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convert reduce-args to a simplifier

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- convert reduce-args to a simplifier. Currently exposed as reduce-args2 tactic until the old tactic code gets removed.
- bug fixes in model_reconstruction trail
  - allow multiple defs to be added with same pool of removed formulas
  - fix tracking of function symbols instead of expressions to filter replay
- add nla_divisions to track (cheap) divisibility lemmas.
-
This commit is contained in:
Nikolaj Bjorner 2023-01-28 20:12:14 -08:00
parent 246d6f7b77
commit 8ea49eed8e
23 changed files with 740 additions and 92 deletions
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2
src/ast/ast_util.h
View file

@ -101,6 +101,8 @@ expr * get_clause_literal(ast_manager & m, expr * cls, unsigned idx);
*/
expr * mk_and(ast_manager & m, unsigned num_args, expr * const * args);
app * mk_and(ast_manager & m, unsigned num_args, app * const * args);
inline expr * mk_and(ast_manager & m, ptr_vector<expr> const& args) { return mk_and(m, args.size(), args.data()); }
inline expr * mk_and(ast_manager & m, ptr_buffer<expr> const& args) { return mk_and(m, args.size(), args.data()); }
inline expr * mk_and(ast_manager & m, expr* a, expr* b) { expr* args[2] = { a, b }; return mk_and(m, 2, args); }
inline app_ref mk_and(app_ref_vector const& args) { return app_ref(mk_and(args.get_manager(), args.size(), args.data()), args.get_manager()); }
inline expr_ref mk_and(expr_ref_vector const& args) { return expr_ref(mk_and(args.get_manager(), args.size(), args.data()), args.get_manager()); }

2
src/ast/converters/generic_model_converter.h
View file

@ -68,8 +68,6 @@ public:
void get_units(obj_map<expr, bool>& units) override;
vector<entry> const& entries() const { return m_entries; }
void shrink(unsigned j) { m_entries.shrink(j); }
};
typedef ref<generic_model_converter> generic_model_converter_ref;

1
src/ast/simplifiers/CMakeLists.txt
View file

@ -19,6 +19,7 @@ z3_add_component(simplifiers
max_bv_sharing.cpp
model_reconstruction_trail.cpp
propagate_values.cpp
reduce_args_simplifier.cpp
solve_context_eqs.cpp
solve_eqs.cpp
COMPONENT_DEPENDENCIES

7
src/ast/simplifiers/dependent_expr_state.cpp
View file

@ -31,8 +31,13 @@ void dependent_expr_state::freeze(func_decl* f) {
}
void dependent_expr_state::freeze(expr* term) {
if (is_app(term))
if (is_app(term) && to_app(term)->get_num_args() == 0)
freeze(to_app(term)->get_decl());
else {
ast_mark visited;
freeze_terms(term, false, visited);
}
}
/**

2
src/ast/simplifiers/dependent_expr_state.h
View file

@ -80,7 +80,7 @@ public:
m_trail.push(value_trail(m_qhead));
m_trail.push(thaw(*this));
}
void pop(unsigned n) { m_trail.pop_scope(n); }
void pop(unsigned n) { m_trail.pop_scope(n); }
void advance_qhead() { freeze_prefix(); m_suffix_frozen = false; m_has_quantifiers = l_undef; m_qhead = qtail(); }
unsigned num_exprs();

36
src/ast/simplifiers/model_reconstruction_trail.cpp
View file

@ -13,6 +13,7 @@ Author:
#include "ast/for_each_expr.h"
#include "ast/ast_ll_pp.h"
#include "ast/rewriter/macro_replacer.h"
#include "ast/simplifiers/model_reconstruction_trail.h"
#include "ast/simplifiers/dependent_expr_state.h"
@ -24,6 +25,10 @@ Author:
// TODO: add filters to skip sections of the trail that do not touch the current free variables.
void model_reconstruction_trail::replay(unsigned qhead, expr_ref_vector& assumptions, dependent_expr_state& st) {
TRACE("simplifier",
for (unsigned i = qhead; i < st.qtail(); ++i)
tout << mk_bounded_pp(st[i].fml(), m) << "\n";
);
ast_mark free_vars;
scoped_ptr<expr_replacer> rp = mk_default_expr_replacer(m, false);
for (unsigned i = qhead; i < st.qtail(); ++i)
@ -32,6 +37,7 @@ void model_reconstruction_trail::replay(unsigned qhead, expr_ref_vector& assumpt
add_vars(a, free_vars);
for (auto& t : m_trail) {
TRACE("simplifier", tout << " active " << t->m_active << " hide " << t->is_hide() << " intersects " << t->intersects(free_vars) << "\n");
if (!t->m_active)
continue;
@ -56,15 +62,17 @@ void model_reconstruction_trail::replay(unsigned qhead, expr_ref_vector& assumpt
if (t->is_def()) {
macro_replacer mrp(m);
app_ref head(m);
func_decl* d = t->m_decl;
ptr_buffer<expr> args;
for (unsigned i = 0; i < d->get_arity(); ++i)
args.push_back(m.mk_var(i, d->get_domain(i)));
head = m.mk_app(d, args);
mrp.insert(head, t->m_def, t->m_dep);
dependent_expr de(m, t->m_def, nullptr, t->m_dep);
add_vars(de, free_vars);
for (auto const& [d, def, dep] : t->m_defs) {
app_ref head(m);
ptr_buffer<expr> args;
for (unsigned i = 0; i < d->get_arity(); ++i)
args.push_back(m.mk_var(i, d->get_domain(i)));
head = m.mk_app(d, args);
mrp.insert(head, def, dep);
TRACE("simplifier", tout << d << " " << def << " " << dep << "\n");
dependent_expr de(m, def, nullptr, dep);
add_vars(de, free_vars);
}
for (unsigned i = qhead; i < st.qtail(); ++i) {
auto [f, p, dep1] = st[i]();
@ -140,6 +148,7 @@ model_converter_ref model_reconstruction_trail::get_model_converter() {
* Append model conversions starting at index i
*/
void model_reconstruction_trail::append(generic_model_converter& mc, unsigned& i) {
TRACE("simplifier", display(tout));
for (; i < m_trail.size(); ++i) {
auto* t = m_trail[i];
if (!t->m_active)
@ -147,7 +156,8 @@ void model_reconstruction_trail::append(generic_model_converter& mc, unsigned& i
else if (t->is_hide())
mc.hide(t->m_decl);
else if (t->is_def())
mc.add(t->m_decl, t->m_def);
for (auto const& [f, def, dep] : t->m_defs)
mc.add(f, def);
else {
for (auto const& [v, def] : t->m_subst->sub())
mc.add(v, def);
@ -167,8 +177,10 @@ std::ostream& model_reconstruction_trail::display(std::ostream& out) const {
continue;
else if (t->is_hide())
out << "hide " << t->m_decl->get_name() << "\n";
else if (t->is_def())
out << t->m_decl->get_name() << " <- " << mk_pp(t->m_def, m) << "\n";
else if (t->is_def()) {
for (auto const& [f, def, dep] : t->m_defs)
out << f->get_name() << " <- " << mk_pp(def, m) << "\n";
}
else {
for (auto const& [v, def] : t->m_subst->sub())
out << mk_pp(v, m) << " <- " << mk_pp(def, m) << "\n";

