars)); }
    
    void showanswer() {
      print("TRUE.");
      for (Var v : vars)
        print("  " + v.getName() + " = " + v);
    }
  }
      
  class Goal {
    Lisp car;
    Goal cdr;
    
    *(Lisp *car, Goal *cdr) {}
    *(Lisp *car) {}
    
    public String toString() {
      ret cdr == null ? car.toString() : car + "; " + cdr;
    }
    
    Goal copy() {
      return new Goal(Prolog.this.copy(car),
        cdr == null ? null : cdr.copy());
    }
    
    Goal append(Goal l) {
      return new Goal(car, cdr == null ? l : cdr.append(l));
    }
    
  } // class Goal
  
  boolean unifyOrRollback(Lisp a, Lisp b) {
    Trail t = Trail_Note();
    if (unify(a, b)) ret true;
    Trail_Undo(t);
    ret false;
  }
  
  boolean unify(Lisp thiz, Lisp t) {
    if (thiz == null) fail("thiz=null");
    if (t == null) fail("t=null");
    
    if (thiz instanceof Var) { // TermVar::unify
      Var v = cast thiz;
      if (v.instance != v)
        return unify(v.instance, t);
      Trail_Push(v);
      v.instance = t;
      return true;
    }
    
    // TermCons::unify
    return unify2(t, thiz);
  }
  
  boolean unify2(Lisp thiz, Lisp t) { 
    if (thiz instanceof Var)
      return unify(thiz, t);
   
    int arity = thiz.size();
    if (neq(thiz.head, t.head) || arity != t.size())
      return false;
    for (int i = 0; i < arity; i++)
      if (!unify(thiz.get(i), t.get(i)))
        return false;
    return true;
  }
  
  Lisp copy(Lisp thiz) {
    if (thiz instanceof Var) {
      Var v = cast thiz;
      if (v.instance == v) {
        Trail_Push(v);
        v.instance = newVar();
      }
      return v.instance;
    }
    
    // copy2 (copy non-var)
    Lisp l = new Lisp(thiz.head);
    for (Lisp arg : thiz)
      l.add(copy(arg));
    ret l;
  }
  
  Var newVar() {
    ret new Var(++varCount);
  }
  
  Var newVar(S name) {
    ret new Var(name);
  }
  
  Clause clause(Lisp head, Goal body) {
    ret prologify(new Clause(head, body));
  }
  
  Clause clause(Lisp rule) {
    L<Lisp> ops = snlSplitOps(rule);
    /*if (showStuff)
      log("clause(Lisp): " + rule + " => " + structure(ops)); */
      
    if (!empty(ops) && last(ops).is("say *"))
      ops.set(l(ops)-1, lisp("then *", lisp("[]", "say", last(ops).get(0))));

    if (!empty(ops) && last(ops).is("then *")) {
      Lisp head = last(ops).get(0);
      Goal goal = null;
      
      // TODO: check the actual words (if/and/...)
      for (int i = l(ops)-2; i >= 0; i--)
        goal = new Goal(ops.get(i).get(0), goal);
        
      ret clause(head, goal);
    } else
      ret clause(rule, (Lisp) null);
  }
  
  Clause clause(Lisp head, Lisp body) {
    ret clause(head, body == null ? null : new Goal(body));
  }
  
  Lisp prologify(Lisp term) {
    ret prologify(term, new HashMap);
  }
  
  Clause prologify(Clause c) {
    new HashMap vars;
    c = new Clause(
      prologify(c.head, vars),
      prologify(c.body, vars),
      c.nat);
    /*if (showStuff)
      log("Clause made: " + structure_seen(c));*/
    ret c;
  }
  
  Goal prologify(Goal goal, Map<S, Var> vars) {
    if (goal == null) ret null;
    ret new Goal(
      prologify(goal.car, vars),
      prologify(goal.cdr, vars));
  }
  
  boolean isVar(Lisp term) {
    ret upperCaseVariables ? snlIsVar(term) : nlIsVar(term);
  }
  
