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());
115 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);
147 codet inc_loop_counter=
155 for(std::vector<exprt>::iterator it=polynomials_hold.begin();
156 it!=polynomials_hold.end();
163 std::cout <<
"Checking following program for inductiveness:\n";
173 std::cout <<
"Not inductive!\n";
182 catch(
const std::string &s)
184 std::cout <<
"Error in inductiveness SAT check: " << s <<
'\n';
187 catch (
const char *s)
189 std::cout <<
"Error in inductiveness SAT check: " << s <<
'\n';
196 std::map<exprt, polynomialt> &polynomials,
205 for(std::map<exprt, polynomialt>::iterator it=polynomials.begin();
206 it!=polynomials.end();
209 it->second.substitute(substitution);
220 for(expr_sett::iterator it=modified.begin();
228 vars.erase(loop_counter_name);
230 for(find_symbols_sett::iterator it=vars.begin();
253 for(patht::reverse_iterator r_it=path.rbegin();
266 if(lhs.
id()==ID_symbol ||
267 lhs.
id()==ID_index ||
268 lhs.
id()==ID_dereference)
277 else if(t->is_assume() || t->is_assert())
286 if(!r_it->guard.is_true() && !r_it->guard.is_nil())
306 if(expr.
id()==ID_index ||
307 expr.
id()==ID_dereference)
309 expr_mapt::iterator it=abstractions.find(expr);
311 if(it==abstractions.end())
338 if(expr.
id()==ID_not &&
339 expr.
op0().
id()==ID_nondet)
343 else if(expr.
id()==ID_equal ||
349 if(expr.
op0().
id()==ID_nondet ||
350 expr.
op1().
id()==ID_nondet)
358 std::map<exprt, polynomialt> polynomials,
392 std::vector<exprt> polynomials_hold;
394 for(std::map<exprt, polynomialt>::iterator it=polynomials.begin();
395 it!=polynomials.end();
399 exprt rhs=it->second.to_expr();
406 for(std::vector<exprt>::iterator it=polynomials_hold.begin();
407 it!=polynomials_hold.end();
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());
426 program.
assume(condition);
431 for(std::map<exprt, polynomialt>::iterator p_it=polynomials.begin();
432 p_it!=polynomials.end();
435 program.
assign(p_it->first, p_it->second.to_expr());
446 std::cout <<
"Checking following program for monotonicity:\n";
455 std::cout <<
"Path is not monotone\n";
461 catch(
const std::string &s)
463 std::cout <<
"Error in monotonicity SAT check: " << s <<
'\n';
468 std::cout <<
"Error in monotonicity SAT check: " << s <<
'\n';
473 std::cout <<
"Path is monotone\n";
487 checker_options.
set_option(
"signed-overflow-check",
true);
488 checker_options.
set_option(
"unsigned-overflow-check",
true);
489 checker_options.
set_option(
"assert-to-assume",
true);
490 checker_options.
set_option(
"assumptions",
true);
496 std::cout <<
"Adding overflow checks at " << now <<
"...\n";
509 std::cout <<
"Done at " << now <<
".\n";
519 for(goto_programt::instructionst::reverse_iterator r_it=loop_body.rbegin();
520 r_it!=loop_body.rend();
523 if(r_it->is_assign())
528 if(assignment.
lhs().
id()==ID_index)
531 assignments.push_back(
532 std::make_pair(assignment.
lhs(), assignment.
rhs()));
536 arrays_written.insert(index_expr.
