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btm.c

#include "btm.h"

/* Private definitions and types */

typedef struct ac_match_pos * Ac_match_pos;
typedef struct ac_match_free_vars_pos * Ac_match_free_vars_pos;

struct btm_state {

    Btm_state parent, next, prev, first_child, last_child;

    Term t1, t2;         /* terms being matched */
    Context c1;          /* context for variables of t1*/

    int varnum;          /* for unbinding when backtracking */
    Context cb;          /* for unbinding when backtracking */

    Unif_alternative alternative;  /* type of alternative (position) */

    /* for commutative unification */
    int flipped;
    Btm_state position_bt;      /* in sequence of alternatives */

    /* for AC matching */
    Ac_match_pos acm;  /* in sequence of AC matchers */
    int partial;               /* partial match for this pair */
    };

struct ac_match_pos {
    Term t1, t2;         /* t1 is pattern, t2 is subject */
    Context c1;          /* context for variables in t1  */
    int n1;              /* number of arguments in t1 */ 
    int n2;              /* size of set of set of args in t2 */
    Term args1[MAX_ACM_ARGS], args2[MAX_ACM_ARGS];  /* the arguments */
           /* position in sequence of matches for complex args of args2 */
    Btm_state bt1[MAX_ACM_ARGS];
           /* flags indicating which of args1 have been matched */
    int match1[MAX_ACM_ARGS];
           /* integer indicating how many of each of args2 have been matched */
    int match2[MAX_ACM_ARGS];
    int mults2[MAX_ACM_ARGS];  /* multiplicities for args2 */
           /* indicates which of args2 are matched by bound vars in args1 */
    int bound_matches[MAX_ACM_ARGS], bound_count;
    int last_a1_symbol;   /* position of last non-variable arg in args1 */
           /* list of backtrack positions for free variables of args1 */
    Ac_match_free_vars_pos free_first, free_last;
           /* # args of unmatched term---used for partial match */
    int partial_term_size;
    Ac_match_pos next;  /* for avail list only */
    };

struct ac_match_free_vars_pos {
    int varnum;                 /* the index of the free variable */
    int coef;                   /* # of occurrences of the var in args1 */
    int targets[MAX_ACM_ARGS];   /* terms in args2 that can go with variable */
    int n;                      /* number of tragets*/
    int combo[MAX_ACM_ARGS];     /* current subset of the targets */
    Ac_match_free_vars_pos prev, next;
    };

/* #define DEBUG */

#define POP       1
#define BACKTRACK 2
#define GO        3
#define SUCCESS   4
#define FAILURE   5

/* Bind a variable, record binding in a bt_node. */

#define BIND_BT(i, c1, t2, c2, bt) {  \
    c1->terms[i] = t2; c1->contexts[i] = c2; \
    bt->varnum = i; bt->cb = c1; }

/* The following declaration is due to mutual recursion with match_bt_guts. */

static int match_commute(Term t1, Context c1, Term t2, Btm_state bt);

/*
 * memory management
 */

static unsigned Ac_match_pos_gets, Ac_match_pos_frees;
static unsigned Ac_match_free_vars_pos_gets, Ac_match_free_vars_pos_frees;
static unsigned Btm_state_gets, Btm_state_frees;

#define BYTES_AC_MATCH_POS sizeof(struct ac_match_pos)
#define PTRS_AC_MATCH_POS BYTES_AC_MATCH_POS%BPP == 0 ? BYTES_AC_MATCH_POS/BPP : BYTES_AC_MATCH_POS/BPP + 1

#define BYTES_AC_MATCH_FREE_VARS_POS sizeof(struct ac_match_free_vars_pos)
#define PTRS_AC_MATCH_FREE_VARS_POS BYTES_AC_MATCH_FREE_VARS_POS%BPP == 0 ? BYTES_AC_MATCH_FREE_VARS_POS/BPP : BYTES_AC_MATCH_FREE_VARS_POS/BPP + 1

#define BYTES_BTM_STATE sizeof(struct btm_state)
#define PTRS_BTM_STATE BYTES_BTM_STATE%BPP == 0 ? BYTES_BTM_STATE/BPP : BYTES_BTM_STATE/BPP + 1

/*************
 *
 *   Ac_match_pos get_ac_match_pos()
 *
 *************/

static
Ac_match_pos get_ac_match_pos(void)
{
  Ac_match_pos p = get_mem(PTRS_AC_MATCH_POS);
  Ac_match_pos_gets++;
  return(p);
}  /* get_ac_match_pos */

/*************
 *
 *    free_ac_match_pos()
 *
 *************/

static
void free_ac_match_pos(Ac_match_pos p)
{
  free_mem(p, PTRS_AC_MATCH_POS);
  Ac_match_pos_frees++;
}  /* free_ac_match_pos */

