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51 if(expr.
id()==ID_symbol ||
52 expr.
id()==ID_index ||
53 expr.
id()==ID_member ||
54 expr.
id()==ID_dereference)
79 for(goto_programt::instructionst::const_iterator
80 it=instructions.begin();
81 it!=instructions.end();
90 for(
const auto &step : path)
98 for(
const auto &step : loop)
109 modified.insert(assignment.
lhs());
114 std::map<exprt, polynomialt> polynomials,
130 std::vector<exprt> polynomials_hold;
135 for(std::map<exprt, polynomialt>::iterator it=polynomials.begin();
136 it!=polynomials.end();
139 const equal_exprt holds(it->first, it->second.to_expr());
142 polynomials_hold.push_back(holds);
155 for(
const auto &p : polynomials_hold)
159 std::cout <<
"Checking following program for inductiveness:\n";
169 std::cout <<
"Not inductive!\n";
178 catch(
const std::string &s)
180 std::cout <<
"Error in inductiveness SAT check: " << s <<
'\n';
183 catch (
const char *s)
185 std::cout <<
"Error in inductiveness SAT check: " << s <<
'\n';
192 std::map<exprt, polynomialt> &polynomials,
201 for(std::map<exprt, polynomialt>::iterator it=polynomials.begin();
202 it!=polynomials.end();
205 it->second.substitute(substitution);
218 vars.erase(loop_counter_name);
241 for(patht::reverse_iterator r_it=path.rbegin();
254 if(lhs.
id()==ID_symbol ||
255 lhs.
id()==ID_index ||
256 lhs.
id()==ID_dereference)
265 else if(t->is_assume() || t->is_assert())
274 if(!r_it->guard.is_true() && !r_it->guard.is_nil())
294 if(expr.
id()==ID_index ||
295 expr.
id()==ID_dereference)
297 expr_mapt::iterator it=abstractions.find(expr);
299 if(it==abstractions.end())
326 if(expr.
id() == ID_not &&
to_not_expr(expr).op().
id() == ID_nondet)
330 else if(expr.
id()==ID_equal ||
337 if(rel_expr.lhs().id() == ID_nondet || rel_expr.rhs().id() == ID_nondet)
345 std::map<exprt, polynomialt> polynomials,
380 std::vector<exprt> polynomials_hold;
382 for(std::map<exprt, polynomialt>::iterator it=polynomials.begin();
383 it!=polynomials.end();
387 exprt rhs=it->second.to_expr();
394 for(std::vector<exprt>::iterator it=polynomials_hold.begin();
395 it!=polynomials_hold.end();
407 for(std::map<exprt, polynomialt>::iterator p_it=polynomials.begin();
408 p_it!=polynomials.end();
411 program.
assign(p_it->first, p_it->second.to_expr());
414 program.
assume(condition);
419 for(std::map<exprt, polynomialt>::iterator p_it=polynomials.begin();
420 p_it!=polynomials.end();
423 program.
assign(p_it->first, p_it->second.to_expr());
434 std::cout <<
"Checking following program for monotonicity:\n";
443 std::cout <<
"Path is not monotone\n";
449 catch(
const std::string &s)
451 std::cout <<
"Error in monotonicity SAT check: " << s <<
'\n';
456 std::cout <<
"Error in monotonicity SAT check: " << s <<
'\n';
461 std::cout <<
"Path is monotone\n";
475 checker_options.
set_option(
"signed-overflow-check",
true);
476 checker_options.
set_option(
"unsigned-overflow-check",
true);
477 checker_options.
set_option(
"assert-to-assume",
true);
478 checker_options.
set_option(
"assumptions",
true);
484 std::cout <<
"Adding overflow checks at " << now <<
"...\n";
497 std::cout <<
"Done at " << now <<
".\n";
507 for(goto_programt::instructionst::reverse_iterator r_it=loop_body.rbegin();
508 r_it!=loop_body.rend();
511 if(r_it->is_assign())
516 if(assignment.
lhs().
id()==ID_index)
519 assignments.push_back(
520 std::make_pair(assignment.
lhs(), assignment.
rhs()));
524 arrays_written.insert(index_expr.
