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Merge branch 'unstable' of https://git01.codeplex.com/z3 into unstable

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This commit is contained in:
Christoph M. Wintersteiger 2013-12-17 13:53:28 +00:00
commit 8fb36bd41d
31 changed files with 2230 additions and 195 deletions
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2
scripts/mk_project.py
View file

@ -55,8 +55,8 @@ def init_project_def():
add_lib('fpa', ['core_tactics', 'bv_tactics', 'sat_tactic'], 'tactic/fpa')
add_lib('smt_tactic', ['smt'], 'smt/tactic')
add_lib('sls_tactic', ['tactic', 'normal_forms', 'core_tactics', 'bv_tactics'], 'tactic/sls')
add_lib('duality', ['smt', 'interp'])
add_lib('qe', ['smt','sat'], 'qe')
add_lib('duality', ['smt', 'interp', 'qe'])
add_lib('muz', ['smt', 'sat', 'smt2parser', 'aig_tactic', 'qe'], 'muz/base')
add_lib('transforms', ['muz', 'hilbert'], 'muz/transforms')
add_lib('rel', ['muz', 'transforms'], 'muz/rel')

52
src/api/api_interp.cpp
View file

@ -42,6 +42,20 @@ Revision History:
using namespace stl_ext;
#endif
#ifndef WIN32
// WARNING: don't make a hash_map with this if the range type
// has a destructor: you'll get an address dependency!!!
namespace stl_ext {
template <>
class hash<Z3_ast> {
public:
size_t operator()(const Z3_ast p) const {
return (size_t) p;
}
};
}
#endif
typedef interpolation_options_struct *Z3_interpolation_options;
extern "C" {
@ -305,8 +319,8 @@ static void get_file_params(const char *filename, hash_map<std::string,std::stri
tokenize(first_line.substr(2,first_line.size()-2),tokens);
for(unsigned i = 0; i < tokens.size(); i++){
std::string &tok = tokens[i];
int eqpos = tok.find('=');
if(eqpos >= 0 && eqpos < (int)tok.size()){
size_t eqpos = tok.find('=');
if(eqpos >= 0 && eqpos < tok.size()){
std::string left = tok.substr(0,eqpos);
std::string right = tok.substr(eqpos+1,tok.size()-eqpos-1);
params[left] = right;
@ -363,8 +377,8 @@ extern "C" {
#else
static Z3_ast and_vec(Z3_context ctx,std::vector<Z3_ast> &c){
return (c.size() > 1) ? Z3_mk_and(ctx,c.size(),&c[0]) : c[0];
static Z3_ast and_vec(Z3_context ctx,svector<Z3_ast> &c){
return (c.size() > 1) ? Z3_mk_and(ctx,c.size(),&c[0]) : c[0];
}
static Z3_ast parents_vector_to_tree(Z3_context ctx, int num, Z3_ast *cnsts, int *parents){
@ -381,15 +395,15 @@ extern "C" {
}
}
else {
std::vector<std::vector<Z3_ast> > chs(num);
std::vector<svector<Z3_ast> > chs(num);
for(int i = 0; i < num-1; i++){
std::vector<Z3_ast> &c = chs[i];
svector<Z3_ast> &c = chs[i];
c.push_back(cnsts[i]);
Z3_ast foo = Z3_mk_interp(ctx,and_vec(ctx,c));
chs[parents[i]].push_back(foo);
}
{
std::vector<Z3_ast> &c = chs[num-1];
svector<Z3_ast> &c = chs[num-1];
c.push_back(cnsts[num-1]);
res = and_vec(ctx,c);
}
@ -454,7 +468,7 @@ extern "C" {
static std::string read_msg;
static std::vector<Z3_ast> read_theory;
static bool iZ3_parse(Z3_context ctx, const char *filename, const char **error, std::vector<Z3_ast> &assertions){
static bool iZ3_parse(Z3_context ctx, const char *filename, const char **error, svector<Z3_ast> &assertions){
read_error.clear();
try {
std::string foo(filename);
@ -496,26 +510,26 @@ extern "C" {
hash_map<std::string,std::string> file_params;
get_file_params(filename,file_params);
int num_theory = 0;
unsigned num_theory = 0;
if(file_params.find("THEORY") != file_params.end())
num_theory = atoi(file_params["THEORY"].c_str());
std::vector<Z3_ast> assertions;
svector<Z3_ast> assertions;
if(!iZ3_parse(ctx,filename,error,assertions))
return false;
if(num_theory > (int)assertions.size())
num_theory = assertions.size();
int num = assertions.size() - num_theory;
if(num_theory > assertions.size())
num_theory = assertions.size();
unsigned num = assertions.size() - num_theory;
read_cnsts.resize(num);
read_parents.resize(num);
read_theory.resize(num_theory);
for(int j = 0; j < num_theory; j++)
for(unsigned j = 0; j < num_theory; j++)
read_theory[j] = assertions[j];
for(int j = 0; j < num; j++)
for(unsigned j = 0; j < num; j++)
read_cnsts[j] = assertions[j+num_theory];
if(ret_num_theory)
@ -529,12 +543,12 @@ extern "C" {
return true;
}
for(int j = 0; j < num; j++)
for(unsigned j = 0; j < num; j++)
read_parents[j] = SHRT_MAX;
hash_map<Z3_ast,int> pred_map;
for(int j = 0; j < num; j++){
for(unsigned j = 0; j < num; j++){
Z3_ast lhs = 0, rhs = read_cnsts[j];
if(Z3_get_decl_kind(ctx,Z3_get_app_decl(ctx,Z3_to_app(ctx,rhs))) == Z3_OP_IMPLIES){
@ -588,7 +602,7 @@ extern "C" {
}
}
for(int j = 0; j < num-1; j++)
for(unsigned j = 0; j < num-1; j++)
if(read_parents[j] == SHRT_MIN){
read_error << "formula " << j+1 << ": unreferenced";
goto fail;

3
src/ast/ast.cpp
View file

@ -3161,3 +3161,6 @@ void prexpr(expr_ref &e){
std::cout << mk_pp(e.get(), e.get_manager()) << std::endl;
}
void ast_manager::show_id_gen(){
std::cout << "id_gen: " << m_expr_id_gen.show_hash() << " " << m_decl_id_gen.show_hash() << "\n";
}

2
src/ast/ast.h
View file

@ -1418,6 +1418,8 @@ protected:
public:
typedef expr_dependency_array_manager::ref expr_dependency_array;
void show_id_gen();
protected:
small_object_allocator m_alloc;
family_manager m_family_manager;

11
src/ast/proof_checker/proof_checker.cpp
View file

@ -479,7 +479,7 @@ bool proof_checker::check1_basic(proof* p, expr_ref_vector& side_conditions) {
// otherwise t2 is also a quantifier.
return true;
}
UNREACHABLE();
IF_VERBOSE(0, verbose_stream() << "does not match last rule: " << mk_pp(p, m) << "\n";);
return false;
}
case PR_DER: {
@ -488,13 +488,12 @@ bool proof_checker::check1_basic(proof* p, expr_ref_vector& side_conditions) {
match_fact(p, fact) &&
match_iff(fact.get(), t1, t2) &&
match_quantifier(t1, is_forall, decls1, body1) &&
is_forall &&
match_or(body1.get(), terms1)) {
is_forall) {
// TBD: check that terms are set of equalities.
// t2 is an instance of a predicate in terms1
return true;
}
UNREACHABLE();
}
IF_VERBOSE(0, verbose_stream() << "does not match last rule: " << mk_pp(p, m) << "\n";);
return false;
}
case PR_HYPOTHESIS: {
@ -832,7 +831,7 @@ bool proof_checker::check1_basic(proof* p, expr_ref_vector& side_conditions) {
}
else {
IF_VERBOSE(0, verbose_stream() << "Could not establish complementarity for:\n" <<
mk_pp(lit1, m) << "\n" << mk_pp(lit2, m) << "\n";);
mk_pp(lit1, m) << "\n" << mk_pp(lit2, m) << "\n" << mk_pp(p, m) << "\n";);
}
fmls[i] = premise1;
}

212
src/duality/duality.h
View file

@ -79,9 +79,36 @@ namespace Duality {
int CumulativeDecisions();
private:
int CountOperators(const Term &t);
Term SubstAtom(hash_map<ast, Term> &memo, const expr &t, const expr &atom, const expr &val);
Term RemoveRedundancy(const Term &t);
bool IsLiteral(const expr &lit, expr &atom, expr &val);
expr Negate(const expr &f);
expr SimplifyAndOr(const std::vector<expr> &args, bool is_and);
expr ReallySimplifyAndOr(const std::vector<expr> &args, bool is_and);
int MaxIndex(hash_map<ast,int> &memo, const Term &t);
bool IsClosedFormula(const Term &t);
Term AdjustQuantifiers(const Term &t);
private:
void SummarizeRec(hash_set<ast> &memo, std::vector<expr> &lits, int &ops, const Term &t);
int CountOperatorsRec(hash_set<ast> &memo, const Term &t);
void RemoveRedundancyOp(bool pol, std::vector<expr> &args, hash_map<ast, Term> &smemo);
Term RemoveRedundancyRec(hash_map<ast, Term> &memo, hash_map<ast, Term> &smemo, const Term &t);
Term SubstAtomTriv(const expr &foo, const expr &atom, const expr &val);
expr ReduceAndOr(const std::vector<expr> &args, bool is_and, std::vector<expr> &res);
expr FinishAndOr(const std::vector<expr> &args, bool is_and);
expr PullCommonFactors(std::vector<expr> &args, bool is_and);
};
@ -142,6 +169,7 @@ namespace Duality {
context *ctx; /** Z3 context for formulas */
solver *slvr; /** Z3 solver */
bool need_goals; /** Can the solver use the goal tree to optimize interpolants? */
solver aux_solver; /** For temporary use -- don't leave assertions here. */
/** Tree interpolation. This method assumes the formulas in TermTree
"assumptions" are currently asserted in the solver. The return
@ -167,6 +195,9 @@ namespace Duality {
/** Assert a background axiom. */
virtual void assert_axiom(const expr &axiom) = 0;
/** Get the background axioms. */
virtual const std::vector<expr> &get_axioms() = 0;
/** Return a string describing performance. */
virtual std::string profile() = 0;
@ -178,6 +209,12 @@ namespace Duality {
/** Cancel, throw Canceled object if possible. */
virtual void cancel(){ }
/* Note: aux solver uses extensional array theory, since it
needs to be able to produce counter-models for
interpolants the have array equalities in them.
*/
LogicSolver(context &c) : aux_solver(c,true){}
virtual ~LogicSolver(){}
};
@ -202,6 +239,10 @@ namespace Duality {
islvr->AssertInterpolationAxiom(axiom);
}
const std::vector<expr> &get_axioms() {
return islvr->GetInterpolationAxioms();
}
std::string profile(){
return islvr->profile();
}
@ -215,7 +256,7 @@ namespace Duality {
}
#endif
iZ3LogicSolver(context &c){
iZ3LogicSolver(context &c) : LogicSolver(c) {
ctx = ictx = &c;
slvr = islvr = new interpolating_solver(*ictx);
need_goals = false;
@ -277,6 +318,7 @@ namespace Duality {
public:
std::list<Edge *> edges;
std::list<Node *> nodes;
std::list<std::pair<Edge *,Term> > constraints;
};
@ -286,7 +328,9 @@ namespace Duality {
literals dualLabels;
std::list<stack_entry> stack;
std::vector<Term> axioms; // only saved here for printing purposes
solver &aux_solver;
hash_set<ast> *proof_core;
public:
/** Construct an RPFP graph with a given interpolating prover context. It is allowed to
@ -296,13 +340,14 @@ namespace Duality {
inherit the axioms.
*/
RPFP(LogicSolver *_ls) : Z3User(*(_ls->ctx), *(_ls->slvr)), dualModel(*(_ls->ctx))
RPFP(LogicSolver *_ls) : Z3User(*(_ls->ctx), *(_ls->slvr)), dualModel(*(_ls->ctx)), aux_solver(_ls->aux_solver)
{
ls = _ls;
nodeCount = 0;
edgeCount = 0;
stack.push_back(stack_entry());
HornClauses = false;
proof_core = 0;
}
~RPFP();
@ -351,10 +396,10 @@ namespace Duality {
bool SubsetEq(const Transformer &other){
Term t = owner->SubstParams(other.IndParams,IndParams,other.Formula);
expr test = Formula && !t;
owner->slvr.push();
owner->slvr.add(test);
check_result res = owner->slvr.check();
owner->slvr.pop(1);
owner->aux_solver.push();
owner->aux_solver.add(test);
check_result res = owner->aux_solver.check();
owner->aux_solver.pop(1);
return res == unsat;
}
@ -444,6 +489,19 @@ namespace Duality {
return n;
}
/** Delete a node. You can only do this if not connected to any edges.*/
void DeleteNode(Node *node){
if(node->Outgoing || !node->Incoming.empty())
throw "cannot delete RPFP node";
for(std::vector<Node *>::iterator it = nodes.end(), en = nodes.begin(); it != en;){
if(*(--it) == node){
nodes.erase(it);
break;
}
}
delete node;
}
/** This class represents a hyper-edge in the RPFP graph */
class Edge
@ -460,6 +518,7 @@ namespace Duality {
hash_map<ast,Term> varMap;
Edge *map;
Term labeled;
std::vector<Term> constraints;
Edge(Node *_Parent, const Transformer &_F, const std::vector<Node *> &_Children, RPFP *_owner, int _number)
: F(_F), Parent(_Parent), Children(_Children), dual(expr(_owner->ctx)) {
@ -480,6 +539,29 @@ namespace Duality {
return e;
}
/** Delete a hyper-edge and unlink it from any nodes. */
void DeleteEdge(Edge *edge){
if(edge->Parent)
edge->Parent->Outgoing = 0;
for(unsigned int i = 0; i < edge->Children.size(); i++){
std::vector<Edge *> &ic = edge->Children[i]->Incoming;
for(std::vector<Edge *>::iterator it = ic.begin(), en = ic.end(); it != en; ++it){
if(*it == edge){
ic.erase(it);
break;
}
}
}
for(std::vector<Edge *>::iterator it = edges.end(), en = edges.begin(); it != en;){
if(*(--it) == edge){
edges.erase(it);
break;
}
}
delete edge;
}
/** Create an edge that lower-bounds its parent. */
Edge *CreateLowerBoundEdge(Node *_Parent)
{
@ -494,13 +576,26 @@ namespace Duality {
void AssertEdge(Edge *e, int persist = 0, bool with_children = false, bool underapprox = false);
/* Constrain an edge by the annotation of one of its children. */
void ConstrainParent(Edge *parent, Node *child);
/** For incremental solving, asserts the negation of the upper bound associated
* with a node.
* */
void AssertNode(Node *n);
/** Assert a constraint on an edge in the SMT context.
*/
void ConstrainEdge(Edge *e, const Term &t);
/** Fix the truth values of atomic propositions in the given
edge to their values in the current assignment. */
void FixCurrentState(Edge *root);
void FixCurrentStateFull(Edge *edge, const expr &extra);
/** Declare a constant in the background theory. */
void DeclareConstant(const FuncDecl &f);
@ -554,9 +649,13 @@ namespace Duality {
lbool Solve(Node *root, int persist);
/** Same as Solve, but annotates only a single node. */
lbool SolveSingleNode(Node *root, Node *node);
/** Get the constraint tree (but don't solve it) */
TermTree *GetConstraintTree(Node *root);
TermTree *GetConstraintTree(Node *root, Node *skip_descendant = 0);
/** Dispose of the dual model (counterexample) if there is one. */
@ -592,6 +691,13 @@ namespace Duality {
Term ComputeUnderapprox(Node *root, int persist);
/** Try to strengthen the annotation of a node by removing disjuncts. */
void Generalize(Node *root, Node *node);
/** Compute disjunctive interpolant for node by case splitting */
void InterpolateByCases(Node *root, Node *node);
/** Push a scope. Assertions made after Push can be undone by Pop. */
void Push();
@ -623,6 +729,16 @@ namespace Duality {
/** Pop a scope (see Push). Note, you cannot pop axioms. */
void Pop(int num_scopes);
/** Erase the proof by performing a Pop, Push and re-assertion of
all the popped constraints */
void PopPush();
/** Return true if the given edge is used in the proof of unsat.
Can be called only after Solve or Check returns an unsat result. */
bool EdgeUsedInProof(Edge *edge);
/** Convert a collection of clauses to Nodes and Edges in the RPFP.
@ -707,8 +823,19 @@ namespace Duality {
// int GetLabelsRec(hash_map<ast,int> *memo, const Term &f, std::vector<symbol> &labels, bool labpos);
/** Compute and save the proof core for future calls to
EdgeUsedInProof. You only need to call this if you will pop
the solver before calling EdgeUsedInProof.
*/
void ComputeProofCore();
private:
void ClearProofCore(){
if(proof_core)
delete proof_core;
proof_core = 0;
}
Term SuffixVariable(const Term &t, int n);
@ -724,10 +851,14 @@ namespace Duality {
Term ReducedDualEdge(Edge *e);
TermTree *ToTermTree(Node *root);
TermTree *ToTermTree(Node *root, Node *skip_descendant = 0);
TermTree *ToGoalTree(Node *root);
void CollapseTermTreeRec(TermTree *root, TermTree *node);
TermTree *CollapseTermTree(TermTree *node);
void DecodeTree(Node *root, TermTree *interp, int persist);
Term GetUpperBound(Node *n);
@ -777,6 +908,11 @@ namespace Duality {
Term UnderapproxFormula(const Term &f, hash_set<ast> &dont_cares);
void ImplicantFullRed(hash_map<ast,int> &memo, const Term &f, std::vector<Term> &lits,
hash_set<ast> &done, hash_set<ast> &dont_cares);
Term UnderapproxFullFormula(const Term &f, hash_set<ast> &dont_cares);
Term ToRuleRec(Edge *e, hash_map<ast,Term> &memo, const Term &t, std::vector<expr> &quants);
hash_map<ast,Term> resolve_ite_memo;
@ -803,6 +939,25 @@ namespace Duality {
Term SubstBound(hash_map<int,Term> &subst, const Term &t);
void ConstrainEdgeLocalized(Edge *e, const Term &t);
void GreedyReduce(solver &s, std::vector<expr> &conjuncts);
void NegateLits(std::vector<expr> &lits);
expr SimplifyOr(std::vector<expr> &lits);
void SetAnnotation(Node *root, const expr &t);
void AddEdgeToSolver(Edge *edge);
void AddToProofCore(hash_set<ast> &core);
void GetGroundLitsUnderQuants(hash_set<ast> *memo, const Term &f, std::vector<Term> &res, int under);
Term StrengthenFormulaByCaseSplitting(const Term &f, std::vector<expr> &case_lits);
expr NegateLit(const expr &f);
};
@ -852,3 +1007,38 @@ namespace Duality {
};
}
// Allow to hash on nodes and edges in deterministic way
namespace hash_space {
template <>
class hash<Duality::RPFP::Node *> {
public:
size_t operator()(const Duality::RPFP::Node *p) const {
return p->number;
}
};
}
namespace hash_space {
template <>
class hash<Duality::RPFP::Edge *> {
public:
size_t operator()(const Duality::RPFP::Edge *p) const {
return p->number;
}
};
}
// allow to walk sets of nodes without address dependency
namespace std {
template <>
class less<Duality::RPFP::Node *> {
public:
bool operator()(Duality::RPFP::Node * const &s, Duality::RPFP::Node * const &t) const {
return s->number < t->number; // s.raw()->get_id() < t.raw()->get_id();
}
};
}