49
src/ast/simplifiers/model_reconstruction_trail.h
View file

@ -39,34 +39,46 @@ class model_reconstruction_trail {
scoped_ptr<expr_substitution> m_subst;
vector<dependent_expr> m_removed;
func_decl_ref m_decl;
expr_ref m_def;
expr_dependency_ref m_dep;
vector<std::tuple<func_decl_ref, expr_ref, expr_dependency_ref>> m_defs;
bool m_active = true;
entry(ast_manager& m, expr_substitution* s, vector<dependent_expr> const& rem) :
m_subst(s), m_removed(rem), m_decl(m), m_def(m), m_dep(m) {}
m_subst(s), m_removed(rem), m_decl(m) {}
entry(ast_manager& m, func_decl* h) : m_decl(h, m), m_def(m), m_dep(m) {}
entry(ast_manager& m, func_decl* h) : m_decl(h, m) {}
entry(ast_manager& m, func_decl* f, expr* def, expr_dependency* dep, vector<dependent_expr> const& rem) :
m_removed(rem), m_decl(f, m), m_def(def, m), m_dep(dep, m) {}
m_removed(rem),
m_decl(m){
m_defs.push_back({ func_decl_ref(f, m), expr_ref(def, m), expr_dependency_ref(dep, m) });
}
entry(ast_manager& m, vector<std::tuple<func_decl_ref, expr_ref, expr_dependency_ref>> const& defs, vector<dependent_expr> const& rem) :
m_removed(rem),
m_decl(m),
m_defs(defs) {
}
bool is_loose() const { return !m_removed.empty(); }
bool intersects(ast_mark const& free_vars) const {
if (is_hide())
return false;
if (is_def())
return free_vars.is_marked(m_decl);
for (auto const& [k, v] : m_subst->sub())
if (free_vars.is_marked(k))
for (auto const& [f, def, dep] : m_defs)
if (free_vars.is_marked(f))
return true;
if (m_subst) {
for (auto const& [k, v] : m_subst->sub())
if (free_vars.is_marked(k))
return true;
}
return false;
}
bool is_hide() const { return m_decl && !m_def; }
bool is_def() const { return m_decl && m_def; }
bool is_subst() const { return !m_decl; }
bool is_hide() const { return m_decl && m_defs.empty(); }
bool is_def() const { return !m_defs.empty(); }
bool is_subst() const { return m_subst && !m_subst->empty(); }
};
ast_manager& m;
@ -76,7 +88,8 @@ class model_reconstruction_trail {
void add_vars(expr* e, ast_mark& free_vars) {
for (expr* t : subterms::all(expr_ref(e, m)))
free_vars.mark(t, true);
if (is_app(t))
free_vars.mark(to_app(t)->get_decl(), true);
}
void add_vars(dependent_expr const& d, ast_mark& free_vars) {
@ -86,7 +99,7 @@ class model_reconstruction_trail {
bool intersects(ast_mark const& free_vars, dependent_expr const& d) {
expr_ref term(d.fml(), m);
auto iter = subterms::all(term);
return any_of(iter, [&](expr* t) { return free_vars.is_marked(t); });
return any_of(iter, [&](expr* t) { return is_app(t) && free_vars.is_marked(to_app(t)->get_decl()); });
}
bool intersects(ast_mark const& free_vars, vector<dependent_expr> const& added) {
@ -126,6 +139,14 @@ public:
m_trail_stack.push(push_back_vector(m_trail));
}
/**
* add definitions
*/
void push(vector<std::tuple<func_decl_ref, expr_ref, expr_dependency_ref>> const& defs, vector<dependent_expr> const& removed) {
m_trail.push_back(alloc(entry, m, defs, removed));
m_trail_stack.push(push_back_vector(m_trail));
}
/**
* register a new depedent expression, update the trail
* by removing substitutions that are not equivalence preserving.

