/*
* Flatten all terms in flat->queue to conjuncts
* - all terms in the queue must also be in the cache
* - f_ite: if true, flatten (ite c a b)
* - f_iff: if true, flatten (iff a b)
*/
static void flattener_build_conjuncts(flattener_t *flat, bool f_ite, bool f_iff) {
term_table_t *terms;
int_queue_t *queue;
composite_term_t *d;
term_t t, u, v;
uint32_t i, n;
queue = &flat->queue;
terms = flat->terms;
while (! int_queue_is_empty(queue)) {
t = int_queue_pop(queue);
switch (term_kind(terms, t)) {
case ITE_TERM:
case ITE_SPECIAL:
d = ite_term_desc(terms, t);
assert(d->arity == 3);
if (f_ite && is_boolean_term(terms, d->arg[1])) {
assert(is_boolean_term(terms, d->arg[2]));
/*
* If t is (ite C A B)
* u := (C => A)
* v := (not C => B)
* Otherwise, t is (not (ite C A B))
* u := (C => not A)
* v := (not C => not B)
*/
u = d->arg[1]; // A
v = d->arg[2]; // B
if (is_neg_term(t)) {
u = opposite_term(u);
v = opposite_term(v);
}
u = mk_implies(flat->manager, d->arg[0], u); // (C => u)
v = mk_implies(flat->manager, opposite_term(d->arg[0]), v); // (not C) => v
flattener_push_term(flat, u);
flattener_push_term(flat, v);
continue;
}
break;
case EQ_TERM:
d = eq_term_desc(terms, t);
assert(d->arity == 2);
if (f_iff && is_boolean_term(terms, d->arg[0])) {
assert(is_boolean_term(terms, d->arg[1]));
/*
* t is either (iff A B) or (not (iff A B)):
*/
u = d->arg[0]; // A
v = d->arg[1]; // B
if (is_neg_term(t)) {
u = opposite_term(u);
}
// flatten to (u => v) and (v => u)
t = mk_implies(flat->manager, u, v); // (u => v)
u = mk_implies(flat->manager, v, u); // (v => u);
flattener_push_term(flat, t);
flattener_push_term(flat, u);
continue;
}
break;
case OR_TERM:
if (is_neg_term(t)) {
/*
* t is (not (or a[0] ... a[n-1]))
* it flattens to (and (not a[0]) ... (not a[n-1]))
*/
d = or_term_desc(terms, t);
n = d->arity;
for (i=0; i<n; i++) {
flattener_push_term(flat, opposite_term(d->arg[i]));
}
continue;
}
break;
default:
break;
}
ivector_push(&flat->resu, t);
}
// clean up the cache
assert(int_queue_is_empty(queue));
int_hset_reset(&flat->cache);
}
/*
* Check whether t occurs in v
* - t must be a free root
* - v must be a valid term
*/
static bool bfs_occurs_check(intern_tbl_t *tbl, term_t t, term_t v) {
term_table_t *terms;
int_queue_t *queue;
int_hset_t *cache;
int32_t x;
bool found;
assert(intern_tbl_root_is_free(tbl, t));
assert(is_pos_term(t) && term_kind(tbl->terms, t) == UNINTERPRETED_TERM);
terms = tbl->terms;
queue = intern_tbl_get_queue(tbl);
cache = intern_tbl_get_cache(tbl);
assert(int_queue_is_empty(queue) && int_hset_is_empty(cache));
bfs_visit_term(tbl, v);
found = false;
do {
x = int_queue_pop(queue);
switch (kind_for_idx(terms, x)) {
case CONSTANT_TERM:
case ARITH_CONSTANT:
case BV64_CONSTANT:
case BV_CONSTANT:
case VARIABLE:
break;
case UNINTERPRETED_TERM:
if (x == index_of(t)) {
// found a cycle
found = true;
goto done;
}
break;
case ARITH_EQ_ATOM:
case ARITH_GE_ATOM:
bfs_visit_term(tbl, integer_value_for_idx(terms, x));
break;
case ITE_TERM:
case ITE_SPECIAL:
case APP_TERM:
case UPDATE_TERM:
case TUPLE_TERM:
case EQ_TERM:
case DISTINCT_TERM:
case FORALL_TERM:
case LAMBDA_TERM:
case OR_TERM:
case XOR_TERM:
case ARITH_BINEQ_ATOM:
case BV_ARRAY:
case BV_DIV:
case BV_REM:
