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arith-theory-axiom reducer to handle arithmetic axioms

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This commit is contained in:
Bernhard Gleiss 2017-12-01 14:21:20 +01:00 • committed by Arie Gurfinkel
parent df2eb771ef
commit de31b07008
2 changed files with 270 additions and 107 deletions
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311
src/muz/spacer/spacer_proof_utils.cpp
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@ -27,6 +27,38 @@ Revision History:
namespace spacer {
// arith lemmas: second parameter specifies exact type of lemma, could be "farkas", "triangle-eq", "eq-propagate", "assign-bounds", maybe also something else
bool is_arith_lemma(ast_manager& m, proof* pr)
{
if (pr->get_decl_kind() == PR_TH_LEMMA)
{
func_decl* d = pr->get_decl();
symbol sym;
if (d->get_num_parameters() >= 1 &&
d->get_parameter(0).is_symbol(sym) && sym == "arith")
{
return true;
}
}
return false;
}
bool is_farkas_lemma(ast_manager& m, proof* pr)
{
if (pr->get_decl_kind() == PR_TH_LEMMA)
{
func_decl* d = pr->get_decl();
symbol sym;
if (d->get_num_parameters() >= 2 && // the Farkas coefficients are saved in the parameters of step
d->get_parameter(0).is_symbol(sym) && sym == "arith" && // the first two parameters are "arith", "farkas",
d->get_parameter(1).is_symbol(sym) && sym == "farkas")
{
return true;
}
}
return false;
}
/*
* ====================================
* methods for proof traversal
@ -153,24 +185,18 @@ proof* ProofIteratorPostOrder::next()
edge_label = "hyp:";
color = "grey";
break;
default:
if (currentNode->get_decl_kind() == PR_TH_LEMMA)
case PR_TH_LEMMA:
if (is_farkas_lemma(m, currentNode))
{
edge_label = "th_axiom:";
func_decl* d = currentNode->get_decl();
symbol sym;
if (d->get_num_parameters() >= 2 && // the Farkas coefficients are saved in the parameters of step
d->get_parameter(0).is_symbol(sym) && sym == "arith" && // the first two parameters are "arith", "farkas",
d->get_parameter(1).is_symbol(sym) && sym == "farkas")
{
edge_label = "th_axiom(farkas):";
}
edge_label = "th_axiom(farkas):";
}
else
{
edge_label = "unknown axiom-type:";
break;
edge_label = "th_axiom:";
}
break;
default:
edge_label = "unknown axiom-type:";
}
}
else
@ -266,32 +292,111 @@ proof* ProofIteratorPostOrder::next()
/*
* ====================================
* methods for reducing hypothesis
* methods for transforming proofs
* ====================================
*/
class reduce_hypotheses {
ast_manager &m;
// tracking all created expressions
expr_ref_vector m_pinned;
void theory_axiom_reducer::reset()
{
m_cache.reset();
m_pinned.reset();
}
proof_ref theory_axiom_reducer::reduce(proof* pr)
{
ProofIteratorPostOrder pit(pr, m);
while (pit.hasNext())
{
proof* p = pit.next();
if (m.get_num_parents(p) == 0 && is_arith_lemma(m, p))
{
// we have an arith-theory-axiom and want to get rid of it
// we need to replace the axiom with 1a) corresponding hypothesis', 1b) a theory lemma and a 1c) a lemma. Furthermore update datastructures
app *cls_fact = to_app(m.get_fact(p));
ptr_buffer<expr> cls;
if (m.is_or(cls_fact)) {
for (unsigned i = 0, sz = cls_fact->get_num_args(); i < sz; ++i)
{ cls.push_back(cls_fact->get_arg(i)); }
} else { cls.push_back(cls_fact); }
// 1a) create hypothesis'
ptr_buffer<proof> hyps;
for (unsigned i=0; i < cls.size(); ++i)
{
expr* hyp_fact = m.is_not(cls[i]) ? to_app(cls[i])->get_arg(0) : m.mk_not(cls[i]);
proof* hyp = m.mk_hypothesis(hyp_fact);
m_pinned.push_back(hyp);
hyps.push_back(hyp);
}
// 1b) create farkas lemma: need to rebuild parameters since mk_th_lemma adds tid as first parameter