array());
530 for(expr_pairst::iterator a_it=assignments.begin();
531 a_it!=assignments.end();
546 std::map<exprt, polynomialt> &polynomials,
551 std::cout <<
"Doing arrays...\n";
560 std::cout <<
"Found " << array_assignments.size()
561 <<
" array assignments\n";
564 if(array_assignments.empty())
574 array_assignments, polynomials, poly_assignments, nondet_indices))
579 std::cout <<
"Couldn't model an array assignment :-(\n";
585 for(expr_sett::iterator it=arrays_written.begin();
586 it!=arrays_written.end();
596 for(polynomial_array_assignmentst::iterator it=poly_assignments.begin();
597 it!=poly_assignments.end();
628 for(expr_sett::iterator a_it=arrays_written.begin();
629 a_it!=arrays_written.end();
633 exprt old_array=substitution[array];
634 std::vector<polynomialt> indices;
635 bool nonlinear_index=
false;
637 for(polynomial_array_assignmentst::iterator it=poly_assignments.begin();
638 it!=poly_assignments.end();
645 indices.push_back(index);
653 nonlinear_index=
true;
675 pos_eliminator=neg_eliminator;
676 pos_eliminator.
mult(-1);
680 for(std::vector<polynomialt>::iterator it=indices.begin();
685 exprt max_idx, min_idx;
693 index.
add(pos_eliminator);
702 index.
add(neg_eliminator);
707 assert(!
"ITSALLGONEWRONG");
713 unchanged_operands.push_back(unchanged_by_this_one);
726 for(std::vector<polynomialt>::iterator it=indices.begin();
730 idx_touched_operands.push_back(
748 implies_exprt idx_not_touched_bound(l_bound, idx_not_touched);
750 idx_never_touched=
exprt(ID_forall);
765 implies_exprt idx_unchanged(idx_never_touched, value_unchanged);
773 program.
assume(array_unchanged);
781 std::map<exprt, polynomialt> &polynomials,
785 for(expr_pairst::iterator it=array_assignments.begin();
786 it!=array_assignments.end();
798 std::cout <<
"Couldn't convert index: "
805 std::cout <<
"Converted index to: "
810 if(it->second.id()==ID_nondet)
812 nondet_indices.push_back(poly_assignment.
index);
814 else if(!
expr2poly(it->second, polynomials, poly_assignment.
value))
818 std::cout <<
"Couldn't convert RHS: " <<
expr2c(it->second,
ns)
826 std::cout <<
"Converted RHS to: "
831 array_polynomials.push_back(poly_assignment);
840 std::map<exprt, polynomialt> &polynomials,
843 exprt subbed_expr=expr;
845 for(std::map<exprt, polynomialt>::iterator it=polynomials.begin();
846 it!=polynomials.end();
849 replace_expr(it->first, it->second.to_expr(), subbed_expr);
853 std::cout <<
"expr2poly(" <<
expr2c(subbed_expr,
ns) <<
")\n";
870 std::map<exprt, polynomialt> &polynomials,
881 std::unordered_set<index_exprt, irep_hash> array_writes;
885 for(std::map<exprt, polynomialt>::iterator it=polynomials.begin();
886 it!=polynomials.end();
889 const exprt &var=it->first;
904 for(expr_sett::iterator it=nonrecursive.begin();
905 it!=nonrecursive.end();
912 for(goto_programt::instructionst::iterator it=body.begin();
918 exprt lhs = it->get_assign().lhs();
919 exprt rhs = it->get_assign().rhs();
921 if(lhs.
id()==ID_dereference)
925 std::cout <<
"Bailing out on write-through-pointer\n";
930 if(lhs.
id()==ID_index)
934 array_writes.insert(lhs_index_expr);
936 if(arrays_written.find(lhs_index_expr.array()) != arrays_written.end())
941 std::cout <<
"Bailing out on array written to twice in loop: "
942 <<
expr2c(lhs_index_expr.array(),
ns) <<
'\n';
947 arrays_written.insert(lhs_index_expr.array());
958 for(expr_sett::iterator it=arrays_written.begin();
959 it!=arrays_written.end();
962 if(arrays_read.find(*it)!=arrays_read.end())
965 std::cout <<
"Bailing out on array read and written on same path\n";
971 for(expr_sett::iterator it=nonrecursive.begin();
972 it!=nonrecursive.end();
975 if(it->id()==ID_symbol)
977 exprt &val=state[*it];
981 std::cout <<
"Fitted nonrecursive: " <<
expr2c(*it,
ns) <<
"=" <<
987 for(
const auto &write : array_writes)
989 const auto &lhs = write;
990 const auto &rhs = state[write];
995 std::cout <<
"Failed to assign a nonrecursive array: " <<
1011 std::cout <<
"Modelling array assignment " <<
expr2c(lhs,
ns) <<
"=" <<
1015 if(lhs.