array());
542 for(expr_pairst::iterator a_it=assignments.begin();
543 a_it!=assignments.end();
558 std::map<exprt, polynomialt> &polynomials,
563 std::cout <<
"Doing arrays...\n";
572 std::cout <<
"Found " << array_assignments.size()
573 <<
" array assignments\n";
576 if(array_assignments.empty())
586 array_assignments, polynomials, poly_assignments, nondet_indices))
591 std::cout <<
"Couldn't model an array assignment :-(\n";
597 for(expr_sett::iterator it=arrays_written.begin();
598 it!=arrays_written.end();
608 for(polynomial_array_assignmentst::iterator it=poly_assignments.begin();
609 it!=poly_assignments.end();
640 for(expr_sett::iterator a_it=arrays_written.begin();
641 a_it!=arrays_written.end();
645 exprt old_array=substitution[array];
646 std::vector<polynomialt> indices;
647 bool nonlinear_index=
false;
649 for(polynomial_array_assignmentst::iterator it=poly_assignments.begin();
650 it!=poly_assignments.end();
657 indices.push_back(index);
665 nonlinear_index=
true;
687 pos_eliminator=neg_eliminator;
688 pos_eliminator.
mult(-1);
692 for(std::vector<polynomialt>::iterator it=indices.begin();
697 exprt max_idx, min_idx;
705 index.
add(pos_eliminator);
714 index.
add(neg_eliminator);
719 assert(!
"ITSALLGONEWRONG");
725 unchanged_operands.push_back(unchanged_by_this_one);
738 for(std::vector<polynomialt>::iterator it=indices.begin();
742 idx_touched_operands.push_back(
760 implies_exprt idx_not_touched_bound(l_bound, idx_not_touched);
762 idx_never_touched=
exprt(ID_forall);
777 implies_exprt idx_unchanged(idx_never_touched, value_unchanged);
785 program.
assume(array_unchanged);
793 std::map<exprt, polynomialt> &polynomials,
797 for(expr_pairst::iterator it=array_assignments.begin();
798 it!=array_assignments.end();
810 std::cout <<
"Couldn't convert index: " 817 std::cout <<
"Converted index to: " 822 if(it->second.id()==ID_nondet)
824 nondet_indices.push_back(poly_assignment.
index);
826 else if(!
expr2poly(it->second, polynomials, poly_assignment.
value))
830 std::cout <<
"Couldn't convert RHS: " <<
expr2c(it->second,
ns)
838 std::cout <<
"Converted RHS to: " 843 array_polynomials.push_back(poly_assignment);
852 std::map<exprt, polynomialt> &polynomials,
855 exprt subbed_expr=expr;
857 for(std::map<exprt, polynomialt>::iterator it=polynomials.begin();
858 it!=polynomials.end();
861 replace_expr(it->first, it->second.to_expr(), subbed_expr);
865 std::cout <<
"expr2poly(" <<
expr2c(subbed_expr,
ns) <<
")\n";
882 std::map<exprt, polynomialt> &polynomials,
897 for(std::map<exprt, polynomialt>::iterator it=polynomials.begin();
898 it!=polynomials.end();
901 const exprt &var=it->first;
916 for(expr_sett::iterator it=nonrecursive.begin();
917 it!=nonrecursive.end();
924 for(goto_programt::instructionst::iterator it=body.begin();
933 if(lhs.
id()==ID_dereference)
937 std::cout <<
"Bailing out on write-through-pointer\n";
942 if(lhs.
id()==ID_index)
945 array_writes.insert(lhs);
947 if(arrays_written.find(lhs.
op0())!=arrays_written.end())
952 std::cout <<
"Bailing out on array written to twice in loop: " <<
958 arrays_written.insert(lhs.
op0());
969 for(expr_sett::iterator it=arrays_written.begin();
970 it!=arrays_written.end();
973 if(arrays_read.find(*it)!=arrays_read.end())
976 std::cout <<
"Bailing out on array read and written on same path\n";
982 for(expr_sett::iterator it=nonrecursive.begin();
983 it!=nonrecursive.end();
986 if(it->id()==ID_symbol)
988 exprt &val=state[*it];
992 std::cout <<
"Fitted nonrecursive: " <<
expr2c(*it,
ns) <<
"=" <<
998 for(expr_sett::iterator it=array_writes.begin();
999 it!=array_writes.end();
1002 const exprt &lhs=*it;
1003 const exprt &rhs=state[*it];
1008 std::cout <<
"Failed to assign a nonrecursive array: " <<
1024 std::cout <<
"Modelling array assignment " <<
expr2c(lhs,
ns) <<
"=" <<
1028 if(lhs.
