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discrim.c

#include "discrim.h"

/* Private definitions and types */

typedef struct flat * Flat;

struct discrim {       /* node in a discrimination tree */
  Discrim   next;      /* sibling */
  union {
    Discrim kids;      /* for internal nodes */
    Plist data;      /* for leaves */
  } u;
  short symbol;  /* variable number or symbol number */
  char type;           /* term type and for ac indexing type */
};

struct flat {  /* for building a stack of states for backtracking */
  Term    t;
  Flat    prev, next, last;
  Discrim alternatives;
  int     bound;           /* (tame) */
  int     varnum;          /* (tame) */
  int     place_holder;
  int     num_ac_args;     /* for AC symbols (wild) */
  int     num_ac_nv_args;  /* for AC symbols (wild) */
  int     commutative;     /* for commutative symbols (wild) */
  int     flip;            /* for commutative symbols (wild) */
};

struct discrim_pos {   /* to save position in set of answers */
  Context  subst;      /* substitution */
  Plist  data;       /* identical terms from leaf of discrim tree */
  Flat     f;          /* stack of states for backtracking */
};

#define GO        1
#define BACKTRACK 2
#define SUCCESS   3
#define FAILURE   4

/* type of discrimination tree node */

#define DVARIABLE       1
#define DRIGID          2
#define AC_ARG_TYPE     3
#define AC_NV_ARG_TYPE  4

#define DVAR(d)  (d->type == DVARIABLE)
 
/*
 * memory management
 */

static unsigned Discrim_gets, Discrim_frees;
static unsigned Flat_gets, Flat_frees;
static unsigned Discrim_pos_gets, Discrim_pos_frees;

#define BYTES_DISCRIM sizeof(struct discrim)
#define PTRS_DISCRIM BYTES_DISCRIM%BPP == 0 ? BYTES_DISCRIM/BPP : BYTES_DISCRIM/BPP + 1

#define BYTES_FLAT sizeof(struct flat)
#define PTRS_FLAT BYTES_FLAT%BPP == 0 ? BYTES_FLAT/BPP : BYTES_FLAT/BPP + 1

#define BYTES_DISCRIM_POS sizeof(struct discrim_pos)
#define PTRS_DISCRIM_POS BYTES_DISCRIM_POS%BPP == 0 ? BYTES_DISCRIM_POS/BPP : BYTES_DISCRIM_POS/BPP + 1

/*************
 *
 *   Discrim get_discrim()
 *
 *************/

static
Discrim get_discrim(void)
{
  Discrim p = get_mem(PTRS_DISCRIM);
  Discrim_gets++;
  return(p);
}  /* get_discrim */

/*************
 *
 *    free_discrim()
 *
 *************/

static
void free_discrim(Discrim p)
{
  free_mem(p, PTRS_DISCRIM);
  Discrim_frees++;
}  /* free_discrim */

/*************
 *
 *   Flat get_flat()
 *
 *************/

static
Flat get_flat(void)
{
  Flat p = get_mem(PTRS_FLAT);
  Flat_gets++;
  return(p);
}  /* get_flat */

/*************
 *
 *    free_flat()
 *
 *************/

static
void free_flat(Flat p)
{
  free_mem(p, PTRS_FLAT);
  Flat_frees++;
}  /* free_flat */

/*************
 *
 *   Discrim_pos get_discrim_pos()
 *
 *************/

static
Discrim_pos get_discrim_pos(void)
{
  Discrim_pos p = get_mem(PTRS_DISCRIM_POS);
  Discrim_pos_gets++;
  return(p);
}  /* get_discrim_pos */

/*************
 *
 *    free_discrim_pos()
 *
 *************/

static
void free_discrim_pos(Discrim_pos p)
{
  free_mem(p, PTRS_DISCRIM_POS);
  Discrim_pos_frees++;
}  /* free_discrim_pos */

/*************
 *
 *   fprint_discrim_mem()
 *
 *************/

/* DOCUMENTATION
This routine prints (to FILE *fp) memory usage statistics for data types
associated with the discrim package.
The Boolean argument heading tells whether to print a heading on the table.
*/

/* PUBLIC */
void fprint_discrim_mem(FILE *fp, BOOL heading)
{
  int n;
  if (heading)
    fprintf(fp, "  type (bytes each)        gets      frees     in use      bytes\n");

  n = BYTES_DISCRIM;
  fprintf(fp, "discrim (%4d)      %11u%11u%11u%9.1f K\n",
          n, Discrim_gets, Discrim_frees,
          Discrim_gets - Discrim_frees,
          ((Discrim_gets - Discrim_frees) * n) / 1024.);

  n = BYTES_FLAT;
  fprintf(fp, "flat (%4d)         %11u%11u%11u%9.1f K\n",
          n, Flat_gets, Flat_frees,
          Flat_gets - Flat_frees,
          ((Flat_gets - Flat_frees) * n) / 1024.);

  n = BYTES_DISCRIM_POS;
  fprintf(fp, "discrim_pos (%4d)  %11u%11u%11u%9.1f K\n",
          n, Discrim_pos_gets, Discrim_pos_frees,
          Discrim_pos_gets - Discrim_pos_frees,
          ((Discrim_pos_gets - Discrim_pos_frees) * n) / 1024.);

}  /* fprint_discrim_mem */

/*************
 *
 *   p_discrim_mem()
 *
 *************/

/* DOCUMENTATION
This routine prints (to stdout) memory usage statistics for data types
associated with the discrim package.
*/

/* PUBLIC */
void p_discrim_mem()
{
  fprint_discrim_mem(stdout, TRUE);
}  /* p_discrim_mem */

/*
 *  end of memory management
 */
/*************
 *
 *   discrim_init()
 *
 *************/

