/*
* Merge the exists and forall variables of constraint i
* - store the variables in solver->all_vars
* - store their values in solver->all_values
*/
static void ef_build_full_map(ef_solver_t *solver, uint32_t i) {
ef_cnstr_t *cnstr;
ivector_t *v;
uint32_t n;
assert(i < ef_prob_num_constraints(solver->prob));
cnstr = solver->prob->cnstr + i;
// collect all variables of cnstr in solver->all_vars
v = &solver->all_vars;
ivector_reset(v);
n = ef_constraint_num_evars(cnstr);
ivector_add(v, cnstr->evars, n);
n = ef_constraint_num_uvars(cnstr);
ivector_add(v, cnstr->uvars, n);
// project the evalues onto the exists variable of constraint i
// store the results in all_values
v = &solver->all_values;
n = ef_constraint_num_evars(cnstr);
resize_ivector(v, n);
v->size = n;
ef_project_exists_model(solver->prob, solver->evalue, cnstr->evars, v->data, n);
// copy the uvalues for constraint i (from uvalue_aux to v)
n = ef_constraint_num_uvars(cnstr);
assert(n == solver->uvalue_aux.size);
ivector_add(v, solver->uvalue_aux.data, n);
#if EF_VERBOSE
printf("Full map\n");
print_full_map(stdout, solver);
fflush(stdout);
#endif
}
/*
* Initialize the exists context
* - asserts all conditions from solver->prob
* - if max_samples is positive, also apply pre-sampling to all the universal constraints
*
* - solver->status is set as follows
* EF_STATUS_SEARCHING: means not solved yet
* EF_STATUS_UNSAT: if the exists context is trivially UNSAT
* EF_STATUS_..._ERROR: if something goes wrong
* EF_STATUS_INTERRUPTED if the pre-sampling is interrupted
*/
static void ef_solver_start(ef_solver_t *solver) {
int32_t code;
uint32_t i, n;
assert(solver->status == EF_STATUS_IDLE);
solver->status = EF_STATUS_SEARCHING;
init_exists_context(solver);
code = exists_context_assert_conditions(solver); // add all conditions
if (code < 0) {
// assertion error
solver->status = EF_STATUS_ASSERT_ERROR;
solver->error_code = code;
} else if (code == TRIVIALLY_UNSAT) {
solver->status = EF_STATUS_UNSAT;
} else if (solver->max_samples > 0) {
/*
* run the pre-sampling stuff
*/
n = ef_prob_num_constraints(solver->prob);
for (i=0; i<n; i++) {
ef_sample_constraint(solver, i);
if (solver->status != EF_STATUS_SEARCHING) break;
}
}
}
/*
* Option 2: generalize by substitution
* - return (prob->cnstr[i].guarantee with y := value)
*/
static term_t ef_generalize2(ef_prob_t *prob, uint32_t i, term_t *value) {
ef_cnstr_t *cnstr;
uint32_t n;
term_t g;
assert(i < ef_prob_num_constraints(prob));
cnstr = prob->cnstr + i;
n = ef_constraint_num_uvars(cnstr);
g = ef_substitution(prob, cnstr->uvars, value, n, cnstr->guarantee);
return g;
}
/*
* Learn a constraint for the exists variable based on the
* existing forall witness for constraint i:
* - the witness is defined by the uvars of constraint i
* and the values stored in uvalue_aux.
*
* This function adds a constraint to the exists_context that will remove the
* current exists model:
* - if solver->option is EF_NOGEN_OPTION, the new constraint is
* of the form (or (/= var[0] eval[k0]) ... (/= var[k-1] eval[k-1]))
* where var[0 ... k-1] are the exist variables of constraint i
* - if solver->option is EF_GEN_BY_SUBST_OPTION, we build a new
* constraint by substitution (option 2)
*
* If something goes wrong, then solver->status is updated to EF_STATUS_ERROR.
* If the new learned assertion makes the exist context trivially unsat
* then context->status is set to EF_STATUS_UNSAT.
* Otherwise context->status is kept as is.
*/
static void ef_solver_learn(ef_solver_t *solver, uint32_t i) {
ef_cnstr_t *cnstr;
term_t *val;
term_t new_constraint;
uint32_t n;
int32_t code;
assert(i < ef_prob_num_constraints(solver->prob));
cnstr = solver->prob->cnstr + i;
switch (solver->option) {
case EF_NOGEN_OPTION:
/*
* project solver->evalues on the existential
* variables that occur in constraint i.