id()==ID_dereference)
1032 std::cout <<
"Bailing out on write-through-pointer\n";
1050 const exprt &fresh_array =
1078 std::cout <<
"Trying to polynomialize " <<
expr2c(idx,
ns) <<
'\n';
1085 if(idx.
id()==ID_pointer_offset)
1098 std::cout <<
"Failed to polynomialize\n";
1112 std::cout <<
"Bailing out on nonlinear index: " 1120 exprt lower_bound=idx;
1121 exprt upper_bound=idx;
1142 std::cout <<
"Bailing out on write to constant array index: " <<
1147 else if(stride == 1 || stride == -1)
1185 exprt fresh_lhs=lhs;
1196 forall.
where() = implies;
1201 program.
assign(arr, fresh_array);
1210 if(e.
id()==ID_index ||
1211 e.
id()==ID_dereference)
1213 arrays.insert(e.
op0());
1224 std::set<std::pair<expr_listt, exprt> > &coefficients,
1227 for(std::set<std::pair<expr_listt, exprt> >::iterator it=coefficients.begin();
1228 it!=coefficients.end();
1233 exprt coefficient=it->second;
1235 std::map<exprt, int> degrees;
1238 monomial.
coeff=mp.to_long();
1240 if(monomial.
coeff==0)
1245 for(
const auto &term : terms)
1247 if(degrees.find(term)!=degrees.end())
1257 for(std::map<exprt, int>::iterator it=degrees.begin();
1263 term.
exp=it->second;
1264 monomial.
terms.push_back(term);
1267 polynomial.
monomials.push_back(monomial);
1273 static int num_symbols=0;
std::list< exprt > expr_listt
The type of an expression, extends irept.
irep_idt name
The unique identifier.
void substitute(substitutiont &substitution)
A base class for relations, i.e., binary predicates.
Generate Equation using Symbolic Execution.
targett assign(const exprt &lhs, const exprt &rhs)
exprt simplify_expr(const exprt &src, const namespacet &ns)
std::ostream & output(const namespacet &ns, const irep_idt &identifier, std::ostream &out) const
Output goto program to given stream.
exprt precondition(patht &path)
std::string to_string(const string_not_contains_constraintt &expr)
Used for debug printing.
void add_overflow_checks()
void copy_to_operands(const exprt &expr)
Copy the given argument to the end of exprt's operands.
const irep_idt & get_identifier() const
Goto Programs with Functions.
const irep_idt & get_value() const
std::set< goto_programt::targett > natural_loopt
const mp_integer binary2integer(const std::string &n, bool is_signed)
convert binary string representation to mp_integer
irep_idt module
Name of module the symbol belongs to.
std::vector< polynomialt > polynomialst
irep_idt pretty_name
Language-specific display name.
typet & type()
Return the type of the expression.
A constant literal expression.
std::vector< termt > terms
std::vector< polynomial_array_assignmentt > polynomial_array_assignmentst
signedbv_typet signed_poly_type()
bool assign_array(const exprt &lhs, const exprt &rhs, scratch_programt &program)
std::list< instructiont > instructionst
exprt conjunction(const exprt::operandst &op)
1) generates a conjunction for two or more operands 2) for one operand, returns the operand 3) return...
const code_assignt & to_code_assign(const codet &code)
const irep_idt & id() const
bool replace_expr(const exprt &what, const exprt &by, exprt &dest)
class symbol_exprt symbol_expr() const
Produces a symbol_exprt for a symbol.
