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z3/lib/dl_util.h
Leonardo de Moura e9eab22e5c Z3 sources
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2012-10-02 11:35:25 -07:00

879 lines
27 KiB
C++

/*++
Copyright (c) 2006 Microsoft Corporation
Module Name:
dl_util.h
Abstract:
Datalog utility function and structures.
Author:
Leonardo de Moura (leonardo) 2010-05-20.
Revision History:
--*/
#ifndef _DL_UTIL_H_
#define _DL_UTIL_H_
#include"ast.h"
#include"hashtable.h"
#include"obj_hashtable.h"
#include"uint_set.h"
#include"horn_subsume_model_converter.h"
#include"replace_proof_converter.h"
#include"substitution.h"
namespace datalog {
class context;
class rule;
class relation_base;
class relation_manager;
class table_base;
class pentagon_relation;
class relation_fact;
class relation_signature;
enum PDR_CACHE_MODE {
NO_CACHE,
HASH_CACHE,
CONSTRAINT_CACHE,
LAST_CACHE_MODE
};
enum DL_ENGINE {
DATALOG_ENGINE,
PDR_ENGINE,
QPDR_ENGINE,
BMC_ENGINE,
LAST_ENGINE
};
struct std_string_hash_proc {
unsigned operator()(const std::string & s) const
{ return string_hash(s.c_str(), static_cast<unsigned>(s.length()), 17); }
};
// typedef int_hashtable<int_hash, default_eq<int> > idx_set;
typedef uint_set idx_set;
typedef idx_set var_idx_set;
typedef u_map<var *> varidx2var_map;
typedef obj_hashtable<func_decl> func_decl_set; //!< Rule dependencies.
typedef vector<std::string> string_vector;
/**
\brief Collect top-level conjunctions and disjunctions.
*/
void flatten_and(expr_ref_vector& result);
void flatten_and(expr* fml, expr_ref_vector& result);
void flatten_or(expr_ref_vector& result);
void flatten_or(expr* fml, expr_ref_vector& result);
/**
Transform
~(a1 | ... | aN)
into
~a1 | ... | ~aN
and
~(a1 & ... & aN)
into
~a1 | ... | ~aN
Return true if something was done.
*/
bool push_toplevel_junction_negation_inside(expr_ref& e);
bool contains_var(expr * trm, unsigned var_idx);
/**
\brief Collect the variables in \c pred.
\pre \c pred must be a valid head or tail.
*/
void collect_vars(ast_manager & m, expr * pred, var_idx_set & result);
void collect_tail_vars(ast_manager & m, rule * r, var_idx_set & result);
void get_free_vars(rule * r, ptr_vector<sort>& sorts);
/**
\brief Return number of arguments of \c pred that are variables
*/
unsigned count_variable_arguments(app * pred);
/**
\brief Store in \c result the set of variables used by \c r when ignoring the tail \c t.
*/
void collect_non_local_vars(ast_manager & m, rule const * r, app * t, var_idx_set & result);
/**
\brief Store in \c result the set of variables used by \c r when ignoring the tail elements \c t_1 and \c t_2.
*/
void collect_non_local_vars(ast_manager & m, rule const * r, app * t_1, app * t_2, var_idx_set & result);
template<typename T>
void copy_nonvariables(app * src, T& tgt)
{
unsigned n = src->get_num_args();
for (unsigned i = 0; i < n; i++) {
expr * arg = src->get_arg(i);
if (!is_var(arg)) {
tgt[i]=arg;
}
}
}
/**
\brief Auxiliary function used to create a tail based on \c pred for a new rule.
The variables in \c pred are re-assigned using \c next_idx and \c varidx2var.
A variable is considered non-local to the rule if it is in the set \c non_local_vars.
Non-local variables are coppied to new_rule_args, and their sorts to \c new_rule_domain.
The new predicate is stored in \c new_pred.