/* DOCUMENTATION
This routine allocates and returns an empty discrimination index.
It can be used for either wild or tame indexing.
*/

/* PUBLIC */
Discrim discrim_init(void)
{
  return get_discrim();
}  /* discrim_init */

/*************
 *
 *   discrim_dealloc(d)
 *
 *************/

/* DOCUMENTATION
This routine frees an empty discrimination index (wild or tame).
*/

/* PUBLIC */
void discrim_dealloc(Discrim d)
{
  if (d->u.kids) {
    fatal_error("discrim_dealloc, nonempty index.");
  }
  else
    free_discrim(d);
}  /* discrim_dealloc */

/*************
 *
 *     print_discrim_tree(fp, d, n, depth)
 *
 *************/

static
void print_discrim_tree(FILE *fp, Discrim d, int n, int depth)
{
  int arity, i;

  for (i = 0; i < depth; i++)
    printf(" -");

  if (depth == 0)
    fprintf(fp, "\nroot");
  else if (DVAR(d))
    fprintf(fp, "v%d", d->symbol);
  else
    fprintf(fp, "%s", sn_to_str(d->symbol));

  fprintf(fp, "(%x)", (unsigned) d);
  if (n == 0) {
    Plist p;
    for (i = 0, p = d->u.data; p; i++, p = p->next);
    fprintf(fp, ": leaf has %d objects.\n", i);
  }
  else {
    Discrim d1;
    fprintf(fp, "\n");
    for (d1 = d->u.kids; d1 != NULL; d1 = d1->next) {
      if (DVAR(d1))
      arity = 0;
      else
      arity = sn_to_arity(d1->symbol);
      print_discrim_tree(fp, d1, n+arity-1, depth+1);
    }
  }
}  /* print_discrim_tree */

/*************
 *
 *   fprint_discrim_tame_index()
 *
 *************/

/* DOCUMENTATION
This routine prints (to FILE *fp) a tame discrimination index.
*/

/* PUBLIC */
void fprint_discrim_tame_index(FILE *fp, Discrim d)
{
  print_discrim_tree(fp, d, 1, 0);
}  /* print_discrim_tame_index */

/*************
 *
 *   p_discrim_tame_index()
 *
 *************/

/* DOCUMENTATION
This routine prints (to stdout) a tame discrimination index.
*/

/* PUBLIC */
void p_discrim_tame_index(Discrim d)
{
    fprint_discrim_tame_index(stdout, d);
}  /* p_discrim_tame_index */

/*************
 *
 *   Discrim discrim_tame_insert_rec(t, d)
 *
 *   Return node of d corresp. to end of term t.  If it does
 *   not exist, add nodes to t so that it does exist.
 *
 *************/

static
Discrim discrim_tame_insert_rec(Term t, Discrim d)
{
  Discrim d1, d2, prev;
  int symbol, i;

  if (VARIABLE(t)) {
    d1 = d->u.kids;
    prev = NULL;
    symbol = VARNUM(t);
    while (d1 && DVAR(d1) && d1->symbol < symbol) {
      prev = d1;
      d1 = d1->next;
    }
    if (d1 == NULL || !DVAR(d1) || d1->symbol != symbol) {
      d2 = get_discrim();
      d2->type = DVARIABLE;
      d2->symbol = VARNUM(t);
      d2->next = d1;
      if (prev == NULL)
      d->u.kids = d2;
      else
      prev->next = d2;
      return d2;
    }
    else  /* found node */
      return d1;
  }

  else {  /* constant || complex */
    d1 = d->u.kids;
    prev = NULL;
    /* arities fixed: handle both NAME and COMPLEX */
    symbol = SYMNUM(t);
    while (d1 && DVAR(d1)) {  /* skip variables */
      prev = d1;
      d1 = d1->next;
    }
    while (d1 && d1->symbol < symbol) {
      prev = d1;
      d1 = d1->next;
    }
    if (d1 == NULL || d1->symbol != symbol) {
      d2 = get_discrim();
      d2->type = DRIGID;
      d2->symbol = symbol;
      d2->next = d1;
      d1 = d2;
    }
    else
      d2 = NULL;  /* new node not required at this level */

    for (i = 0; i < t->arity; i++)
      d1 = discrim_tame_insert_rec(t->args[i], d1);

    if (d2 != NULL) {  /* link in new subtree (possibly a leaf) */
      if (prev == NULL)
      d->u.kids = d2;
      else
      prev->next = d2;
    }
          
    return d1;  /* d1 is leaf corresp. to end of input term */
  }
}  /* discrim_tame_insert_rec */

/*************
 *
 *    discrim_tame_insert(t, root, object)
 *
 *************/

static
void discrim_tame_insert(Term t, Discrim root, void *object)
{
  Discrim d;
  Plist gp1, gp2;

  d = discrim_tame_insert_rec(t, root);
  gp1 = get_plist();
  gp1->v = object;

  /* Install at end of list. */
  if (d->u.data == NULL)
    d->u.data = gp1;
  else {
    for (gp2 = d->u.data; gp2->next != NULL; gp2 = gp2->next);
    gp2->next = gp1;
  }
}  /* discrim_tame_insert */

/*************
 *
 *    Discrim discrim_end(t, d, path_p)
 *
 *    Given a discrimination tree (or a subtree) and a term, return the 
 *    node in the tree that corresponds to the last symbol in t (or NULL
 *    if the node doesn't exist).  *path_p is a list that is extended by
 *    this routine.  It is a list of pointers to the
 *    nodes in path from the parent of the returned node up to imd. 
 *    (It is useful for deletions, because nodes do not have pointers to
 *    parents.) 
 *
 *************/

static
Discrim discrim_end(Term t, Discrim d, Plist *path_p)
{
  Discrim d1;
  Plist dp;
  int symbol, sym;