/*************
 *
 *   Ac_match_free_vars_pos get_ac_match_free_vars_pos()
 *
 *************/

static
Ac_match_free_vars_pos get_ac_match_free_vars_pos(void)
{
  Ac_match_free_vars_pos p = get_mem(PTRS_AC_MATCH_FREE_VARS_POS);
  Ac_match_free_vars_pos_gets++;
  return(p);
}  /* get_ac_match_free_vars_pos */

/*************
 *
 *    free_ac_match_free_vars_pos()
 *
 *************/

static
void free_ac_match_free_vars_pos(Ac_match_free_vars_pos p)
{
  free_mem(p, PTRS_AC_MATCH_FREE_VARS_POS);
  Ac_match_free_vars_pos_frees++;
}  /* free_ac_match_free_vars_pos */

/*************
 *
 *   Btm_state get_btm_state()
 *
 *************/

static
Btm_state get_btm_state(void)
{
  Btm_state p = get_mem(PTRS_BTM_STATE);
  p->varnum = -1;
  p->alternative = NO_ALT;
  Btm_state_gets++;
  return(p);
}  /* get_btm_state */

/*************
 *
 *    free_btm_state()
 *
 *************/

static
void free_btm_state(Btm_state p)
{
  free_mem(p, PTRS_BTM_STATE);
  Btm_state_frees++;
}  /* free_btm_state */

/*************
 *
 *   fprint_btm_mem()
 *
 *************/

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

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

  n = BYTES_AC_MATCH_POS;
  fprintf(fp, "ac_match_pos (%4d)%11u%11u%11u%9.1f K\n",
          n, Ac_match_pos_gets, Ac_match_pos_frees,
          Ac_match_pos_gets - Ac_match_pos_frees,
          ((Ac_match_pos_gets - Ac_match_pos_frees) * n) / 1024.);

  n = BYTES_AC_MATCH_FREE_VARS_POS;
  fprintf(fp, "ac_match_free_vars_pos (%4d)\n                    %11u%11u%11u%9.1f K\n",
          n, Ac_match_free_vars_pos_gets, Ac_match_free_vars_pos_frees,
          Ac_match_free_vars_pos_gets - Ac_match_free_vars_pos_frees,
          ((Ac_match_free_vars_pos_gets - Ac_match_free_vars_pos_frees) * n) / 1024.);

  n = BYTES_BTM_STATE;
  fprintf(fp, "btm_state (%4d)    %11u%11u%11u%9.1f K\n",
          n, Btm_state_gets, Btm_state_frees,
          Btm_state_gets - Btm_state_frees,
          ((Btm_state_gets - Btm_state_frees) * n) / 1024.);

}  /* fprint_btm_mem */

/*************
 *
 *   p_btm_mem()
 *
 *************/

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

/* PUBLIC */
void p_btm_mem()
{
  fprint_btm_mem(stdout, TRUE);
}  /* p_btm_mem */

/*
 *  end of memory management
 */
/*************
 *
 *    flatten_mult
 *
 *    Flatten an AC term into an array, collapsing multiple occurrences
 *    into one, filling in a parallel array with multiplicities.
 *    Also return a count of the total number of arguments.
 *
 *    The index (*ip) must be initialized by the calling routine.
 *
 *************/

static
void flatten_mult(Term t, Term *a, int *m, int *ip, int *totp,
              int (*comp_proc) (void *, void *))
{
  Term t1;
  int sn, i;

  sn = SYMNUM(t);
  for (i = 0; i < ARITY(t); i++) {
    t1 = t->args[i];
    if (SYMNUM(t1) == sn)
      flatten_mult(t1, a, m, ip, totp, comp_proc);
    else {
      (*totp)++;
      if (*ip > 0 && (*comp_proc)(t1, a[(*ip)-1]) == SAME_AS)
      m[(*ip)-1]++;
      else {
      if (*ip >= MAX_ACM_ARGS) {
        fprint_term(stdout, t);
        fatal_error("flatten_mult, too many arguments.");
      }
      a[*ip] = t1;
      m[*ip] = 1;
      (*ip)++;
      }
    }
  }
}  /* flatten_mult */

/*************
 *
 *    macbv_rec -- match (identically) all args of an AC term.
 *
 *    Called by match_ac_bound_vars.
 *
 *************/

static
int macbv_rec(int ac_sn, Term t, Term *args2, int *mults2,
            int *match2, int n2, int *bound_matches, int *bp)
{
  int i, available;
    
  if (!COMPLEX(t) || SYMNUM(t) != ac_sn) {
    for (i = 0; i < n2; i++) {
      available = mults2[i] - match2[i];
      if (available > 0 && term_ident(t, args2[i])) {
      match2[i]++;
      bound_matches[(*bp)++] = i;
      return(1);
      }
    }
    return(0);
  }
  else {
    if (!macbv_rec(ac_sn,t->args[0],args2,mults2,match2,n2,
               bound_matches,bp))
      return(0);
    else
      return(macbv_rec(ac_sn,t->args[1],args2,mults2,match2,n2,
                   bound_matches,bp));
  }
}  /* macbv_rec */