case BV_SDIV:
case BV_SREM:
case BV_SMOD:
case BV_SHL:
case BV_LSHR:
case BV_ASHR:
case BV_EQ_ATOM:
case BV_GE_ATOM:
case BV_SGE_ATOM:
bfs_visit_composite(tbl, composite_for_idx(terms, x));
break;
case BIT_TERM:
case SELECT_TERM:
bfs_visit_term(tbl, select_for_idx(terms, x)->arg);
break;
case POWER_PRODUCT:
bfs_visit_pprod(tbl, pprod_for_idx(terms, x));
break;
case ARITH_POLY:
bfs_visit_poly(tbl, polynomial_for_idx(terms, x));
break;
case BV64_POLY:
bfs_visit_bvpoly64(tbl, bvpoly64_for_idx(terms, x));
break;
case BV_POLY:
bfs_visit_bvpoly(tbl, bvpoly_for_idx(terms, x));
break;
default:
assert(false);
abort();
break;
}
} while (! int_queue_is_empty(queue));
done:
int_hset_reset(cache);
int_queue_reset(queue);
return found;
}
/*
* Process disjuncts and universal quantifiers
* - input = all terms in the queue
* - f_ite: if true, flatten (ite c a b)
* - f_iff: if true, flatten (iff a b)
*/
static void flattener_forall_disjuncts(flattener_t *flat, bool f_ite, bool f_iff) {
term_table_t *terms;
int_queue_t *queue;
composite_term_t *d;
term_t t, u, v;
uint32_t i, n;
queue = &flat->queue;
terms = flat->terms;
while (! int_queue_is_empty(queue)) {
t = int_queue_pop(queue);
switch (term_kind(terms, t)) {
case ITE_TERM:
case ITE_SPECIAL:
d = ite_term_desc(terms, t);
assert(d->arity == 3);
if (f_ite && is_boolean_term(terms, d->arg[1])) {
assert(is_boolean_term(terms, d->arg[2]));
/*
* If t is (ite C A B)
* u := (C AND A)
* v := (not C AND B)
* Otherwise, t is (not (ite C A B))
* u := (C AND not A)
* v := (not C AND not B)
*/
u = d->arg[1]; // A
v = d->arg[2]; // B
if (is_neg_term(t)) {
u = opposite_term(u); // NOT A
v = opposite_term(v); // NOT B
}
u = mk_binary_and(flat->manager, d->arg[0], u); // (C AND u)
v = mk_binary_and(flat->manager, opposite_term(d->arg[0]), v); // (not C) AND v
flattener_push_term(flat, u);
flattener_push_term(flat, v);
continue;
}
break;
case EQ_TERM:
d = eq_term_desc(terms, t);
assert(d->arity == 2);
if (f_iff && is_boolean_term(terms, d->arg[0])) {
assert(is_boolean_term(terms, d->arg[1]));
/*
* t is either (iff A B) or (not (iff A B)):
*/
u = d->arg[0]; // A
v = d->arg[1]; // B
if (is_neg_term(t)) {
u = opposite_term(u);
}
// flatten to (u AND v) or ((not u) AND (not v))
t = mk_binary_and(flat->manager, u, v); // (u AND v)
u = mk_binary_and(flat->manager, opposite_term(u), opposite_term(v)); // (not u AND not v);
flattener_push_term(flat, t);
flattener_push_term(flat, u);
continue;
}
break;
case OR_TERM:
if (is_pos_term(t)) {
/*
* t is (or a[0] ... a[n-1])
*/
d = or_term_desc(terms, t);
n = d->arity;
for (i=0; i<n; i++) {
flattener_push_term(flat, d->arg[i]);
}
continue;
}
break;
case FORALL_TERM:
if (is_pos_term(t)) {
d = forall_term_desc(terms, t);
n = d->arity;
assert(n >= 2);
/*
* t is (FORALL x_0 ... x_k : body)
* body is the last argument in the term descriptor
*/
flattener_push_term(flat, d->arg[n-1]);
continue;
}
break;
default:
break;
}
ivector_push(&flat->resu, t);
}
// clean up the cache
assert(int_queue_is_empty(queue));
int_hset_reset(&flat->cache);
}
/*
* Check whether f is a range constraint
* - if so return a term t and fill in vector v with the formula's constants
* - otherwise, return NULL_TERM
*
* Side effect: use queue and cache.