unsigned num_params = p->get_decl()->get_num_parameters();
parameter const* params = p->get_decl()->get_parameters();
vector<parameter> parameters;
for (unsigned i = 1; i < num_params; ++i) {
parameters.push_back(params[i]);
}
SASSERT(params[0].is_symbol());
family_id tid = m.mk_family_id(params[0].get_symbol());
SASSERT(tid != null_family_id);
proof* th_lemma = m.mk_th_lemma(tid, m.mk_false(),hyps.size(), hyps.c_ptr(), num_params-1, parameters.c_ptr());
SASSERT(is_arith_lemma(m, th_lemma));
// 1c) create lemma
proof* res = m.mk_lemma(th_lemma, cls_fact);
SASSERT(m.get_fact(res) == m.get_fact(p));
m_pinned.push_back(res);
m_cache.insert(p, res);
}
else
{
bool dirty = false; // proof is dirty, if a subproof of one of its premises has been transformed
// cache for the transformation
obj_map<proof, proof*> m_cache;
ptr_buffer<proof> args;
for (unsigned i = 0, sz = m.get_num_parents(p); i < sz; ++i)
{
proof* pp = m.get_parent(p, i);
proof* tmp;
if (m_cache.find(pp, tmp))
{
args.push_back(tmp);
dirty = dirty || pp != tmp;
}
else
{
SASSERT(false);
}
}
if (!dirty) // if not dirty just use the old step
{
m_cache.insert(p, p);
}
else // otherwise create new step with the corresponding proofs of the premises
{
if (m.has_fact(p)) { args.push_back(to_app(m.get_fact(p))); }
SASSERT(p->get_decl()->get_arity() == args.size());
proof* res = m.mk_app(p->get_decl(), args.size(), (expr * const*)args.c_ptr());
m_pinned.push_back(res);
m_cache.insert(p, res);
}
}
}
proof* res;
bool found = m_cache.find(pr,res);
SASSERT(found);
DEBUG_CODE(proof_checker pc(m);
expr_ref_vector side(m);
SASSERT(pc.check(res, side));
);
return proof_ref(res,m);
}
// map from unit literals to their hypotheses-free derivations
obj_map<expr, proof*> m_units;
// -- all hypotheses in the the proof
obj_hashtable<expr> m_hyps;
// marks hypothetical proofs
ast_mark m_hypmark;
// stack
ptr_vector<proof> m_todo;
void reset()
void hypothesis_reducer::reset()
{
m_cache.reset();
m_units.reset();
@ -299,14 +404,35 @@ class reduce_hypotheses {
m_hypmark.reset();
m_pinned.reset();
}
void hypothesis_reducer::compute_hypmarks_and_hyps(proof* pr)
{
proof *p;
ProofIteratorPostOrder pit(pr, m);
while (pit.hasNext()) {
p = pit.next();
if (m.is_hypothesis(p))
{
m_hypmark.mark(p, true);
m_hyps.insert(m.get_fact(p));
}
else
{
compute_hypmark_from_parents(p);
}
}
}
bool compute_mark1(proof *pr)
bool hypothesis_reducer::compute_hypmark_from_parents(proof *pr)
{
bool hyp_mark = false;
// lemmas clear all hypotheses
if (!m.is_lemma(pr)) {
for (unsigned i = 0, sz = m.get_num_parents(pr); i < sz; ++i) {
if (m_hypmark.is_marked(m.get_parent(pr, i))) {
if (!m.is_lemma(pr)) // lemmas clear all hypotheses
{
for (unsigned i = 0, sz = m.get_num_parents(pr); i < sz; ++i)
{
if (m_hypmark.is_marked(m.get_parent(pr, i)))
{
hyp_mark = true;
break;
}
@ -316,22 +442,13 @@ class reduce_hypotheses {
return hyp_mark;
}
void compute_marks(proof* pr)
// collect all units that are hyp-free and are used as hypotheses somewhere
// requires that m_hypmarks and m_hyps have been computed
void hypothesis_reducer::collect_units(proof* pr)
{
proof *p;
ProofIteratorPostOrder pit(pr, m);
while (pit.hasNext()) {
p = pit.next();
if (m.is_hypothesis(p)) {
m_hypmark.mark(p, true);
m_hyps.insert(m.get_fact(p));
} else {
compute_mark1(p);
}
}
ProofIteratorPostOrder pit2(pr, m);
while (pit2.hasNext()) {
p = pit2.next();
proof* p = pit.next();
if (!m.is_hypothesis(p))
{
// collect units that are hyp-free and are used as hypotheses somewhere
@ -342,12 +459,25 @@ class reduce_hypotheses {
}
}
}
void find_units(proof *pr)
{
// optional. not implemented yet.