/*************
 *
 *    match_ac_bound_vars -- match (identically) a set of bound variables.
 *
 *    For each bound variable of args1, find an identical match in args2.
 *    If bound to an AC term t, (with same AC symbol) find an identical
 *    match for each argument of t.  Record the positions of the matched
 *    terms in `bound_matches', so that they can be unmached on backtracking.
 *
 *************/

static
int match_ac_bound_vars(int ac_sn, Term *args1, int n1,
                  Term *args2, int *mults2, int *match2,
                  int n2, int begin,
                  int *bound_matches, int *bp, Context c1)
{
  int i, ok, vn;
  Term t;

  for (i=begin, ok=1, *bp=0; i < n1 && ok; i++) {
    vn = VARNUM(args1[i]);
    t = c1->terms[vn];
    if (t)
      ok = macbv_rec(ac_sn,t,args2,mults2,match2,n2,bound_matches,bp);
  }
  if (!ok) {
    /* Subtract any matches that were made before failure. */
    for (i = 0; i < *bp; i++)
      match2[bound_matches[i]] -= 1;
    *bp = 0;  /* Not really necessary, but helpful for debugging. */
  }
  return(ok);
}  /* match_ac_bound_vars */

/*************
 *
 *    set_up_free_vars
 *
 *    Build a list of the set of free variables in args1.  Each node
 *    contains the number of occurrences (coef) of the variable.
 *    Sort the list---nonincreasing coef.
 *
 *    Variables are partitioned into `free' and `bound' according to
 *    their state after all nonvariable terms have been matched.
 *    A variable is called `bound' iff it occurs in a nonvariable term.
 *   
 *    Since the partition does not change during backtracking, this
 *    routine needs to be called only once, after all nonvariable
 *    terms have been matched for the first time.
 *
 *************/

static
void set_up_free_vars(Ac_match_pos ac, Context c1)
{
  Ac_match_free_vars_pos p1, p2;
  Term t;
  int i, temp;

  ac->free_first = NULL; ac->free_last = NULL;
  for (i = ac->last_a1_symbol+1; i < ac->n1; i++) {
    t = ac->args1[i];
    if (c1->terms[VARNUM(t)] == NULL) {
      /* We have a free variable. */
      for (p1=ac->free_first; p1 && p1->varnum!=VARNUM(t); p1=p1->next);
      if (p1 != NULL)
      (p1->coef)++;
      else {
      p1 = get_ac_match_free_vars_pos();
      p1->varnum = VARNUM(t);
      p1->coef = 1;
      p1->next = NULL;
      p1->prev = ac->free_last;
      if (ac->free_last)
        ac->free_last->next = p1;
      else
        ac->free_first = p1;
      ac->free_last = p1;
      }
    }
  }
  /* Now sort -- nonincreasing coefficients. */
  /* There won't be many, so use a quadratic sort. */
  p1 = ac->free_first;
  if (p1) {
    while (p1->next) {
      for (p2 = p1->next; p2; p2 = p2->next) {
      if (p1->coef < p2->coef) {
        temp = p2->coef;
        p2->coef = p1->coef;
        p1->coef = temp;
        temp = p2->varnum;
        p2->varnum = p1->varnum;
        p1->varnum = temp;
      }
      }
      p1 = p1->next;
    }
  }
}  /* set_up_free_vars */

/*************
 *
 *    unbind_free_var
 *
 *    This routine takes an `ac match free variable position' and
 *    unbinds the free variable.  If the variable is bound to a
 *    compound AC term that was created just for the binding,
 *    then the new parts of the term are deleted.
 *
 *************/

static
void unbind_free_var(Ac_match_free_vars_pos pos, Context c)
{
  int i, j;
  Term t, t1;

  /* Free the temporary substitution term, if necessary. */

  /* First count how many nodes have to be deleted. */
  for (i = j = 0; i < pos->n; i++)
    if (pos->combo[i])
      j++;
    
  t = c->terms[pos->varnum];
  for (i = 0; i < j-1; i++) {
    t1 = t->args[1];
    free_term(t);
    t = t1;
  }
    
  /* unbind variable */
  c->terms[pos->varnum] = NULL;
    