*/
void mk_new_rule_tail(ast_manager & m, app * pred,
var_idx_set const & non_local_vars,
unsigned & next_idx, varidx2var_map & varidx2var,
sort_ref_buffer & new_rule_domain, expr_ref_buffer & new_rule_args,
app_ref & new_pred);
/**
\brief Simpler version of the previous function. Initializes next_idx with 0, and
an empty varid2var
*/
inline void mk_new_rule_tail(ast_manager & m, app * pred,
var_idx_set const & non_local_vars,
sort_ref_buffer & new_rule_domain, expr_ref_buffer & new_rule_args,
app_ref & new_pred) {
unsigned next_idx = 0;
varidx2var_map varidx2var;
mk_new_rule_tail(m, pred, non_local_vars, next_idx, varidx2var, new_rule_domain, new_rule_args, new_pred);
}
/**
\brief Print a predicate \c f to the stream \c out.
*/
void display_predicate(context & ctx, app * f, std::ostream & out);
/**
\brief Like \c display_predicate, just without the final '\n' character.
*/
void output_predicate(context & ctx, app * f, std::ostream & out);
/**
\brief Print a fact \c f to the stream \c out in a format conforming to Bddbddb.
*/
void display_fact(context & ctx, app * f, std::ostream & out);
class scoped_coarse_proof {
ast_manager& m;
proof_gen_mode m_mode;
public:
scoped_coarse_proof(ast_manager& m): m(m) {
m_mode = m.proof_mode();
m.toggle_proof_mode(PGM_COARSE);
}
~scoped_coarse_proof() {
m.toggle_proof_mode(m_mode);
}
};
class variable_intersection
{
bool values_match(const expr * v1, const expr * v2);
ast_manager & m_manager;
unsigned_vector m_args1;
unsigned_vector m_args2;
unsigned_vector m_const_indexes;
app_ref_vector m_consts;
static unsigned expr_cont_get_size(app * a) { return a->get_num_args(); }
static expr * expr_cont_get(app * a, unsigned i) { return a->get_arg(i); }
static unsigned expr_cont_get_size(const ptr_vector<expr> & v) { return v.size(); }
static expr * expr_cont_get(const ptr_vector<expr> & v, unsigned i) { return v[i]; }
public:
variable_intersection(ast_manager & m) : m_manager(m), m_consts(m) {}
unsigned size() const {
return m_args1.size();
}
const unsigned * get_cols1() const {
return m_args1.c_ptr();
}
const unsigned * get_cols2() const {
return m_args2.c_ptr();
}
bool empty() const {
return size()==0;
}
void get(unsigned i, unsigned & index1, unsigned & index2) const {
index1=m_args1[i];
index2=m_args2[i];
}
void reset() {
m_args1.reset();
m_args2.reset();
m_const_indexes.reset();
m_consts.reset();
}
bool args_match(const app * f1, const app * f2);
bool args_self_match(const app * f);
/**
\brief Fill arguments of \c f1 into corresponding positions in
\c tgt using its \c operator[].
*/
template<typename T>
void fill_into_second(const app * f1, T & tgt) const {
unsigned n=size();
for(unsigned i=0; i<n; i++) {
unsigned f1_index, tgt_index;
get(i, f1_index, tgt_index);
tgt[tgt_index]=f1->get_arg(f1_index);
}
}
void add_pair(unsigned idx1, unsigned idx2) {
m_args1.push_back(idx1);
m_args2.push_back(idx2);
}
/**
Find pairs of indexes of arguments of \c a1 and \c a2 that correspond to the same
variable. Here we do not detect the constant arguments in \c a1 and \c a2.
*/
template<typename T1, typename T2>
void populate(const T1 & a1, const T2 & a2)
{
//TODO: optimize quadratic complexity
//TODO: optimize number of checks when variable occurs multiple times
unsigned a1num = expr_cont_get_size(a1);
unsigned a2num = expr_cont_get_size(a2);
for(unsigned i1=0; i1<a1num; i1++) {
expr * e1=expr_cont_get(a1,i1);
if(!is_var(e1)) {
continue;
}
var* v1=to_var(e1);
for(unsigned i2=0; i2<a2num; i2++) {
expr * e2=expr_cont_get(a2,i2);
if(!is_var(e2)) {
continue;
}
var* v2=to_var(e2);
if(v1->get_idx()==v2->get_idx()) {
add_pair(i1, i2);
}
}
}
}
/**
Find pairs of indexes of arguments of \c a that correspond to the same variable
and indexes that correspond to a constant.