    /* add current node to the front of the path list. */

  dp = get_plist();
  dp->v = d;
  dp->next = *path_p;
  *path_p = dp;

  if (VARIABLE(t)) {
    d1 = d->u.kids;
    symbol = VARNUM(t);
    while (d1 && DVAR(d1) && d1->symbol < symbol) 
      d1 = d1->next;

    if (d1 == NULL || !DVAR(d1) || d1->symbol != symbol)
      return NULL;
    else   /* found node */
      return d1;
  }

  else {  /* constant || complex */
    d1 = d->u.kids;
    sym = SYMNUM(t);  /* arities fixed: handle both NAME and COMPLEX */
    while (d1 && DVAR(d1))  /* skip variables */
      d1 = d1->next;
    while (d1 && d1->symbol < sym)
      d1 = d1->next;

    if (d1 == NULL || d1->symbol != sym)
      return NULL;
    else {
      int i;
      for (i = 0; d1 && i < t->arity; i++)
      d1 = discrim_end(t->args[i], d1, path_p);
      return d1;
    }
  }
}  /* discrim_end */

/*************
 *
 *    discrim_tame_delete(t, root, object)
 *
 *************/

static
void discrim_tame_delete(Term t, Discrim root, void *object)
{
  Discrim end, d2, d3, parent;
  Plist tp1, tp2;
  Plist dp1, path;

    /* First find the correct leaf.  path is used to help with  */
    /* freeing nodes, because nodes don't have parent pointers. */

  path = NULL;
  end = discrim_end(t, root, &path);
  if (end == NULL) {
    fatal_error("discrim_tame_delete, cannot find end.");
  }

    /* Free the pointer in the leaf-list */

  tp1 = end->u.data;
  tp2 = NULL;
  while(tp1 && tp1->v != object) {
    tp2 = tp1;
    tp1 = tp1->next;
  }
  if (tp1 == NULL) {
    fatal_error("discrim_tame_delete, cannot find term.");
  }

  if (tp2 == NULL)
    end->u.data = tp1->next;
  else
    tp2->next = tp1->next;
  free_plist(tp1);

  if (end->u.data == NULL) {
    /* free tree nodes from bottom up, using path to get parents */
    end->u.kids = NULL;  /* probably not necessary */
    dp1 = path;
    while (end->u.kids == NULL && end != root) {
      parent = (Discrim) dp1->v;
      dp1 = dp1->next;
      d2 = parent->u.kids;
      d3 = NULL;
      while (d2 != end) {
      d3 = d2;
      d2 = d2->next;
      }
      if (d3 == NULL)
      parent->u.kids = d2->next;
      else
      d3->next = d2->next;
      free_discrim(d2);
      end = parent;
    }
  }

  /* free path list */

  while (path) {
    dp1 = path;
    path = path->next;
    free_plist(dp1);
  }

}  /* discrim_tame_delete */

/*************
 *
 *   discrim_tame_update()
 *
 *************/

/* DOCUMENTATION
This routine inserts (op==INSERT) or deletes (op==DELETE)
an object into/from a tame discrimination index.
Term t is the key, root is the root of the discrimination tree,
and *object is a pointer (in many cases, *object will be t).
See discrim_tame_retrieve_first().
<P>
A fatal error occurs if yout ry to delete an object that was not
previouly inserted.
*/

/* PUBLIC */
void discrim_tame_update(Term t, Discrim root, void *object, Indexop op)
{
  if (op == INSERT)
    discrim_tame_insert(t, root, object);
  else
    discrim_tame_delete(t, root, object);
}  /* discrim_tame_update */

/*************
 *
 *  check_flat
 *
 *************/

static
Flat check_flat(Flat f)
{
  Flat last;
  int i, arity;

  if (f->next != NULL && f->next->prev != f)
    fprintf(stderr, "check_flat: next-prev error\n");

  if (f->place_holder)
    arity = 0;
  else
    arity = ARITY(f->t);
  
  last = f;
  for (i = 0; i < arity; i++) 
    last = check_flat(last->next);
  if (f->last != last)
    fprintf(stderr, "check_flat: last is wrong\n");
  return last;
}  /* check_flat */

/*************
 *
 *  p_flat
 *
 *************/

void p_flat(Flat f)
{
  while (f != NULL) {
    printf("%s", VARIABLE(f->t) ? "*" : sn_to_str(SYMNUM(f->t)));
    if (f->place_holder)
      printf("[]");
    f = f->next;
    if (f != NULL)
      printf("-");
  }
  printf("\n");
}  /* p_flat */

/*************
 *
 *  flip_flat
 *
 *************/

static
void flip_flat(Flat f)
{
  /* Assume f is binary. */
  Flat arg1 = f->next;
  Flat arg2 = arg1->last->next;
  Flat after = f->last->next;
  Flat p;
  
  f->next = arg2;
  arg2->last->next = arg1;
  arg1->last->next = after;
  f->last = arg1->last;
  arg2->prev = f;
  arg1->prev = arg2->last;
  if (after != NULL)
    after->prev = arg1->last;

  /* arg2->last is the old end of f */

  for (p = f->prev; p != NULL; p = p->prev)
    if (p->last == arg2->last)
      p->last = f->last;
#if 0
  for (p = f; p->prev != NULL; p = p->prev);
  check_flat(p);
#endif
}  /* flip_flat */