428
src/ast/simplifiers/reduce_args_simplifier.cpp Normal file
View file

@ -0,0 +1,428 @@
/*++
Copyright (c) 2012 Microsoft Corporation
Module Name:
reduce_args_simplifier.cpp
Abstract:
Reduce the number of arguments in function applications.
Author:
Leonardo (leonardo) 2012-02-19
Notes:
--*/
#include "util/map.h"
#include "ast/ast_smt2_pp.h"
#include "ast/ast_util.h"
#include "ast/has_free_vars.h"
#include "ast/rewriter/rewriter_def.h"
#include "ast/simplifiers/dependent_expr_state.h"
/**
\brief Reduce the number of arguments in function applications.
Example, suppose we have a function f with 2 arguments.
There are 1000 applications of this function, but the first argument is always "a", "b" or "c".
Thus, we replace the f(t1, t2)
with
f_a(t2) if t1 = a
f_b(t2) if t2 = b
f_c(t2) if t2 = c
Since f_a, f_b, f_c are new symbols, satisfiability is preserved.
This transformation is very similar in spirit to the Ackermman's reduction.
This transformation should work in the following way:
1- Create a mapping decl2arg_map from declarations to tuples of booleans, an entry [f -> (true, false, true)]
means that f is a declaration with 3 arguments where the first and third arguments are always values.
2- Traverse the formula and populate the mapping.
For each function application f(t1, ..., tn) do
a) Create a boolean tuple (is_value(t1), ..., is_value(tn)) and do
the logical-and with the tuple that is already in the mapping. If there is no such tuple
in the mapping, we just add a new entry.
If all entries are false-tuples, then there is nothing to be done. The transformation is not applicable.
Now, we create a mapping decl2new_decl from (decl, val_1, ..., val_n) to decls. Note that, n may be different for each entry,
but it is the same for the same declaration.
For example, suppose we have [f -> (true, false, true)] in decl2arg_map, and applications f(1, a, 2), f(1, b, 2), f(1, b, 3), f(2, b, 3), f(2, c, 3) in the formula.
Then, decl2arg_map would contain
(f, 1, 2) -> f_1_2
(f, 1, 3) -> f_1_3
(f, 2, 3) -> f_2_3
where f_1_2, f_1_3 and f_2_3 are new function symbols.
Using the new map, we can replace the occurrences of f.
*/
class reduce_args_simplifier : public dependent_expr_simplifier {
bv_util m_bv;
static bool is_var_plus_offset(ast_manager& m, bv_util& bv, expr* e, expr*& base) {
expr *lhs, *rhs;
if (bv.is_bv_add(e, lhs, rhs) && bv.is_numeral(lhs))
base = rhs;
else
base = e;
return !has_free_vars(base);
}
static bool may_be_unique(ast_manager& m, bv_util& bv, expr* e, expr*& base) {
base = nullptr;
return m.is_unique_value(e) || is_var_plus_offset(m, bv, e, base);
}
static bool may_be_unique(ast_manager& m, bv_util& bv, expr* e) {
expr* base;
return may_be_unique(m, bv, e, base);
}
struct find_non_candidates_proc {
ast_manager & m;
bv_util & m_bv;
obj_hashtable<func_decl> & m_non_candidates;
find_non_candidates_proc(ast_manager & m, bv_util & bv, obj_hashtable<func_decl> & non_candidates):
m(m),
m_bv(bv),
m_non_candidates(non_candidates) {
}
void operator()(var * n) {}
void operator()(quantifier *n) {}
void operator()(app * n) {
if (!is_uninterp(n))
return;
func_decl * d;
if (n->get_num_args() == 0)
return; // ignore constants
d = n->get_decl();
if (m_non_candidates.contains(d))
return; // it is already in the set.
for (expr* arg : *n)
if (may_be_unique(m, m_bv, arg))
return;
m_non_candidates.insert(d);
}
};
/**
\brief Populate the table non_candidates with function declarations \c f
such that there is a function application (f t1 ... tn) where t1 ... tn are not values.
*/
void find_non_candidates(obj_hashtable<func_decl> & non_candidates) {
non_candidates.reset();
find_non_candidates_proc proc(m, m_bv, non_candidates);
expr_fast_mark1 visited;
for (auto i : indices())
quick_for_each_expr(proc, visited, m_fmls[i].fml());
TRACE("reduce_args", tout << "non_candidates:\n"; for (func_decl* d : non_candidates) tout << d->get_name() << "\n";);
}
struct populate_decl2args_proc {
reduce_args_simplifier& m_owner;
ast_manager & m;
bv_util & m_bv;
obj_hashtable<func_decl> & m_non_candidates;
obj_map<func_decl, bit_vector> & m_decl2args;
obj_map<func_decl, svector<expr*> > m_decl2base; // for args = base + offset
populate_decl2args_proc(reduce_args_simplifier& o, ast_manager & m, bv_util & bv, obj_hashtable<func_decl> & nc, obj_map<func_decl, bit_vector> & d):
m_owner(o), m(m), m_bv(bv), m_non_candidates(nc), m_decl2args(d) {}
void operator()(var * n) {}
void operator()(quantifier * n) {}
void operator()(app * n) {
if (n->get_num_args() == 0)
return; // ignore constants
func_decl * d = n->get_decl();
if (d->get_family_id() != null_family_id)
return; // ignore interpreted symbols
if (m_non_candidates.contains(d))
return; // declaration is not a candidate
if (m_owner.m_fmls.frozen(d))
return;
unsigned j = n->get_num_args();
obj_map<func_decl, bit_vector>::iterator it = m_decl2args.find_iterator(d);
expr* base;
if (it == m_decl2args.end()) {
m_decl2args.insert(d, bit_vector());
svector<expr*>& bases = m_decl2base.insert_if_not_there(d, svector<expr*>());
bases.resize(j);
it = m_decl2args.find_iterator(d);
SASSERT(it != m_decl2args.end());
it->m_value.reserve(j);
while (j > 0) {
--j;
it->m_value.set(j, may_be_unique(m, m_bv, n->get_arg(j), base));
bases[j] = base;
}
} else {
svector<expr*>& bases = m_decl2base[d];
SASSERT(j == it->m_value.size());
while (j > 0) {
--j;
it->m_value.set(j, it->m_value.get(j) && may_be_unique(m, m_bv, n->get_arg(j), base) && bases[j] == base);
}
}
}
};
void populate_decl2args(obj_hashtable<func_decl> & non_candidates,
obj_map<func_decl, bit_vector> & decl2args) {
expr_fast_mark1 visited;
decl2args.reset();
populate_decl2args_proc proc(*this, m, m_bv, non_candidates, decl2args);
for (auto i : indices())
quick_for_each_expr(proc, visited, m_fmls[i].fml());
// Remove all cases where the simplification is not applicable.
ptr_buffer<func_decl> bad_decls;
for (auto const& [k, v] : decl2args)
if (all_of(v, [&](auto b) { return !b;}))
bad_decls.push_back(k);
for (func_decl* a : bad_decls)
decl2args.erase(a);
TRACE("reduce_args", tout << "decl2args:" << std::endl;
for (auto const& [k, v] : decl2args) {