759
src/duality/duality_rpfp.cpp
View file

@ -25,6 +25,8 @@ Revision History:
#include "duality_profiling.h"
#include <algorithm>
#include <fstream>
#include <set>
#include <iterator>
#ifndef WIN32
// #define Z3OPS
@ -89,15 +91,17 @@ namespace Duality {
if(memo.find(t) != memo.end())
return;
memo.insert(t);
decl_kind k = t.decl().get_decl_kind();
if(k == And || k == Or || k == Not || k == Implies || k == Iff){
ops++;
int nargs = t.num_args();
for(int i = 0; i < nargs; i++)
SummarizeRec(memo,lits,ops,t.arg(i));
if(t.is_app()){
decl_kind k = t.decl().get_decl_kind();
if(k == And || k == Or || k == Not || k == Implies || k == Iff){
ops++;
int nargs = t.num_args();
for(int i = 0; i < nargs; i++)
SummarizeRec(memo,lits,ops,t.arg(i));
return;
}
}
else
lits.push_back(t);
lits.push_back(t);
}
int Z3User::CumulativeDecisions(){
@ -123,6 +127,32 @@ namespace Duality {
}
}
int Z3User::CountOperatorsRec(hash_set<ast> &memo, const Term &t){
if(memo.find(t) != memo.end())
return 0;
memo.insert(t);
if(t.is_app()){
decl_kind k = t.decl().get_decl_kind();
if(k == And || k == Or){
int count = 1;
int nargs = t.num_args();
for(int i = 0; i < nargs; i++)
count += CountOperatorsRec(memo,t.arg(i));
return count;
}
return 0;
}
if(t.is_quantifier())
return CountOperatorsRec(memo,t.body())+2; // count 2 for a quantifier
return 0;
}
int Z3User::CountOperators(const Term &t){
hash_set<ast> memo;
return CountOperatorsRec(memo,t);
}
Z3User::Term Z3User::conjoin(const std::vector<Term> &args){
return ctx.make(And,args);
}
@ -183,6 +213,7 @@ namespace Duality {
return clone_quantifier(t,new_body);
}
RPFP::Term RPFP::LocalizeRec(Edge *e, hash_map<ast,Term> &memo, const Term &t)
{
std::pair<ast,Term> foo(t,expr(ctx));
@ -272,16 +303,21 @@ namespace Duality {
return implies(b, Localize(e, e->F.Formula));
}
TermTree *RPFP::ToTermTree(Node *root)
TermTree *RPFP::ToTermTree(Node *root, Node *skip_descendant)
{
if(skip_descendant && root == skip_descendant)
return new TermTree(ctx.bool_val(true));
Edge *e = root->Outgoing;
if(!e) return new TermTree(ctx.bool_val(true), std::vector<TermTree *>());
std::vector<TermTree *> children(e->Children.size());
for(unsigned i = 0; i < children.size(); i++)
children[i] = ToTermTree(e->Children[i]);
children[i] = ToTermTree(e->Children[i],skip_descendant);
// Term top = ReducedDualEdge(e);
Term top = e->dual.null() ? ctx.bool_val(true) : e->dual;
return new TermTree(top, children);
TermTree *res = new TermTree(top, children);
for(unsigned i = 0; i < e->constraints.size(); i++)
res->addTerm(e->constraints[i]);
return res;
}
TermTree *RPFP::GetGoalTree(Node *root){
@ -321,11 +357,229 @@ namespace Duality {
res = f(args.size(),&args[0]);
}
else if (t.is_quantifier())
res = CloneQuantifier(t,SubstRec(memo, t.body()));
{
std::vector<expr> pats;
t.get_patterns(pats);
for(unsigned i = 0; i < pats.size(); i++)
pats[i] = SubstRec(memo,pats[i]);
Term body = SubstRec(memo,t.body());
res = clone_quantifier(t, body, pats);
}
// res = CloneQuantifier(t,SubstRec(memo, t.body()));
else res = t;
return res;
}
bool Z3User::IsLiteral(const expr &lit, expr &atom, expr &val){
if(!(lit.is_quantifier() && IsClosedFormula(lit))){
if(!lit.is_app())
return false;
decl_kind k = lit.decl().get_decl_kind();
if(k == Not){
if(IsLiteral(lit.arg(0),atom,val)){
val = eq(val,ctx.bool_val(true)) ? ctx.bool_val(false) : ctx.bool_val(true);
return true;
}
return false;
}
if(k == And || k == Or || k == Iff || k == Implies)
return false;
}
atom = lit;
val = ctx.bool_val(true);
return true;
}
expr Z3User::Negate(const expr &f){
if(f.is_app() && f.decl().get_decl_kind() == Not)
return f.arg(0);
else if(eq(f,ctx.bool_val(true)))
return ctx.bool_val(false);
else if(eq(f,ctx.bool_val(false)))
return ctx.bool_val(true);
return !f;
}
expr Z3User::ReduceAndOr(const std::vector<expr> &args, bool is_and, std::vector<expr> &res){
for(unsigned i = 0; i < args.size(); i++)
if(!eq(args[i],ctx.bool_val(is_and))){
if(eq(args[i],ctx.bool_val(!is_and)))
return ctx.bool_val(!is_and);
res.push_back(args[i]);
}
return expr();
}
expr Z3User::FinishAndOr(const std::vector<expr> &args, bool is_and){
if(args.size() == 0)
return ctx.bool_val(is_and);
if(args.size() == 1)
return args[0];
return ctx.make(is_and ? And : Or,args);
}
expr Z3User::SimplifyAndOr(const std::vector<expr> &args, bool is_and){
std::vector<expr> sargs;
expr res = ReduceAndOr(args,is_and,sargs);
if(!res.null()) return res;
return FinishAndOr(sargs,is_and);
}
expr Z3User::PullCommonFactors(std::vector<expr> &args, bool is_and){
// first check if there's anything to do...
if(args.size() < 2)
return FinishAndOr(args,is_and);
for(unsigned i = 0; i < args.size(); i++){
const expr &a = args[i];
if(!(a.is_app() && a.decl().get_decl_kind() == (is_and ? Or : And)))
return FinishAndOr(args,is_and);
}
std::vector<expr> common;
for(unsigned i = 0; i < args.size(); i++){
unsigned n = args[i].num_args();
std::vector<expr> v(n),w;
for(unsigned j = 0; j < n; j++)
v[j] = args[i].arg(j);
std::less<ast> comp;
std::sort(v.begin(),v.end(),comp);
if(i == 0)
common.swap(v);
else {
std::set_intersection(common.begin(),common.end(),v.begin(),v.end(),std::inserter(w,w.begin()),comp);
common.swap(w);
}
}
if(common.empty())
return FinishAndOr(args,is_and);
std::set<ast> common_set(common.begin(),common.end());
for(unsigned i = 0; i < args.size(); i++){
unsigned n = args[i].num_args();
std::vector<expr> lits;
for(unsigned j = 0; j < n; j++){
const expr b = args[i].arg(j);
if(common_set.find(b) == common_set.end())
lits.push_back(b);
}
args[i] = SimplifyAndOr(lits,!is_and);
}
common.push_back(SimplifyAndOr(args,is_and));
return SimplifyAndOr(common,!is_and);
}
expr Z3User::ReallySimplifyAndOr(const std::vector<expr> &args, bool is_and){
std::vector<expr> sargs;
expr res = ReduceAndOr(args,is_and,sargs);
if(!res.null()) return res;
return PullCommonFactors(sargs,is_and);
}
Z3User::Term Z3User::SubstAtomTriv(const expr &foo, const expr &atom, const expr &val){
if(eq(foo,atom))
return val;
else if(foo.is_app() && foo.decl().get_decl_kind() == Not && eq(foo.arg(0),atom))
return Negate(val);
else
return foo;
}
Z3User::Term Z3User::SubstAtom(hash_map<ast, Term> &memo, const expr &t, const expr &atom, const expr &val){
std::pair<ast,Term> foo(t,expr(ctx));
std::pair<hash_map<ast,Term>::iterator, bool> bar = memo.insert(foo);
Term &res = bar.first->second;
if(!bar.second) return res;
if (t.is_app()){
func_decl f = t.decl();
decl_kind k = f.get_decl_kind();
// TODO: recur here, but how much? We don't want to be quadractic in formula size
if(k == And || k == Or){
int nargs = t.num_args();
std::vector<Term> args(nargs);
for(int i = 0; i < nargs; i++)
args[i] = SubstAtom(memo,t.arg(i),atom,val);
res = ReallySimplifyAndOr(args, k==And);
return res;
}
}
else if(t.is_quantifier() && atom.is_quantifier()){
if(eq(t,atom))
res = val;
else
res = clone_quantifier(t,SubstAtom(memo,t.body(),atom,val));
return res;
}
res = SubstAtomTriv(t,atom,val);
return res;
}
void Z3User::RemoveRedundancyOp(bool pol, std::vector<expr> &args, hash_map<ast, Term> &smemo){
for(unsigned i = 0; i < args.size(); i++){
const expr &lit = args[i];
expr atom, val;
if(IsLiteral(lit,atom,val)){
for(unsigned j = 0; j < args.size(); j++)
if(j != i){
smemo.clear();
args[j] = SubstAtom(smemo,args[j],atom,pol ? val : !val);
}
}
}
}
Z3User::Term Z3User::RemoveRedundancyRec(hash_map<ast, Term> &memo, hash_map<ast, Term> &smemo, const Term &t)
{
std::pair<ast,Term> foo(t,expr(ctx));
std::pair<hash_map<ast,Term>::iterator, bool> bar = memo.insert(foo);
Term &res = bar.first->second;
if(!bar.second) return res;
if (t.is_app())
{
func_decl f = t.decl();
std::vector<Term> args;
int nargs = t.num_args();
for(int i = 0; i < nargs; i++)
args.push_back(RemoveRedundancyRec(memo, smemo, t.arg(i)));
decl_kind k = f.get_decl_kind();
if(k == And){
RemoveRedundancyOp(true,args,smemo);
res = ReallySimplifyAndOr(args, true);
}
else if(k == Or){
RemoveRedundancyOp(false,args,smemo);
res = ReallySimplifyAndOr(args, false);
}
else {
if(k == Equal && args[0].get_id() > args[1].get_id())
std::swap(args[0],args[1]);
res = f(args.size(),&args[0]);
}
}
else if (t.is_quantifier())
{
Term body = RemoveRedundancyRec(memo,smemo,t.body());
res = clone_quantifier(t, body);
}
else res = t;
return res;
}
Z3User::Term Z3User::RemoveRedundancy(const Term &t){
hash_map<ast, Term> memo;
hash_map<ast, Term> smemo;
return RemoveRedundancyRec(memo,smemo,t);
}
Z3User::Term Z3User::AdjustQuantifiers(const Term &t)
{
if(t.is_quantifier() || (t.is_app() && t.has_quantifiers()))
return t.qe_lite();
return t;
}
Z3User::Term Z3User::SubstRecHide(hash_map<ast, Term> &memo, const Term &t, int number)
{
std::pair<ast,Term> foo(t,expr(ctx));
@ -373,6 +627,19 @@ namespace Duality {
x = x && y;
}
void RPFP::SetAnnotation(Node *root, const expr &t){
hash_map<ast, Term> memo;
Term b;
std::vector<Term> v;
RedVars(root, b, v);
memo[b] = ctx.bool_val(true);
for (unsigned i = 0; i < v.size(); i++)
memo[v[i]] = root->Annotation.IndParams[i];
Term annot = SubstRec(memo, t);
// Strengthen(ref root.Annotation.Formula, annot);
root->Annotation.Formula = annot;
}
void RPFP::DecodeTree(Node *root, TermTree *interp, int persist)
{
std::vector<TermTree *> &ic = interp->getChildren();
@ -382,16 +649,7 @@ namespace Duality {
for (unsigned i = 0; i < nc.size(); i++)
DecodeTree(nc[i], ic[i], persist);
}
hash_map<ast, Term> memo;
Term b;
std::vector<Term> v;
RedVars(root, b, v);
memo[b] = ctx.bool_val(true);
for (unsigned i = 0; i < v.size(); i++)
memo[v[i]] = root->Annotation.IndParams[i];
Term annot = SubstRec(memo, interp->getTerm());
// Strengthen(ref root.Annotation.Formula, annot);
root->Annotation.Formula = annot;
SetAnnotation(root,interp->getTerm());
#if 0
if(persist != 0)
Z3_persist_ast(ctx,root->Annotation.Formula,persist);
@ -509,6 +767,10 @@ namespace Duality {
timer_stop("solver add");
}
void RPFP::ConstrainParent(Edge *parent, Node *child){
ConstrainEdgeLocalized(parent,GetAnnotation(child));
}
/** For incremental solving, asserts the negation of the upper bound associated
* with a node.
@ -524,6 +786,24 @@ namespace Duality {
}
}
/** Assert a constraint on an edge in the SMT context.
*/
void RPFP::ConstrainEdge(Edge *e, const Term &t)
{
Term tl = Localize(e, t);
ConstrainEdgeLocalized(e,tl);
}
void RPFP::ConstrainEdgeLocalized(Edge *e, const Term &tl)
{
e->constraints.push_back(tl);
stack.back().constraints.push_back(std::pair<Edge *,Term>(e,tl));
slvr.add(tl);
}
/** Declare a constant in the background theory. */
void RPFP::DeclareConstant(const FuncDecl &f){
@ -592,6 +872,7 @@ namespace Duality {
TermTree *goals = NULL;
if(ls->need_goals)
goals = GetGoalTree(root);
ClearProofCore();
// if (dualModel != null) dualModel.Dispose();
// if (dualLabels != null) dualLabels.Dispose();
@ -613,11 +894,54 @@ namespace Duality {
return res;
}
void RPFP::CollapseTermTreeRec(TermTree *root, TermTree *node){
root->addTerm(node->getTerm());
std::vector<Term> &cnsts = node->getTerms();
for(unsigned i = 0; i < cnsts.size(); i++)
root->addTerm(cnsts[i]);
std::vector<TermTree *> &chs = node->getChildren();
for(unsigned i = 0; i < chs.size(); i++){
CollapseTermTreeRec(root,chs[i]);
}
}
TermTree *RPFP::CollapseTermTree(TermTree *node){
std::vector<TermTree *> &chs = node->getChildren();
for(unsigned i = 0; i < chs.size(); i++)
CollapseTermTreeRec(node,chs[i]);
for(unsigned i = 0; i < chs.size(); i++)
delete chs[i];
chs.clear();
return node;
}
lbool RPFP::SolveSingleNode(Node *root, Node *node)
{
timer_start("Solve");
TermTree *tree = CollapseTermTree(GetConstraintTree(root,node));
tree->getChildren().push_back(CollapseTermTree(ToTermTree(node)));
TermTree *interpolant = NULL;
ClearProofCore();
timer_start("interpolate_tree");
lbool res = ls->interpolate_tree(tree, interpolant, dualModel,0,true);
timer_stop("interpolate_tree");
if (res == l_false)
{
DecodeTree(node, interpolant->getChildren()[0], 0);
delete interpolant;
}
delete tree;
timer_stop("Solve");
return res;
}
/** Get the constraint tree (but don't solve it) */
TermTree *RPFP::GetConstraintTree(Node *root)
TermTree *RPFP::GetConstraintTree(Node *root, Node *skip_descendant)
{
return AddUpperBound(root, ToTermTree(root));
return AddUpperBound(root, ToTermTree(root,skip_descendant));
}
/** Dispose of the dual model (counterexample) if there is one. */
@ -646,6 +970,7 @@ namespace Duality {
check_result RPFP::Check(Node *root, std::vector<Node *> underapproxes, std::vector<Node *> *underapprox_core )
{
ClearProofCore();
// if (dualModel != null) dualModel.Dispose();
check_result res;
if(!underapproxes.size())
@ -682,6 +1007,7 @@ namespace Duality {
check_result RPFP::CheckUpdateModel(Node *root, std::vector<expr> assumps){
// check_result temp1 = slvr.check(); // no idea why I need to do this
ClearProofCore();
check_result res = slvr.check_keep_model(assumps.size(),&assumps[0]);
dualModel = slvr.get_model();
return res;
@ -1062,7 +1388,8 @@ namespace Duality {
}
}
/* Unreachable! */
throw "error in RPFP::ImplicantRed";
// TODO: need to indicate this failure to caller
// std::cerr << "error in RPFP::ImplicantRed";
goto done;
}
else if(k == Not) {
@ -1081,6 +1408,31 @@ namespace Duality {
done[truth].insert(f);
}
void RPFP::ImplicantFullRed(hash_map<ast,int> &memo, const Term &f, std::vector<Term> &lits,
hash_set<ast> &done, hash_set<ast> &dont_cares){
if(done.find(f) != done.end())
return; /* already processed */
if(f.is_app()){
int nargs = f.num_args();
decl_kind k = f.decl().get_decl_kind();
if(k == Implies || k == Iff || k == And || k == Or || k == Not){
for(int i = 0; i < nargs; i++)
ImplicantFullRed(memo,f.arg(i),lits,done,dont_cares);
goto done;
}
}
{
if(dont_cares.find(f) == dont_cares.end()){
int b = SubtermTruth(memo,f);
if(b != 0 && b != 1) goto done;
expr bv = (b==1) ? f : !f;
lits.push_back(bv);
}
}
done:
done.insert(f);
}
RPFP::Term RPFP::ResolveIte(hash_map<ast,int> &memo, const Term &t, std::vector<Term> &lits,
hash_set<ast> *done, hash_set<ast> &dont_cares){
if(resolve_ite_memo.find(t) != resolve_ite_memo.end())
@ -1143,6 +1495,16 @@ namespace Duality {
return conjoin(lits);
}
RPFP::Term RPFP::UnderapproxFullFormula(const Term &f, hash_set<ast> &dont_cares){
/* first compute truth values of subterms */
hash_map<ast,int> memo;
hash_set<ast> done;
std::vector<Term> lits;
ImplicantFullRed(memo,f,lits,done,dont_cares);
/* return conjunction of literals */
return conjoin(lits);
}
struct VariableProjector : Z3User {
struct elim_cand {
@ -1669,6 +2031,121 @@ namespace Duality {
return eu;
}
void RPFP::FixCurrentState(Edge *edge){
hash_set<ast> dont_cares;
resolve_ite_memo.clear();
timer_start("UnderapproxFormula");
Term dual = edge->dual.null() ? ctx.bool_val(true) : edge->dual;
Term eu = UnderapproxFormula(dual,dont_cares);
timer_stop("UnderapproxFormula");
ConstrainEdgeLocalized(edge,eu);
}
void RPFP::FixCurrentStateFull(Edge *edge, const expr &extra){
hash_set<ast> dont_cares;
resolve_ite_memo.clear();
timer_start("UnderapproxFormula");
Term dual = edge->dual.null() ? ctx.bool_val(true) : edge->dual;
for(unsigned i = 0; i < edge->constraints.size(); i++)
dual = dual && edge->constraints[i];
// dual = dual && extra;
Term eu = UnderapproxFullFormula(dual,dont_cares);
timer_stop("UnderapproxFormula");
ConstrainEdgeLocalized(edge,eu);
}
void RPFP::GetGroundLitsUnderQuants(hash_set<ast> *memo, const Term &f, std::vector<Term> &res, int under){
if(memo[under].find(f) != memo[under].end())
return;
memo[under].insert(f);
if(f.is_app()){
if(!under && !f.has_quantifiers())
return;
decl_kind k = f.decl().get_decl_kind();
if(k == And || k == Or || k == Implies || k == Iff){
int num_args = f.num_args();
for(int i = 0; i < num_args; i++)
GetGroundLitsUnderQuants(memo,f.arg(i),res,under);
return;
}
}
else if (f.is_quantifier()){
#if 0
// treat closed quantified formula as a literal 'cause we hate nested quantifiers
if(under && IsClosedFormula(f))
res.push_back(f);
else
#endif
GetGroundLitsUnderQuants(memo,f.body(),res,1);
return;
}
if(under && f.is_ground())
res.push_back(f);
}
RPFP::Term RPFP::StrengthenFormulaByCaseSplitting(const Term &f, std::vector<expr> &case_lits){
hash_set<ast> memo[2];
std::vector<Term> lits;
GetGroundLitsUnderQuants(memo, f, lits, 0);
hash_set<ast> lits_hash;
for(unsigned i = 0; i < lits.size(); i++)
lits_hash.insert(lits[i]);
hash_map<ast,expr> subst;
hash_map<ast,int> stt_memo;
std::vector<expr> conjuncts;
for(unsigned i = 0; i < lits.size(); i++){
const expr &lit = lits[i];
if(lits_hash.find(NegateLit(lit)) == lits_hash.end()){
case_lits.push_back(lit);
bool tval = false;
expr atom = lit;
if(lit.is_app() && lit.decl().get_decl_kind() == Not){
tval = true;
atom = lit.arg(0);
}
expr etval = ctx.bool_val(tval);
if(atom.is_quantifier())
subst[atom] = etval; // this is a bit desperate, since we can't eval quants
else {
int b = SubtermTruth(stt_memo,atom);
if(b == (tval ? 1 : 0))
subst[atom] = etval;
else {
if(b == 0 || b == 1){
etval = ctx.bool_val(b ? true : false);
subst[atom] = etval;
conjuncts.push_back(b ? atom : !atom);
}
}
}
}
}
expr g = f;
if(!subst.empty()){
g = SubstRec(subst,f);
if(conjuncts.size())
g = g && ctx.make(And,conjuncts);
g = g.simplify();
}
#if 1
expr g_old = g;
g = RemoveRedundancy(g);
bool changed = !eq(g,g_old);
g = g.simplify();
if(changed) { // a second pass can get some more simplification
g = RemoveRedundancy(g);
g = g.simplify();
}
#else
g = RemoveRedundancy(g);
g = g.simplify();
#endif
g = AdjustQuantifiers(g);
return g;
}
RPFP::Term RPFP::ModelValueAsConstraint(const Term &t){
if(t.is_array()){
@ -1712,6 +2189,167 @@ namespace Duality {
res = CreateRelation(p->Annotation.IndParams,funder);
}
#if 0
void RPFP::GreedyReduce(solver &s, std::vector<expr> &conjuncts){
// verify
s.push();
expr conj = ctx.make(And,conjuncts);
s.add(conj);
check_result res = s.check();
if(res != unsat)
throw "should be unsat";
s.pop(1);
for(unsigned i = 0; i < conjuncts.size(); ){
std::swap(conjuncts[i],conjuncts.back());
expr save = conjuncts.back();
conjuncts.pop_back();
s.push();
expr conj = ctx.make(And,conjuncts);
s.add(conj);
check_result res = s.check();
s.pop(1);
if(res != unsat){
conjuncts.push_back(save);
std::swap(conjuncts[i],conjuncts.back());
i++;
}
}
}
#endif
void RPFP::GreedyReduce(solver &s, std::vector<expr> &conjuncts){
std::vector<expr> lits(conjuncts.size());
for(unsigned i = 0; i < lits.size(); i++){
func_decl pred = ctx.fresh_func_decl("@alit", ctx.bool_sort());
lits[i] = pred();
s.add(ctx.make(Implies,lits[i],conjuncts[i]));
}
// verify
check_result res = s.check(lits.size(),&lits[0]);
if(res != unsat){
// add the axioms in the off chance they are useful
const std::vector<expr> &theory = ls->get_axioms();
for(unsigned i = 0; i < theory.size(); i++)
s.add(theory[i]);
if(s.check(lits.size(),&lits[0]) != unsat)
throw "should be unsat";
}
for(unsigned i = 0; i < conjuncts.size(); ){
std::swap(conjuncts[i],conjuncts.back());
std::swap(lits[i],lits.back());
check_result res = s.check(lits.size()-1,&lits[0]);
if(res != unsat){
std::swap(conjuncts[i],conjuncts.back());
std::swap(lits[i],lits.back());
i++;
}
else {
conjuncts.pop_back();
lits.pop_back();
}
}
}
expr RPFP::NegateLit(const expr &f){
if(f.is_app() && f.decl().get_decl_kind() == Not)
return f.arg(0);
else
return !f;
}
void RPFP::NegateLits(std::vector<expr> &lits){
for(unsigned i = 0; i < lits.size(); i++){
expr &f = lits[i];
if(f.is_app() && f.decl().get_decl_kind() == Not)
f = f.arg(0);
else
f = !f;
}
}
expr RPFP::SimplifyOr(std::vector<expr> &lits){
if(lits.size() == 0)
return ctx.bool_val(false);
if(lits.size() == 1)
return lits[0];
return ctx.make(Or,lits);
}
// set up edge constraint in aux solver
void RPFP::AddEdgeToSolver(Edge *edge){
if(!edge->dual.null())
aux_solver.add(edge->dual);
for(unsigned i = 0; i < edge->constraints.size(); i++){
expr tl = edge->constraints[i];
aux_solver.add(tl);
}
}
void RPFP::InterpolateByCases(Node *root, Node *node){
aux_solver.push();
AddEdgeToSolver(node->Outgoing);
node->Annotation.SetEmpty();
hash_set<ast> *core = new hash_set<ast>;
core->insert(node->Outgoing->dual);
while(1){
aux_solver.push();
expr annot = !GetAnnotation(node);
aux_solver.add(annot);
if(aux_solver.check() == unsat){
aux_solver.pop(1);
break;
}
dualModel = aux_solver.get_model();
aux_solver.pop(1);
Push();
FixCurrentStateFull(node->Outgoing,annot);
ConstrainEdgeLocalized(node->Outgoing,!GetAnnotation(node));
check_result foo = Check(root);
if(foo != unsat)
throw "should be unsat";
AddToProofCore(*core);
Transformer old_annot = node->Annotation;
SolveSingleNode(root,node);
{
expr itp = GetAnnotation(node);
dualModel = aux_solver.get_model();
std::vector<expr> case_lits;
itp = StrengthenFormulaByCaseSplitting(itp, case_lits);
SetAnnotation(node,itp);
}
if(node->Annotation.IsEmpty()){
std::cout << "bad in InterpolateByCase -- core:\n";
std::vector<expr> assumps;
slvr.get_proof().get_assumptions(assumps);
for(unsigned i = 0; i < assumps.size(); i++)
assumps[i].show();
throw "ack!";
}
Pop(1);
node->Annotation.UnionWith(old_annot);
}
if(proof_core)
delete proof_core; // shouldn't happen
proof_core = core;
aux_solver.pop(1);
}
void RPFP::Generalize(Node *root, Node *node){
aux_solver.push();
AddEdgeToSolver(node->Outgoing);
expr fmla = GetAnnotation(node);
std::vector<expr> conjuncts;
CollectConjuncts(fmla,conjuncts,false);
GreedyReduce(aux_solver,conjuncts); // try to remove conjuncts one at a tme
aux_solver.pop(1);
NegateLits(conjuncts);
SetAnnotation(node,SimplifyOr(conjuncts));
}
/** Push a scope. Assertions made after Push can be undone by Pop. */
@ -1733,10 +2371,26 @@ namespace Duality {
(*it)->dual = expr(ctx,NULL);
for(std::list<Node *>::iterator it = back.nodes.begin(), en = back.nodes.end(); it != en; ++it)
(*it)->dual = expr(ctx,NULL);
for(std::list<std::pair<Edge *,Term> >::iterator it = back.constraints.begin(), en = back.constraints.end(); it != en; ++it)
(*it).first->constraints.pop_back();
stack.pop_back();
}
}
/** Erase the proof by performing a Pop, Push and re-assertion of
all the popped constraints */
void RPFP::PopPush(){
slvr.pop(1);
slvr.push();
stack_entry &back = stack.back();
for(std::list<Edge *>::iterator it = back.edges.begin(), en = back.edges.end(); it != en; ++it)
slvr.add((*it)->dual);
for(std::list<Node *>::iterator it = back.nodes.begin(), en = back.nodes.end(); it != en; ++it)
slvr.add((*it)->dual);
for(std::list<std::pair<Edge *,Term> >::iterator it = back.constraints.begin(), en = back.constraints.end(); it != en; ++it)
slvr.add((*it).second);
}
@ -1880,6 +2534,37 @@ namespace Duality {
return SubstBoundRec(memo, subst, 0, t);
}
int Z3User::MaxIndex(hash_map<ast,int> &memo, const Term &t)
{
std::pair<ast,int> foo(t,-1);
std::pair<hash_map<ast,int>::iterator, bool> bar = memo.insert(foo);
int &res = bar.first->second;
if(!bar.second) return res;
if (t.is_app()){
func_decl f = t.decl();
int nargs = t.num_args();
for(int i = 0; i < nargs; i++){
int m = MaxIndex(memo, t.arg(i));
if(m > res)
res = m;
}
}
else if (t.is_quantifier()){
int bound = t.get_quantifier_num_bound();
res = MaxIndex(memo,t.body()) - bound;
}
else if (t.is_var()) {
res = t.get_index_value();
}
return res;
}
bool Z3User::IsClosedFormula(const Term &t){
hash_map<ast,int> memo;
return MaxIndex(memo,t) < 0;
}
/** Convert a collection of clauses to Nodes and Edges in the RPFP.
Predicate unknowns are uninterpreted predicates not
@ -2169,8 +2854,32 @@ namespace Duality {
}
void RPFP::AddToProofCore(hash_set<ast> &core){
std::vector<expr> assumps;
slvr.get_proof().get_assumptions(assumps);
for(unsigned i = 0; i < assumps.size(); i++)
core.insert(assumps[i]);
}
void RPFP::ComputeProofCore(){
if(!proof_core){
proof_core = new hash_set<ast>;
AddToProofCore(*proof_core);
}
}
bool RPFP::EdgeUsedInProof(Edge *edge){
ComputeProofCore();
if(!edge->dual.null() && proof_core->find(edge->dual) != proof_core->end())
return true;
for(unsigned i = 0; i < edge->constraints.size(); i++)
if(proof_core->find(edge->constraints[i]) != proof_core->end())
return true;
return false;
}
RPFP::~RPFP(){
ClearProofCore();
for(unsigned i = 0; i < nodes.size(); i++)
delete nodes[i];
for(unsigned i = 0; i < edges.size(); i++)