/*************
 *
 *    discrim_retrieve_leaf(t_in, root, subst, ppos)
 *
 *************/

static
Plist discrim_retrieve_leaf(Term t_in, Discrim root,
                        Context subst, Flat *ppos)
{
  Flat f, f1, f2, f_save;
  Term t = NULL;
  Discrim d = NULL;
  int symbol = 0;
  int match = 0;
  int bound = 0;
  int status = 0;

  f = *ppos;  /* Don't forget to reset before return. */
  t = t_in;
  f_save = NULL;

  if (t != NULL) {  /* if first call */
    d = root->u.kids;
    if (d != NULL) {
      f = get_flat();
      f->t = t;
      f->last = f;
      f->prev = NULL;
      f->place_holder = (COMPLEX(t));
      status = GO;
    }
    else
      status = FAILURE;
  }
  else
    status = BACKTRACK;

  while (status == GO || status == BACKTRACK) {
    if (status == BACKTRACK) {
      while (f && !f->alternatives) {  /* clean up HERE??? */
      if (f->bound) {
        subst->terms[f->varnum] = NULL;
        f->bound = 0;
      }
      if (f->commutative && f->flip == 2) {
          /* commutative with no alternative */
          flip_flat(f);   /* un-flip */
#if 0
          printf("AFTER un-flip: "); p_flat(f);
#endif
          f->flip = 0;
        }
      f_save = f;
      f = f->prev;
      }
      if (f != NULL) {
      if (f->bound) {
        subst->terms[f->varnum] = NULL;
        f->bound = 0;
      }
      
      if (f->commutative && f->flip == 1) {
        flip_flat(f);   /* flip */
#if 0
        printf("AFTER flip: "); p_flat(f);
#endif
        f->flip = 2;
      }
      d = f->alternatives;
      f->alternatives = NULL;
      status = GO;
      }
      else
      status = FAILURE;
    }

    if (status == GO) {
      match = 0;
      while (!match && d && DVAR(d)) {
      symbol = d->symbol;
      if (subst->terms[symbol]) { /* if already bound */
        match = term_ident(subst->terms[symbol], f->t);
        bound = 0;
      }
      else { /* bind variable in discrim tree */
        match = 1;
        subst->terms[symbol] = f->t;
        bound = 1;
      }
      if (!match)
        d = d->next;
      }
      if (match) {
      /* push alternatives */
      f->alternatives = d->next;
      f->bound = bound;
      f->varnum = symbol;
      f = f->last;
      }
      else if (VARIABLE(f->t))
      status = BACKTRACK;
      else {
      symbol = SYMNUM(f->t);
      while (d && d->symbol < symbol)
        d = d->next;
      if (!d || d->symbol != symbol)
        status = BACKTRACK;
      else if (f->place_holder) {
        int i;
        /* insert skeleton in place_holder */
        f1 = get_flat();
        f1->t = f->t;
        f1->prev = f->prev;
        f1->last = f;
        f_save = f1;
        if (f1->prev)
          f1->prev->next = f1;
                
        t = f->t;
        for (i = 0; i < t->arity; i++) {
          if (i < t->arity-1)
            f2 = get_flat();
          else
            f2 = f;
          f2->place_holder = COMPLEX(t->args[i]);
          f2->t = t->args[i];
          f2->last = f2;
          f2->prev = f1;
          f1->next = f2;
          f1 = f2;
        }
        f = f_save;
        if (is_commutative(SYMNUM(f->t)) &&
            !term_ident(f->t->args[0], f->t->args[1]))
          f->commutative = 1;
      }  /* if f->place_holder */
      if (f->commutative && f->flip == 0) {
        f->alternatives = d;
        f->flip = 1;
      }
      }
      if (status == GO) {
      if (f->next) {
        f = f->next;
        d = d->u.kids;
      }
      else
        status = SUCCESS;
      }
    }
  }
  if (status == SUCCESS) {
    *ppos = f;
    return d->u.data;
  }
  else {
    /* Free flats. */
    while (f_save) {
      f1 = f_save;
      f_save = f_save->next;
      free_flat(f1);
    }
    return NULL;
  }
         
}  /* discrim_retrieve_leaf */

/*************
 *
 *    discrim_tame_retrieve_first(t, root, subst, ppos)
 *
 *    Get the first object associated with a term more general than t.
 *
 *    Remember to call discrim_tame_cancel(*ppos) if you don't want the
 *    whole sequence.
 *
 *************/

/* DOCUMENTATION
This routine, along with discrim_tame_retrieve_next(), gets answers from
a tame discrimination index.
This routine retrieves the first object associated with a term, say ft,
more general than Term t.  (NULL is returned if there is none.)
The substitution for variables of ft is placed into Context subst.
<P>
If an object is returned, Discrim_pos *ppos is set to the retrieval
state and is used for subsequent discrim_tame_retrieve_next() calls.
<P>
If you to get some, but not all answers, you must call
discrim_tame_cancel() to clear the substitution and free memory
associated with the Discrim_pos.
*/

/* PUBLIC */
void *discrim_tame_retrieve_first(Term t, Discrim root,
                       Context subst, Discrim_pos *ppos)
{
  Plist tp;
  Flat f;
  Discrim_pos gp;

  tp = discrim_retrieve_leaf(t, root, subst, &f);
  if (tp == NULL)
    return NULL;
  else {
    gp = get_discrim_pos();
    gp->subst = subst;
    gp->f = f;
    gp->data = tp;
    *ppos = gp;
    return tp->v;
  }
}  /* discrim_tame_retrieve_first */

/*************
 *
 *    discrim_tame_retrieve_next(ppos)
 *
 *    Get the next object associated with a term more general than t.
 *
 *    Remember to call discrim_tame_cancel(*ppos) if you don't want the
 *    whole sequence.
 *
 *************/

/* DOCUMENTATION
This routine retrieves the next object in the sequence of answers to
a query of a tame discrimination tree.
You must <I>not</I> explicitly clear the Context you gave to
discrim_tame_retrieve_first()---that is handled internally.
See discrim_tame_retrieve_first().
*/