}  /* unbind_free_var */

/*************
 *
 *  free_var_match
 *
 *  Find the first or next match for a free variable.  If (match_all)
 *  then all remaining arguments of args2 must be matched.
 *  Otherwise, backtracking will produce matches in all combinations.
 *
 *************/

static
int free_var_match(Ac_match_free_vars_pos pos, Term *args2,
               int *mults2, int *match2, int n2, Context c1,
               int symbol, int match_all)
{
  Term t;
  int i, j, k, n, ok, go, avail;

  t = c1->terms[pos->varnum];

  if (!t) {
    /* It is not a continuation, so set up everything.
     *
     * Loop through args2, collecting targets, combinations of which
     * can be substituted for the current variable.
     * Example: current variable is 2x; terms available for
     * matching are 4a, 3b, 2c, 1d; targets are a,a,b,c.
     */
  
  n = 0;
    for (i = 0; i < n2; i++) {
      avail = mults2[i] - match2[i];
      if (match_all && (avail % pos->coef != 0))
      return 0; /* Fail, because there will be unmatched term(s) */
      j = avail / pos->coef;  /* integer division */
      for (k = 0; k < j; k++)
      pos->targets[n++] = i;
    }

    pos->n = n;
    if (n == 0)
      return 0;
    else {
      for (i = 0; i < n; i++)
      pos->combo[i] = 1;
    }
  }
  else {
    /* continutation */
    unbind_free_var(pos, c1);

    /* unmark args2 terms */
    for (i = 0; i < pos->n; i++)
      if (pos->combo[i]) {
      match2[pos->targets[i]] -= pos->coef;
      }

    if (match_all) {
      for (i = 0; i < pos->n; i++)
      pos->combo[i] = 0;
      return 0;
    }
    else {
      go = 1;
      while (go) {
      /* subtract 1 from  combo */
      for (i = (pos->n)-1; i >= 0 && pos->combo[i] == 0; i--)
        pos->combo[i] = 1;
      if (i < 0)
        return(0);
      else {
        pos->combo[i] = 0;
        /* Check redundancy condition. */
        for (i = 0, ok = 1; i < (pos->n)-1 && ok; i++)
          if (pos->targets[i] == pos->targets[i+1] &&
            pos->combo[i] < pos->combo[i+1])
            ok = 0;
        go = !ok;
      }
      }

      /* Now make sure that combo is not empty. */
      for (i = 0, ok = 0; i < pos->n && !ok; i++)
      ok = pos->combo[i];
      if (!ok)
      return 0;
    }
  }

  /* All is well---we have a match for the current variable. */
  /* Build a temporary substitution term, if necessary. */
  /* Note order in which it is built---this makes it AC canonical. */

  t = NULL;
  for (i = pos->n-1; i >= 0; i--) 
    if (pos->combo[i]) {
      if (t == NULL)
      t = args2[pos->targets[i]];
      else
      t = build_binary_term(symbol, args2[pos->targets[i]], t);
    }

  /* Bind variable. */
  c1->terms[pos->varnum] = t;
    
  /* Mark args2 terms matched to the current variable. */
  for (i = 0; i < pos->n; i++)
    if (pos->combo[i])
      match2[pos->targets[i]] += pos->coef;

  return 1;
}  /* free_var_match */

/*************
 *
 *    build_partial_term
 *
 *    When partial match has been found, this routine collects the
 *    unmatched arguments of args2 and builds and returns an AC term.
 *    The size of the new term is stored in the AC position so that
 *    it can easily be freed.
 *
 *************/

static
Term build_partial_term(Ac_match_pos ac)
{
  int i, j, k, n;
  Term t;

  t = NULL; k = 0;
  for (i = 0; i < ac->n2; i++) {
    n = ac->mults2[i] - ac->match2[i];
    for (j = 0; j < n; j++) {
      k++;
      if (!t)
      t = ac->args2[i];
      else
      t = build_binary_term(SYMNUM(ac->t1), ac->args2[i], t);
    }
  }
  ac->partial_term_size = k;
  return t;
}  /* build_partial_term */

/*************
 *
 *    clear_partial_term
 *
 *    Remove the partial term from the substitution and free the
 *    appropriate parts fo the partial term.
 *
 *************/

static
void clear_partial_term(Ac_match_pos ac)
{
  int i;
  Term t, t1;

  t = ac->c1->partial_term;
  ac->c1->partial_term = NULL;
    
  for (i = 0; i < ac->partial_term_size - 1; i++) {
    t1 = t->args[1];
    free_term(t);
    t = t1;
  }
  ac->partial_term_size = 0;
}  /* clear_partial_term */

#define GO_FUNCTORS   1
#define GO_BOUND_VARS 2
#define GO_FREE_VARS  3
#define SUCCESS       4
#define FAILURE       5