id()==ID_dereference)
1019 std::cout <<
"Bailing out on write-through-pointer\n";
1037 const exprt &fresh_array =
1065 std::cout <<
"Trying to polynomialize " <<
expr2c(idx,
ns) <<
'\n';
1072 if(idx.
id()==ID_pointer_offset)
1085 std::cout <<
"Failed to polynomialize\n";
1099 std::cout <<
"Bailing out on nonlinear index: "
1107 exprt lower_bound=idx;
1108 exprt upper_bound=idx;
1129 std::cout <<
"Bailing out on write to constant array index: " <<
1134 else if(stride == 1 || stride == -1)
1172 exprt fresh_lhs=lhs;
1183 forall.
where() = implies;
1188 program.
assign(arr, fresh_array);
1197 if(e.
id() == ID_index)
1201 else if(e.
id() == ID_dereference)
1214 std::set<std::pair<expr_listt, exprt> > &coefficients,
1217 for(std::set<std::pair<expr_listt, exprt> >::iterator it=coefficients.begin();
1218 it!=coefficients.end();
1223 exprt coefficient=it->second;
1225 std::map<exprt, int> degrees;
1228 monomial.
coeff = numeric_cast_v<int>(mp);
1230 if(monomial.
coeff==0)
1235 for(
const auto &term : terms)
1237 if(degrees.find(term)!=degrees.end())
1247 for(std::map<exprt, int>::iterator it=degrees.begin();
1253 term.
exp=it->second;
1254 monomial.
terms.push_back(term);
1257 polynomial.
monomials.push_back(monomial);
1263 static int num_symbols=0;
symbol_tablet & symbol_table
void copy_to_operands(const exprt &expr)
Copy the given argument to the end of exprt's operands.
void from_expr(const exprt &expr)
dstringt has one field, an unsigned integer no which is an index into a static table of strings.
Generate Equation using Symbolic Execution.
const char * c_str() const
const unary_exprt & to_unary_expr(const exprt &expr)
Cast an exprt to a unary_exprt.
void add(polynomialt &other)
const symbolt & lookup_ref(const irep_idt &name) const
Find a symbol in the symbol table for read-only access.
exprt conjunction(const exprt::operandst &op)
1) generates a conjunction for two or more operands 2) for one operand, returns the operand 3) return...
#define Forall_operands(it, expr)
bool do_assumptions(std::map< exprt, polynomialt > polynomials, patht &body, exprt &guard, guard_managert &guard_manager)
std::vector< expr_pairt > expr_pairst
The type of an expression, extends irept.
symbolt fresh_symbol(std::string base, typet type)
void push_nondet(exprt &expr)
void find_symbols_or_nexts(const exprt &src, find_symbols_sett &dest)
Add to the set dest the sub-expressions of src with id ID_symbol or ID_next_symbol.
const index_exprt & to_index_expr(const exprt &expr)
Cast an exprt to an index_exprt.
std::list< exprt > expr_listt
typet type
Type of symbol.
std::list< instructiont > instructionst
bool assign_array(const index_exprt &lhs, const exprt &rhs, scratch_programt &program)
message_handlert & message_handler
targett add(instructiont &&instruction)
Adds a given instruction at the end.
The plus expression Associativity is not specified.
bool do_arrays(goto_programt::instructionst &loop_body, std::map< exprt, polynomialt > &polynomials, substitutiont &substitution, scratch_programt &program)
Base class for all expressions.
irep_idt base_name
Base (non-scoped) name.
void set_option(const std::string &option, const bool value)
std::string to_string(const string_not_contains_constraintt &expr)
Used for debug printing.
bool check_inductive(std::map< exprt, polynomialt > polynomials, patht &path, guard_managert &guard_manager)
Expression to hold a symbol (variable)
std::vector< monomialt > monomials
static instructiont make_assignment(const code_assignt &_code, const source_locationt &l=source_locationt::nil())
Create an assignment instruction.
unsignedbv_typet unsigned_poly_type()
void find_modified(const patht &path, expr_sett &modified)
irep_idt pretty_name
Language-specific display name.