  Lisp prologify(Lisp term, Map<S, Var> vars) {
    if (term == null) ret null;
    if (isVar(term)) {
      Var v = vars.get(term.head);
      if (v == null)
        vars.put(term.head, v = newVar(term.head));
      ret v;
    } else {
      Lisp l = new Lisp(term.head);
      for (Lisp arg : term)
        l.add(prologify(arg, vars));
      ret l;
    }
  }
  
  L<Var> findVars(Goal g) {
    new IdentityHashMap<Var, Boolean> map;
    while (g != null) {
      findVars(g.car, map);
      g = g.cdr;
    }
    ret asList(map.keySet());
  }
  
  L<Var> findVars(Lisp term) {
    new IdentityHashMap<Var, Boolean> map;
    findVars(term, map);
    ret asList(map.keySet());
  }
  
  void findVars(Lisp term, IdentityHashMap<Var, Boolean> map) {
    if (term instanceof Var)
      map.put((Var) term, Boolean.TRUE);
    else
      for (Lisp arg : term)
        findVars(arg, map);
  }
  
  static Map<S, Var> makeVarMap(L<Var> vars) {
    new HashMap<S, Var> map;
    for (Var v : vars)
      map.put(v.getName(), v);
    ret map;
  }
  
  new L<Clause> emptyProgram;
  
  // Executor stack entry
  class Entry {
    Goal goal;
    L<Clause> program; // full program or filtered by arity
    int programIdx = -1; // -1 is natives
    Trail trail;
    boolean trailSet;

    *(Goal *goal) {
      Lisp car = resolve1(goal.car);
      if (car instanceof Var) {
        if (showStuff)
          log("Weird: Goal is variable: " + car);
        program = Prolog.this.program;
      } else {
        int arity = car.size();
        if (showStuff)
          log("Goal arity " + arity + ": " + car);
        program = arity >= l(programByArity) ? emptyProgram : programByArity.get(arity);
      }
    }
  }
  
  void start(Lisp goal) {
    start(new Goal(prologify(goal)));
  }
  
  // warning: doesn't prologify the goal
  void start(Goal goal) {
    if (showStuff)
      log("Starting on goal: " + structure_seen(goal));
    steps = 0;
    stack = new L;
    Trail_Undo(null);
    stackAdd(new Entry(goal));
    startTime = now();
  }
  
  void log(S s) {
    if (log != null) {
      if (l(log) == maxLogSize)
        log.add("[Log overflow]");
      else if (l(log) < maxLogSize)
        log.add(s);
    } else if (showStuff)
      print("prolog: " + s);
  }
    
  int level() {
    ret l(stack)-1;
  }
  
  boolean done() {
    boolean result = empty(stack);
    if (showStuff && result)
      log("Done with goal!");
    ret result;
  }

  boolean gnext(Goal g) {  
    Goal gdash = g.cdr;
    if (gdash == null) {
      if (showStuff)
        log("gnext true");
      ret true;
    } else {
      stackAdd(new Entry(gdash));
      ret false;
    }
  }
  
  void stackPop() {
    Entry e = popLast(stack);
    if (e.trailSet)
      Trail_Undo(e.trail);
  }
  
  void backToCutPoint(int n) {
    if (showStuff)
      log("back to cut point " + n);
    while (l(stack) >= n) {
      if (showStuff)
        log("cut: dropping " + structure(last(stack).goal));
      stackPop();
    }
  }

  boolean step() {
    if (done()) fail("done!"); // safety
    if (now() >= startTime+timeLimit*1000)
      fail("time limit reached: " + timeLimit + " s");
    
    ++steps;
    Entry e = last(stack);
    
    if (e.trailSet) {
      Trail_Undo(e.trail);
      e.trailSet = false;
    }
    
    e.trail = Trail_Note();
    e.trailSet = true;
    