280
src/duality/duality_solver.cpp
View file

@ -184,7 +184,7 @@ namespace Duality {
best.insert(*it);
}
#else
virtual void ChooseExpand(const std::set<RPFP::Node *> &choices, std::set<RPFP::Node *> &best, bool high_priority=false){
virtual void ChooseExpand(const std::set<RPFP::Node *> &choices, std::set<RPFP::Node *> &best, bool high_priority=false, bool best_only=false){
if(high_priority) return;
int best_score = INT_MAX;
int worst_score = 0;
@ -194,13 +194,13 @@ namespace Duality {
best_score = std::min(best_score,score);
worst_score = std::max(worst_score,score);
}
int cutoff = best_score + (worst_score-best_score)/2;
int cutoff = best_only ? best_score : (best_score + (worst_score-best_score)/2);
for(std::set<Node *>::iterator it = choices.begin(), en = choices.end(); it != en; ++it)
if(scores[(*it)->map].updates <= cutoff)
best.insert(*it);
}
#endif
/** Called when done expanding a tree */
virtual void Done() {}
};
@ -1270,18 +1270,24 @@ namespace Duality {
}
}
bool UpdateNodeToNode(Node *node, Node *top){
if(!node->Annotation.SubsetEq(top->Annotation)){
reporter->Update(node,top->Annotation);
indset->Update(node,top->Annotation);
updated_nodes.insert(node->map);
node->Annotation.IntersectWith(top->Annotation);
return true;
}
return false;
}
/** Update the unwinding solution, using an interpolant for the
derivation tree. */
void UpdateWithInterpolant(Node *node, RPFP *tree, Node *top){
if(top->Outgoing)
for(unsigned i = 0; i < top->Outgoing->Children.size(); i++)
UpdateWithInterpolant(node->Outgoing->Children[i],tree,top->Outgoing->Children[i]);
if(!node->Annotation.SubsetEq(top->Annotation)){
reporter->Update(node,top->Annotation);
indset->Update(node,top->Annotation);
updated_nodes.insert(node->map);
node->Annotation.IntersectWith(top->Annotation);
}
UpdateNodeToNode(node, top);
heuristic->Update(node);
}
@ -1305,7 +1311,8 @@ namespace Duality {
if(node->Bound.IsFull()) return true;
reporter->Bound(node);
int start_decs = rpfp->CumulativeDecisions();
DerivationTree dt(this,unwinding,reporter,heuristic,FullExpand);
DerivationTree *dtp = new DerivationTreeSlow(this,unwinding,reporter,heuristic,FullExpand);
DerivationTree &dt = *dtp;
bool res = dt.Derive(unwinding,node,UseUnderapprox);
int end_decs = rpfp->CumulativeDecisions();
// std::cout << "decisions: " << (end_decs - start_decs) << std::endl;
@ -1321,6 +1328,7 @@ namespace Duality {
UpdateWithInterpolant(node,dt.tree,dt.top);
delete dt.tree;
}
delete dtp;
return !res;
}
@ -1491,7 +1499,7 @@ namespace Duality {
return res != unsat;
}
bool Build(){
virtual bool Build(){
#ifdef EFFORT_BOUNDED_STRAT
start_decs = tree->CumulativeDecisions();
#endif
@ -1545,7 +1553,7 @@ namespace Duality {
}
}
void ExpandNode(RPFP::Node *p){
virtual void ExpandNode(RPFP::Node *p){
// tree->RemoveEdge(p->Outgoing);
Edge *edge = duality->GetNodeOutgoing(p->map,last_decs);
std::vector<RPFP::Node *> &cs = edge->Children;
@ -1573,6 +1581,7 @@ namespace Duality {
}
#else
#if 0
void ExpansionChoices(std::set<Node *> &best){
std::vector <Node *> unused_set, used_set;
std::set<Node *> choices;
@ -1598,12 +1607,12 @@ namespace Duality {
heuristic->ChooseExpand(choices, best);
}
#else
void ExpansionChoicesFull(std::set<Node *> &best, bool high_priority){
void ExpansionChoicesFull(std::set<Node *> &best, bool high_priority, bool best_only = false){
std::set<Node *> choices;
for(std::list<RPFP::Node *>::iterator it = leaves.begin(), en = leaves.end(); it != en; ++it)
if (high_priority || !tree->Empty(*it)) // if used in the counter-model
choices.insert(*it);
heuristic->ChooseExpand(choices, best, high_priority);
heuristic->ChooseExpand(choices, best, high_priority, best_only);
}
void ExpansionChoicesRec(std::vector <Node *> &unused_set, std::vector <Node *> &used_set,
@ -1641,9 +1650,9 @@ namespace Duality {
std::set<Node *> old_choices;
void ExpansionChoices(std::set<Node *> &best, bool high_priority){
void ExpansionChoices(std::set<Node *> &best, bool high_priority, bool best_only = false){
if(!underapprox || constrained || high_priority){
ExpansionChoicesFull(best, high_priority);
ExpansionChoicesFull(best, high_priority,best_only);
return;
}
std::vector <Node *> unused_set, used_set;
@ -1668,28 +1677,259 @@ namespace Duality {
#endif
#endif
bool ExpandSomeNodes(bool high_priority = false){
bool ExpandSomeNodes(bool high_priority = false, int max = INT_MAX){
#ifdef EFFORT_BOUNDED_STRAT
last_decs = tree->CumulativeDecisions() - start_decs;
#endif
timer_start("ExpandSomeNodes");
timer_start("ExpansionChoices");
std::set<Node *> choices;
ExpansionChoices(choices,high_priority);
ExpansionChoices(choices,high_priority,max != INT_MAX);
timer_stop("ExpansionChoices");
std::list<RPFP::Node *> leaves_copy = leaves; // copy so can modify orig
leaves.clear();
int count = 0;
for(std::list<RPFP::Node *>::iterator it = leaves_copy.begin(), en = leaves_copy.end(); it != en; ++it){
if(choices.find(*it) != choices.end())
if(choices.find(*it) != choices.end() && count < max){
count++;
ExpandNode(*it);
}
else leaves.push_back(*it);
}
timer_stop("ExpandSomeNodes");
return !choices.empty();
}
void RemoveExpansion(RPFP::Node *p){
Edge *edge = p->Outgoing;
Node *parent = edge->Parent;
std::vector<RPFP::Node *> cs = edge->Children;
tree->DeleteEdge(edge);
for(unsigned i = 0; i < cs.size(); i++)
tree->DeleteNode(cs[i]);
leaves.push_back(parent);
}
};
class DerivationTreeSlow : public DerivationTree {
public:
struct stack_entry {
unsigned level; // SMT solver stack level
std::vector<Node *> expansions;
};
std::vector<stack_entry> stack;
hash_map<Node *, expr> updates;
DerivationTreeSlow(Duality *_duality, RPFP *rpfp, Reporter *_reporter, Heuristic *_heuristic, bool _full_expand)
: DerivationTree(_duality, rpfp, _reporter, _heuristic, _full_expand) {
stack.push_back(stack_entry());
}
virtual bool Build(){
stack.back().level = tree->slvr.get_scope_level();
while (true)
{
lbool res;
unsigned slvr_level = tree->slvr.get_scope_level();
if(slvr_level != stack.back().level)
throw "stacks out of sync!";
// res = tree->Solve(top, 1); // incremental solve, keep interpolants for one pop
check_result foo = tree->Check(top);
res = foo == unsat ? l_false : l_true;
if (res == l_false) {
if (stack.empty()) // should never happen
return false;
{
std::vector<Node *> &expansions = stack.back().expansions;
int update_count = 0;
for(unsigned i = 0; i < expansions.size(); i++){
Node *node = expansions[i];
tree->SolveSingleNode(top,node);
if(expansions.size() == 1 && NodeTooComplicated(node))
SimplifyNode(node);
tree->Generalize(top,node);
if(RecordUpdate(node))
update_count++;
}
if(update_count == 0)
reporter->Message("backtracked without learning");
}
tree->ComputeProofCore(); // need to compute the proof core before popping solver
while(1) {
std::vector<Node *> &expansions = stack.back().expansions;
bool prev_level_used = LevelUsedInProof(stack.size()-2); // need to compute this before pop
tree->Pop(1);
hash_set<Node *> leaves_to_remove;
for(unsigned i = 0; i < expansions.size(); i++){
Node *node = expansions[i];
// if(node != top)
// tree->ConstrainParent(node->Incoming[0],node);
std::vector<Node *> &cs = node->Outgoing->Children;
for(unsigned i = 0; i < cs.size(); i++){
leaves_to_remove.insert(cs[i]);
UnmapNode(cs[i]);
if(std::find(updated_nodes.begin(),updated_nodes.end(),cs[i]) != updated_nodes.end())
throw "help!";
}
}
RemoveLeaves(leaves_to_remove); // have to do this before actually deleting the children
for(unsigned i = 0; i < expansions.size(); i++){
Node *node = expansions[i];
RemoveExpansion(node);
}
stack.pop_back();
if(prev_level_used || stack.size() == 1) break;
RemoveUpdateNodesAtCurrentLevel(); // this level is about to be deleted -- remove its children from update list
std::vector<Node *> &unused_ex = stack.back().expansions;
for(unsigned i = 0; i < unused_ex.size(); i++)
heuristic->Update(unused_ex[i]->map); // make it less likely to expand this node in future
}
HandleUpdatedNodes();
if(stack.size() == 1)
return false;
}
else {
tree->Push();
std::vector<Node *> &expansions = stack.back().expansions;
for(unsigned i = 0; i < expansions.size(); i++){
tree->FixCurrentState(expansions[i]->Outgoing);
}
#if 0
if(tree->slvr.check() == unsat)
throw "help!";
#endif
stack.push_back(stack_entry());
stack.back().level = tree->slvr.get_scope_level();
if(ExpandSomeNodes(false,1)){
continue;
}
while(stack.size() > 1){
tree->Pop(1);
stack.pop_back();
}
return true;
}
}
}
bool NodeTooComplicated(Node *node){
return tree->CountOperators(node->Annotation.Formula) > 3;
}
void SimplifyNode(Node *node){
// have to destroy the old proof to get a new interpolant
tree->PopPush();
tree->InterpolateByCases(top,node);
}
bool LevelUsedInProof(unsigned level){
std::vector<Node *> &expansions = stack[level].expansions;
for(unsigned i = 0; i < expansions.size(); i++)
if(tree->EdgeUsedInProof(expansions[i]->Outgoing))
return true;
return false;
}
void RemoveUpdateNodesAtCurrentLevel() {
for(std::list<Node *>::iterator it = updated_nodes.begin(), en = updated_nodes.end(); it != en;){
Node *node = *it;
if(AtCurrentStackLevel(node->Incoming[0]->Parent)){
std::list<Node *>::iterator victim = it;
++it;
updated_nodes.erase(victim);
}
else
++it;
}
}
void RemoveLeaves(hash_set<Node *> &leaves_to_remove){
std::list<RPFP::Node *> leaves_copy;
leaves_copy.swap(leaves);
for(std::list<RPFP::Node *>::iterator it = leaves_copy.begin(), en = leaves_copy.end(); it != en; ++it){
if(leaves_to_remove.find(*it) == leaves_to_remove.end())
leaves.push_back(*it);
}
}
hash_map<Node *, std::vector<Node *> > node_map;
std::list<Node *> updated_nodes;
virtual void ExpandNode(RPFP::Node *p){
stack.back().expansions.push_back(p);
DerivationTree::ExpandNode(p);
std::vector<Node *> &new_nodes = p->Outgoing->Children;
for(unsigned i = 0; i < new_nodes.size(); i++){
Node *n = new_nodes[i];
node_map[n->map].push_back(n);
}
}
bool RecordUpdate(Node *node){
bool res = duality->UpdateNodeToNode(node->map,node);
if(res){
std::vector<Node *> to_update = node_map[node->map];
for(unsigned i = 0; i < to_update.size(); i++){
Node *node2 = to_update[i];
// maintain invariant that no nodes on updated list are created at current stack level
if(node2 == node || !(node->Incoming.size() > 0 && AtCurrentStackLevel(node2->Incoming[0]->Parent))){
updated_nodes.push_back(node2);
if(node2 != node)
node2->Annotation = node->Annotation;
}
}
}
return res;
}
void HandleUpdatedNodes(){
for(std::list<Node *>::iterator it = updated_nodes.begin(), en = updated_nodes.end(); it != en;){
Node *node = *it;
node->Annotation = node->map->Annotation;
if(node->Incoming.size() > 0)
tree->ConstrainParent(node->Incoming[0],node);
if(AtCurrentStackLevel(node->Incoming[0]->Parent)){
std::list<Node *>::iterator victim = it;
++it;
updated_nodes.erase(victim);
}
else
++it;
}
}
bool AtCurrentStackLevel(Node *node){
std::vector<Node *> vec = stack.back().expansions;
for(unsigned i = 0; i < vec.size(); i++)
if(vec[i] == node)
return true;
return false;
}
void UnmapNode(Node *node){
std::vector<Node *> &vec = node_map[node->map];
for(unsigned i = 0; i < vec.size(); i++){
if(vec[i] == node){
std::swap(vec[i],vec.back());
vec.pop_back();
return;
}
}
throw "can't unmap node";
}
};
class Covering {
struct cover_info {
@ -2084,7 +2324,7 @@ namespace Duality {
return name;
}
virtual void ChooseExpand(const std::set<RPFP::Node *> &choices, std::set<RPFP::Node *> &best, bool high_priority){
virtual void ChooseExpand(const std::set<RPFP::Node *> &choices, std::set<RPFP::Node *> &best, bool high_priority, bool best_only){
if(!high_priority || !old_cex.tree){
Heuristic::ChooseExpand(choices,best,false);
return;