/* PUBLIC */
void *discrim_tame_retrieve_next(Discrim_pos pos)
{
  Plist tp;
    
  tp = pos->data->next;
  if (tp != NULL) {  /* if any more terms in current leaf */
    pos->data = tp;
    return tp->v;
  }
  else {  /* try for another leaf */
    tp = discrim_retrieve_leaf((Term) NULL, (Discrim) NULL,
                         pos->subst, &(pos->f));
    if (tp != NULL) {
      pos->data = tp;
      return tp->v;
    }
    else {
      free_discrim_pos(pos);
      return NULL;
    }
  }
}  /* discrim_tame_retrieve_next */

/*************
 *
 *    discrim_tame_cancel(pos)
 *
 *************/

/* DOCUMENTATION
This routine <I>must</I> be called if you get some, but not all
answers to a tame discrimintaion query.
The Context (which was given to the discrim_tame_retrieve_first() call) is
cleared, and the memory associated the retrieval state is freed.
*/

/* PUBLIC */
void discrim_tame_cancel(Discrim_pos pos)
{
  Flat f1, f2;

  f1 = pos->f;
  while (f1) {
    if (f1->bound)
      pos->subst->terms[f1->varnum] = NULL;
    f2 = f1;
    f1 = f1->prev;
    free_flat(f2);
  }
  free_discrim_pos(pos);
}  /* discrim_tame_cancel */

/* ******************************** WILD **************************** */

/*************
 *
 *     num_ac_args(t, symbol)
 *
 *************/

static
int num_ac_args(struct term *t, int symbol)
{
  if (!COMPLEX(t) || SYMNUM(t) != symbol)
    return 1;
  else
    return (num_ac_args(t->args[0], symbol) +
          num_ac_args(t->args[1], symbol));
}  /* num_ac_args */

/*************
 *
 *     num_ac_nv_args(t, symbol)
 *
 *************/

static
int num_ac_nv_args(struct term *t, int symbol)
{
  if (!COMPLEX(t) || SYMNUM(t) != symbol)
    return (VARIABLE(t) ? 0 : 1);
  else
    return (num_ac_nv_args(t->args[0], symbol) +
          num_ac_nv_args(t->args[1], symbol));
}  /* num_ac_nv_args */

/*************
 *
 *     print_discrim_wild_tree()
 *
 *************/

static
void print_discrim_wild_tree(FILE *fp, Discrim d, int n, int depth)
{
  int arity, i;

  for (i = 0; i < depth; i++)
    fprintf(fp, " -");

  if (depth == 0)
    fprintf(fp, "\nroot");
  else if (d->type == AC_ARG_TYPE)
    fprintf(fp, "AC %d args", d->symbol);
  else if (d->type == AC_NV_ARG_TYPE)
    fprintf(fp, "AC %d NV args", d->symbol);
  else if (DVAR(d))
    fprintf(fp, "*");
  else
    fprintf(fp, "%s", sn_to_str(d->symbol));

  fprintf(fp, " (%x)", (unsigned) d);

  if (n == 0) {
    Plist p;
    for (i = 0, p = d->u.data; p; i++, p = p->next);
    fprintf(fp, ": leaf has %d objects.\n", i);
  }
  else {
    Discrim d1;
    fprintf(fp, "\n");
    for (d1 = d->u.kids; d1 != NULL; d1 = d1->next) {
      if (d1->type == AC_ARG_TYPE || d1->type == AC_NV_ARG_TYPE)
      arity = 0;
      else if (DVAR(d1))
      arity = 0;
      else
      arity = sn_to_arity(d1->symbol);
      print_discrim_wild_tree(fp, d1, n+arity-1, depth+1);
    }
  }
}  /* print_discrim_wild_tree */

/*************
 *
 *   fprint_discrim_wild_index()
 *
 *************/

/* DOCUMENTATION
This routine prints (to FILE *fp) a wild discrimination index.
*/

/* PUBLIC */
void fprint_discrim_wild_index(FILE *fp, Discrim d)
{
  print_discrim_wild_tree(fp, d, 1, 0);
}  /* fprint_discrim_wild_index */

/*************
 *
 *   p_discrim_wild_index()
 *
 *************/

/* DOCUMENTATION
This routine prints (to stdout) a wild discrimination index.
*/

/* PUBLIC */
void p_discrim_wild_index(Discrim d)
{
  fprint_discrim_wild_index(stdout, d);
}  /* p_discrim_wild_index */

/*************
 *
 *     discrim_wild_insert_ac(t, d)
 *
 *************/

static
Discrim discrim_wild_insert_ac(Term t, Discrim d)
{
  int num_args, num_nv_args;
  Discrim d1, d2, dnew, prev;

  num_args = num_ac_args(t, SYMNUM(t));

  for (d1 = d->u.kids, prev = NULL;
       d1 && d1->symbol < num_args;
       prev = d1, d1 = d1->next);
  if (d1 == NULL || d1->symbol != num_args) {
    dnew = get_discrim();
    dnew->type = AC_ARG_TYPE;
    dnew->symbol = num_args;
    dnew->next = d1;
    if (prev != NULL)
      prev->next = dnew;
    else
      d->u.kids = dnew;
    d1 = dnew;
  }

  num_nv_args = num_ac_nv_args(t, SYMNUM(t));

  for (d2 = d1->u.kids, prev = NULL;
       d2 && d2->symbol < num_nv_args;
       prev = d2, d2 = d2->next);
  if (!d2 || d2->symbol != num_nv_args) {
    dnew = get_discrim();
    dnew->type = AC_NV_ARG_TYPE;
    dnew->symbol = num_nv_args;
    dnew->next = d2;
    if (prev != NULL)
      prev->next = dnew;
    else
      d1->u.kids = dnew;
    d2 = dnew;
  }
  return d2;
    