}
void reduce(proof* pf, proof_ref &out)
proof_ref hypothesis_reducer::reduce(proof* pr)
{
compute_hypmarks_and_hyps(pr);
collect_units(pr);
proof* res = compute_transformed_proof(pr);
SASSERT(res != nullptr);
proof_ref res_ref(res,m);
reset();
DEBUG_CODE(proof_checker pc(m);
expr_ref_vector side(m);
SASSERT(pc.check(res, side));
);
return res_ref;
}
proof* hypothesis_reducer::compute_transformed_proof(proof* pf)
{
proof *res = NULL;
@ -383,9 +513,14 @@ class reduce_hypotheses {
if (todo_sz < m_todo.size()) { continue; }
else { m_todo.pop_back(); }
if (m.is_hypothesis(p)) {
// here the transformation begins
// INV: for each premise of p, we have computed the transformed proof.
if (m.is_hypothesis(p))
{
// hyp: replace by a corresponding unit
if (m_units.find(m.get_fact(p), tmp)) {
if (m_units.find(m.get_fact(p), tmp))
{
// if the transformed subproof ending in the unit has already been computed, use it
if (m_cache.find(tmp,tmp2))
{
@ -406,11 +541,11 @@ class reduce_hypotheses {
//lemma: reduce the premise; remove reduced consequences from conclusion
SASSERT(args.size() == 1);
res = mk_lemma_core(args.get(0), m.get_fact(p));
compute_mark1(res);
compute_hypmark_from_parents(res);
} else if (m.is_unit_resolution(p)) {
// unit: reduce untis; reduce the first premise; rebuild unit resolution
res = mk_unit_resolution_core(args.size(), args.c_ptr());
compute_mark1(res);
compute_hypmark_from_parents(res);
} else {
// if any literal is false, we don't need a step
bool has_empty_clause_premise = false;
@ -431,21 +566,22 @@ class reduce_hypotheses {
SASSERT(p->get_decl()->get_arity() == args.size());
res = m.mk_app(p->get_decl(), args.size(), (expr * const*)args.c_ptr());
m_pinned.push_back(res);
compute_mark1(res);
compute_hypmark_from_parents(res);
}
}
SASSERT(res);
m_cache.insert(p, res);
if (!m_hypmark.is_marked(res) && m.has_fact(res) && m.is_false(m.get_fact(res))) { break; }
if (!m_hypmark.is_marked(res) && m.has_fact(res) && m.is_false(m.get_fact(res)))
{
return res;
}
}
out = res;
}
// returns true if (hypothesis (not a)) would be reduced
bool is_reduced(expr *a)
bool hypothesis_reducer::is_reduced(expr *a)
{
expr_ref e(m);
if (m.is_not(a)) { e = to_app(a)->get_arg(0); }
@ -453,7 +589,8 @@ class reduce_hypotheses {
return m_units.contains(e);
}
proof *mk_lemma_core(proof *pf, expr *fact)
proof* hypothesis_reducer::mk_lemma_core(proof *pf, expr *fact)
{
ptr_buffer<expr> args;
expr_ref lemma(m);
@ -486,7 +623,7 @@ class reduce_hypotheses {
return res;
}
proof *mk_unit_resolution_core(unsigned num_args, proof* const *args)
proof* hypothesis_reducer::mk_unit_resolution_core(unsigned num_args, proof* const *args)
{
ptr_buffer<proof> pf_args;
@ -542,42 +679,4 @@ class reduce_hypotheses {
return res;
}
}