tout << k->get_name() << ": ";
for (unsigned i = 0; i < v.size(); ++i)
tout << (v.get(i) ? "1" : "0");
tout << std::endl;
});
}
struct arg2func_hash_proc {
bit_vector const & m_bv;
arg2func_hash_proc(bit_vector const & bv):m_bv(bv) {}
unsigned operator()(app const * n) const {
// compute the hash-code using only the arguments where m_bv is true.
unsigned a = 0x9e3779b9;
unsigned num_args = n->get_num_args();
for (unsigned i = 0; i < num_args; i++) {
if (!m_bv.get(i))
continue; // ignore argument
a = hash_u_u(a, n->get_arg(i)->get_id());
}
return a;
}
};
struct arg2func_eq_proc {
bit_vector const & m_bv;
arg2func_eq_proc(bit_vector const & bv):m_bv(bv) {}
bool operator()(app const * n1, app const * n2) const {
// compare only the arguments where m_bv is true
SASSERT(n1->get_num_args() == n2->get_num_args());
unsigned num_args = n1->get_num_args();
for (unsigned i = 0; i < num_args; i++) {
if (!m_bv.get(i))
continue; // ignore argument
if (n1->get_arg(i) != n2->get_arg(i))
return false;
}
return true;
}
};
typedef map<app *, func_decl *, arg2func_hash_proc, arg2func_eq_proc> arg2func;
typedef obj_map<func_decl, arg2func *> decl2arg2func_map;
struct reduce_args_ctx {
ast_manager & m;
decl2arg2func_map m_decl2arg2funcs;
reduce_args_ctx(ast_manager & m): m(m) {
}
~reduce_args_ctx() {
for (auto const& [_, map] : m_decl2arg2funcs) {
for (auto const& [k, v] : *map) {
m.dec_ref(k);
m.dec_ref(v);
}
dealloc(map);
}
}
};
struct reduce_args_rw_cfg : public default_rewriter_cfg {
ast_manager & m;
reduce_args_simplifier& m_owner;
obj_map<func_decl, bit_vector> & m_decl2args;
decl2arg2func_map & m_decl2arg2funcs;
reduce_args_rw_cfg(reduce_args_simplifier& owner, obj_map<func_decl, bit_vector> & decl2args, decl2arg2func_map & decl2arg2funcs):
m(owner.m),
m_owner(owner),
m_decl2args(decl2args),
m_decl2arg2funcs(decl2arg2funcs) {
}
br_status reduce_app(func_decl * f, unsigned num, expr * const * args, expr_ref & result, proof_ref & result_pr) {
result_pr = nullptr;
if (f->get_arity() == 0)
return BR_FAILED; // ignore constants
if (f->get_family_id() != null_family_id)
return BR_FAILED; // ignore interpreted symbols
obj_map<func_decl, bit_vector>::iterator it = m_decl2args.find_iterator(f);
if (it == m_decl2args.end())
return BR_FAILED;
bit_vector & bv = it->m_value;
arg2func *& map = m_decl2arg2funcs.insert_if_not_there(f, 0);
if (!map) {
map = alloc(arg2func, arg2func_hash_proc(bv), arg2func_eq_proc(bv));
}
app_ref tmp(m.mk_app(f, num, args), m);
func_decl *& new_f = map->insert_if_not_there(tmp, nullptr);
if (!new_f) {
// create fresh symbol
ptr_buffer<sort> domain;
unsigned arity = f->get_arity();
for (unsigned i = 0; i < arity; ++i) {
if (!bv.get(i))
domain.push_back(f->get_domain(i));
}
new_f = m.mk_fresh_func_decl(f->get_name(), symbol::null, domain.size(), domain.data(), f->get_range());
m.inc_ref(tmp);
m.inc_ref(new_f);
}
ptr_buffer<expr> new_args;
for (unsigned i = 0; i < num; i++) {
if (!bv.get(i))
new_args.push_back(args[i]);
}
result = m.mk_app(new_f, new_args.size(), new_args.data());
return BR_DONE;
}
};
struct reduce_args_rw : rewriter_tpl<reduce_args_rw_cfg> {
reduce_args_rw_cfg m_cfg;
public:
reduce_args_rw(reduce_args_simplifier & owner, obj_map<func_decl, bit_vector> & decl2args, decl2arg2func_map & decl2arg2funcs):
rewriter_tpl<reduce_args_rw_cfg>(owner.m, false, m_cfg),
m_cfg(owner, decl2args, decl2arg2funcs) {
}
};
void mk_mc(obj_map<func_decl, bit_vector> & decl2args, decl2arg2func_map & decl2arg2funcs, vector<dependent_expr> const& removed) {
ptr_buffer<expr> new_args;
var_ref_vector new_vars(m);
ptr_buffer<expr> new_eqs;
generic_model_converter * f_mc = alloc(generic_model_converter, m, "reduce_args");
for (auto const& [f, map] : decl2arg2funcs)
for (auto const& [t, new_def] : *map)
m_fmls.model_trail().hide(new_def);
vector<std::tuple<func_decl_ref, expr_ref, expr_dependency_ref>> defs;
for (auto const& [f, map] : decl2arg2funcs) {
expr * def = nullptr;
SASSERT(decl2args.contains(f));
bit_vector & bv = decl2args.find(f);
new_vars.reset();
new_args.reset();
for (unsigned i = 0; i < f->get_arity(); i++) {
new_vars.push_back(m.mk_var(i, f->get_domain(i)));
if (!bv.get(i))
new_args.push_back(new_vars.back());
}
for (auto const& [t, new_def] : *map) {
SASSERT(new_def->get_arity() == new_args.size());
app * new_t = m.mk_app(new_def, new_args);
if (def == nullptr) {
def = new_t;
}
else {
new_eqs.reset();
for (unsigned i = 0; i < f->get_arity(); i++)
if (bv.get(i))
new_eqs.push_back(m.mk_eq(new_vars.get(i), t->get_arg(i)));
SASSERT(new_eqs.size() > 0);
expr * cond = mk_and(m, new_eqs);
def = m.mk_ite(cond, new_t, def);
}
}
SASSERT(def);
expr_dependency* dep = nullptr;
defs.push_back({ func_decl_ref(f,m), expr_ref(def, m), expr_dependency_ref(dep, m) });
}
m_fmls.model_trail().push(defs, removed);
}
unsigned m_num_decls = 0;
public:
reduce_args_simplifier(ast_manager& m, dependent_expr_state& st, params_ref const& p) :
dependent_expr_simplifier(m, st),
m_bv(m)
{}
~reduce_args_simplifier() override {}
char const* name() const override { return "reduce-args"; }
void collect_statistics(statistics& st) const override {
st.update("reduced-funcs", m_num_decls);
}
void reset_statistics() override {
m_num_decls = 0;
}
void reduce() override {
m_fmls.freeze_suffix();
obj_hashtable<func_decl> non_candidates;
obj_map<func_decl, bit_vector> decl2args;
find_non_candidates(non_candidates);
populate_decl2args(non_candidates, decl2args);
if (decl2args.empty())
return;
m_num_decls += decl2args.size();
reduce_args_ctx ctx(m);
reduce_args_rw rw(*this, decl2args, ctx.m_decl2arg2funcs);
vector<dependent_expr> removed;
// if not global scope then what?
// cannot just use in incremental mode.
for (auto i : indices()) {
auto [f, p, d] = m_fmls[i]();
if (p)
continue;
expr_ref new_f(m);
rw(f, new_f);
if (f != new_f) {
removed.push_back(m_fmls[i]);
m_fmls.update(i, dependent_expr(m, new_f, p, d));
}
}
mk_mc(decl2args, ctx.m_decl2arg2funcs, removed);
}
};
dependent_expr_simplifier* mk_reduce_args_simplifier(ast_manager & m, dependent_expr_state& st, params_ref const & p) {
return alloc(reduce_args_simplifier, m, st, p);
}