* then build (or (/= evar[0] val[0]) ... (/= evar[n-1] val[n-1]))
*/
n = ef_constraint_num_evars(cnstr);
resize_ivector(&solver->evalue_aux, n);
solver->evalue_aux.size = n;
val = solver->evalue_aux.data;
ef_project_exists_model(solver->prob, solver->evalue, cnstr->evars, val, n);
new_constraint = ef_generalize1(solver->prob, cnstr->evars, val, n);
break;
case EF_GEN_BY_SUBST_OPTION:
val = solver->uvalue_aux.data;
new_constraint = ef_generalize2(solver->prob, i, val);
if (new_constraint < 0) {
// error in substitution
solver->status = EF_STATUS_SUBST_ERROR;
solver->error_code = new_constraint;
return;
}
break;
case EF_GEN_BY_PROJ_OPTION:
default: // added this to prevent bogus GCC warning
new_constraint = ef_generalize3(solver, i);
if (new_constraint < 0) {
return;
}
break;
}
// add the new constraint to the exists context
code = update_exists_context(solver, new_constraint);
if (code == TRIVIALLY_UNSAT) {
solver->status = EF_STATUS_UNSAT;
} else if (code < 0) {
solver->status = EF_STATUS_ASSERT_ERROR;
solver->error_code = code;
}
}
/*
* Show witness found for constraint i
*/
void print_forall_witness(FILE *f, ef_solver_t *solver, uint32_t i) {
ef_prob_t *prob;
ef_cnstr_t *cnstr;
uint32_t j, n;
prob = solver->prob;
assert(i < ef_prob_num_constraints(prob));
cnstr = prob->cnstr + i;
n = ef_constraint_num_uvars(cnstr);
for (j=0; j<n; j++) {
fprintf(f, "%s := ", yices_get_term_name(cnstr->uvars[j]));
yices_pp_term(f, solver->uvalue_aux.data[j], 100, 1, 10);
}
}
/*
* Check whether the current exists_model can be falsified by one
* of the universal constraints.
* - scan the universal constraints starting from solver->scan_idx
* - the current exists model is defined by
* the mapping from solver->prob->evars to solver->evalues
*
* Update the solver->status as follows:
* - if no constraint falsifies the model, solver->status = EF_STATUS_SAT
* - if some constraint falsifies the model, then solver->status may be
* updated to EF_STATUS_UNSAT (trivially unsat after learning)
* - if something goes wrong, solver->status = EF_STATUS_ERROR
*
* If constraint i falsifies the model then solver->scan_idx is
* set to (i+1) modulo num_constraints.
*/
static void ef_solver_check_exists_model(ef_solver_t *solver) {
smt_status_t status;
uint32_t i, n;
n = ef_prob_num_constraints(solver->prob);
/*
* Special case: if there are no universal constraints
* we return SAT immediately.
*/
if (n == 0) {
solver->status = EF_STATUS_SAT;
return;
}
i = solver->scan_idx;
do {
tprintf(solver->trace, 4, "(EF: testing candidate against constraint %"PRIu32")\n", i);
status = ef_solver_test_exists_model(solver, i);
trace_candidate_check(solver, i, status);
switch (status) {
case STATUS_SAT:
case STATUS_UNKNOWN:
#if EF_VERBOSE
printf("Counterexample for constraint[%"PRIu32"]\n", i);
print_forall_witness(stdout, solver, i);
printf("\n");
fflush(stdout);
#endif
ef_solver_learn(solver, i);
default:
i ++;
if (i == n) {
i = 0;
}
break;
}
} while (status == STATUS_UNSAT && i != solver->scan_idx);
solver->scan_idx = i; // prepare for the next call
if (status == STATUS_UNSAT) {
// done a full scan
solver->status = EF_STATUS_SAT;
}
}
/*
* Compute an implicant for constraint i
* - we must have an assignment for the exists variable in solver->evalue
* and an assignment for the universal variables of constraints i in
* solver->uvalue_aux.