/*************
 *
 *    match_ac -- associative-commutative matching.
 *
 *    Get the first (bt->alternative == NO_ALT) or next AC matcher.
 *    I intend for this to be called from `match_bt_guts'.  
 *    It assumed that the root symbols of the input terms are AC. 
 *
 *    Call match_ac_cancel(ac) if you quit before getting all matchers. 
 *
 *    t1 -- pattern term
 *    c1 -- context (substitution table) for t1
 *    t2 -- subject term
 *    bt -- backtrack position
 *
 *************/

static
int match_ac(Term t1, Context c1, Term t2, Btm_state bt)
{
  int status, n1, n2, total2, i, ok, a1_pos, a2_pos;
  int free_var_forward;
  Term a1, a2;
  Ac_match_pos ac;
  Ac_match_free_vars_pos free_pos, p1, p2;
  Btm_state bt1 = NULL;

  a1_pos = a2_pos = free_var_forward = 0;  /* to quiet compiler */
  free_pos = NULL;  /* to quiet compiler */

  if (bt->alternative == NO_ALT) {  /* initialize, get first matcher */
    ac = get_ac_match_pos();
    bt->acm = ac;
    ac->t1 = t1; ac->t2 = t2; ac->c1 = c1;
    ac->free_first = NULL; ac->partial_term_size = 0;
    n1 = 0; n2 = 0; total2 = 0; 
    flatten(t1, ac->args1, &n1);
    flatten_mult(t2, ac->args2, ac->mults2, &n2, &total2,
             (int (*)(void*,void*)) term_compare_ncv);
    if (n1 > total2)  /* fail if t1 has more arguments */
      status = FAILURE;
    else {
      /* Assume inputs are ac_canonical, so don't sort.       */
      /* Don't bother to eliminate common arguments, because  */
      /* It usually doesn't pay off.                          */
      ac->n1 = n1; ac->n2 = n2;
      for (i = 0; i < n1; i++)
      ac->match1[i] = -1;
      for (i = 0; i < n2; i++)
      ac->match2[i] = 0;
      for (i = 0; i < n1 && !VARIABLE(ac->args1[i]); i++);
      ac->last_a1_symbol = i-1;
      a1_pos = 0; a2_pos = 0; bt1 = NULL;
      status = GO_FUNCTORS;
    }
  }
  else {  /* continuation, get next matcher */
    ac = bt->acm;
    if (bt->partial) {
      printf("WARNING: partial match_ac on continuation.\n");
      if (c1->partial_term)
      clear_partial_term(ac);
    }
    n1 = ac->n1; n2 = ac->n2;
    if (n1 == 0 && n2 == 0)  /* vacuous success last time */
      status = FAILURE;
    else {
      free_pos = ac->free_last;
      free_var_forward = 0;
      status = GO_FREE_VARS;
    }
  }
    
  while (status != SUCCESS && status != FAILURE) {
    while (status == GO_FUNCTORS) {
      if (a1_pos > ac->last_a1_symbol)
      status = GO_BOUND_VARS;
      else if (a1_pos < 0)
      status = FAILURE;
      else {
      if (bt1) {
        /* remove arrow */
        ac->match1[a1_pos] = -1;
        ac->bt1[a1_pos] = NULL;
        ac->match2[a2_pos]--;
        /* Try for another match with this pair. */
        bt1 = match_bt_next(bt1);
        if (!bt1)
          a2_pos++;
      }

      if (!bt1) {
        /* Look for a match for a1, starting with a2. */
        a1 = ac->args1[a1_pos];
        while (bt1 == NULL && a2_pos < ac->n2) {
          a2 = ac->args2[a2_pos];
          if (SYMNUM(a1) == SYMNUM(a2) &&
            ac->match2[a2_pos] < ac->mults2[a2_pos])
            bt1 = match_bt_first(a1, c1, a2, 0);
          if (bt1 == NULL)
            a2_pos++;
        }
      }

      if (bt1) {   /* We have a match: a1->a2. */
        /* draw arrow */
        ac->match1[a1_pos] = a2_pos;
        ac->bt1[a1_pos] = bt1;
        ac->match2[a2_pos]++;
        a1_pos++; a2_pos = 0; bt1 = NULL;
      }
      else {  /* back up */
        a1_pos--;
        a2_pos = ac->match1[a1_pos];
        bt1 = ac->bt1[a1_pos];
      }
      }
    }  /* while GO_FUNCTORS */
      
    if (status == GO_BOUND_VARS) {
      /* Try to macth (identically) bound variables. */
      ok = match_ac_bound_vars(SYMNUM(t1), ac->args1, n1,
                         ac->args2, ac->mults2, ac->match2, n2,
                         ac->last_a1_symbol+1, ac->bound_matches,
                         &(ac->bound_count), c1);
      if (ok) {
      free_pos = ac->free_first;
      free_var_forward = 1;
      status = GO_FREE_VARS;
      }
      else {  /* backup */
      a1_pos = ac->last_a1_symbol;
      if (a1_pos >= 0) {
        a2_pos = ac->match1[a1_pos];
        bt1 = ac->bt1[a1_pos];
      }
      status = GO_FUNCTORS;
      }
    }