16
src/ast/simplifiers/reduce_args_simplifier.h Normal file
View file

@ -0,0 +1,16 @@
/*++
Copyright (c) 2012 Microsoft Corporation
Module Name:
reduce_args_simplifier.h
Abstract:
Reduce the number of arguments in function applications.
--*/
#pragma once
dependent_expr_simplifier* mk_reduce_args_simplifier(ast_manager & m, dependent_expr_state& st, params_ref const & p);

1
src/math/lp/CMakeLists.txt
View file

@ -34,6 +34,7 @@ z3_add_component(lp
nla_basics_lemmas.cpp
nla_common.cpp
nla_core.cpp
nla_divisions.cpp
nla_grobner.cpp
nla_intervals.cpp
nla_monotone_lemmas.cpp

9
src/math/lp/nla_core.cpp
View file

@ -30,6 +30,7 @@ core::core(lp::lar_solver& s, reslimit & lim) :
m_order(this),
m_monotone(this),
m_powers(*this),
m_divisions(*this),
m_intervals(this, lim),
m_monomial_bounds(this),
m_horner(this),
@ -136,6 +137,11 @@ void core::add_monic(lpvar v, unsigned sz, lpvar const* vs) {
}
m_emons.add(v, m_add_buffer);
}
void core::add_idivision(lpvar r, lpvar x, lpvar y) {
m_divisions.add_idivision(r, x, y);
}
void core::push() {
TRACE("nla_solver_verbose", tout << "\n";);
@ -1519,6 +1525,9 @@ lbool core::check(vector<lemma>& l_vec) {
if (l_vec.empty() && !done())
m_basics.basic_lemma(false);
if (l_vec.empty() && !done())
m_divisions.check(l_vec);
#if 0
if (l_vec.empty() && !done() && !run_horner)
m_horner.horner_lemmas();

4
src/math/lp/nla_core.h
View file

@ -20,6 +20,7 @@
#include "math/lp/nla_monotone_lemmas.h"
#include "math/lp/nla_grobner.h"
#include "math/lp/nla_powers.h"
#include "math/lp/nla_divisions.h"
#include "math/lp/emonics.h"
#include "math/lp/nla_settings.h"
#include "math/lp/nex.h"
@ -88,6 +89,7 @@ class core {
order m_order;
monotone m_monotone;
powers m_powers;
divisions m_divisions;
intervals m_intervals;
monomial_bounds m_monomial_bounds;
nla_settings m_nla_settings;
@ -199,8 +201,10 @@ public:
void deregister_monic_from_tables(const monic & m, unsigned i);
void add_monic(lpvar v, unsigned sz, lpvar const* vs);
void add_idivision(lpvar r, lpvar x, lpvar y);
void push();
void pop(unsigned n);
trail_stack& trail() { return m_emons.get_trail_stack(); }
rational mon_value_by_vars(unsigned i) const;
rational product_value(const monic & m) const;