}  /* discrim_wild_insert_ac */

/*************
 *
 *    Discrim discrim_wild_insert_rec(t, d)
 *
 *************/

static
Discrim discrim_wild_insert_rec(Term t, Discrim d)
{
  Discrim d1, prev, d2;
  int sym;

  if (VARIABLE(t)) {
    d1 = d->u.kids;
    if (d1 == NULL || !DVAR(d1)) {
      d2 = get_discrim();
      d2->type = DVARIABLE;
      d2->symbol = 0;    /* HERE */
      d2->next = d1;
      d->u.kids = d2;
      return d2;
    }
    else  /* found node */
      return d1;
  }

  else {  /* constant || complex */
    d1 = d->u.kids;
    prev = NULL;
    /* arities fixed: handle both NAME and COMPLEX */
    sym = SYMNUM(t);
    if (d1 && DVAR(d1)) {  /* skip variable */
      prev = d1;
      d1 = d1->next;
    }
    while (d1 && d1->symbol < sym) {
      prev = d1;
      d1 = d1->next;
    }
    if (d1 == NULL || d1->symbol != sym) {
      d2 = get_discrim();
      d2->type = DRIGID;
      d2->symbol = sym;
      d2->next = d1;
      d1 = d2;
    }
    else
      d2 = NULL;  /* new node not required at this level */

    if (is_assoc_comm(SYMNUM(t))) {
      d1 = discrim_wild_insert_ac(t, d1);
    }
    else {
      int i;
      for (i = 0; i < t->arity; i++)
      d1 = discrim_wild_insert_rec(t->args[i], d1);
    }

    if (d2 != NULL) {  /* link in new subtree (possibly a leaf) */
      if (prev == NULL)
      d->u.kids = d2;
      else
      prev->next = d2;
    }
          
    return d1;  /* d1 is leaf corresp. to end of input term */
  }
}  /* discrim_wild_insert_rec */

/*************
 *
 *    discrim_wild_insert(t, root, object)
 *
 *************/

static
void discrim_wild_insert(Term t, Discrim root, void *object)
{
  Discrim d;
  Plist gp1, gp2;

  d = discrim_wild_insert_rec(t, root);
  gp1 = get_plist();
  gp1->v = object;

  /* Install at end of list. */
  if (d->u.data == NULL)
    d->u.data = gp1;
  else {
    for (gp2 = d->u.data; gp2->next; gp2 = gp2->next);
    gp2->next = gp1;
  }
}  /* discrim_wild_insert */

/*************
 *
 *    Discrim discrim_wild_end(t, is, path_p)
 *
 *    Given a discrimination tree (or a subtree) and a term, return the 
 *    node in the tree that corresponds to the last symbol in t (or NULL
 *    if the node doesn't exist).  *path_p is a list that is extended by
 *    this routine.  It is a list of pointers to the
 *    nodes in path from the parent of the returned node up to imd. 
 *    (It is needed for deletions, because nodes do not have pointers to
 *    parents.) 
 *
 *************/

static
Discrim discrim_wild_end(Term t, Discrim d,
                            Plist *path_p)
{
  Discrim d1;
  Plist p;
  int sym;

  /* add current node to the front of the path list. */

  p = get_plist();
  p->v = d;
  p->next = *path_p;
  *path_p = p;

  if (VARIABLE(t)) {
    d1 = d->u.kids;
    if (d1 && DVAR(d1))
      return d1;
    else
      return NULL;
  }

  else {  /* constant || complex */
    d1 = d->u.kids;
    sym = SYMNUM(t);
    if (d1 && DVAR(d1))  /* skip variables */
      d1 = d1->next;
    while (d1 && d1->symbol < sym)
      d1 = d1->next;

    if (d1 == NULL || d1->symbol != sym)
      return NULL;
    else if (is_assoc_comm(SYMNUM(t))) {
      int num_args, num_nv_args;
      Discrim d2, d3;
            
      num_args = num_ac_args(t, SYMNUM(t));
      num_nv_args = num_ac_nv_args(t, SYMNUM(t));
            
      for (d2 = d1->u.kids; d2 && d2->symbol != num_args; d2 = d2->next);
      if (d2 == NULL)
      return NULL;
      else {
      for (d3 = d2->u.kids; d3 && d3->symbol != num_nv_args; d3 = d3->next);
      if (d3 == NULL)
        return NULL;
      else {
        p = get_plist();
        p->v = d1;
        p->next = *path_p;
        *path_p = p;
        p = get_plist();
        p->v = d2;
        p->next = *path_p;
        *path_p = p;
        return d3;
      }
      }
    }
    else {
      int i;
      for (i = 0; d1 && i < t->arity; i++)
      d1 = discrim_wild_end(t->args[i], d1, path_p);
      return d1;
    }
  }
}  /* discrim_wild_end */

/*************
 *
 *    discrim_wild_delete(t, root, object)
 *
 *************/

static
void discrim_wild_delete(Term t, Discrim root, void *object)
{
  Discrim end, i2, i3, parent;
  Plist tp1, tp2;
  Plist isp1, path;

    /* First find the correct leaf.  path is used to help with  */
    /* freeing nodes, because nodes don't have parent pointers. */

  path = NULL;
  end = discrim_wild_end(t, root, &path);
  if (end == NULL) {
    fatal_error("discrim_wild_delete, cannot find end.");
  }