    else if (status == GO_FREE_VARS) {
      if (ac->free_first == NULL) {
      set_up_free_vars(ac, c1);
      free_pos = ac->free_first;
      }
      while (free_pos) {
      if (free_var_match(free_pos, ac->args2, ac->mults2,
                     ac->match2, ac->n2, c1, SYMNUM(ac->t1),
                     !bt->partial && free_pos->next == NULL)) {
        free_pos = free_pos->next;
        free_var_forward = 1;
      }
      else {
        free_pos = free_pos->prev;
        free_var_forward = 0;
      }
      }
      if (free_var_forward) {
      /* Check for non-matched a2 terms. */
      for (i = 0, ok = 1; i < n2 && ok; i++)
        ok = ac->mults2[i] == ac->match2[i];
      if (!ok) {
        /*  Have at least 1 non-matched a2 term. */
        if (bt->partial) {
          c1->partial_term = build_partial_term(ac);
          status = SUCCESS;
        }
        else
          status = GO_FUNCTORS;  /* set up below */
      }
      else
        status = SUCCESS;
      }
      else
      status = GO_FUNCTORS;

      if (status == GO_FUNCTORS) {
      /* Unmark bound variable matches. */
      for (i = 0; i < ac->bound_count; i++)
        ac->match2[ac->bound_matches[i]] -= 1;
      a1_pos = ac->last_a1_symbol;
      if (a1_pos >= 0) {
        a2_pos = ac->match1[a1_pos];
        bt1 = ac->bt1[a1_pos];
      }
      }
    }  /* if GO_FREE_VARS */
  }  /* while !SUCCESS && !FAILURE */

  if (status == SUCCESS)
    bt->alternative = AC_ALT;
  else {
    /* free memory */
    p1 = ac->free_first;
    while (p1) {
      p2 = p1;
      p1 = p1->next;
      free_ac_match_free_vars_pos(p2);
    }
    free_ac_match_pos(ac);
    bt->alternative = NO_ALT;
  }
  return(status == SUCCESS);
}    /* match_ac */

/*************
 *
 *    match_ac_cancel
 *
 *    Free an AC match position.  This is to be used when you have obtained
 *    one or more AC matchers by calling match_ac, but you do not wish
 *    to backtrack to obtain additional AC matchers.  Do not call this
 *    routine if match_ac returned 0.
 *
 *************/

static
void match_ac_cancel(Ac_match_pos ac)
{
  Ac_match_free_vars_pos p1, p2;
  int i;
    
  for (i = 0; i <= ac->last_a1_symbol; i++)
    match_bt_cancel(ac->bt1[i]);
  p1 = ac->free_first;
  while (p1) {
    unbind_free_var(p1, ac->c1);
    p2 = p1;
    p1 = p1->next;
    free_ac_match_free_vars_pos(p2);
  }
  if (ac->partial_term_size > 0)
    clear_partial_term(ac);
  free_ac_match_pos(ac);
}  /* match_ac_cancel */

/*************
 *
 *    Btm_state match_bt_backup(bt)
 *
 *    Back up (freeing nodes) to the most recent node with an alternative.
 *
 *************/

static
Btm_state match_bt_backup(Btm_state bt1)
{
  Btm_state bt2, bt3;

  while (bt1 != NULL && bt1->alternative == NO_ALT) {

    if (bt1->cb) {  /* unbind variable */
      bt1->cb->terms[bt1->varnum] = NULL;
      bt1->cb->contexts[bt1->varnum] = NULL;
    }
      
    if (bt1->prev) {
      bt1 = bt1->prev;
      while (bt1->last_child)
      bt1 = bt1->last_child;
    }
    else {
      bt2 = bt1;
      bt1 = bt1->parent;

      while (bt2) {
      bt3 = bt2;
      bt2 = bt2->next;
      free_btm_state(bt3);
      }

      if (bt1)
      bt1->first_child = bt1->last_child = NULL;
    }
  }
    
  return(bt1);
      
}  /* match_bt_backup */

/*************
 *
 *    match_bt_guts
 *
 *    Main loop for backtracking matching.
 *
 *************/

static
Btm_state match_bt_guts(Btm_state bt1)
{
  Term t1, t2;
  Context c1;
  int vn1, status;
  Btm_state bt2, bt3;

  status = GO;

  while (status == GO) {

    t1 = bt1->t1;
    t2 = bt1->t2;
    c1 = bt1->c1;

    if (bt1->alternative == COMM_ALT) {
      if (match_commute(t1, c1, t2, bt1))
      status = POP;
      else
      status = BACKTRACK;
    }
    else if (bt1->alternative == AC_ALT) {
      if (match_ac(t1, c1, t2, bt1))
      status = POP;
      else
      status = BACKTRACK;
    }
    else if (VARIABLE(t1)) {
      vn1 = VARNUM(t1);
      if (c1->terms[vn1]) {
      if (term_ident(c1->terms[vn1], t2))
        status = POP;
      else
        status = BACKTRACK;
      }
      else {
      BIND_BT(vn1, c1, t2, NULL, bt1)
        status = POP;
      }
    }
      
    else if (VARIABLE(t2))
      status = BACKTRACK;

    else if (SYMNUM(t1) != SYMNUM(t2))
      status = BACKTRACK;
      
    else if (CONSTANT(t1))
      status = POP;
      