* - this builds and store the full model for constraint i in solver->full_model
* then construct and store the implicant in solver->implicant
*
* Error codes: set solver->status to EF_STATUS_ERROR
* - this may happen if yices_model_from_map or yices_implicant_for_fomuulas fail
*/
static void ef_build_implicant(ef_solver_t *solver, uint32_t i) {
model_t *mdl;
ef_cnstr_t *cnstr;
term_vector_t *v;
term_t a[2];
uint32_t n;
int32_t code;
assert(i < ef_prob_num_constraints(solver->prob));
// free the current full model if any
if (solver->full_model != NULL) {
yices_free_model(solver->full_model);
solver->full_model = NULL;
}
// build the full_map and the correspongin model.
ef_build_full_map(solver, i);
n = solver->all_vars.size;
assert(n == solver->all_values.size);
mdl = yices_model_from_map(n, solver->all_vars.data, solver->all_values.data);
if (mdl == NULL) {
// error in the model construction
solver->status = EF_STATUS_ERROR; // TODO: add another code
solver->error_code = yices_error_code();
return;
}
solver->full_model = mdl;
cnstr = solver->prob->cnstr + i;
a[0] = cnstr->assumption;
a[1] = opposite_term(cnstr->guarantee);
v = &solver->implicant;
v->size = 0;
code = yices_implicant_for_formulas(mdl, 2, a, v);
if (code < 0) {
solver->status = EF_STATUS_ERROR;
solver->error_code = yices_error_code();
}
#if 1
printf("Implicant\n");
yices_pp_term_array(stdout, v->size, v->data, 120, UINT32_MAX, 0, 0);
printf("(%"PRIu32" literals)\n", v->size);
#endif
}
/*
* Sampling for the i-th constraint in solver->prob
* - search for at most max_samples y's that satisfy the assumption of constraint i in prob
* - for each such y, add a new constraint to the exist context ctx
* - max_samples = bound on the number of samples to take (must be positive)
*
* Constraint i is of the form
* (FORALL Y_i: B_i(Y_i) => C(X_i, Y_i))
* - every sample is a model y_i that satisfies B_i.
* - for each sample, we learn that any good candidate X_i must satisfy C(X_i, y_i).
* So we add the constraint C(X_i, y_i) to ctx.
*
* Update the solver->status to
* - EF_STATUS_UNSAT if the exits context is trivially unsat
* - EF_STATUS_..._ERRORif something goes wrong
* - EF_STATUS_INTERRUPTED if a call to check/recheck context is interrupted
* keep it unchanged otherwise (should be EF_STATUS_SEARCHING).
*/
static void ef_sample_constraint(ef_solver_t *solver, uint32_t i) {
context_t *sampling_ctx;
ef_cnstr_t *cnstr;
term_t *value;
uint32_t nvars, samples;
int32_t ucode, ecode;
smt_status_t status;
term_t cnd;
assert(i < ef_prob_num_constraints(solver->prob) && solver->max_samples > 0);
cnstr = solver->prob->cnstr + i;
/*
* make uvalue_aux large enough
* its size = number of universal variables in constraint i
*/
nvars = ef_constraint_num_uvars(cnstr);
resize_ivector(&solver->uvalue_aux, nvars);
solver->uvalue_aux.size = nvars;
value = solver->uvalue_aux.data;
samples = solver->max_samples;
/*
* assert the assumption in the forall context
*/
sampling_ctx = get_forall_context(solver);
ucode = assert_formula(sampling_ctx, cnstr->assumption);
while (ucode == CTX_NO_ERROR) {
status = satisfy_context(sampling_ctx, solver->parameters, cnstr->uvars, nvars, value, NULL);
switch (status) {
case STATUS_SAT:
case STATUS_UNKNOWN:
// learned condition on X:
cnd = ef_substitution(solver->prob, cnstr->uvars, value, nvars, cnstr->guarantee);
if (cnd < 0) {
solver->status = EF_STATUS_SUBST_ERROR;
solver->error_code = cnd;
goto done;
}
ecode = update_exists_context(solver, cnd);
if (ecode < 0) {
solver->status = EF_STATUS_ASSERT_ERROR;
solver->error_code = ecode;