// reduce all units, if any unit reduces to false return true and put its proof into out
bool reduce_units(proof_ref &out)
{
proof_ref res(m);
for (auto entry : m_units) {
reduce(entry.get_value(), res);
if (m.is_false(m.get_fact(res))) {
out = res;
return true;
}
res.reset();
}
return false;
}
public:
reduce_hypotheses(ast_manager &m) : m(m), m_pinned(m) {}
void operator()(proof_ref &pr)
{
compute_marks(pr);
reduce(pr.get(), pr);
reset();
}
};
void reduce_hypotheses(proof_ref &pr)
{
ast_manager &m = pr.get_manager();
class reduce_hypotheses hypred(m);
hypred(pr);
DEBUG_CODE(proof_checker pc(m);
expr_ref_vector side(m);
SASSERT(pc.check(pr, side));
);
}
}

66
src/muz/spacer/spacer_proof_utils.h
View file

@ -22,6 +22,7 @@ Revision History:
namespace spacer {
bool is_arith_lemma(ast_manager& m, proof* pr);
bool is_farkas_lemma(ast_manager& m, proof* pr);
/*
* iterator, which traverses the proof in depth-first post-order.
@ -46,8 +47,71 @@ private:
class iuc_proof;
void pp_proof_dot(ast_manager& m, proof* pr, iuc_proof* iuc_pr = nullptr);
class theory_axiom_reducer
{
public:
theory_axiom_reducer(ast_manager& m) : m(m), m_pinned(m) {}
// reduce theory axioms and return transformed proof
proof_ref reduce(proof* pr);
private:
ast_manager &m;
// tracking all created expressions
expr_ref_vector m_pinned;
// maps each proof of a clause to the transformed subproof of that clause
obj_map<proof, proof*> m_cache;
void reset();
};
void reduce_hypotheses(proof_ref &pr);
class hypothesis_reducer
{
public:
hypothesis_reducer(ast_manager &m) : m(m), m_pinned(m) {}
// reduce hypothesis and return transformed proof
proof_ref reduce(proof* pf);
private:
typedef obj_hashtable<expr> expr_set;
ast_manager &m;
// tracking all created expressions
expr_ref_vector m_pinned;
// maps each proof of a clause to the transformed subproof of that clause
obj_map<proof, proof*> m_cache;
// maps each unit literals to the transformed subproof of that unit
obj_map<expr, proof*> m_units;
// -- all hypotheses in the the proof
obj_hashtable<expr> m_hyps;
// marks hypothetical proofs
ast_mark m_hypmark;
std::vector<expr_set> m_pinned_hyp_sets; // tracking all created sets of hypothesis
obj_map<expr, expr_set*> m_hyp_anchestor; // maps each proof to the set of hypothesis it contains, needed to avoid creating cycles in the proof.
// stack
ptr_vector<proof> m_todo;
void reset();
proof* compute_transformed_proof(proof* pf);
void compute_hypmarks_and_hyps(proof* pr);
bool compute_hypmark_from_parents(proof *pr);
void collect_units(proof* pr);
// returns true if (hypothesis (not a)) would be reduced
bool is_reduced(expr *a);
proof* mk_lemma_core(proof *pf, expr *fact);
proof* mk_unit_resolution_core(unsigned num_args, proof* const *args);
};
}
#endif