    /* Free the pointer in the leaf-list */

  tp1 = end->u.data;
  tp2 = NULL;
  while(tp1 && tp1->v != object) {
    tp2 = tp1;
    tp1 = tp1->next;
  }
  if (tp1 == NULL) {
    fatal_error("discrim_wild_delete, cannot find term.");
  }

  if (tp2 == NULL)
    end->u.data = tp1->next;
  else
    tp2->next = tp1->next;
  free_plist(tp1);

  if (!end->u.data) {
    /* free tree nodes from bottom up, using path to get parents */
    end->u.kids = NULL;  /* not really necessary */
    isp1 = path;
    while (!end->u.kids && end != root) {
      parent = (Discrim) isp1->v;
      isp1 = isp1->next;
      i2 = parent->u.kids;
      i3 = NULL;
      while (i2 != end) {
      i3 = i2;
      i2 = i2->next;
      }
      if (i3 == NULL)
      parent->u.kids = i2->next;
      else
      i3->next = i2->next;
      free_discrim(i2);
      end = parent;
    }
  }

  /* free path list */

  while (path) {
    isp1 = path;
    path = path->next;
    free_plist(isp1);
  }
}  /* discrim_wild_delete */

/*************
 *
 *   discrim_wild_update()
 *
 *************/

/* DOCUMENTATION
This routine inserts (op==INSERT) or deletes (op==DELETE)
an object into/from a wild discrimination index.
Term t is the key, root is the root of the discrimination tree,
and *object is a pointer (in many cases, *object will be t).
See discrim_tame_retrieve_first().
<P>
A fatal error occurs if yout ry to delete an object that was not
previouly inserted.
*/

/* PUBLIC */
void discrim_wild_update(Term t, Discrim root, void *object, Indexop op)
{
  if (op == INSERT)
    discrim_wild_insert(t, root, object);
  else
    discrim_wild_delete(t, root, object);
}  /* discrim_wild_update */

/*************
 *
 *    discrim_wild_retrieve_leaf(t_in, root, ppos)
 *
 *************/

static
Plist discrim_wild_retrieve_leaf(Term t_in, Discrim root, Flat *ppos)
{
  Flat f, f1, f2;
  Flat f_save = NULL;
  Term t;
  Discrim d = NULL;
  int symbol, status;

  f = *ppos;  /* Don't forget to reset before return. */
  t = t_in;

  if (t != NULL) {  /* if first call */
    d = root->u.kids;
    if (d != NULL) {
      f = get_flat();
      f->t = t;
      f->last = f;
      f->prev = NULL;
      f->next = NULL;
      f->place_holder = COMPLEX(t);
      status = GO;
    }
    else
      status = FAILURE;
  }
  else
    status = BACKTRACK;

  while (status == GO || status == BACKTRACK) {

    /* Three things determine the state at this point.
     * 1. d is the current node in the discrimination tree.
     * 2. f is the current node in the stack of flats.
     * 3. status is either GO or BACKTRACK.
     *
     * Commutative symbols:
     * This is more complicated than it needs to be, because
     * alternatives are handled awkwardly.
     * flip == 0 means that we haven't descended into the commutative term.
     * flip == 1 means that we are in the unflipped commutative term, and
     * flip == 2 means that we are in the flipped commutative term.
     */

    if (status == BACKTRACK) {
#if 0
      printf("backtracking\n");
#endif
      /* Back up to a place with an aternate branch. */
      while (f != NULL  && f->alternatives == NULL) {
      if (f->commutative && f->flip == 2) {
        /* commutative with no alternative */
        flip_flat(f);   /* un-flip */
#if 0
        printf("AFTER un-flip: "); p_flat(f);
#endif
        f->flip = 0;
      }
      f_save = f;
      f = f->prev;
      }

      if (f != NULL) {
#if 0
      printf("alternative: (%x)\n", (unsigned) f->alternatives);
#endif
      if (f->commutative && f->flip == 1) {
      flip_flat(f);   /* flip */
#if 0
      printf("AFTER flip: "); p_flat(f);
#endif
      f->flip = 2;
      }


      d = f->alternatives;
      f->alternatives = NULL;
      status = GO;
      }
      else {
      /* Free stack of flats and fail. */
      while (f_save != NULL) {
        f1 = f_save;
        f_save = f_save->next;
        free_flat(f1);
      }
      status = FAILURE;
      }
    }  /* backtrack */

    if (status == GO) {
#if 0
      printf("go with (%x) %s\n", (unsigned) d,
           DVAR(d) ? "*" : sn_to_str(d->symbol));
#endif
      if (d && d->type == AC_ARG_TYPE) {
      if (d->symbol <= f->num_ac_args)
        f->alternatives = d->next;
      else
        status = BACKTRACK;
      }
      else if (d && d->type == AC_NV_ARG_TYPE) {
      if (d->symbol <= f->num_ac_nv_args)
        f->alternatives = d->next;
      else
        status = BACKTRACK;
      }
      else if (d && DVAR(d)) {
      /* push alternatives */
      f->alternatives = d->next;
      f = f->last;
      }
      else if (VARIABLE(f->t))
      status = BACKTRACK;
      else {
      symbol = SYMNUM(f->t);
      while (d && d->symbol < symbol)
        d = d->next;

      if (!d || d->symbol != symbol)
        status = BACKTRACK;
      else {
        if (f->place_holder) {

          /* Insert skeleton in place_holder.  This is tricky, because 
           * someone's "last" pointer may be pointing to f.  Therefore,
           * f becomes the last argument of the skeleton.
           */

          if (is_assoc_comm(SYMNUM(f->t))) {  /* AC case */
            f1 = get_flat();
            f1->t = f->t;
            f1->prev = f->prev;
            f1->last = f;
            if (f1->prev)
            f1->prev->next = f1;

            f2 = get_flat();
            f2->prev = f1;
            f2->last = f2;
            f2->next = f;
            f->prev = f2;
            f1->next = f2;
            f->last = f;