*/
void populate_self(const app * a);
};
template<class T>
void project_out_vector_columns(T & container, unsigned removed_col_cnt, const unsigned * removed_cols) {
if(removed_col_cnt==0) {
return;
}
unsigned n = container.size();
unsigned ofs = 1;
unsigned r_i = 1;
for(unsigned i=removed_cols[0]+1; i<n; i++) {
if(r_i!=removed_col_cnt && removed_cols[r_i]==i) {
r_i++;
ofs++;
continue;
}
container[i-ofs] = container[i];
}
SASSERT(r_i==removed_col_cnt);
container.resize(n-removed_col_cnt);
}
template<class T, class M>
void project_out_vector_columns(ref_vector<T,M> & container, unsigned removed_col_cnt,
const unsigned * removed_cols) {
if(removed_col_cnt==0) {
return;
}
unsigned n = container.size();
unsigned ofs = 1;
int r_i = 1;
for(unsigned i=removed_cols[0]+1; i<n; i++) {
if(r_i!=removed_col_cnt && removed_cols[r_i]==i) {
r_i++;
ofs++;
continue;
}
container.set(i-ofs, container.get(i));
}
SASSERT(r_i==removed_col_cnt);
container.resize(n-removed_col_cnt);
}
template<class T>
void project_out_vector_columns(T & container, const unsigned_vector removed_cols) {
project_out_vector_columns(container, removed_cols.size(), removed_cols.c_ptr());
}
/**
\brief Take a single cycle permutation and store it in the form of a cycle.
The function modifies the \c permutation vector
*/
void cycle_from_permutation(unsigned_vector & permutation, unsigned_vector & cycle);
/**
\brief If \c permutation is an identity, return false. Otherwise remove one cycle from the
permutation, store it in the form of a cycle in \c cycle and return true.
Using this function one can retrieve all cycles in a permutation.
\c cycle must be empty before calling the function.
*/
bool try_remove_cycle_from_permutation(unsigned_vector & permutation, unsigned_vector & cycle);
void collect_sub_permutation(const unsigned_vector & permutation, const unsigned_vector & translation,
unsigned_vector & res, bool & identity);
template<class T>
void permutate_by_cycle(T & container, unsigned cycle_len, const unsigned * permutation_cycle) {
if(cycle_len<2) {
return;
}
typename T::data aux = container[permutation_cycle[0]];
for(unsigned i=1; i<cycle_len; i++) {
container[permutation_cycle[i-1]]=container[permutation_cycle[i]];
}
container[permutation_cycle[cycle_len-1]]=aux;
}
template<class T, class M>
void permutate_by_cycle(ref_vector<T,M> & container, unsigned cycle_len, const unsigned * permutation_cycle) {
if(cycle_len<2) {
return;
}
T * aux = container.get(permutation_cycle[0]);
for(unsigned i=1; i<cycle_len; i++) {
container.set(permutation_cycle[i-1], container.get(permutation_cycle[i]));
}
container.set(permutation_cycle[cycle_len-1], aux);
}
template<class T>
void permutate_by_cycle(T & container, const unsigned_vector permutation_cycle) {
permutate_by_cycle(container, permutation_cycle.size(), permutation_cycle.c_ptr());
}
class counter {
protected:
typedef u_map<int> map_impl;
map_impl m_data;
const bool m_stay_non_negative;
public:
typedef map_impl::iterator iterator;
counter(bool stay_non_negative = true) : m_stay_non_negative(stay_non_negative) {}
iterator begin() const { return m_data.begin(); }
iterator end() const { return m_data.end(); }
void update(unsigned el, int delta);
int & get(unsigned el);
/**
\brief Increase values of elements in \c els by \c delta.
The function returns a reference to \c *this to allow for expressions like
counter().count(sz, arr).get_positive_count()
*/
counter & count(unsigned sz, const unsigned * els, int delta = 1);
counter & count(const unsigned_vector & els, int delta = 1) {
return count(els.size(), els.c_ptr(), delta);
}
void collect_positive(idx_set & acc) const;
unsigned get_positive_count() const;
bool get_max_positive(unsigned & res) const;
unsigned get_max_positive() const;
/**
Since the default counter value of a counter is zero, the result is never negative.