98
src/duality/duality_wrapper.cpp
View file

@ -26,16 +26,23 @@ Revision History:
#include "expr_abstract.h"
#include "stopwatch.h"
#include "model_smt2_pp.h"
#include "qe_lite.h"
namespace Duality {
solver::solver(Duality::context& c) : object(c), the_model(c) {
solver::solver(Duality::context& c, bool extensional) : object(c), the_model(c) {
params_ref p;
p.set_bool("proof", true); // this is currently useless
p.set_bool("model", true);
p.set_bool("unsat_core", true);
p.set_bool("mbqi",true);
p.set_str("mbqi.id","itp"); // use mbqi for quantifiers in interpolants
p.set_uint("mbqi.max_iterations",1); // use mbqi for quantifiers in interpolants
if(true || extensional)
p.set_bool("array.extensional",true);
scoped_ptr<solver_factory> sf = mk_smt_solver_factory();
m_solver = (*sf)(m(), p, true, true, true, ::symbol::null);
m_solver->updt_params(p); // why do we have to do this?
canceled = false;
}
@ -323,6 +330,14 @@ expr context::make_quant(decl_kind op, const std::vector<sort> &_sorts, const st
return simplify(p);
}
expr expr::qe_lite() const {
::qe_lite qe(m());
expr_ref result(to_expr(raw()),m());
proof_ref pf(m());
qe(result,pf);
return ctx().cook(result);
}
expr clone_quantifier(const expr &q, const expr &b){
return q.ctx().cook(q.m().update_quantifier(to_quantifier(q.raw()), to_expr(b.raw())));
}
@ -425,15 +440,18 @@ expr context::make_quant(decl_kind op, const std::vector<sort> &_sorts, const st
static int linearize_assumptions(int num,
TermTree *assumptions,
std::vector<expr> &linear_assumptions,
std::vector<std::vector <expr> > &linear_assumptions,
std::vector<int> &parents){
for(unsigned i = 0; i < assumptions->getChildren().size(); i++)
num = linearize_assumptions(num, assumptions->getChildren()[i], linear_assumptions, parents);
linear_assumptions[num] = assumptions->getTerm();
// linear_assumptions[num].push_back(assumptions->getTerm());
for(unsigned i = 0; i < assumptions->getChildren().size(); i++)
parents[assumptions->getChildren()[i]->getNumber()] = num;
parents[num] = SHRT_MAX; // in case we have no parent
linear_assumptions[num] = assumptions->getTerm();
linear_assumptions[num].push_back(assumptions->getTerm());
std::vector<expr> &ts = assumptions->getTerms();
for(unsigned i = 0; i < ts.size(); i++)
linear_assumptions[num].push_back(ts[i]);
return num + 1;
}
@ -462,14 +480,15 @@ expr context::make_quant(decl_kind op, const std::vector<sort> &_sorts, const st
{
int size = assumptions->number(0);
std::vector<expr> linear_assumptions(size);
std::vector<std::vector<expr> > linear_assumptions(size);
std::vector<int> parents(size);
linearize_assumptions(0,assumptions,linear_assumptions,parents);
ptr_vector< ::ast> _interpolants(size-1);
ptr_vector< ::ast>_assumptions(size);
vector<ptr_vector< ::ast> >_assumptions(size);
for(int i = 0; i < size; i++)
_assumptions[i] = linear_assumptions[i];
for(unsigned j = 0; j < linear_assumptions[i].size(); j++)
_assumptions[i].push_back(linear_assumptions[i][j]);
::vector<int> _parents; _parents.resize(parents.size());
for(unsigned i = 0; i < parents.size(); i++)
_parents[i] = parents[i];
@ -477,11 +496,12 @@ expr context::make_quant(decl_kind op, const std::vector<sort> &_sorts, const st
for(unsigned i = 0; i < theory.size(); i++)
_theory[i] = theory[i];
push();
if(!incremental){
push();
for(unsigned i = 0; i < linear_assumptions.size(); i++)
add(linear_assumptions[i]);
for(unsigned j = 0; j < linear_assumptions[i].size(); j++)
add(linear_assumptions[i][j]);
}
check_result res = check();
@ -517,7 +537,8 @@ expr context::make_quant(decl_kind op, const std::vector<sort> &_sorts, const st
}
#endif
pop();
if(!incremental)
pop();
return (res == unsat) ? l_false : ((res == sat) ? l_true : l_undef);
@ -549,6 +570,29 @@ expr context::make_quant(decl_kind op, const std::vector<sort> &_sorts, const st
return "";
}
static void get_assumptions_rec(stl_ext::hash_set<ast> &memo, const proof &pf, std::vector<expr> &assumps){
if(memo.find(pf) != memo.end())return;
memo.insert(pf);
pfrule dk = pf.rule();
if(dk == PR_ASSERTED){
expr con = pf.conc();
assumps.push_back(con);
}
else {
unsigned nprems = pf.num_prems();
for(unsigned i = 0; i < nprems; i++){
proof arg = pf.prem(i);
get_assumptions_rec(memo,arg,assumps);
}
}
}
void proof::get_assumptions(std::vector<expr> &assumps){
stl_ext::hash_set<ast> memo;
get_assumptions_rec(memo,*this,assumps);
}
void ast::show() const{
std::cout << mk_pp(raw(), m()) << std::endl;
@ -559,6 +603,40 @@ expr context::make_quant(decl_kind op, const std::vector<sort> &_sorts, const st
std::cout << std::endl;
}
void model::show_hash() const {
std::ostringstream ss;
model_smt2_pp(ss, m(), *m_model, 0);
hash_space::hash<std::string> hasher;
unsigned h = hasher(ss.str());
std::cout << "model hash: " << h << "\n";
}
void solver::show() {
unsigned n = m_solver->get_num_assertions();
if(!n)
return;
ast_smt_pp pp(m());
for (unsigned i = 0; i < n-1; ++i)
pp.add_assumption(m_solver->get_assertion(i));
pp.display_smt2(std::cout, m_solver->get_assertion(n-1));
}
void solver::show_assertion_ids() {
#if 0
unsigned n = m_solver->get_num_assertions();
std::cerr << "assertion ids: ";
for (unsigned i = 0; i < n-1; ++i)
std::cerr << " " << m_solver->get_assertion(i)->get_id();
std::cerr << "\n";
#else
unsigned n = m_solver->get_num_assertions();
std::cerr << "assertion ids hash: ";
unsigned h = 0;
for (unsigned i = 0; i < n-1; ++i)
h += m_solver->get_assertion(i)->get_id();
std::cerr << h << "\n";
#endif
}
void include_ast_show(ast &a){
a.show();

64
src/duality/duality_wrapper.h
View file

@ -393,6 +393,7 @@ namespace Duality {
sort array_range() const;
};
class func_decl : public ast {
public:
func_decl() : ast() {}
@ -412,6 +413,7 @@ namespace Duality {
expr operator()(unsigned n, expr const * args) const;
expr operator()(const std::vector<expr> &args) const;
expr operator()() const;
expr operator()(expr const & a) const;
expr operator()(int a) const;
expr operator()(expr const & a1, expr const & a2) const;
@ -455,6 +457,8 @@ namespace Duality {
bool is_quantifier() const {return raw()->get_kind() == AST_QUANTIFIER;}
bool is_var() const {return raw()->get_kind() == AST_VAR;}
bool is_label (bool &pos,std::vector<symbol> &names) const ;
bool is_ground() const {return to_app(raw())->is_ground();}
bool has_quantifiers() const {return to_app(raw())->has_quantifiers();}
// operator Z3_app() const { assert(is_app()); return reinterpret_cast<Z3_app>(m_ast); }
func_decl decl() const {return func_decl(ctx(),to_app(raw())->get_decl());}
@ -554,6 +558,8 @@ namespace Duality {
expr simplify(params const & p) const;
expr qe_lite() const;
friend expr clone_quantifier(const expr &, const expr &);
friend expr clone_quantifier(const expr &q, const expr &b, const std::vector<expr> &patterns);
@ -593,6 +599,36 @@ namespace Duality {
};
typedef ::decl_kind pfrule;
class proof : public ast {
public:
proof(context & c):ast(c) {}
proof(context & c, ::proof *s):ast(c, s) {}
proof(proof const & s):ast(s) {}
operator ::proof*() const { return to_app(raw()); }
proof & operator=(proof const & s) { return static_cast<proof&>(ast::operator=(s)); }
pfrule rule() const {
::func_decl *d = to_app(raw())->get_decl();
return d->get_decl_kind();
}
unsigned num_prems() const {
return to_app(raw())->get_num_args() - 1;
}
expr conc() const {
return ctx().cook(to_app(raw())->get_arg(num_prems()));
}
proof prem(unsigned i) const {
return proof(ctx(),to_app(to_app(raw())->get_arg(i)));
}
void get_assumptions(std::vector<expr> &assumps);
};
#if 0
#if Z3_MAJOR_VERSION > 4 || Z3_MAJOR_VERSION == 4 && Z3_MINOR_VERSION >= 3
@ -691,6 +727,7 @@ namespace Duality {
}
void show() const;
void show_hash() const;
unsigned num_consts() const {return m_model.get()->get_num_constants();}
unsigned num_funcs() const {return m_model.get()->get_num_functions();}
@ -775,7 +812,7 @@ namespace Duality {
model the_model;
bool canceled;
public:
solver(context & c);
solver(context & c, bool extensional = false);
solver(context & c, ::solver *s):object(c),the_model(c) { m_solver = s; canceled = false;}
solver(solver const & s):object(s), the_model(s.the_model) { m_solver = s.m_solver; canceled = false;}
~solver() {
@ -867,6 +904,16 @@ namespace Duality {
if(m_solver)
m_solver->cancel();
}
unsigned get_scope_level(){return m_solver->get_scope_level();}
void show();
void show_assertion_ids();
proof get_proof(){
return proof(ctx(),m_solver->get_proof());
}
};
#if 0
@ -1144,6 +1191,9 @@ namespace Duality {
inline expr func_decl::operator()(const std::vector<expr> &args) const {
return operator()(args.size(),&args[0]);
}
inline expr func_decl::operator()() const {
return operator()(0,0);
}
inline expr func_decl::operator()(expr const & a) const {
return operator()(1,&a);
}
@ -1199,6 +1249,8 @@ namespace Duality {
inline expr getTerm(){return term;}
inline std::vector<expr> &getTerms(){return terms;}
inline std::vector<TermTree *> &getChildren(){
return children;
}
@ -1215,6 +1267,8 @@ namespace Duality {
}
inline void setTerm(expr t){term = t;}
inline void addTerm(expr t){terms.push_back(t);}
inline void setChildren(const std::vector<TermTree *> & _children){
children = _children;
@ -1231,6 +1285,7 @@ namespace Duality {
private:
expr term;
std::vector<expr> terms;
std::vector<TermTree *> children;
int num;
};
@ -1277,6 +1332,7 @@ namespace Duality {
void SetWeakInterpolants(bool weak);
void SetPrintToFile(const std::string &file_name);
const std::vector<expr> &GetInterpolationAxioms() {return theory;}
const char *profile();
private:
@ -1331,7 +1387,8 @@ namespace std {
class less<Duality::ast> {
public:
bool operator()(const Duality::ast &s, const Duality::ast &t) const {
return s.raw() < t.raw(); // s.raw()->get_id() < t.raw()->get_id();
// return s.raw() < t.raw();
return s.raw()->get_id() < t.raw()->get_id();
}
};
}
@ -1362,7 +1419,8 @@ namespace std {
class less<Duality::func_decl> {
public:
bool operator()(const Duality::func_decl &s, const Duality::func_decl &t) const {
return s.raw() < t.raw(); // s.raw()->get_id() < t.raw()->get_id();
// return s.raw() < t.raw();
return s.raw()->get_id() < t.raw()->get_id();
}
};
}

12
src/interp/iz3base.h
View file

@ -24,6 +24,16 @@ Revision History:
#include "iz3mgr.h"
#include "iz3scopes.h"
namespace hash_space {
template <>
class hash<func_decl *> {
public:
size_t operator()(func_decl * const &s) const {
return (size_t) s;
}
};
}
/* Base class for interpolators. Includes an AST manager and a scoping
object as bases. */
@ -182,6 +192,4 @@ class iz3base : public iz3mgr, public scopes {
#endif

7
src/interp/iz3foci.cpp
View file

@ -51,6 +51,13 @@ public:
typedef hash_map<foci2::ast,ast> NodeToAst;
NodeToAst node_to_ast; // maps Z3 ast's to foci expressions
// We only use this for FuncDeclToSymbol, which has no range destructor
struct symb_hash {
size_t operator()(const symb &s) const {
return (size_t) s;
}
};
typedef hash_map<symb,foci2::symb> FuncDeclToSymbol;
FuncDeclToSymbol func_decl_to_symbol; // maps Z3 func decls to symbols

2
src/interp/iz3hash.h
View file

@ -141,6 +141,7 @@ namespace std {
#ifndef WIN32
#if 0
namespace stl_ext {
template <class T>
class hash<T *> {
@ -150,6 +151,7 @@ namespace stl_ext {
}
};
}
#endif
#endif

65
src/interp/iz3interp.cpp
View file

@ -75,15 +75,16 @@ struct frame_reducer : public iz3mgr {
}
}
void get_frames(const std::vector<ast> &z3_preds,
void get_frames(const std::vector<std::vector<ast> >&z3_preds,
const std::vector<int> &orig_parents,
std::vector<ast> &assertions,
std::vector<std::vector<ast> >&assertions,
std::vector<int> &parents,
z3pf proof){
frames = z3_preds.size();
orig_parents_copy = orig_parents;
for(unsigned i = 0; i < z3_preds.size(); i++)
frame_map[z3_preds[i]] = i;
for(unsigned j = 0; j < z3_preds[i].size(); j++)
frame_map[z3_preds[i][j]] = i;
used_frames.resize(frames);
hash_set<ast> memo;
get_proof_assumptions_rec(proof,memo,used_frames);
@ -202,7 +203,7 @@ public:
}
void proof_to_interpolant(z3pf proof,
const std::vector<ast> &cnsts,
const std::vector<std::vector<ast> > &cnsts,
const std::vector<int> &parents,
std::vector<ast> &interps,
const std::vector<ast> &theory,
@ -212,11 +213,12 @@ public:
test_secondary(cnsts,parents,interps);
return;
#endif
profiling::timer_start("Interpolation prep");
// get rid of frames not used in proof
std::vector<ast> cnsts_vec;
std::vector<std::vector<ast> > cnsts_vec;
std::vector<int> parents_vec;
frame_reducer fr(*this);
fr.get_frames(cnsts,parents,cnsts_vec,parents_vec,proof);
@ -235,10 +237,7 @@ public:
#define BINARY_INTERPOLATION
#ifndef BINARY_INTERPOLATION
// create a translator
std::vector<std::vector<ast> > cnsts_vec_vec(cnsts_vec.size());
for(unsigned i = 0; i < cnsts_vec.size(); i++)
cnsts_vec_vec[i].push_back(cnsts_vec[i]);
iz3translation *tr = iz3translation::create(*this,sp,cnsts_vec_vec,parents_vec,theory);
iz3translation *tr = iz3translation::create(*this,sp,cnsts_vec,parents_vec,theory);
tr_killer.set(tr);
// set the translation options, if needed
@ -273,7 +272,8 @@ public:
std::vector<std::vector<ast> > cnsts_vec_vec(2);
for(unsigned j = 0; j < cnsts_vec.size(); j++){
bool is_A = the_base.in_range(j,rng);
cnsts_vec_vec[is_A ? 0 : 1].push_back(cnsts_vec[j]);
for(unsigned k = 0; k < cnsts_vec[j].size(); k++)
cnsts_vec_vec[is_A ? 0 : 1].push_back(cnsts_vec[j][k]);
}
killme<iz3translation> tr_killer_i;
@ -308,6 +308,19 @@ public:
}
void proof_to_interpolant(z3pf proof,
std::vector<ast> &cnsts,
const std::vector<int> &parents,
std::vector<ast> &interps,
const std::vector<ast> &theory,
interpolation_options_struct *options = 0
){
std::vector<std::vector<ast> > cnsts_vec(cnsts.size());
for(unsigned i = 0; i < cnsts.size(); i++)
cnsts_vec[i].push_back(cnsts[i]);
proof_to_interpolant(proof,cnsts_vec,parents,interps,theory,options);
}
// same as above, but represents the tree using an ast
void proof_to_interpolant(const z3pf &proof,
@ -322,7 +335,6 @@ public:
to_parents_vec_representation(_cnsts, tree, cnsts, parents, theory, pos_map);
//use the parents vector representation to compute interpolant
proof_to_interpolant(proof,cnsts,parents,interps,theory,options);
@ -397,6 +409,35 @@ void iz3interpolate(ast_manager &_m_manager,
interps[i] = itp.uncook(_interps[i]);
}
void iz3interpolate(ast_manager &_m_manager,
ast *proof,
const ::vector<ptr_vector<ast> > &cnsts,
const ::vector<int> &parents,
ptr_vector<ast> &interps,
const ptr_vector<ast> &theory,
interpolation_options_struct * options)
{
iz3interp itp(_m_manager);
if(options)
options->apply(itp);
std::vector<std::vector<iz3mgr::ast> > _cnsts(cnsts.size());
std::vector<int> _parents(parents.size());
std::vector<iz3mgr::ast> _interps;
std::vector<iz3mgr::ast> _theory(theory.size());
for(unsigned i = 0; i < cnsts.size(); i++)
for(unsigned j = 0; j < cnsts[i].size(); j++)
_cnsts[i].push_back(itp.cook(cnsts[i][j]));
for(unsigned i = 0; i < parents.size(); i++)
_parents[i] = parents[i];
for(unsigned i = 0; i < theory.size(); i++)
_theory[i] = itp.cook(theory[i]);
iz3mgr::ast _proof = itp.cook(proof);
itp.proof_to_interpolant(_proof,_cnsts,_parents,_interps,_theory,options);
interps.resize(_interps.size());
for(unsigned i = 0; i < interps.size(); i++)
interps[i] = itp.uncook(_interps[i]);
}
void iz3interpolate(ast_manager &_m_manager,
ast *proof,
const ptr_vector<ast> &cnsts,
@ -461,5 +502,3 @@ void interpolation_options_struct::apply(iz3base &b){
b.set_option((*it).first,(*it).second);
}