    // cut operator - suceeds first time
    if (e.goal.car.is("!", 1)) {
      if (showStuff)
        log("cut " + e.programIdx + ". " + structure(e.goal));
      if (e.programIdx == -1) {
        ++e.programIdx;
        ret gnext(e.goal);
      } else if (e.programIdx == 0) {
        ++e.programIdx;
        // fails 2nd time and cuts
        //e.goal.car.head = "false"; // super-hack :D
        backToCutPoint(parseInt(e.goal.car.get(0).raw()));
        ret false;
      } else {
        stackPop();
        ret false;
      }
    }

    if (e.programIdx >= l(e.program)) { // program loop ends
      removeLast(stack);
      ret false;
    }
      
    if (e.programIdx == -1) {
      ++e.programIdx;
        
      // try native functions
      if (goNative(e.goal.car)) {
        if (showStuff)
          log(indent(level()) + "native!");
          
        ret gnext(e.goal);
      }
      
      ret false;
    }
      
    // now in program loop
    
    Clause c = e.program.get(e.programIdx).copy();
    ++e.programIdx;
    Trail_Undo(e.trail);
    S text = null;
    if (showStuff)
      text = "  Goal: " + e.goal + ". Got clause: " + c;
    ++topUnifications;
    if (unify(e.goal.car, c.head)) {
      if (showStuff) {
        log(indent(level()) + text);
        log(indent(level()) + "  Clause unifies to: " + c);
      }
      Goal gdash;
      if (c.nat != null) {
        if (showStuff)
          log(indent(level()) + " Clause is native.");
        if (!c.nat.yo(this, c.head)) {
          if (showStuff)
            log(indent(level()) + "Native clause fails");
          ret false;
        }
        gdash = e.goal.cdr;
      } else
        gdash = c.body == null ? e.goal.cdr : resolveCut(c.body).append(e.goal.cdr);
      if (showStuff)
        log(indent(level()) + "  gdash: " + gdash);
        
      if (gdash == null) {
        if (showStuff)
          log("SUCCESS!");
        ret true;
      } else {
        Entry e2 = new Entry(gdash);
        if (showStuff)
          log(indent(level()) + "New goal: " + gdash);
        stackAdd(e2);
        ret false;
      }
    } /*else
      if (showStuff)
        log(indent(level()) + "No match for clause.");*/
        
    ret false;
  }
  
  // resolve cut in clause body
  Goal resolveCut(Goal g) {
    if (g.car.is("!", 0))
      ret fixCut(g);
    if (g.cdr == null)
      ret g;
    ret new Goal(g.car, resolveCut(g.cdr));
  }
  
  // note stack length in cut
  Goal fixCut(Goal g) {
    ret new Goal(lisp("!", lstr(stack)), g.cdr); // max. one cut per clause
  }
  
  void stackAdd(Entry e) {
    stack.add(e);
    int n = l(stack);
    if (n > maxLevel) fail("Maximum stack level reached: " + n);
    if (n > maxLevelSeen) maxLevelSeen = n;
  }
  
  void addClause(S text) {
    addClause(nlParse(text));
  }
  
  void addClause(Lisp c) {
    addClause(clause(c));
  }
  
  void addClause(Clause c) {
    program.add(c);
    int arity = c.head.size();
    while (arity >= l(programByArity))
      programByArity.add(new L);
    programByArity.get(arity).add(c);
  }
  
  boolean canSolve(Lisp goal) {
    ret canSolve(new Goal(prologify(goal)));
  }
  
  boolean canSolve(Goal goal) {
    start(goal);
    while (!done())
      if (step())
        ret true;
    ret false;
  }
  
  // return variable map or null if unsolved
  Map<S, Lisp> solve(Lisp goal) {
    start(new Goal(prologify(goal)));
    ret nextSolution();
  }
  
  Map<S, Lisp> solve(S text) {
    ret solve(nlParse(text));
  }
  
  Map<S, Lisp> getUserVarMap() {
    Goal g = stack.get(0).goal;
    new HashMap<S, Lisp> map;
    for (Var v : findVars(g))
      if (v.isUserVar())
        map.put(v.getName(), resolve(v));
    ret map;
  }
  