bool array_assignments2polys(expr_pairst &array_assignments, std::map< exprt, polynomialt > &polynomials, polynomial_array_assignmentst &array_polynomials, polynomialst &nondet_indices)
unsignedbv_typet unsigned_poly_type()
void ensure_no_overflows(scratch_programt &program)
std::vector< expr_pairt > expr_pairst
std::unordered_set< exprt, irep_hash > expr_sett
targett assume(const exprt &guard)
symbolt fresh_symbol(std::string base, typet type)
exprt eval(const exprt &e)
void stash_variables(scratch_programt &program, expr_sett modified, substitutiont &substitution)
void abstract_arrays(exprt &expr, expr_mapt &abstractions)
API to expression classes.
bool do_arrays(goto_programt::instructionst &loop_body, std::map< exprt, polynomialt > &polynomials, substitutiont &substitution, scratch_programt &program)
std::list< path_nodet > patht
instructionst::const_iterator const_targett
void find_modified(const patht &path, expr_sett &modified)
A side_effect_exprt that returns a non-deterministically chosen value.
void gather_array_accesses(const exprt &expr, expr_sett &arrays)
#define forall_operands(it, expr)
The plus expression Associativity is not specified.
const symbol_exprt & to_symbol_expr(const exprt &expr)
Cast an exprt to a symbol_exprt.
void extract_polynomial(scratch_programt &program, std::set< std::pair< expr_listt, exprt > > &coefficients, polynomialt &polynomial)
dstringt has one field, an unsigned integer no which is an index into a static table of strings.
bool check_inductive(std::map< exprt, polynomialt > polynomials, patht &path)
bool check_sat(bool do_slice)
bool expr2poly(exprt &expr, std::map< exprt, polynomialt > &polynomials, polynomialt &poly)
const constant_exprt & to_constant_expr(const exprt &expr)
Cast an exprt to a constant_exprt.
The Boolean constant false.
int max_degree(const exprt &var)
std::vector< exprt > operandst
void gather_rvalues(const exprt &expr, expr_sett &rvalues)
int coeff(const exprt &expr)
A generic container class for the GOTO intermediate representation of one function.
bool do_assumptions(std::map< exprt, polynomialt > polynomials, patht &body, exprt &guard)
typet type
Type of symbol.
void append_path(patht &path)
void from_expr(const exprt &expr)
targett add_instruction()
Adds an instruction at the end.
Base class for all expressions.
std::map< exprt, exprt > substitutiont
irep_idt base_name
Base (non-scoped) name.
std::string expr2c(const exprt &expr, const namespacet &ns, const expr2c_configurationt &configuration)
const source_locationt & source_location() const
void add(polynomialt &other)
message_handlert & message_handler
std::unordered_map< exprt, exprt, irep_hash > replace_mapt
#define Forall_operands(it, expr)
bool do_nonrecursive(goto_programt::instructionst &loop_body, std::map< exprt, polynomialt > &polynomials, substitutiont &substitution, expr_sett &nonrecursive, scratch_programt &program)
void push_nondet(exprt &expr)
symbol_tablet & symbol_table
Expression to hold a symbol (variable)
const char * c_str() const
bool add(const symbolt &symbol)
Add a new symbol to the symbol table.
void set_option(const std::string &option, const bool value)
Data structure for representing an arbitrary statement in a program.
std::unordered_set< irep_idt > find_symbols_sett
const symbolt * lookup(const irep_idt &name) const
Find a symbol in the symbol table for read-only access.
#define forall_goto_program_instructions(it, program)
const index_exprt & to_index_expr(const exprt &expr)
Cast an exprt to an index_exprt.
void find_symbols(const exprt &src, find_symbols_sett &dest)
A codet representing an assignment in the program.
std::unordered_map< exprt, exprt, irep_hash > expr_mapt
expr_pairst gather_array_assignments(goto_programt::instructionst &loop_body, expr_sett &arrays_written)
std::vector< monomialt > monomials
bool simplify(exprt &expr, const namespacet &ns)
void stash_polynomials(scratch_programt &program, std::map< exprt, polynomialt > &polynomials, std::map< exprt, exprt > &stashed, patht &path)