10
src/interp/iz3interp.h
View file

@ -56,6 +56,16 @@ void iz3interpolate(ast_manager &_m_manager,
const ptr_vector<ast> &theory,
interpolation_options_struct * options = 0);
/* Same as above, but each constraint is a vector of formulas. */
void iz3interpolate(ast_manager &_m_manager,
ast *proof,
const vector<ptr_vector<ast> > &cnsts,
const ::vector<int> &parents,
ptr_vector<ast> &interps,
const ptr_vector<ast> &theory,
interpolation_options_struct * options = 0);
/* Compute an interpolant from a proof. This version uses the ast
representation, for compatibility with the new API. */

42
src/interp/iz3mgr.cpp
View file

@ -190,7 +190,7 @@ iz3mgr::ast iz3mgr::make_quant(opr op, const std::vector<ast> &bvs, ast &body){
op == Forall,
names.size(), &types[0], &names[0], abs_body.get(),
0,
symbol(),
symbol("itp"),
symbol(),
0, 0,
0, 0
@ -761,6 +761,19 @@ int iz3mgr::occurs_in(ast var, ast e){
}
bool iz3mgr::solve_arith(const ast &v, const ast &x, const ast &y, ast &res){
if(op(x) == Plus){
int n = num_args(x);
for(int i = 0; i < n; i++){
if(arg(x,i) == v){
res = z3_simplify(make(Sub, y, make(Sub, x, v)));
return true;
}
}
}
return false;
}
// find a controlling equality for a given variable v in a term
// a controlling equality is of the form v = t, which, being
// false would force the formula to have the specifid truth value
@ -774,6 +787,9 @@ iz3mgr::ast iz3mgr::cont_eq(stl_ext::hash_set<ast> &cont_eq_memo, bool truth, as
if(!truth && op(e) == Equal){
if(arg(e,0) == v) return(arg(e,1));
if(arg(e,1) == v) return(arg(e,0));
ast res;
if(solve_arith(v,arg(e,0),arg(e,1),res)) return res;
if(solve_arith(v,arg(e,1),arg(e,0),res)) return res;
}
if((!truth && op(e) == And) || (truth && op(e) == Or)){
int nargs = num_args(e);
@ -815,11 +831,35 @@ iz3mgr::ast iz3mgr::subst(ast var, ast t, ast e){
return subst(memo,var,t,e);
}
iz3mgr::ast iz3mgr::subst(stl_ext::hash_map<ast,ast> &subst_memo,ast e){
std::pair<ast,ast> foo(e,ast());
std::pair<hash_map<ast,ast>::iterator,bool> bar = subst_memo.insert(foo);
ast &res = bar.first->second;
if(bar.second){
int nargs = num_args(e);
std::vector<ast> args(nargs);
for(int i = 0; i < nargs; i++)
args[i] = subst(subst_memo,arg(e,i));
opr f = op(e);
if(f == Equal && args[0] == args[1]) res = mk_true();
else res = clone(e,args);
}
return res;
}
// apply a quantifier to a formula, with some optimizations
// 1) bound variable does not occur -> no quantifier
// 2) bound variable must be equal to some term -> substitute
iz3mgr::ast iz3mgr::apply_quant(opr quantifier, ast var, ast e){
if((quantifier == Forall && op(e) == And)
|| (quantifier == Exists && op(e) == Or)){
int n = num_args(e);
std::vector<ast> args(n);
for(int i = 0; i < n; i++)
args[i] = apply_quant(quantifier,var,arg(e,i));
return make(op(e),args);
}
if(!occurs_in(var,e))return e;
hash_set<ast> cont_eq_memo;
ast cterm = cont_eq(cont_eq_memo, quantifier == Forall, var, e);

19
src/interp/iz3mgr.h
View file

@ -65,7 +65,7 @@ class ast_i {
return _ast == other._ast;
}
bool lt(const ast_i &other) const {
return _ast < other._ast;
return _ast->get_id() < other._ast->get_id();
}
friend bool operator==(const ast_i &x, const ast_i&y){
return x.eq(y);
@ -76,7 +76,7 @@ class ast_i {
friend bool operator<(const ast_i &x, const ast_i&y){
return x.lt(y);
}
size_t hash() const {return (size_t)_ast;}
size_t hash() const {return _ast->get_id();}
bool null() const {return !_ast;}
};
@ -140,7 +140,8 @@ namespace std {
class less<ast_r> {
public:
bool operator()(const ast_r &s, const ast_r &t) const {
return s.raw() < t.raw(); // s.raw()->get_id() < t.raw()->get_id();
// return s.raw() < t.raw();
return s.raw()->get_id() < t.raw()->get_id();
}
};
}
@ -359,6 +360,12 @@ class iz3mgr {
return fid == m().get_basic_family_id() && k == BOOL_SORT;
}
bool is_array_type(type t){
family_id fid = to_sort(t)->get_family_id();
decl_kind k = to_sort(t)->get_decl_kind();
return fid == m_array_fid && k == ARRAY_SORT;
}
type get_range_type(symb s){
return to_func_decl(s)->get_range();
}
@ -631,6 +638,9 @@ class iz3mgr {
ast subst(ast var, ast t, ast e);
// apply a substitution defined by a map
ast subst(stl_ext::hash_map<ast,ast> &map, ast e);
// apply a quantifier to a formula, with some optimizations
// 1) bound variable does not occur -> no quantifier
// 2) bound variable must be equal to some term -> substitute
@ -683,13 +693,14 @@ class iz3mgr {
protected:
ast_manager &m_manager;
int occurs_in(ast var, ast e);
private:
ast mki(family_id fid, decl_kind sk, int n, raw_ast **args);
ast make(opr op, int n, raw_ast **args);
ast make(symb sym, int n, raw_ast **args);
int occurs_in1(stl_ext::hash_map<ast,bool> &occurs_in_memo, ast var, ast e);
int occurs_in(ast var, ast e);
bool solve_arith(const ast &v, const ast &x, const ast &y, ast &res);
ast cont_eq(stl_ext::hash_set<ast> &cont_eq_memo, bool truth, ast v, ast e);
ast subst(stl_ext::hash_map<ast,ast> &subst_memo, ast var, ast t, ast e);

14
src/interp/iz3pp.cpp
View file

@ -40,6 +40,20 @@ Revision History:
using namespace stl_ext;
#endif
#ifndef WIN32
// We promise not to use this for hash_map with range destructor
namespace stl_ext {
template <>
class hash<expr *> {
public:
size_t operator()(const expr *p) const {
return (size_t) p;
}
};
}
#endif
// TBD: algebraic data-types declarations will not be printed.
class free_func_visitor {
ast_manager& m;