            /* Now, f2 is the AC_ARGS node, and f is the AC_NV_ARGS node. */
            f2->num_ac_args = num_ac_args(f1->t, SYMNUM(f1->t));
            f->num_ac_nv_args = num_ac_nv_args(f1->t, SYMNUM(f1->t));

            f = f1;
          }

          else {  /* non AC case */
            int i;
            f1 = get_flat();
            f1->t = f->t;
            f1->prev = f->prev;
            f1->last = f;
            f_save = f1;
            if (f1->prev)
            f1->prev->next = f1;

            t = f->t;
            for (i = 0; i < t->arity; i++) {
            if (i < t->arity-1)
              f2 = get_flat();
            else
              f2 = f;
            f2->place_holder = COMPLEX(t->args[i]);
            f2->t = t->args[i];
            f2->last = f2;
            f2->prev = f1;
            f1->next = f2;
            f1 = f2;
            }
            f = f_save;
            if (is_commutative(SYMNUM(f->t)) &&
              !term_ident(f->t->args[0], f->t->args[1]))
            f->commutative = 1;
          }  /* non-AC */
        }  /* if f->place_holder */
        if (f->commutative && f->flip == 0) {
          f->alternatives = d;
          f->flip = 1;
        }
      }  /* rigid symbols match */
      }  /* non-variable */
      if (status == GO) {
      if (f->next) {
        f = f->next;
        d = d->u.kids;
      }
      else
        status = SUCCESS;
      }  /* if go */
    }  /* if go */
  }  /* while go or backtrack */
  if (status == SUCCESS) {
    *ppos = f;
    return d->u.data;
  }
  else
    return NULL;
}  /* discrim_wild_retrieve_leaf */

/*************
 *
 *    discrim_wild_retrieve_first(t, root, ppos)
 *
 *    Get the first object associated with a term more general than t.
 *
 *    Remember to call discrim_wild_cancel(pos) if you don't
 *    want the whole sequence.
 *
 *************/

/* DOCUMENTATION
This routine, along with discrim_wild_retrieve_next(), gets answers from
a wild discrimination index.
This routine retrieves the first object associated with a term
more general than Term t.  (NULL is returned if there is none.)
<P>
If an object is returned, Discrim_pos *ppos is set to the retrieval
state and is used for subsequent discrim_tame_retrieve_next() calls.
<P>
If you to get some, but not all answers, you must call
discrim_wild_cancel() to clear the substitution and free memory
associated with the Discrim_pos.
*/

/* PUBLIC */
void *discrim_wild_retrieve_first(Term t, Discrim root,
                          Discrim_pos *ppos)
{
  Plist tp;
  Flat f;
  Discrim_pos gp;

  tp = discrim_wild_retrieve_leaf(t, root, &f);
  if (tp == NULL)
    return NULL;
  else {
    gp = get_discrim_pos();
    gp->f = f;
    gp->data = tp;
    *ppos = gp;
    return tp->v;
  }
}  /* discrim_wild_retrieve_first */

/*************
 *
 *    discrim_wild_retrieve_next(pos)
 *
 *    Get the next object associated with a term more general than t.
 *
 *    Remember to call discrim_wild_cancel(pos) if you don't
 *    want the whole sequence.
 *
 *************/

/* DOCUMENTATION
This routine retrieves the next object in the sequence of answers to
a query of a wild discrimination tree.
See discrim_wild_retrieve_first().
*/

/* PUBLIC */
void *discrim_wild_retrieve_next(Discrim_pos pos)
{
  Plist tp;
    
  tp = pos->data->next;
  if (tp != NULL) {  /* if any more terms in current leaf */
    pos->data = tp;
    return tp->v;
  }
  else {  /* try for another leaf */
    tp = discrim_wild_retrieve_leaf((Term) NULL, (Discrim) NULL, &(pos->f));
                              
    if (tp != NULL) {
      pos->data = tp;
      return tp->v;
    }
    else {
      free_discrim_pos(pos);
      return NULL;
    }
  }
}  /* discrim_wild_retrieve_next */

/*************
 *
 *    discrim_wild_cancel(pos)
 *
 *************/

/* DOCUMENTATION
This routine should be called if you get some, but not all
answers to a wild discrimintaion query.
The memory associated the retrieval state is freed.
*/

/* PUBLIC */
void discrim_wild_cancel(Discrim_pos pos)
{
  Flat f1, f2;

  f1 = pos->f;
  while (f1) {
    f2 = f1;
    f1 = f1->prev;
    free_flat(f2);
  }
  free_discrim_pos(pos);
}  /* discrim_wild_cancel */

/*************
 *
 *   zap_discrim_tree()
 *
 *************/

static
void zap_discrim_tree(Discrim d, int n)
{
  if (n == 0) {
    zap_plist(d->u.data);
  }
  else {
    int arity;
    Discrim k, prev;

    k = d->u.kids;
    while (k != NULL) {
      if (k->type == AC_ARG_TYPE || k->type == AC_NV_ARG_TYPE)
      arity = 0;
      else if (DVAR(k))
      arity = 0;
      else
      arity = sn_to_arity(k->symbol);
      prev = k;
      k = k->next;
      zap_discrim_tree(prev, n+arity-1);
    }
  }
  free_discrim(d);
}  /* zap_discrim_tree */

/*************
 *
 *   destroy_discrim_tree()
 *
 *************/

/* DOCUMENTATION
This routine frees all the memory associated with a discrimination
index.  It can be used with either wild or tame trees.
*/

/* PUBLIC */
void destroy_discrim_tree(Discrim d)
{
  zap_discrim_tree(d, 1);
}  /* destroy_discrim_tree */

/*************
 *
 *   discrim_empty()
 *
 *************/

/* DOCUMENTATION
This Boolean function checks if a discrimination index is empty.
It can be used with either wild or tame trees.
*/

/* PUBLIC */
BOOL discrim_empty(Discrim d)
{
  return (d == NULL ? TRUE : (d->u.kids == NULL ? TRUE : FALSE));
}  /* discrim_empty */


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