  Map<S, Lisp> nextSolution() {
    if (showStuff)
      log("nextSolution");
    int n = 0;
    while (!done()) {
      ++n;
      if (step()) {
        if (showStuff)
          log("  solution found in step " + n);
        ret getUserVarMap();
      }
    }
    if (showStuff)
      log("No solution");
    ret null;
  }
  
  void addTheory(S text) {
    Lisp tree = nlParse(text);
    if (nlIsMultipleStatements(text))
      for (Lisp part : tree)
        addClause(part);
    else
      addClause(tree);
  }
  
  // shouldn't use anymore
  void addClauses(Lisp tree) {
    if (isJuxta(tree) && snlSplitOps(tree) == null)
      for (Lisp part : tree)
        addClause(part);
    else
      addClause(tree);
  }
  
  boolean goNative(Lisp term) {
    term = resolve(term);
    
    for (Native n : natives) {
      Trail t = Trail_Note();
      boolean result;
      try {
        result = n.yo(this, term);
      } catch (Exception e) {
        Trail_Undo(t);
        continue;
      }
      if (!result) {
        Trail_Undo(t);
        continue;
      }
      ret true;
    }

    if (term.is("nativeTest", 0))
      ret true;
      
    if (term.is("isQuoted", 1)) {
      Lisp x = term.get(0);
      ret !(x instanceof Var) && x.isLeaf() && isQuoted(x.head);
    }
      
    ret false;
  }
  
  // Resolve top-level only
  Lisp resolve1(Lisp term) {
    if (term instanceof Var)
      ret ((Var) term).getValue();
    ret term;
  }
  
  // resolve all variables
  Lisp resolve(Lisp term) {
    term = resolve1(term);
      
    // smart recurse
    for (int i = 0; i < term.size(); i++) {
      Lisp l = term.get(i);
      Lisp r = resolve(l);
      if (l != r) {
        Lisp x = new Lisp(term.head);
        for (int j = 0; j < i; j++)
          x.add(term.get(j));
        x.add(r);
        for (i++; i < term.size(); i++)
          x.add(resolve(term.get(i)));
        ret x;
      }
    }
    
    ret term;
  }
  
  // looks for a bodyless rule in the program that matches the term
  boolean containsStatement(Lisp term) {
    for (Clause c : program)
      if (c.body == null && c.nat == null && eq(c.head, term))
        ret true;
    ret false;
  }
  
  // closed == contains no variables
  boolean isClosedTerm(Lisp term) {
    if (term instanceof Var)
      ret false;
    else
      for (Lisp arg : term)
        if (!isClosedTerm(arg))
          ret false;
    ret true;
  }
  
  void addNative(Native n) {
    if (n instanceof BaseNative)
      addNative(((BaseNative) n).pat, n);
    else
      natives.add(n);
  }
  
  void addNatives(Native... l) {
    for (Native n : l)
      addNative(n);
  }
    
  void addNatives(L<Native> l) {
    for (Native n : l)
      addNative(n);
  }
  
  void addNative(S text, Native n) {
    addClause(prologify(new Clause(nlParse(text), n)));
  }
  
  L<Lisp> getStackTerms() {
    new L<Lisp> l;
    for (Entry e : stack)
      l.add(e.goal.car);
    ret l;
  }
  
  void logOn() {
    log = new L;
    showStuff = true;
  }

  static abstract class BaseNative implements Native {
    S pat;
    Prolog p;
    Map<S, Lisp> m;
    
    *(S *pat) {}
    
    abstract boolean yo();
    
    public boolean yo(Prolog p, Lisp term) {
      m = new HashMap;
      this.p = p;
      try {
        ret nlMatch(pat, p.resolve(term), m) && yo();
      } catch (Exception e) {
        ++p.exceptions;
        if (p.showStuff)
          p.log("Exception in native: " + e);
        ret false;
      } finally {
        this.p = null;
      }
    }
    
    boolean unify(S var, Lisp term) {
      Lisp v = m.get(var);
      if (v == null)
        fail("Variable " + var + " not found");
      ret p.unify(v, term);
    }
  } // BaseNative
  
  // Prolog constructor
  *() {
    addClause(lisp("true"));
  }
} // class Prolog