628
src/interp/iz3proof_itp.cpp
View file

@ -118,6 +118,30 @@ class iz3proof_itp_impl : public iz3proof_itp {
where t is an arbitrary term */
symb rewrite_B;
/* a normalization step is of the form (lhs=rhs) : proof, where "proof"
is a proof of lhs=rhs and lhs is a mixed term. If rhs is a mixed term
then it must have a greater index than lhs. */
symb normal_step;
/* A chain of normalization steps is either "true" (the null chain)
or normal_chain(<step> <tail>), where step is a normalization step
and tail is a normalization chain. The lhs of <step> must have
a less term index than any lhs in the chain. Moreover, the rhs of
<step> may not occur as the lhs of step in <tail>. If we wish to
add lhs=rhs to the beginning of <tail> and rhs=rhs' occurs in <tail>
we must apply transitivity, transforming <step> to lhs=rhs'. */
symb normal_chain;
/* If p is a proof of Q and c is a normalization chain, then normal(p,c)
is a proof of Q(c) (that is, Q with all substitutions in c performed). */
symb normal;
/** Stand-ins for quantifiers */
symb sforall, sexists;
ast get_placeholder(ast t){
hash_map<ast,ast>::iterator it = placeholders.find(t);
@ -209,6 +233,10 @@ class iz3proof_itp_impl : public iz3proof_itp {
ast neg_pivot_lit = mk_not(atom);
if(op(pivot) != Not)
std::swap(premise1,premise2);
if(op(pivot) == Equal && op(arg(pivot,0)) == Select && op(arg(pivot,1)) == Select){
neg_pivot_lit = mk_not(neg_pivot_lit);
std::swap(premise1,premise2);
}
return resolve_arith_rec1(memo, neg_pivot_lit, premise1, premise2);
}
@ -333,7 +361,13 @@ class iz3proof_itp_impl : public iz3proof_itp {
break;
}
default:
res = itp2;
{
symb s = sym(itp2);
if(s == sforall || s == sexists)
res = make(s,arg(itp2,0),resolve_arith_rec2(memo, pivot1, conj1, arg(itp2,1)));
else
res = itp2;
}
}
}
return res;
@ -363,7 +397,13 @@ class iz3proof_itp_impl : public iz3proof_itp {
break;
}
default:
res = itp1;
{
symb s = sym(itp1);
if(s == sforall || s == sexists)
res = make(s,arg(itp1,0),resolve_arith_rec1(memo, neg_pivot_lit, arg(itp1,1), itp2));
else
res = itp1;
}
}
}
return res;
@ -451,7 +491,12 @@ class iz3proof_itp_impl : public iz3proof_itp {
hash_map<ast,ast> simplify_memo;
ast simplify(const ast &t){
return simplify_rec(t);
ast res = normalize(simplify_rec(t));
#ifdef BOGUS_QUANTS
if(localization_vars.size())
res = add_quants(z3_simplify(res));
#endif
return res;
}
ast simplify_rec(const ast &e){
@ -521,12 +566,18 @@ class iz3proof_itp_impl : public iz3proof_itp {
throw cannot_simplify();
}
bool is_normal_ineq(const ast &ineq){
if(sym(ineq) == normal)
return is_ineq(arg(ineq,0));
return is_ineq(ineq);
}
ast simplify_sum(std::vector<ast> &args){
ast cond = mk_true();
ast Aproves = mk_true(), Bproves = mk_true();
ast ineq = args[0];
if(!is_ineq(ineq)) throw cannot_simplify();
sum_cond_ineq(ineq,cond,args[1],args[2]);
return my_implies(cond,ineq);
if(!is_normal_ineq(ineq)) throw cannot_simplify();
sum_cond_ineq(ineq,args[1],args[2],Aproves,Bproves);
return my_and(Aproves,my_implies(Bproves,ineq));
}
ast simplify_rotate_sum(const ast &pl, const ast &pf){
@ -539,29 +590,42 @@ class iz3proof_itp_impl : public iz3proof_itp {
return sym(chain) == concat;
}
ast ineq_from_chain(const ast &chain, ast &cond){
if(is_rewrite_chain(chain)){
ast last = chain_last(chain);
ast rest = chain_rest(chain);
if(is_true(rest) && is_rewrite_side(LitA,last)
&& is_true(rewrite_lhs(last))){
cond = my_and(cond,rewrite_cond(last));
return rewrite_rhs(last);
}
if(is_rewrite_side(LitB,last) && is_true(rewrite_cond(last)))
return ineq_from_chain(rest,cond);
#if 0
ast ineq_from_chain_simple(const ast &chain, ast &cond){
if(is_true(chain))
return chain;
ast last = chain_last(chain);
ast rest = chain_rest(chain);
if(is_true(rest) && is_rewrite_side(LitA,last)
&& is_true(rewrite_lhs(last))){
cond = my_and(cond,rewrite_cond(last));
return rewrite_rhs(last);
}
if(is_rewrite_side(LitB,last) && is_true(rewrite_cond(last)))
return ineq_from_chain_simple(rest,cond);
return chain;
}
#endif
ast ineq_from_chain(const ast &chain, ast &Aproves, ast &Bproves){
if(is_rewrite_chain(chain))
return rewrite_chain_to_normal_ineq(chain,Aproves,Bproves);
return chain;
}
void sum_cond_ineq(ast &ineq, ast &cond, const ast &coeff2, const ast &ineq2){
void sum_cond_ineq(ast &ineq, const ast &coeff2, const ast &ineq2, ast &Aproves, ast &Bproves){
opr o = op(ineq2);
if(o == Implies){
sum_cond_ineq(ineq,cond,coeff2,arg(ineq2,1));
cond = my_and(cond,arg(ineq2,0));
sum_cond_ineq(ineq,coeff2,arg(ineq2,1),Aproves,Bproves);
Bproves = my_and(Bproves,arg(ineq2,0));
}
else {
ast the_ineq = ineq_from_chain(ineq2,cond);
ast the_ineq = ineq_from_chain(ineq2,Aproves,Bproves);
if(sym(ineq) == normal || sym(the_ineq) == normal){
sum_normal_ineq(ineq,coeff2,the_ineq,Aproves,Bproves);
return;
}
if(is_ineq(the_ineq))
linear_comb(ineq,coeff2,the_ineq);
else
@ -569,6 +633,27 @@ class iz3proof_itp_impl : public iz3proof_itp {
}
}
void destruct_normal(const ast &pf, ast &p, ast &n){
if(sym(pf) == normal){
p = arg(pf,0);
n = arg(pf,1);
}
else {
p = pf;
n = mk_true();
}
}
void sum_normal_ineq(ast &ineq, const ast &coeff2, const ast &ineq2, ast &Aproves, ast &Bproves){
ast in1,in2,n1,n2;
destruct_normal(ineq,in1,n1);
destruct_normal(ineq2,in2,n2);
ast dummy1, dummy2;
sum_cond_ineq(in1,coeff2,in2,dummy1,dummy2);
n1 = merge_normal_chains(n1,n2, Aproves, Bproves);
ineq = make_normal(in1,n1);
}
bool is_ineq(const ast &ineq){
opr o = op(ineq);
if(o == Not) o = op(arg(ineq,0));
@ -577,6 +662,12 @@ class iz3proof_itp_impl : public iz3proof_itp {
// divide both sides of inequality by a non-negative integer divisor
ast idiv_ineq(const ast &ineq1, const ast &divisor){
if(sym(ineq1) == normal){
ast in1,n1;
destruct_normal(ineq1,in1,n1);
in1 = idiv_ineq(in1,divisor);
return make_normal(in1,n1);
}
if(divisor == make_int(rational(1)))
return ineq1;
ast ineq = ineq1;
@ -585,17 +676,23 @@ class iz3proof_itp_impl : public iz3proof_itp {
return make(op(ineq),mk_idiv(arg(ineq,0),divisor),mk_idiv(arg(ineq,1),divisor));
}
ast rotate_sum_rec(const ast &pl, const ast &pf, ast &cond, ast &ineq){
ast rotate_sum_rec(const ast &pl, const ast &pf, ast &Bproves, ast &ineq){
if(pf == pl)
return my_implies(cond,simplify_ineq(ineq));
return my_implies(Bproves,simplify_ineq(ineq));
if(op(pf) == Uninterpreted && sym(pf) == sum){
if(arg(pf,2) == pl){
sum_cond_ineq(ineq,cond,make_int("1"),arg(pf,0));
ast Aproves = mk_true();
sum_cond_ineq(ineq,make_int("1"),arg(pf,0),Aproves,Bproves);
if(!is_true(Aproves))
throw "help!";
ineq = idiv_ineq(ineq,arg(pf,1));
return my_implies(cond,ineq);
return my_implies(Bproves,ineq);
}
sum_cond_ineq(ineq,cond,arg(pf,1),arg(pf,2));
return rotate_sum_rec(pl,arg(pf,0),cond,ineq);
ast Aproves = mk_true();
sum_cond_ineq(ineq,arg(pf,1),arg(pf,2),Aproves,Bproves);
if(!is_true(Aproves))
throw "help!";
return rotate_sum_rec(pl,arg(pf,0),Bproves,ineq);
}
throw cannot_simplify();
}
@ -605,28 +702,30 @@ class iz3proof_itp_impl : public iz3proof_itp {
ast equality = arg(neg_equality,0);
ast x = arg(equality,0);
ast y = arg(equality,1);
ast cond1 = mk_true();
ast xleqy = round_ineq(ineq_from_chain(arg(pf,1),cond1));
ast yleqx = round_ineq(ineq_from_chain(arg(pf,2),cond1));
ast Aproves1 = mk_true(), Bproves1 = mk_true();
ast xleqy = round_ineq(ineq_from_chain(arg(pf,1),Aproves1,Bproves1));
ast yleqx = round_ineq(ineq_from_chain(arg(pf,2),Aproves1,Bproves1));
ast ineq1 = make(Leq,make_int("0"),make_int("0"));
sum_cond_ineq(ineq1,cond1,make_int("-1"),xleqy);
sum_cond_ineq(ineq1,cond1,make_int("-1"),yleqx);
cond1 = my_and(cond1,z3_simplify(ineq1));
ast cond2 = mk_true();
sum_cond_ineq(ineq1,make_int("-1"),xleqy,Aproves1,Bproves1);
sum_cond_ineq(ineq1,make_int("-1"),yleqx,Aproves1,Bproves1);
Bproves1 = my_and(Bproves1,z3_simplify(ineq1));
ast Aproves2 = mk_true(), Bproves2 = mk_true();
ast ineq2 = make(Leq,make_int("0"),make_int("0"));
sum_cond_ineq(ineq2,cond2,make_int("1"),xleqy);
sum_cond_ineq(ineq2,cond2,make_int("1"),yleqx);
cond2 = z3_simplify(ineq2);
sum_cond_ineq(ineq2,make_int("1"),xleqy,Aproves2,Bproves2);
sum_cond_ineq(ineq2,make_int("1"),yleqx,Aproves2,Bproves2);
Bproves2 = z3_simplify(ineq2);
if(!is_true(Aproves1) || !is_true(Aproves2))
throw "help!";
if(get_term_type(x) == LitA){
ast iter = z3_simplify(make(Plus,x,get_ineq_rhs(xleqy)));
ast rewrite1 = make_rewrite(LitA,top_pos,cond1,make(Equal,x,iter));
ast rewrite2 = make_rewrite(LitB,top_pos,cond2,make(Equal,iter,y));
ast rewrite1 = make_rewrite(LitA,top_pos,Bproves1,make(Equal,x,iter));
ast rewrite2 = make_rewrite(LitB,top_pos,Bproves2,make(Equal,iter,y));
return chain_cons(chain_cons(mk_true(),rewrite1),rewrite2);
}
if(get_term_type(y) == LitA){
ast iter = z3_simplify(make(Plus,y,get_ineq_rhs(yleqx)));
ast rewrite2 = make_rewrite(LitA,top_pos,cond1,make(Equal,iter,y));
ast rewrite1 = make_rewrite(LitB,top_pos,cond2,make(Equal,x,iter));
ast rewrite2 = make_rewrite(LitA,top_pos,Bproves1,make(Equal,iter,y));
ast rewrite1 = make_rewrite(LitB,top_pos,Bproves2,make(Equal,x,iter));
return chain_cons(chain_cons(mk_true(),rewrite1),rewrite2);
}
throw cannot_simplify();
@ -649,11 +748,18 @@ class iz3proof_itp_impl : public iz3proof_itp {
ast equa = sep_cond(arg(pf,0),cond);
if(is_equivrel_chain(equa)){
ast lhs,rhs; eq_from_ineq(arg(neg_equality,0),lhs,rhs); // get inequality we need to prove
ast ineqs= chain_ineqs(op(arg(neg_equality,0)),LitA,equa,lhs,rhs); // chain must be from lhs to rhs
cond = my_and(cond,chain_conditions(LitA,equa));
ast Bconds = chain_conditions(LitB,equa);
if(is_true(Bconds) && op(ineqs) != And)
return my_implies(cond,ineqs);
LitType lhst = get_term_type(lhs), rhst = get_term_type(rhs);
if(lhst != LitMixed && rhst != LitMixed){
ast ineqs= chain_ineqs(op(arg(neg_equality,0)),LitA,equa,lhs,rhs); // chain must be from lhs to rhs
cond = my_and(cond,chain_conditions(LitA,equa));
ast Bconds = z3_simplify(chain_conditions(LitB,equa));
if(is_true(Bconds) && op(ineqs) != And)
return my_implies(cond,ineqs);
}
else {
ast itp = make(Leq,make_int(rational(0)),make_int(rational(0)));
return make_normal(itp,cons_normal(fix_normal(lhs,rhs,equa),mk_true()));
}
}
}
throw cannot_simplify();
@ -757,11 +863,57 @@ class iz3proof_itp_impl : public iz3proof_itp {
chain = concat_rewrite_chain(chain,split[1]);
}
}
else // if not an equivalence, must be of form T <-> pred
else { // if not an equivalence, must be of form T <-> pred
chain = concat_rewrite_chain(P,PeqQ);
}
return chain;
}
void get_subterm_normals(const ast &ineq1, const ast &ineq2, const ast &chain, ast &normals,
const ast &pos, hash_set<ast> &memo, ast &Aproves, ast &Bproves){
opr o1 = op(ineq1);
opr o2 = op(ineq2);
if(o1 == Not || o1 == Leq || o1 == Lt || o1 == Geq || o1 == Gt || o1 == Plus || o1 == Times){
int n = num_args(ineq1);
if(o2 != o1 || num_args(ineq2) != n)
throw "bad inequality rewriting";
for(int i = 0; i < n; i++){
ast new_pos = add_pos_to_end(pos,i);
get_subterm_normals(arg(ineq1,i), arg(ineq2,i), chain, normals, new_pos, memo, Aproves, Bproves);
}
}
else if(get_term_type(ineq2) == LitMixed && memo.find(ineq2) == memo.end()){
memo.insert(ineq2);
ast sub_chain = extract_rewrites(chain,pos);
if(is_true(sub_chain))
throw "bad inequality rewriting";
ast new_normal = make_normal_step(ineq2,ineq1,reverse_chain(sub_chain));
normals = merge_normal_chains(normals,cons_normal(new_normal,mk_true()), Aproves, Bproves);
}
}
ast rewrite_chain_to_normal_ineq(const ast &chain, ast &Aproves, ast &Bproves){
ast tail, pref = get_head_chain(chain,tail,false); // pref is x=y, tail is x=y -> x'=y'
ast head = chain_last(pref);
ast ineq1 = rewrite_rhs(head);
ast ineq2 = apply_rewrite_chain(ineq1,tail);
ast nc = mk_true();
hash_set<ast> memo;
get_subterm_normals(ineq1,ineq2,tail,nc,top_pos,memo, Aproves, Bproves);
ast itp;
if(is_rewrite_side(LitA,head)){
itp = ineq1;
ast mc = z3_simplify(chain_side_proves(LitB,pref));
Bproves = my_and(Bproves,mc);
}
else {
itp = make(Leq,make_int(rational(0)),make_int(rational(0)));
ast mc = z3_simplify(chain_side_proves(LitA,pref));
Aproves = my_and(Aproves,mc);
}
return make_normal(itp,nc);
}
/* Given a chain rewrite chain deriving not P and a rewrite chain deriving P, return an interpolant. */
ast contra_chain(const ast &neg_chain, const ast &pos_chain){
// equality is a special case. we use the derivation of x=y to rewrite not(x=y) to not(y=y)
@ -790,11 +942,18 @@ class iz3proof_itp_impl : public iz3proof_itp {
}
ast simplify_modpon(const std::vector<ast> &args){
ast cond = mk_true();
ast chain = simplify_modpon_fwd(args,cond);
ast Q2 = sep_cond(args[2],cond);
ast interp = is_negation_chain(chain) ? contra_chain(chain,Q2) : contra_chain(Q2,chain);
return my_implies(cond,interp);
ast Aproves = mk_true(), Bproves = mk_true();
ast chain = simplify_modpon_fwd(args,Bproves);
ast Q2 = sep_cond(args[2],Bproves);
ast interp;
if(is_normal_ineq(Q2)){ // inequalities are special
ast nQ2 = rewrite_chain_to_normal_ineq(chain,Aproves,Bproves);
sum_cond_ineq(nQ2,make_int(rational(1)),Q2,Aproves,Bproves);
interp = normalize(nQ2);
}
else
interp = is_negation_chain(chain) ? contra_chain(chain,Q2) : contra_chain(Q2,chain);
return my_and(Aproves,my_implies(Bproves,interp));
}
@ -1035,6 +1194,12 @@ class iz3proof_itp_impl : public iz3proof_itp {