65
src/math/lp/nla_divisions.cpp Normal file
View file

@ -0,0 +1,65 @@
/*++
Copyright (c) 2017 Microsoft Corporation
Module Name:
nla_divisions.cpp
Author:
Lev Nachmanson (levnach)
Nikolaj Bjorner (nbjorner)
Description:
Check divisions
--*/
#include "math/lp/nla_core.h"
namespace nla {
void divisions::add_idivision(lpvar r, lpvar x, lpvar y) {
m_idivisions.push_back({r, x, y});
m_core.trail().push(push_back_vector(m_idivisions));
}
typedef lp::lar_term term;
// y1 >= y2 > 0 & x1 <= x2 => x1/y1 <= x2/y2
// y2 <= y1 < 0 & x1 >= x2 => x1/y1 <= x2/y2
void divisions::check(vector<lemma>& lemmas) {
core& c = m_core;
if (c.use_nra_model())
return;
for (auto const & [r, x, y] : m_idivisions) {
auto xval = c.val(x);
auto yval = c.val(y);
auto rval = c.val(r);
if (!c.var_is_int(x))
continue;
if (yval == 0)
continue;
// idiv semantics
if (rval == div(xval, yval))
continue;
for (auto const& [r2, x2, y2] : m_idivisions) {
if (r2 == r)
continue;
auto x2val = c.val(x2);
auto y2val = c.val(y2);
auto r2val = c.val(r2);
if (yval >= y2val && y2val > 0 && xval <= x2val && rval > r2val) {
new_lemma lemma(c, "y1 >= y2 > 0 & x1 <= x2 => x1/y1 <= x2/y2");
lemma |= ineq(term(y, rational(-1), y2), llc::LT, rational::zero());
lemma |= ineq(y2, llc::LE, rational::zero());
lemma |= ineq(term(x, rational(-1), x2), llc::GT, rational::zero());
lemma |= ineq(term(r, rational(-1), r2), llc::LE, rational::zero());
return;
}
}
}
}
}

31
src/math/lp/nla_divisions.h Normal file
View file

@ -0,0 +1,31 @@
/*++
Copyright (c) 2017 Microsoft Corporation
Module Name:
nla_divisions.h
Author:
Lev Nachmanson (levnach)
Nikolaj Bjorner (nbjorner)
Description:
Check division constraints.
--*/
#include "math/lp/nla_types.h"
namespace nla {
class core;
class divisions {
core& m_core;
vector<std::tuple<lpvar, lpvar, lpvar>> m_idivisions;
public:
divisions(core& c):m_core(c) {}
void add_idivision(lpvar r, lpvar x, lpvar y);
void check(vector<lemma>&);
};
}

4
src/math/lp/nla_solver.cpp
View file

@ -22,6 +22,10 @@ namespace nla {
void solver::add_monic(lpvar v, unsigned sz, lpvar const* vs) {
m_core->add_monic(v, sz, vs);
}
void solver::add_idivision(lpvar r, lpvar x, lpvar y) {
m_core->add_idivision(r, x, y);
}
bool solver::is_monic_var(lpvar v) const {
return m_core->is_monic_var(v);

1
src/math/lp/nla_solver.h
View file

@ -25,6 +25,7 @@ namespace nla {
core* m_core;
public:
void add_monic(lpvar v, unsigned sz, lpvar const* vs);
void add_idivision(lpvar r, lpvar x, lpvar y);
solver(lp::lar_solver& s, reslimit& limit);
~solver();
nla_settings& settings();

3
src/math/lp/var_eqs.h
View file

@ -68,8 +68,7 @@ class var_eqs {
T* m_merge_handler;
union_find<var_eqs> m_uf;
lp::incremental_vector<std::pair<signed_var, signed_var>>
m_trail;
lp::incremental_vector<std::pair<signed_var, signed_var>> m_trail;
vector<svector<eq_edge>> m_eqs; // signed_var.index() -> the edges adjacent to signed_var.index()
trail_stack m_stack;