    else {  /* both COMPLEX with same symbol (and same arity) */
      int arity = ARITY(t1);

      if (arity == 2 && is_commutative(SYMNUM(t1))) {
      if (match_commute(t1, c1, t2, bt1))
        status = POP;
      else
        status = BACKTRACK;
      }
      else if (arity == 2 && is_assoc_comm(SYMNUM(t1))) {
      if (match_ac(t1, c1, t2, bt1))
        status = POP;
      else
        status = BACKTRACK;
      }
      else {
      int i;
      /* Set up children corresponding to args of <t1,t2>. */
      /* Order not important for correctness. */
      /* AC kids last for efficiency, but keep in order otherwise. */
      bt3 = NULL;
      for (i = 0; i < arity; i++) {

        bt2 = get_btm_state();
        bt2->t1 = t1->args[i];
        bt2->t2 = t2->args[i];
        bt2->c1 = c1;
        bt2->parent = bt1;

        if (is_assoc_comm(SYMNUM(bt2->t1))) {
          /* insert at end */
          bt2->prev = bt1->last_child;
          if (bt1->last_child)
            bt1->last_child->next = bt2;
          else
            bt1->first_child = bt2;
          bt1->last_child = bt2;
        }
        else {
          if (bt3) {
            /* insert after bt3 */
            bt2->next = bt3->next;
            bt2->prev = bt3;
            bt3->next = bt2;
            if (bt2->next)
            bt2->next->prev = bt2;
            else
            bt1->last_child = bt2;
          }
          else {
            /* insert at beginning */
            bt2->next = bt1->first_child;
            if (bt2->next)
            bt2->next->prev = bt2;
            else
            bt1->last_child = bt2;
            bt1->first_child = bt2;
          }
          bt3 = bt2;
        }
      }

      bt1 = bt1->first_child;
      status = GO;
      }
    }
      
    if (status == POP) {
      while (!bt1->next && bt1->parent)
      bt1 = bt1->parent;
      if (!bt1->next)
      status = SUCCESS;
      else {
      bt1 = bt1->next;
      status = GO;
      }
    }
    else if (status == BACKTRACK) {
      bt1 = match_bt_backup(bt1);
      if (bt1)
      status = GO;
      else
      status = FAILURE;
    }
  }
  return(bt1);
}  /* match_bt_guts */

/*************
 *
 *  match_commute()
 *
 *  There is nothing fancy here.  We simply try to unify both ways.
 *  We can get redundant matches if both ways match, for example,
 *  f(a,x) and f(a,a) match twice, both times with the same substitution.
 *
 *************/

static
int match_commute(Term t1, Context c1, Term t2, Btm_state bt)
{
  Btm_state bt1, bt2;

  if (bt->alternative == NO_ALT) {  /* first call */
    bt->alternative = COMM_ALT;
    bt->flipped = 0;

    /* Set up 2 subproblems, then match guts. */

    bt1 = get_btm_state();  bt2 = get_btm_state();
    bt1->next = bt2; bt2->prev = bt1;
    bt1->c1 = c1;
    bt2->c1 = c1;
    bt1->t1 = t1->args[0]; bt1->t2 = t2->args[0];
    bt2->t1 = t1->args[1]; bt2->t2 = t2->args[1];

    bt->position_bt = match_bt_guts(bt1);
  }
  else  /* continuation */
    bt->position_bt = match_bt_next(bt->position_bt);

  if (!bt->position_bt && !bt->flipped) {

    /* Set up 2 subproblems, with t2 flipped, then match guts. */

    bt1 = get_btm_state();  bt2 = get_btm_state();
    bt1->next = bt2; bt2->prev = bt1;
    bt1->c1 = c1;
    bt2->c1 = c1;
    bt1->t1=t1->args[0]; bt1->t2=t2->args[1];
    bt2->t1=t1->args[1]; bt2->t2=t2->args[0];

    bt->flipped = 1;
    bt->position_bt = match_bt_guts(bt1);
  }

  if (bt->position_bt)
    return(1);
  else {
    bt->alternative = NO_ALT;
    return(0);
  }
    
}  /* match_commute */

/*************
 *
 *    p_acm -- print an ac match position.
 *
 *************/

static
void p_acm(Ac_match_pos ac)
{
  int i;
  Ac_match_free_vars_pos p;
  
  printf("Ac_match_pos %x.\n", (unsigned) ac);
  printf("t1: "); p_term(ac->t1);
  printf("t2: "); p_term(ac->t2);
  for (i = 0; i < ac->n1; i++) {
    fprint_term(stdout, ac->args1[i]);
    printf(" %d ",ac->match1[i]);
  }
  printf("\n");
  for (i = 0; i < ac->n2; i++) {
    fprint_term(stdout, ac->args2[i]);
    printf(" <%d,%d> ",ac->mults2[i],ac->match2[i]);
  }
  printf("\n");

  printf("last_a1_symbol=%d.\n",ac->last_a1_symbol);
  printf("free vars list <symbol,coef>:\n");
  for (p = ac->free_first; p; p = p->next) {
    printf("<%d,%d>, ", p->varnum, p->coef);
    for (i = 0; i < p->n; i++) {
      fprint_term(stdout,ac->args2[p->targets[i]]);
      printf(":%d ",p->combo[i]);
    }
    printf("\n");
  }
  printf("\n");
}  /* p_acm */