This is unused by this implementation of guards, but can be used by other implementations of the same...
void stash_polynomials(scratch_programt &program, std::map< exprt, polynomialt > &polynomials, std::map< exprt, exprt > &stashed, patht &path)
typet & type()
Return the type of the expression.
int coeff(const exprt &expr)
int max_degree(const exprt &var)
static instructiont make_assertion(const exprt &g, const source_locationt &l=source_locationt::nil())
bool expr2poly(exprt &expr, std::map< exprt, polynomialt > &polynomials, polynomialt &poly)
std::ostream & output(const namespacet &ns, const irep_idt &identifier, std::ostream &out) const
Output goto program to given stream.
#define forall_operands(it, expr)
signedbv_typet signed_poly_type()
std::string expr2c(const exprt &expr, const namespacet &ns, const expr2c_configurationt &configuration)
exprt eval(const exprt &e)
const irep_idt & get_identifier() const
class symbol_exprt symbol_expr() const
Produces a symbol_exprt for a symbol.
exprt precondition(patht &path)
bool simplify(exprt &expr, const namespacet &ns)
exprt simplify_expr(exprt src, const namespacet &ns)
std::unordered_set< exprt, irep_hash > expr_sett
void ensure_no_overflows(scratch_programt &program)
void extract_polynomial(scratch_programt &program, std::set< std::pair< expr_listt, exprt >> &coefficients, polynomialt &polynomial)
const symbol_exprt & to_symbol_expr(const exprt &expr)
Cast an exprt to a symbol_exprt.
targett assume(const exprt &guard)
const irep_idt & id() const
std::vector< polynomial_array_assignmentt > polynomial_array_assignmentst
std::vector< exprt > operandst
The Boolean constant false.
void abstract_arrays(exprt &expr, expr_mapt &abstractions)
void append_path(patht &path)
bool array_assignments2polys(expr_pairst &array_assignments, std::map< exprt, polynomialt > &polynomials, polynomial_array_assignmentst &array_polynomials, polynomialst &nondet_indices)
parentt::loopt natural_loopt
A side_effect_exprt that returns a non-deterministically chosen value.
std::map< exprt, exprt > substitutiont
bool add(const symbolt &symbol)
Add a new symbol to the symbol table.
const dereference_exprt & to_dereference_expr(const exprt &expr)
Cast an exprt to a dereference_exprt.
expr_pairst gather_array_assignments(goto_programt::instructionst &loop_body, expr_sett &arrays_written)
std::unordered_set< irep_idt > find_symbols_sett
const code_assignt & to_code_assign(const codet &code)
std::list< path_nodet > patht
const not_exprt & to_not_expr(const exprt &expr)
Cast an exprt to an not_exprt.
void substitute(substitutiont &substitution)
bool replace_expr(const exprt &what, const exprt &by, exprt &dest)
std::unordered_map< exprt, exprt, irep_hash > replace_mapt
const mp_integer binary2integer(const std::string &n, bool is_signed)
convert binary string representation to mp_integer
void gather_array_accesses(const exprt &expr, expr_sett &arrays)
A base class for relations, i.e., binary predicates whose two operands have the same type.
std::vector< polynomialt > polynomialst
Goto Programs with Functions.
A generic container class for the GOTO intermediate representation of one function.
instructionst::const_iterator const_targett
void stash_variables(scratch_programt &program, expr_sett modified, substitutiont &substitution)
static instructiont make_assumption(const exprt &g, const source_locationt &l=source_locationt::nil())
bool check_sat(bool do_slice, guard_managert &guard_manager)
A codet representing an assignment in the program.
A constant literal expression.
irep_idt module
Name of module the symbol belongs to.
std::unordered_map< exprt, exprt, irep_hash > expr_mapt
API to expression classes.
targett assign(const exprt &lhs, const exprt &rhs)
void gather_rvalues(const exprt &expr, expr_sett &rvalues)
const binary_relation_exprt & to_binary_relation_expr(const exprt &expr)
Cast an exprt to a binary_relation_exprt.
const irep_idt & get_value() const
const source_locationt & source_location() const
irep_idt name
The unique identifier.
void add_overflow_checks()
#define forall_goto_program_instructions(it, program)
std::vector< termt > terms
bool do_nonrecursive(goto_programt::instructionst &loop_body, std::map< exprt, polynomialt > &polynomials, substitutiont &substitution, expr_sett &nonrecursive, scratch_programt &program)
const constant_exprt & to_constant_expr(const exprt &expr)
Cast an exprt to a constant_exprt.