72
src/sat/sat_solver/sat_smt_solver.cpp
View file

@ -161,7 +161,6 @@ class sat_smt_solver : public solver {
expr_ref_vector m_assumptions, m_core, m_ors, m_aux_fmls, m_internalized_fmls;
atom2bool_var m_map;
generic_model_converter_ref m_mc;
unsigned m_mc_size = 0;
mutable model_converter_ref m_cached_mc;
mutable ref<sat2goal::mc> m_sat_mc;
std::string m_unknown = "no reason given";
@ -180,8 +179,7 @@ public:
m_trail(m_preprocess_state.m_trail),
m_dep(m, m_trail),
m_assumptions(m), m_core(m), m_ors(m), m_aux_fmls(m), m_internalized_fmls(m),
m_map(m),
m_mc(alloc(generic_model_converter, m, "sat-smt-solver")) {
m_map(m) {
updt_params(p);
init_preprocess();
m_solver.set_incremental(true);
@ -211,7 +209,6 @@ public:
for (expr* f : m_internalized_fmls) result->m_internalized_fmls.push_back(tr(f));
if (m_mc) result->m_mc = dynamic_cast<generic_model_converter*>(m_mc->translate(tr));
result->m_dep.copy(tr, m_dep);
result->m_mc_size = m_mc_size;
if (m_sat_mc) result->m_sat_mc = dynamic_cast<sat2goal::mc*>(m_sat_mc->translate(tr));
result->m_internalized_converted = m_internalized_converted;
return result;
@ -291,7 +288,6 @@ public:
m_preprocess.push();
m_trail.push(restore_vector(m_assumptions));
m_trail.push(restore_vector(m_fmls));
m_trail.push(value_trail(m_mc_size));
}
void pop(unsigned n) override {
@ -302,7 +298,6 @@ public:
m_map.pop(n);
m_goal2sat.user_pop(n);
m_solver.user_pop(n);
m_mc->shrink(m_mc_size);
}
void set_phase(expr* e) override {
@ -549,6 +544,7 @@ public:
model_converter_ref get_model_converter() const override {
const_cast<sat_smt_solver*>(this)->convert_internalized();
verbose_stream() << "get model converter " << (m_cached_mc.get() != nullptr) << "\n";
if (m_cached_mc)
return m_cached_mc;
if (is_internalized() && m_internalized_converted) {
@ -660,6 +656,7 @@ private:
if (!m.inc())
return l_undef;
m_preprocess_state.advance_qhead();
m_mc = alloc(generic_model_converter, m, "sat-model-converter");
m_preprocess_state.append(*m_mc);
m_solver.pop_to_base_level();
m_aux_fmls.reset();
@ -754,42 +751,43 @@ private:
if (m_sat_mc)
(*m_sat_mc)(mdl);
m_goal2sat.update_model(mdl);
TRACE("sat", m_mc->display(tout););
(*m_mc)(mdl);
TRACE("sat", model_smt2_pp(tout, m, *mdl, 0););
if (!gparams::get_ref().get_bool("model_validate", false))
return;
IF_VERBOSE(1, verbose_stream() << "Verifying solution\n";);
model_evaluator eval(*mdl);
eval.set_model_completion(true);
bool all_true = true;
for (dependent_expr const& d : m_fmls) {
if (has_quantifiers(d.fml()))
continue;
expr_ref tmp(m);
eval(d.fml(), tmp);
if (m.limit().is_canceled())
return;
CTRACE("sat", !m.is_true(tmp),
tout << "Evaluation failed: " << mk_pp(d.fml(), m) << " to " << tmp << "\n";
model_smt2_pp(tout, m, *(mdl.get()), 0););
if (m.is_false(tmp)) {
IF_VERBOSE(0, verbose_stream() << "failed to verify: " << mk_pp(d.fml(), m) << "\n");
IF_VERBOSE(0, verbose_stream() << "evaluated to " << tmp << "\n");
all_true = false;
if (gparams::get_ref().get_bool("model_validate", false)) {
IF_VERBOSE(1, verbose_stream() << "Verifying solution\n";);
model_evaluator eval(*mdl);
eval.set_model_completion(true);
bool all_true = true;
for (dependent_expr const& d : m_fmls) {
if (has_quantifiers(d.fml()))
continue;
expr_ref tmp(m);
eval(d.fml(), tmp);
if (m.limit().is_canceled())
return;
CTRACE("sat", !m.is_true(tmp),
tout << "Evaluation failed: " << mk_pp(d.fml(), m) << " to " << tmp << "\n";
model_smt2_pp(tout, m, *(mdl.get()), 0););
if (m.is_false(tmp)) {
IF_VERBOSE(0, verbose_stream() << "failed to verify: " << mk_pp(d.fml(), m) << "\n");
IF_VERBOSE(0, verbose_stream() << "evaluated to " << tmp << "\n");
all_true = false;
}
}
if (!all_true) {
IF_VERBOSE(0, verbose_stream() << m_params << "\n");
IF_VERBOSE(0, if (m_mc) m_mc->display(verbose_stream() << "mc0\n"));
IF_VERBOSE(0, for (auto const& kv : m_map) verbose_stream() << mk_pp(kv.m_key, m) << " |-> " << kv.m_value << "\n");
exit(0);
}
else {
IF_VERBOSE(1, verbose_stream() << "solution verified\n");
}
}
if (!all_true) {
IF_VERBOSE(0, verbose_stream() << m_params << "\n");
IF_VERBOSE(0, if (m_mc) m_mc->display(verbose_stream() << "mc0\n"));
IF_VERBOSE(0, for (auto const& kv : m_map) verbose_stream() << mk_pp(kv.m_key, m) << " |-> " << kv.m_value << "\n");
exit(0);
}
else {
IF_VERBOSE(1, verbose_stream() << "solution verified\n");
}
TRACE("sat", m_mc->display(tout););
(*m_mc)(mdl);
}
};

7
src/smt/theory_lra.cpp
View file

@ -435,6 +435,13 @@ class theory_lra::imp {
app_ref mod(a.mk_mod(n1, n2), m);
ctx().internalize(mod, false);
if (ctx().relevancy()) ctx().add_relevancy_dependency(n, mod);
#if 0
// shortcut to create non-linear division axioms.
theory_var r = mk_var(n);
theory_var x = mk_var(n1);
theory_var y = mk_var(n2);
m_nla->add_idivision(get_lpvar(n), get_lpvar(n1), get_lpvar(n2));
#endif
}
else if (a.is_mod(n, n1, n2)) {
if (!a.is_numeral(n2, r) || r.is_zero()) found_underspecified(n);

10
src/tactic/core/reduce_args_tactic.cpp
View file

@ -18,6 +18,7 @@ Notes:
--*/
#include "tactic/tactical.h"
#include "ast/ast_smt2_pp.h"
#include "ast/ast_util.h"
#include "ast/array_decl_plugin.h"
#include "ast/has_free_vars.h"
#include "util/map.h"
@ -397,7 +398,7 @@ struct reduce_args_tactic::imp {
ptr_buffer<expr> new_args;
var_ref_vector new_vars(m);
ptr_buffer<expr> new_eqs;
generic_model_converter * f_mc = alloc(generic_model_converter, m, "reduce_args");
generic_model_converter * f_mc = alloc(generic_model_converter, m, "reduce_args");
for (auto const& [f, map] : decl2arg2funcs)
for (auto const& [t, new_def] : *map)
f_mc->hide(new_def);
@ -414,7 +415,6 @@ struct reduce_args_tactic::imp {
new_args.push_back(new_vars.back());
}
for (auto const& [t, new_def] : *map) {
// f_mc->hide(new_def);
SASSERT(new_def->get_arity() == new_args.size());
app * new_t = m.mk_app(new_def, new_args);
if (def == nullptr) {
@ -427,11 +427,7 @@ struct reduce_args_tactic::imp {
new_eqs.push_back(m.mk_eq(new_vars.get(i), t->get_arg(i)));
}
SASSERT(new_eqs.size() > 0);
expr * cond;
if (new_eqs.size() == 1)
cond = new_eqs[0];
else
cond = m.mk_and(new_eqs);
expr * cond = mk_and(m, new_eqs);
def = m.mk_ite(cond, new_t, def);
}
}