*/
int get_max_counter_value() const;
};
class var_counter : public counter {
ptr_vector<sort> m_sorts;
expr_fast_mark1 m_visited;
ptr_vector<expr> m_todo;
unsigned_vector m_scopes;
unsigned get_max_var(bool & has_var);
public:
var_counter(bool stay_non_negative = true) : counter(stay_non_negative) {}
void count_vars(ast_manager & m, const app * t, int coef = 1);
void count_vars(ast_manager & m, const rule * r, int coef = 1);
unsigned get_max_var(const rule& r);
unsigned get_max_var(expr* e);
unsigned get_next_var(expr* e);
};
class ast_counter {
typedef obj_map<ast, int> map_impl;
map_impl m_data;
bool m_stay_non_negative;
public:
typedef map_impl::iterator iterator;
ast_counter(bool stay_non_negative = true) : m_stay_non_negative(stay_non_negative) {}
iterator begin() const { return m_data.begin(); }
iterator end() const { return m_data.end(); }
int & get(ast * el) {
return m_data.insert_if_not_there2(el, 0)->get_data().m_value;
}
void update(ast * el, int delta){
get(el)+=delta;
SASSERT(!m_stay_non_negative || get(el)>=0);
}
void inc(ast * el) { update(el, 1); }
void dec(ast * el) { update(el, -1); }
};
void del_rule(horn_subsume_model_converter* mc, rule& r);
void resolve_rule(replace_proof_converter* pc, rule& r1, rule& r2, unsigned idx,
expr_ref_vector const& s1, expr_ref_vector const& s2, rule& res);
model_converter* mk_skip_model_converter();
proof_converter* mk_skip_proof_converter();
/**
Return maximal variable number, or zero is there isn't any
*/
// unsigned get_max_var(const rule & r, ast_manager & m);
void reverse_renaming(ast_manager & m, const expr_ref_vector & src, expr_ref_vector & tgt);
/**
\brief Populate vector \c renaming_args so that it can be used as an argument to \c var_subst.
The renaming we want is one that transforms variables with numbers of indexes of \c map into the
values of at those indexes. If a value if \c UINT_MAX, it means we do not transform the index
corresponding to it.
*/
void get_renaming_args(const unsigned_vector & map, const relation_signature & orig_sig,
expr_ref_vector & renaming_arg);
void print_renaming(const expr_ref_vector & cont, std::ostream & out);
/**
\brief Update tgt with effect of applying substitution from 'sub' to it.
tgt is extended by variables that are substituted by 'sub'.
We use the convention that the entry at index 'i' corresponds to variable
with de-Bruijn index 'i'.
*/
void apply_subst(expr_ref_vector& tgt, expr_ref_vector const& sub);
// -----------------------------------
//
// container functions
//
// -----------------------------------
template<class Set>
void set_intersection(Set & tgt, const Set & src) {
svector<typename Set::data> to_remove;
typename Set::iterator vit = tgt.begin();
typename Set::iterator vend = tgt.end();
for(;vit!=vend;++vit) {
typename Set::data itm=*vit;
if(!src.contains(itm)) {
to_remove.push_back(itm);
}
}
while(!to_remove.empty()) {
tgt.remove(to_remove.back());
to_remove.pop_back();
}
}
template<class Set>
void set_difference(Set & tgt, const Set & to_remove) {
typename Set::iterator vit = to_remove.begin();
typename Set::iterator vend = to_remove.end();
for(;vit!=vend;++vit) {
typename Set::data itm=*vit;
tgt.remove(itm);
}
}
template<class Set>
void set_union(Set & tgt, const Set & to_add) {
typename Set::iterator vit = to_add.begin();
typename Set::iterator vend = to_add.end();
for(;vit!=vend;++vit) {
typename Set::data itm=*vit;
tgt.insert(itm);
}
}
void idx_set_union(idx_set & tgt, const idx_set & src);
template<class T>
void unite_disjoint_maps(T & tgt, const T & src) {
typename T::iterator it = src.begin();