goto done;
}
if (ecode == TRIVIALLY_UNSAT) {
solver->status = EF_STATUS_UNSAT;
goto done;
}
break;
case STATUS_UNSAT:
// no more samples for this constraints
goto done;
case STATUS_INTERRUPTED:
solver->status = EF_STATUS_INTERRUPTED;
goto done;
default:
solver->status = EF_STATUS_CHECK_ERROR;
solver->error_code = status;
goto done;
}
samples --;
if (samples == 0) goto done;
ucode = assert_blocking_clause(sampling_ctx);
}
/*
* if ucode < 0, something went wrong in assert_formula
* or in assert_blocking_clause
*/
if (ucode < 0) {
solver->status = EF_STATUS_ASSERT_ERROR;
solver->error_code = ucode;
}
done:
clear_forall_context(solver, true);
}
/*
* Test the current exists model using universal constraint i
* - i must be a valid index (i.e., 0 <= i < solver->prob->num_cnstr)
* - this checks the assertion B_i and not C_i after replacing existential
* variables by their values (stored in evalue)
* - return code:
* if STATUS_SAT (or STATUS_UNKNOWN): a model of (B_i and not C_i)
* is found and stored in uvalue_aux
* if STATUS_UNSAT: no model found (current exists model is good as
* far as constraint i is concerned)
* anything else: an error or interruption
*
* - if we get an error or interruption, solver->status is updated
* otherwise, it is kept as is (should be EF_STATUS_SEARCHING)
*/
static smt_status_t ef_solver_test_exists_model(ef_solver_t *solver, uint32_t i) {
context_t *forall_ctx;
ef_cnstr_t *cnstr;
term_t *value;
term_t g;
uint32_t n;
int32_t code;
smt_status_t status;
assert(i < ef_prob_num_constraints(solver->prob));
cnstr = solver->prob->cnstr + i;
n = ef_prob_num_evars(solver->prob);
g = ef_substitution(solver->prob, solver->prob->all_evars, solver->evalue, n, cnstr->guarantee);
if (g < 0) {
// error in substitution
solver->status = EF_STATUS_SUBST_ERROR;
solver->error_code = g;
return STATUS_ERROR;
}
/*
* make uvalue_aux large enough
*/
n = ef_constraint_num_uvars(cnstr);
resize_ivector(&solver->uvalue_aux, n);
solver->uvalue_aux.size = n;
value = solver->uvalue_aux.data;
forall_ctx = get_forall_context(solver);
code = forall_context_assert(solver, cnstr->assumption, g); // assert B_i(Y_i) and not g(Y_i)
if (code == CTX_NO_ERROR) {
status = satisfy_context(forall_ctx, solver->parameters, cnstr->uvars, n, value, NULL);
switch (status) {
case STATUS_SAT:
case STATUS_UNKNOWN:
case STATUS_UNSAT:
break;
case STATUS_INTERRUPTED:
solver->status = EF_STATUS_INTERRUPTED;
break;
default:
solver->status = EF_STATUS_CHECK_ERROR;
solver->error_code = status;
break;
}
} else if (code == TRIVIALLY_UNSAT) {
assert(context_status(forall_ctx) == STATUS_UNSAT);
status = STATUS_UNSAT;
} else {
// error in assertion
solver->status = EF_STATUS_ASSERT_ERROR;
solver->error_code = code;
status = STATUS_ERROR;
}
clear_forall_context(solver, true);
return status;
}
/*
* Sample exists models
* - stop when we find one that's not refuted by the forall constraints
* - or when we reach the iteration bound
*
* Result:
* - solver->status = EF_STATUS_ERROR if something goes wrong
* - solver->status = EF_STATUS_INTERRUPTED if one of the calls to
* check_context is interrupted
* - solver->status = EF_STATUS_UNSAT if all efmodels have been tried and none
* of them worked
* - solver->status = EF_STATUS_UNKNOWN if the iteration limit is reached
* - solver->status = EF_STATUS_SAT if a good model is found
*
* In the later case,
* - the model is stored in solver->exists_model
* - also it's available as a mapping form solver->prob->evars to solver->evalues
*
* Also solver->iters stores the number of iterations used.