return make(add_pos,make_int(rational(arg)),pos);
}
ast add_pos_to_end(const ast &pos, int i){
if(pos == top_pos)
return pos_add(i,pos);
return make(add_pos,arg(pos,0),add_pos_to_end(arg(pos,1),i));
}
/* return the argument number of position, if not top */
int pos_arg(const ast &pos){
rational r;
@ -1170,6 +1335,10 @@ class iz3proof_itp_impl : public iz3proof_itp {
return make(sym(rew),pos_add(apos,arg(rew,0)),arg(rew,1),arg(rew,2));
}
ast rewrite_pos_set(const ast &pos, const ast &rew){
return make(sym(rew),pos,arg(rew,1),arg(rew,2));
}
ast rewrite_up(const ast &rew){
return make(sym(rew),arg(arg(rew,0),1),arg(rew,1),arg(rew,2));
}
@ -1317,6 +1486,28 @@ class iz3proof_itp_impl : public iz3proof_itp {
split_chain_rec(chain,res);
}
ast extract_rewrites(const ast &chain, const ast &pos){
if(is_true(chain))
return chain;
ast last = chain_last(chain);
ast rest = chain_rest(chain);
ast new_rest = extract_rewrites(rest,pos);
ast p1 = rewrite_pos(last);
ast diff;
switch(pos_diff(p1,pos,diff)){
case -1: {
ast new_last = rewrite_pos_set(diff, last);
return chain_cons(new_rest,new_last);
}
case 1:
if(rewrite_lhs(last) != rewrite_rhs(last))
throw "bad rewrite chain";
break;
default:;
}
return new_rest;
}
ast down_chain(const ast &chain){
ast split[2];
split_chain(chain,split);
@ -1381,7 +1572,7 @@ class iz3proof_itp_impl : public iz3proof_itp {
// ast s = ineq_to_lhs(ineq);
// ast srhs = arg(s,1);
ast srhs = arg(ineq,0);
if(op(srhs) == Plus && num_args(srhs) == 2){
if(op(srhs) == Plus && num_args(srhs) == 2 && arg(ineq,1) == make_int(rational(0))){
lhs = arg(srhs,0);
rhs = arg(srhs,1);
// if(op(lhs) == Times)
@ -1393,6 +1584,11 @@ class iz3proof_itp_impl : public iz3proof_itp {
return;
}
}
if(op(ineq) == Leq || op(ineq) == Geq){
lhs = srhs;
rhs = arg(ineq,1);
return;
}
throw "bad ineq";
}
@ -1404,7 +1600,204 @@ class iz3proof_itp_impl : public iz3proof_itp {
return chain_cons(rest,last);
}
ast apply_rewrite_chain(const ast &t, const ast &chain){
if(is_true(chain))
return t;
ast last = chain_last(chain);
ast rest = chain_rest(chain);
ast mid = apply_rewrite_chain(t,rest);
ast res = subst_in_pos(mid,rewrite_pos(last),rewrite_rhs(last));
return res;
}
ast drop_rewrites(LitType t, const ast &chain, ast &remainder){
if(!is_true(chain)){
ast last = chain_last(chain);
ast rest = chain_rest(chain);
if(is_rewrite_side(t,last)){
ast res = drop_rewrites(t,rest,remainder);
remainder = chain_cons(remainder,last);
return res;
}
}
remainder = mk_true();
return chain;
}
// Normalization chains
ast cons_normal(const ast &first, const ast &rest){
return make(normal_chain,first,rest);
}
ast normal_first(const ast &t){
return arg(t,0);
}
ast normal_rest(const ast &t){
return arg(t,1);
}
ast normal_lhs(const ast &t){
return arg(arg(t,0),0);
}
ast normal_rhs(const ast &t){
return arg(arg(t,0),1);
}
ast normal_proof(const ast &t){
return arg(t,1);
}
ast make_normal_step(const ast &lhs, const ast &rhs, const ast &proof){
return make(normal_step,make_equiv(lhs,rhs),proof);
}
ast make_normal(const ast &ineq, const ast &nrml){
if(!is_ineq(ineq))
throw "what?";
return make(normal,ineq,nrml);
}
ast fix_normal(const ast &lhs, const ast &rhs, const ast &proof){
LitType rhst = get_term_type(rhs);
if(rhst != LitMixed || ast_id(lhs) < ast_id(rhs))
return make_normal_step(lhs,rhs,proof);
else
return make_normal_step(rhs,lhs,reverse_chain(proof));
}
ast chain_side_proves(LitType side, const ast &chain){
LitType other_side = side == LitA ? LitB : LitA;
return my_and(chain_conditions(other_side,chain),my_implies(chain_conditions(side,chain),chain_formulas(side,chain)));
}
// Merge two normalization chains
ast merge_normal_chains_rec(const ast &chain1, const ast &chain2, hash_map<ast,ast> &trans, ast &Aproves, ast &Bproves){
if(is_true(chain1))
return chain2;
if(is_true(chain2))
return chain1;
ast f1 = normal_first(chain1);
ast f2 = normal_first(chain2);
ast lhs1 = normal_lhs(f1);
ast lhs2 = normal_lhs(f2);
int id1 = ast_id(lhs1);
int id2 = ast_id(lhs2);
if(id1 < id2) return cons_normal(f1,merge_normal_chains_rec(normal_rest(chain1),chain2,trans,Aproves,Bproves));
if(id2 < id1) return cons_normal(f2,merge_normal_chains_rec(chain1,normal_rest(chain2),trans,Aproves,Bproves));
ast rhs1 = normal_rhs(f1);
ast rhs2 = normal_rhs(f2);
LitType t1 = get_term_type(rhs1);
LitType t2 = get_term_type(rhs2);
int tid1 = ast_id(rhs1);
int tid2 = ast_id(rhs2);
ast pf1 = normal_proof(f1);
ast pf2 = normal_proof(f2);
ast new_normal;
if(t1 == LitMixed && (t2 != LitMixed || tid2 > tid1)){
ast new_proof = concat_rewrite_chain(reverse_chain(pf1),pf2);
new_normal = f2;
trans[rhs1] = make_normal_step(rhs1,rhs2,new_proof);
}
else if(t2 == LitMixed && (t1 != LitMixed || tid1 > tid2))
return merge_normal_chains_rec(chain2,chain1,trans,Aproves,Bproves);
else if(t1 == LitA && t2 == LitB){
ast new_proof = concat_rewrite_chain(reverse_chain(pf1),pf2);
ast Bproof, Aproof = drop_rewrites(LitB,new_proof,Bproof);
ast mcA = chain_side_proves(LitB,Aproof);
Bproves = my_and(Bproves,mcA);
ast mcB = chain_side_proves(LitA,Bproof);
Aproves = my_and(Aproves,mcB);
ast rep = apply_rewrite_chain(rhs1,Aproof);
new_proof = concat_rewrite_chain(pf1,Aproof);
new_normal = make_normal_step(rhs1,rep,new_proof);
}
else if(t1 == LitA && t2 == LitB)
return merge_normal_chains_rec(chain2,chain1,trans,Aproves,Bproves);
else if(t1 == LitA) {
ast new_proof = concat_rewrite_chain(reverse_chain(pf1),pf2);
ast mc = chain_side_proves(LitB,new_proof);
Bproves = my_and(Bproves,mc);
new_normal = f1; // choice is arbitrary
}
else { /* t1 = t2 = LitB */
ast new_proof = concat_rewrite_chain(reverse_chain(pf1),pf2);
ast mc = chain_side_proves(LitA,new_proof);
Aproves = my_and(Aproves,mc);
new_normal = f1; // choice is arbitrary
}
return cons_normal(new_normal,merge_normal_chains_rec(normal_rest(chain1),normal_rest(chain2),trans,Aproves,Bproves));
}
ast trans_normal_chain(const ast &chain, hash_map<ast,ast> &trans){
if(is_true(chain))
return chain;
ast f = normal_first(chain);
ast r = normal_rest(chain);
ast rhs = normal_rhs(f);
hash_map<ast,ast>::iterator it = trans.find(rhs);
ast new_normal;
if(it != trans.end()){
const ast &f2 = it->second;
ast pf = concat_rewrite_chain(normal_proof(f),normal_proof(f2));
new_normal = make_normal_step(normal_lhs(f),normal_rhs(f2),pf);
}
else
new_normal = f;
return cons_normal(new_normal,trans_normal_chain(r,trans));
}
ast merge_normal_chains(const ast &chain1, const ast &chain2, ast &Aproves, ast &Bproves){
hash_map<ast,ast> trans;
ast res = merge_normal_chains_rec(chain1,chain2,trans,Aproves,Bproves);
res = trans_normal_chain(res,trans);
return res;
}
bool destruct_cond_ineq(ast t, ast &Aproves, ast &Bproves, ast&ineq){
if(op(t) == And){
Aproves = arg(t,0);
t = arg(t,1);
}
else
Aproves = mk_true();
if(op(t) == Implies){
Bproves = arg(t,0);
t = arg(t,1);
}
else
Bproves = mk_true();
if(is_normal_ineq(t)){
ineq = t;
return true;
}
return false;
}
ast cons_cond_ineq(const ast &Aproves, const ast &Bproves, const ast &ineq){
return my_and(Aproves,my_implies(Bproves,ineq));
}
ast normalize(const ast &ct){
ast Aproves,Bproves,t;
if(!destruct_cond_ineq(ct,Aproves,Bproves,t))
return ct;
if(sym(t) != normal)
return ct;
ast chain = arg(t,1);
hash_map<ast,ast> map;
for(ast c = chain; !is_true(c); c = normal_rest(c)){
ast first = normal_first(c);
ast lhs = normal_lhs(first);
ast rhs = normal_rhs(first);
map[lhs] = rhs;
}
ast res = subst(map,arg(t,0));
return cons_cond_ineq(Aproves,Bproves,res);
}
/** Make an assumption node. The given clause is assumed in the given frame. */
virtual node make_assumption(int frame, const std::vector<ast> &assumption){
if(!weak){
@ -1522,9 +1915,22 @@ class iz3proof_itp_impl : public iz3proof_itp {
return itp;
}
ast capture_localization(ast e){
// #define CAPTURE_LOCALIZATION
#ifdef CAPTURE_LOCALIZATION
for(int i = localization_vars.size() - 1; i >= 0; i--){
LocVar &lv = localization_vars[i];
if(occurs_in(lv.var,e)){
symb q = (pv->in_range(lv.frame,rng)) ? sexists : sforall;
e = make(q,make(Equal,lv.var,lv.term),e); // use Equal because it is polymorphic
}
}
#endif
return e;
}
/** Make an axiom node. The conclusion must be an instance of an axiom. */
virtual node make_axiom(const std::vector<ast> &conclusion){
prover::range frng = pv->range_full();
virtual node make_axiom(const std::vector<ast> &conclusion, prover::range frng){
int nargs = conclusion.size();
std::vector<ast> largs(nargs);
std::vector<ast> eqs;
@ -1546,7 +1952,11 @@ class iz3proof_itp_impl : public iz3proof_itp {
for(unsigned i = 0; i < eqs.size(); i++)
itp = make_mp(eqs[i],itp,pfs[i]);
return itp;
return capture_localization(itp);
}
virtual node make_axiom(const std::vector<ast> &conclusion){
return make_axiom(conclusion,pv->range_full());
}
/** Make a Contra node. This rule takes a derivation of the form
@ -1939,6 +2349,8 @@ class iz3proof_itp_impl : public iz3proof_itp {
*/
ast make_refl(const ast &e){
if(get_term_type(e) == LitA)
return mk_false();
return mk_true(); // TODO: is this right?
}
@ -1972,7 +2384,8 @@ class iz3proof_itp_impl : public iz3proof_itp {
int nargs = num_args(e);
if(nargs > 0 /* && (!is_local(e) || flo <= hi || fhi >= lo) */){
prover::range frng = rng;
if(op(e) == Uninterpreted){
opr o = op(e);
if(o == Uninterpreted){
symb f = sym(e);
prover::range srng = pv->sym_range(f);
if(pv->ranges_intersect(srng,rng)) // localize to desired range if possible
@ -1980,6 +2393,9 @@ class iz3proof_itp_impl : public iz3proof_itp {
else
frng = srng; // this term will be localized
}
else if(o == Plus || o == Times){ // don't want bound variables inside arith ops
frng = erng; // this term will be localized
}
std::vector<ast> largs(nargs);
std::vector<ast> eqs;
std::vector<ast> pfs;
@ -2006,6 +2422,9 @@ class iz3proof_itp_impl : public iz3proof_itp {
if(pv->ranges_intersect(pv->ast_scope(e),rng))
return e; // this term occurs in range, so it's O.K.
if(is_array_type(get_type(e)))
throw "help!";
// choose a frame for the constraint that is close to range
int frame = pv->range_near(pv->ast_scope(e),rng);
@ -2018,12 +2437,89 @@ class iz3proof_itp_impl : public iz3proof_itp {
return new_var;
}
ast delete_quant(hash_map<ast,ast> &memo, const ast &v, const ast &e){
std::pair<ast,ast> foo(e,ast());
std::pair<hash_map<ast,ast>::iterator,bool> bar = memo.insert(foo);
ast &res = bar.first->second;
if(bar.second){
opr o = op(e);
switch(o){
case Or:
case And:
case Implies: {
unsigned nargs = num_args(e);
std::vector<ast> args; args.resize(nargs);
for(unsigned i = 0; i < nargs; i++)
args[i] = delete_quant(memo, v, arg(e,i));
res = make(o,args);
break;
}
case Uninterpreted: {
symb s = sym(e);
ast w = arg(arg(e,0),0);
if(s == sforall || s == sexists){
res = delete_quant(memo,v,arg(e,1));
if(w != v)
res = make(s,w,res);
break;
}
}
default:
res = e;
}
}
return res;
}
ast insert_quants(hash_map<ast,ast> &memo, const ast &e){
std::pair<ast,ast> foo(e,ast());
std::pair<hash_map<ast,ast>::iterator,bool> bar = memo.insert(foo);
ast &res = bar.first->second;
if(bar.second){
opr o = op(e);
switch(o){
case Or:
case And:
case Implies: {
unsigned nargs = num_args(e);
std::vector<ast> args; args.resize(nargs);
for(unsigned i = 0; i < nargs; i++)
args[i] = insert_quants(memo, arg(e,i));
res = make(o,args);
break;
}
case Uninterpreted: {
symb s = sym(e);
if(s == sforall || s == sexists){
opr q = (s == sforall) ? Forall : Exists;
ast v = arg(arg(e,0),0);
hash_map<ast,ast> dmemo;
ast body = delete_quant(dmemo,v,arg(e,1));
body = insert_quants(memo,body);
res = apply_quant(q,v,body);
break;
}
}
default:
res = e;
}
}
return res;
}
ast add_quants(ast e){
#ifdef CAPTURE_LOCALIZATION
if(!localization_vars.empty()){
hash_map<ast,ast> memo;
e = insert_quants(memo,e);
}
#else
for(int i = localization_vars.size() - 1; i >= 0; i--){
LocVar &lv = localization_vars[i];
opr quantifier = (pv->in_range(lv.frame,rng)) ? Exists : Forall;
e = apply_quant(quantifier,lv.var,e);
}
#endif
return e;
}
@ -2035,7 +2531,11 @@ class iz3proof_itp_impl : public iz3proof_itp {
/* Return an interpolant from a proof of false */
ast interpolate(const node &pf){
// proof of false must be a formula, with quantified symbols
#ifndef BOGUS_QUANTS
return add_quants(z3_simplify(pf));
#else
return z3_simplify(pf);
#endif
}
ast resolve_with_quantifier(const ast &pivot1, const ast &conj1,
@ -2055,7 +2555,7 @@ class iz3proof_itp_impl : public iz3proof_itp {
ast npP = make_mp(make(Iff,nPloc,nP),npPloc,neqpf);
ast nrP = make_resolution(nP,conj2,npP);
ast res = make_resolution(Ploc,rP,nrP);
return res;
return capture_localization(res);
}
ast get_contra_coeff(const ast &f){
@ -2141,6 +2641,16 @@ public:
m().inc_ref(rewrite_A);
rewrite_B = function("@rewrite_B",3,boolboolbooldom,bool_type());
m().inc_ref(rewrite_B);
normal_step = function("@normal_step",2,boolbooldom,bool_type());
m().inc_ref(normal_step);
normal_chain = function("@normal_chain",2,boolbooldom,bool_type());
m().inc_ref(normal_chain);
normal = function("@normal",2,boolbooldom,bool_type());
m().inc_ref(normal);
sforall = function("@sforall",2,boolbooldom,bool_type());
m().inc_ref(sforall);
sexists = function("@sexists",2,boolbooldom,bool_type());
m().inc_ref(sexists);
}
~iz3proof_itp_impl(){