typename T::iterator end = src.end();
for(; it!=end; ++it) {
SASSERT(!tgt.contains(it->m_key));
tgt.insert(it->m_key, it->m_value);
}
}
template<class T, class U>
void collect_map_range(T & acc, const U & map) {
typename U::iterator it = map.begin();
typename U::iterator end = map.end();
for(; it!=end; ++it) {
acc.push_back(it->m_value);
}
}
template<class T>
void print_container(const T & begin, const T & end, std::ostream & out) {
T it = begin;
out << "(";
bool first = true;
for(; it!=end; ++it) {
if(first) { first = false; } else { out << ","; }
out << (*it);
}
out << ")";
}
template<class T>
void print_container(const T & cont, std::ostream & out) {
print_container(cont.begin(), cont.end(), out);
}
template<class T, class M>
void print_container(const ref_vector<T,M> & cont, std::ostream & out) {
print_container(cont.c_ptr(), cont.c_ptr() + cont.size(), out);
}
template<class T>
void print_map(const T & cont, std::ostream & out) {
typename T::iterator it = cont.begin();
typename T::iterator end = cont.end();
out << "(";
bool first = true;
for(; it!=end; ++it) {
if(first) { first = false; } else { out << ","; }
out << it->m_key << "->" << it->m_value;
}
out << ")";
}
template<class It, class V>
unsigned find_index(const It & begin, const It & end, const V & val) {
unsigned idx = 0;
It it = begin;
for(; it!=end; it++, idx++) {
if(*it==val) {
return idx;
}
}
return UINT_MAX;
}
template<class T, class U>
bool containers_equal(const T & begin1, const T & end1, const U & begin2, const U & end2) {
T it1 = begin1;
U it2 = begin2;
for(; it1!=end1 && it2!=end2; ++it1, ++it2) {
if(*it1!=*it2) {
return false;
}
}
return it1==end1 && it2==end2;
}
template<class T, class U>
bool vectors_equal(const T & c1, const U & c2) {
if(c1.size()!=c2.size()) {
return false;
}
typename T::data * it1 = c1.c_ptr();
typename T::data * end1 = c1.c_ptr()+c1.size();
typename U::data * it2 = c2.c_ptr();
for(; it1!=end1; ++it1, ++it2) {
if(*it1!=*it2) {
return false;
}
}
return true;
}
template<class T>
unsigned int_vector_hash(const T & cont) {
return string_hash(reinterpret_cast<const char *>(cont.c_ptr()),
cont.size()*sizeof(typename T::data), 0);
}
template<class T>
struct int_vector_hash_proc {
unsigned operator()(const T & cont) const {
return int_vector_hash(cont);
}
};
template<class T>
struct vector_eq_proc {
bool operator()(const T & c1, const T & c2) const { return vectors_equal(c1, c2); }
};
template<class T>
void dealloc_ptr_vector_content(ptr_vector<T> & v) {
typename ptr_vector<T>::iterator it = v.begin();
typename ptr_vector<T>::iterator end = v.end();
for(; it!=end; ++it) {
dealloc(*it);
}
}
void dealloc_ptr_vector_content(ptr_vector<relation_base> & v);
/**
\brief Add elements from an iterable object \c src into the vector \c vector.
*/
template<class VectType, class U>
void push_into_vector(VectType & vector, const U & src) {
typename U::iterator it = src.begin();
typename U::iterator end = src.end();
for(; it!=end; ++it) {
vector.push_back(*it);
}
}
template<class VectType, class U, class M>
void push_into_vector(VectType & vector, const ref_vector<U,M> & src) {
U * const * it = src.begin();
U * const * end = src.end();
for(; it!=end; ++it) {
vector.push_back(*it);
}
}
template<class SetType, class U>
void insert_into_set(SetType & tgt, const U & src) {
typename U::const_iterator it = src.begin();
typename U::const_iterator end = src.end();
for(; it!=end; ++it) {
tgt.insert(*it);
}
}
/**
\brief Remove the first occurence of \c el from \c v and return \c true. If
\c el is not present in \c v, return \c false. The order of elements in \c v
is not preserved.