*/
static void ef_solver_search(ef_solver_t *solver) {
smt_status_t stat;
uint32_t i, max;
max = solver->max_iters;
i = 0;
assert(max > 0);
#if 0
printf("\nEF search: %"PRIu32" constraints, %"PRIu32" exists vars, %"PRIu32" forall vars\n",
ef_prob_num_constraints(solver->prob),
ef_prob_num_evars(solver->prob),
ef_prob_num_uvars(solver->prob));
// printf("\nConditions on the exists variables:\n");
// yices_pp_term_array(stdout, ef_prob_num_conditions(solver->prob), solver->prob->conditions, 120, UINT32_MAX, 0, 0);
#endif
ef_solver_start(solver);
while (solver->status == EF_STATUS_SEARCHING && i < max) {
#if 0
printf("\n--- Iteration %"PRIu32" (scan_idx = %"PRIu32") ---\n", i, solver->scan_idx);
#endif
stat = ef_solver_check_exists(solver);
switch (stat) {
case STATUS_SAT:
case STATUS_UNKNOWN:
// we have a candidate exists model
// check it and learn what we can
#if 0
// FOR DEBUGGING
printf("Candidate exists model:\n");
print_ef_solution(stdout, solver);
printf("\n");
#endif
ef_solver_check_exists_model(solver);
break;
case STATUS_UNSAT:
solver->status = EF_STATUS_UNSAT;
break;
case STATUS_INTERRUPTED:
solver->status = EF_STATUS_INTERRUPTED;
break;
default:
solver->status = EF_STATUS_CHECK_ERROR;
solver->error_code = stat;
break;
}
i ++;
}
/*
* Cleanup and set status if i == max
*/
if (solver->status != EF_STATUS_SAT && solver->exists_model != NULL) {
yices_free_model(solver->exists_model);
solver->exists_model = NULL;
if (solver->status == EF_STATUS_SEARCHING) {
assert(i == max);
solver->status = EF_STATUS_UNKNOWN;
}
}
solver->iters = i;
}
/*
* Option 3: generalize by computing an implicant then
* applying projection.
*/
static term_t ef_generalize3(ef_solver_t *solver, uint32_t i) {
model_t *mdl;
ef_cnstr_t *cnstr;
ivector_t *v, *w;
term_t a[2];
uint32_t n;
int32_t code;
proj_flag_t pflag;
term_t result;
assert(i < ef_prob_num_constraints(solver->prob));
// free the current full model if any
if (solver->full_model != NULL) {
yices_free_model(solver->full_model);
solver->full_model = NULL;
}
// build the full_map and the corresponding model.
ef_build_full_map(solver, i);
n = solver->all_vars.size;
assert(n == solver->all_values.size);
mdl = yices_model_from_map(n, solver->all_vars.data, solver->all_values.data);
if (mdl == NULL) {
// error in the model construction
solver->status = EF_STATUS_MDL_ERROR;
solver->error_code = yices_error_code();
return NULL_TERM;
}
solver->full_model = mdl;
// Constraint
cnstr = solver->prob->cnstr + i;
a[0] = cnstr->assumption; // B(y)
a[1] = opposite_term(cnstr->guarantee); // not C(x, y)
#if EF_VERBOSE
printf("Constraint:\n");
yices_pp_term_array(stdout, 2, a, 120, UINT32_MAX, 0, 0);
printf("(%"PRIu32" literals)\n", 2);
#endif
// Compute the implicant
v = &solver->implicant;
ivector_reset(v);
code = get_implicant(mdl, solver->prob->manager, LIT_COLLECTOR_ALL_OPTIONS, 2, a, v);
if (code < 0) {
solver->status = EF_STATUS_IMPLICANT_ERROR;
solver->error_code = code;
return NULL_TERM;
}
#if EF_VERBOSE
printf("Implicant:\n");
yices_pp_term_array(stdout, v->size, v->data, 120, UINT32_MAX, 0, 0);
printf("(%"PRIu32" literals)\n", v->size);
#endif
// Projection
w = &solver->projection;
ivector_reset(w);
n = ef_constraint_num_uvars(cnstr);
#if EF_VERBOSE
printf("(%"PRIu32" universals)\n", n);
yices_pp_term_array(stdout, n, cnstr->uvars, 120, UINT32_MAX, 0, 0);
#endif
pflag = project_literals(mdl, solver->prob->manager, v->size, v->data, n, cnstr->uvars, w);
if (pflag != PROJ_NO_ERROR) {
solver->status = EF_STATUS_PROJECTION_ERROR;
solver->error_code = pflag;
return NULL_TERM;
}
#if EF_VERBOSE
printf("Projection:\n");
yices_pp_term_array(stdout, w->size, w->data, 120, UINT32_MAX, 0, 0);
printf("(%"PRIu32" literals)\n", w->size);
#endif
switch (w->size) {
case 0:
result = true_term;
break;
case 1:
result = w->data[0];
break;
default:
result = mk_and(solver->prob->manager, w->size, w->data);
break;
}
return opposite_term(result);
}