10
src/tactic/core/reduce_args_tactic.h
View file

@ -63,6 +63,8 @@ It creates a fresh function for each of the different values at position `i`.
#pragma once
#include "util/params.h"
#include "ast/simplifiers/reduce_args_simplifier.h"
#include "tactic/dependent_expr_state_tactic.h"
class ast_manager;
class tactic;
@ -71,3 +73,11 @@ tactic * mk_reduce_args_tactic(ast_manager & m, params_ref const & p = params_re
ADD_TACTIC("reduce-args", "reduce the number of arguments of function applications, when for all occurrences of a function f the i-th is a value.", "mk_reduce_args_tactic(m, p)")
*/
inline tactic* mk_reduce_args_tactic2(ast_manager& m, params_ref const& p = params_ref()) {
return alloc(dependent_expr_state_tactic, m, p,
[](auto& m, auto& p, auto& s) -> dependent_expr_simplifier* { return mk_reduce_args_simplifier(m, s, p); });
}
/*
ADD_TACTIC("reduce-args2", "reduce the number of arguments of function applications, when for all occurrences of a function f the i-th is a value.", "mk_reduce_args_tactic2(m, p)")
*/

56
src/tactic/dependent_expr_state_tactic.h
View file

@ -23,13 +23,14 @@ class dependent_expr_state_tactic : public tactic, public dependent_expr_state {
public:
using factoryTy = dependent_expr_simplifier(*(*)(ast_manager& m, params_ref const& p, dependent_expr_state& s));
private:
ast_manager& m;
ast_manager& m;
params_ref m_params;
trail_stack m_trail;
goal_ref m_goal;
dependent_expr m_dep;
statistics m_st;
factoryTy m_factory;
expr_ref_vector m_frozen;
scoped_ptr<dependent_expr_simplifier> m_simp;
scoped_ptr<model_reconstruction_trail> m_model_trail;
@ -37,6 +38,9 @@ private:
if (!m_simp) {
m_simp = m_factory(m, m_params, *this);
m_st.reset();
push();
for (expr* e : m_frozen)
freeze(e);
}
if (!m_model_trail)
m_model_trail = alloc(model_reconstruction_trail, m, m_trail);
@ -44,14 +48,20 @@ private:
public:
dependent_expr_state_tactic(ast_manager& m, params_ref const& p, factoryTy f):
dependent_expr_state_tactic(ast_manager& m, params_ref const& p, factoryTy f) :
dependent_expr_state(m),
m(m),
m_params(p),
m_dep(m, m.mk_true(), nullptr, nullptr),
m_factory(f)
m_factory(f),
m_frozen(m)
{}
~dependent_expr_state_tactic() override {
if (m_simp)
pop(1);
}
/**
* size(), [](), update() and inconsisent() implement the abstract interface of dependent_expr_state
*/
@ -61,14 +71,14 @@ public:
m_dep = dependent_expr(m, m_goal->form(i), m_goal->pr(i), m_goal->dep(i));
return m_dep;
}
void update(unsigned i, dependent_expr const& j) override {
if (inconsistent())
return;
auto [f, p, d] = j();
m_goal->update(i, f, p, d);
}
void add(dependent_expr const& j) override {
if (inconsistent())
return;
@ -83,10 +93,10 @@ public:
model_reconstruction_trail& model_trail() override {
return *m_model_trail;
}
char const* name() const override { return m_simp?m_simp->name():"null"; }
void updt_params(params_ref const & p) override {
char const* name() const override { return m_simp ? m_simp->name() : "null"; }
void updt_params(params_ref const& p) override {
m_params.append(p);
init();
m_simp->updt_params(m_params);
@ -97,12 +107,12 @@ public:
m_simp->collect_param_descrs(r);
}
tactic * translate(ast_manager & m) override {
tactic* translate(ast_manager& m) override {
return alloc(dependent_expr_state_tactic, m, m_params, m_factory);
}
void operator()(goal_ref const & in,
goal_ref_buffer & result) override {
void operator()(goal_ref const& in,
goal_ref_buffer& result) override {
init();
statistics_report sreport(*this);
tactic_report report(name(), *in);
@ -124,25 +134,39 @@ public:
}
void cleanup() override {
if (m_simp)
if (m_simp) {
m_simp->collect_statistics(m_st);
pop(1);
}
m_simp = nullptr;
m_model_trail = nullptr;
m_goal = nullptr;
m_dep = dependent_expr(m, m.mk_true(), nullptr, nullptr);
}
void collect_statistics(statistics & st) const override {
if (m_simp)
void collect_statistics(statistics& st) const override {
if (m_simp)
m_simp->collect_statistics(st);
else
st.copy(m_st);
}
void reset_statistics() override {
if (m_simp)
m_simp->reset_statistics();
m_st.reset();
}
};
void user_propagate_register_expr(expr* e) override {
freeze(e);
m_frozen.push_back(e);
}
void user_propagate_clear() override {
if (m_simp) {
pop(1);
push();
}
m_frozen.reset();
}
};

16
src/util/bit_vector.h
View file

@ -211,6 +211,22 @@ public:
bool contains(const bit_vector & other) const;
class iterator {
bit_vector const& b;
unsigned m_curr;
public:
iterator(bit_vector const& b, unsigned i) : b(b), m_curr(i) {}
bool operator*(unsigned i) const { return b.get(m_curr); }
bool operator*() const { return b.get(m_curr); }
iterator& operator++() { ++m_curr; return *this; }
iterator operator++(int) { iterator tmp = *this; ++* this; return tmp; }
bool operator==(iterator const& it) const { return m_curr == it.m_curr; }
bool operator!=(iterator const& it) const { return m_curr != it.m_curr; }
};
iterator begin() const { return iterator(*this, 0); }
iterator end() const { return iterator(*this, size()); }
};
inline std::ostream & operator<<(std::ostream & out, bit_vector const & b) {