/*************
 *
 *   p_btm_state()
 *
 *************/

/* DOCUMENTATION
This routine prints (to stdout) a Btm_state.  It is not pretty.
*/

/* PUBLIC */
void p_btm_state(Btm_state bt)
{
  printf("\nBtm node %x.\n", (unsigned) bt);
  printf("t1: "); p_term(bt->t1);
  printf("t2: "); p_term(bt->t2);
  printf("c1: "); p_context(bt->c1);
  printf("varnum: %d\n", bt->varnum);
  printf("cb: "); p_context(bt->c1);
  printf("alternative: %d\n", bt->alternative);
  printf("flipped: %d\n", bt->alternative);
  printf("position_bt: %x\n", (unsigned) bt->position_bt);
  printf("partial: %d\n", bt->partial);
  p_acm(bt->acm);
}  /* p_btm_state */

/*************
 *
 *    match_bt_first
 *
 *
 *************/

/* DOCUMENTATION
This is backtracking matching, to be used when there
can be more than one unifier.  This version handles (any number of)
commutative (C) and associative-commutative (AC) function symbols.
<P>
The flag `partial' says that if the top level is AC, then
not all arguments of t2 have to be matched.  The non-matched
args are put in c1->partial_term.  Partial matches are allowed
for the top level only.  This is useful for AC rewriting.
<P>
If any AC terms are in t1 or t2, then both t1 and t2 should be
in `ac_canonical()' form before the call, that is, AC terms are
right associated and sorted.  C terms are in t1 or t2
need not be c_canonical.  (Commutatvie matching is primitive,
and you can get duplicate unifiers.)
<P>
Get first matching substitution.  Return position for match_bt_next()
calls.  Here is an example.  Assume we have terms t1 and t2.
<PRE>
  {
    Context c1 = get_context();
    Btm_state bt = match_bt_first(t1, c1, t2, 0);
    while (bt != NULL) {
        Term t3 = apply(t1, c1);
        zap_term(t3);
        bt = match_bt_next(bt);
        }
    free_context(c1);
  }
</PRE>
If you quit before NULL is returned, call match_bt_cancel(bt)
to clear substitutions and free memory.
*/

/* PUBLIC */
Btm_state match_bt_first(Term t1, Context c1, Term t2, int partial)
{
  Btm_state bt;

  bt = get_btm_state();
  bt->t1 = t1; bt->t2 = t2; bt->c1 = c1;
  bt->partial = partial;
  return(match_bt_guts(bt));

}  /* match_bt */

/*************
 *
 *    match_bt_next -- see match_bt_first
 *
 *    Get next unifier.  Return position for subsequent calls.
 *
 *************/

/* DOCUMENTATION
This routine gets the next matching substitution.
See match_bt_first() for details.
*/

/* PUBLIC */
Btm_state match_bt_next(Btm_state bt1)
{
  /* Go to last node in tree, then back up to a node with an alternative. */

  while (bt1->next)
    bt1 = bt1->next;
  while (bt1->last_child)
    bt1 = bt1->last_child;

  bt1 = match_bt_backup(bt1);

  if (bt1)
    return(match_bt_guts(bt1));
  else
    return NULL;
}  /* match_bt_next */

/*************
 *
 *    match_bt_cancel
 *
 *    This routine should be called if the rest of a sequence of
 *    unifiers is not called for.  It clears substitutions and
 *    frees memory.
 *
 *************/

/* DOCUMENTATION
This routine clears any substitution and frees memory associated
with a backtrack matching state.  This should be called if you
get some, but not all, matching substitutions in backtrack matching.
See match_bt_first().
*/

/* PUBLIC */
void match_bt_cancel(Btm_state bt)
{
  Btm_state bt1, bt2;

  for (bt1 = bt; bt1 != NULL; ) {

    match_bt_cancel(bt1->first_child);
      
    if (bt1->alternative == COMM_ALT)
      /* match_bt_guts leaves us at the second child. */
      match_bt_cancel(bt1->position_bt->prev);
    else if (bt1->alternative == AC_ALT) {
      match_ac_cancel(bt1->acm);
    }
    else if (bt1->cb) {
      bt1->cb->terms[bt1->varnum] = NULL;
      bt1->cb->contexts[bt1->varnum] = NULL;
    }
    bt2 = bt1;
    bt1 = bt1->next;
    free_btm_state(bt2);
  }
}  /* match_bt_cancel */


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