* v may be modified even if the function returns NULL_TERM.
*/
static term_t formula_is_range_constraint(sym_breaker_t *breaker, term_t f, ivector_t *v) {
int_queue_t *queue;
int_hset_t *cache;
term_table_t *terms;
intern_tbl_t *intern;
term_t r, t;
term_t x, a, y, b;
uint32_t neqs;
queue = &breaker->queue;
cache = &breaker->cache;
terms = breaker->terms;
intern = &breaker->ctx->intern;
assert(int_queue_is_empty(queue) && int_hset_is_empty(cache));
push_term(queue, cache, f);
neqs = 0;
t = NULL_TERM;
y = NULL_TERM; // prevent GCC warning
b = NULL_TERM; // prevent GCC warning
/*
* Invariants:
* - neqs = number of equality atoms seen so far
* - if neq == 1, then the first equality is stored as (y == b) where b is a constant
* - if neq >= 2, then all equalities seen so far were of the form (x == constant)
*/
do {
// r := root of the first term in the queue
r = intern_tbl_get_root(intern, int_queue_pop(queue));
switch (match_term(breaker->ctx, r, &a, &x)) {
case MATCH_FALSE: // skip false terms
break;
case MATCH_OR:
push_children(queue, cache, or_term_desc(terms, r));
break;
case MATCH_EQ:
assert(term_is_constant(terms, a));
if (neqs == 0) {
y = x; b = a;
} else if (neqs == 1) {
/*
* First equality: (y == b). Second equality: (x == a)
*/
if (y == x) {
// y is the common term, a and b are constant
ivector_push(v, b);
ivector_push(v, a);
} else if (y == a && term_is_uconst(terms, x)) {
// y is the common term, b and x are constant
ivector_push(v, b);
ivector_push(v, a);
} else if (x == b && term_is_uconst(terms, y)) {
// b is the common term, y and a are constant
ivector_push(v, y);
ivector_push(v, a);
y = b;
} else if (a == b && term_is_uconst(terms, y) && term_is_uconst(terms, x)) {
// b is the common term, y and x are constant
ivector_push(v, y);
ivector_push(v, x);
y = b;
} else {
// abort
goto done;
}
} else {
/*
* All equalities so far have the form (y == constant)
* - the current equality is (x == a)
*/
if (y == x) {
ivector_push(v, a); // match
} else if (y == a && term_is_constant(terms, x)) {
ivector_push(v, x); // swap a and x
} else {
// no match
goto done;
}
}
neqs ++;
break;
case MATCH_IFF:
/*
* the returned term x is equivalent to t
*/
push_term(queue, cache, x);
break;
default:
// abort
goto done;
}
} while (! int_queue_is_empty(queue));
assert(y != NULL_TERM && t == NULL_TERM);
if (neqs >= 2) {
assert(v->size == neqs);
t = y;
}
done:
int_queue_reset(queue);
int_hset_reset(cache);
return t;
}