*/
template<class T>
bool remove_from_vector(T & v, const typename T::data & el) {
unsigned sz = v.size();
for(unsigned i=0; i<sz; i++) {
if(v[i]==el) {
std::swap(v[i], v.back());
v.pop_back();
return true;
}
}
return false;
}
/**
\brief Reset and deallocate the values stored in a mapping of the form obj_map<Key, Value*>
*/
template<typename Key, typename Value, typename Hash, typename Eq>
void reset_dealloc_values(map<Key, Value*, Hash, Eq> & m) {
typename map<Key, Value*, Hash, Eq>::iterator it = m.begin();
typename map<Key, Value*, Hash, Eq>::iterator end = m.end();
for (; it != end; ++it) {
dealloc(it->m_value);
}
m.reset();
}
template<class T>
struct aux__index_comparator {
T* m_keys;
aux__index_comparator(T* keys) : m_keys(keys) {}
bool operator()(unsigned a, unsigned b) {
return m_keys[a]<m_keys[b];
}
};
template<class T, class U>
void sort_two_arrays(unsigned len, T* keys, U* vals) {
if(len<2) {
return;
}
if(len==2) {
if(keys[0]>keys[1]) {
std::swap(keys[0], keys[1]);
std::swap(vals[0], vals[1]);
}
return;
}
unsigned_vector numbers;
for(unsigned i=0; i<len; i++) {
numbers.push_back(i);
}
aux__index_comparator<T> cmp(keys);
std::sort(numbers.begin(), numbers.end(), cmp);
for(unsigned i=0; i<len; i++) {
unsigned prev_i = i;
for(;;) {
unsigned src_i = numbers[prev_i];
numbers[prev_i]=prev_i;
if(src_i==i) {
break;
}
std::swap(keys[prev_i], keys[src_i]);
std::swap(vals[prev_i], vals[src_i]);
prev_i = src_i;
}
}
}
/**
\brief Consider \c translation as a map from indexes to values. Iterate through \c src and store
transformed values of elements into \c res unless they are equal to \c UINT_MAX.
*/
void collect_and_transform(const unsigned_vector & src, const unsigned_vector & translation,
unsigned_vector & res);
/**
\brief Insert into \c res values of \c src transformed by \c map (understood as a function
from its indexes to the values stored in it).
*/
void transform_set(const unsigned_vector & map, const idx_set & src, idx_set & result);
void add_sequence(unsigned start, unsigned count, unsigned_vector & v);
template<class Container>
void add_sequence_without_set(unsigned start, unsigned count, const Container & complement, unsigned_vector & v) {
unsigned after_last = start+count;
for(unsigned i=start; i<after_last; i++) {
if(!complement.contains(i)) {
v.push_back(i);
}
}
}
// -----------------------------------
//
// filesystem functions
//
// -----------------------------------
void get_file_names(std::string directory, std::string extension, bool traverse_subdirs,
string_vector & res);
bool file_exists(std::string name);
bool is_directory(std::string name);
std::string get_file_name_without_extension(std::string name);
// -----------------------------------
//
// misc
//
// -----------------------------------
struct uint64_hash {
typedef uint64 data;
unsigned operator()(uint64 x) const { return hash_ull(x); }
};
template<class T>
void universal_delete(T* ptr) {
dealloc(ptr);
}
void universal_delete(relation_base* ptr);
void universal_delete(table_base* ptr);
template<typename T>
class scoped_rel {
T* m_t;
public:
scoped_rel(T* t) : m_t(t) {}
~scoped_rel() { if (m_t) { universal_delete(m_t); } }
scoped_rel() : m_t(0) {}
scoped_rel& operator=(T* t) { if (m_t) { universal_delete(m_t); } m_t = t; return *this; }
T* operator->() { return m_t; }
const T* operator->() const { return m_t; }
T& operator*() { return *m_t; }
const T& operator*() const { return *m_t; }
operator bool() const { return m_t!=0; }
T* get() { return m_t; }
/**
\brief Remove object from \c scoped_rel without deleting it.
*/
T* release() {
T* res = m_t;
m_t = 0;
return res;
}
};
/**
\brief If it is possible to convert the beginning of \c s to uint64,
store the result of conversion and return true; otherwise return false.
*/
bool string_to_uint64(const char * s, uint64 & res);
std::string to_string(uint64 num);
/**
\brief Read the sequence of decimal digits starting at \c s and interpret it as
uint64. If successful, \c res will contain the read number and \c s will point
to the first non-digit character, and true is returned. If the first character
is not a digit, no parameter is modified and false is returned. If the uint64
overflows, \c points to the character which caused the overflow and false is
returned.
*/
bool read_uint64(const char * & s, uint64 & res);
};
#endif /* _DL_UTIL_H_ */