3
src/interp/iz3proof_itp.h
View file

@ -70,6 +70,9 @@ class iz3proof_itp : public iz3mgr {
/** Make an axiom node. The conclusion must be an instance of an axiom. */
virtual node make_axiom(const std::vector<ast> &conclusion) = 0;
/** Make an axiom node. The conclusion must be an instance of an axiom. Localize axiom instance to range*/
virtual node make_axiom(const std::vector<ast> &conclusion, prover::range) = 0;
/** Make a Contra node. This rule takes a derivation of the form
Gamma |- False and produces |- \/~Gamma. */

72
src/interp/iz3translate.cpp
View file

@ -109,36 +109,49 @@ public:
symbols and assign each to a frame. THe assignment is heuristic.
*/
void scan_skolems_rec(hash_set<ast> &memo, const ast &proof){
std::pair<hash_set<ast>::iterator,bool> bar = memo.insert(proof);
if(!bar.second)
return;
int scan_skolems_rec(hash_map<ast,int> &memo, const ast &proof, int frame){
std::pair<ast,int> foo(proof,INT_MAX);
std::pair<AstToInt::iterator, bool> bar = memo.insert(foo);
int &res = bar.first->second;
if(!bar.second) return res;
pfrule dk = pr(proof);
if(dk == PR_SKOLEMIZE){
if(dk == PR_ASSERTED){
ast ass = conc(proof);
res = frame_of_assertion(ass);
}
else if(dk == PR_SKOLEMIZE){
ast quanted = arg(conc(proof),0);
if(op(quanted) == Not)
quanted = arg(quanted,0);
range r = ast_range(quanted);
if(range_is_empty(r))
r = ast_scope(quanted);
// range r = ast_range(quanted);
// if(range_is_empty(r))
range r = ast_scope(quanted);
if(range_is_empty(r))
throw "can't skolemize";
int frame = range_max(r);
if(frame == INT_MAX || !in_range(frame,r))
frame = range_max(r); // this is desperation -- may fail
if(frame >= frames) frame = frames - 1;
add_frame_range(frame,arg(conc(proof),1));
r = ast_scope(arg(conc(proof),1));
}
else if(dk==PR_MODUS_PONENS_OEQ){
frame = scan_skolems_rec(memo,prem(proof,0),frame);
scan_skolems_rec(memo,prem(proof,1),frame);
}
else {
unsigned nprems = num_prems(proof);
for(unsigned i = 0; i < nprems; i++){
scan_skolems_rec(memo,prem(proof,i));
int bar = scan_skolems_rec(memo,prem(proof,i),frame);
if(res == INT_MAX || res == bar) res = bar;
else if(bar != INT_MAX) res = -1;
}
}
return res;
}
void scan_skolems(const ast &proof){
hash_set<ast> memo;
scan_skolems_rec(memo,proof);
hash_map<ast,int> memo;
scan_skolems_rec(memo,proof, INT_MAX);
}
// determine locality of a proof term
@ -1364,6 +1377,18 @@ public:
return eq2;
}
bool get_store_array(const ast &t, ast &res){
if(op(t) == Store){
res = t;
return true;
}
int nargs = num_args(t);
for(int i = 0; i < nargs; i++)
if(get_store_array(arg(t,i),res))
return true;
return false;
}
// translate a Z3 proof term into interpolating proof system
Iproof::node translate_main(ast proof, bool expect_clause = true){
@ -1448,6 +1473,21 @@ public:
}
}
/* this is the symmetry rule for ~=, that is, takes x ~= y and yields y ~= x.
the proof idiom uses commutativity, monotonicity and mp, but we replace it here
with symmtrey and resolution, that is, we prove y = x |- x = y, then resolve
with the proof of ~(x=y) to get ~y=x. */
if(dk == PR_MODUS_PONENS && pr(prem(proof,1)) == PR_MONOTONICITY && pr(prem(prem(proof,1),0)) == PR_COMMUTATIVITY && num_prems(prem(proof,1)) == 1){
Iproof::node ante = translate_main(prem(proof,0),false);
ast eq0 = arg(conc(prem(prem(proof,1),0)),0);
ast eq1 = arg(conc(prem(prem(proof,1),0)),1);
Iproof::node eq1hy = iproof->make_hypothesis(eq1);
Iproof::node eq0pf = iproof->make_symmetry(eq0,eq1,eq1hy);
std::vector<ast> clause; // just a dummy
res = iproof->make_resolution(eq0,clause,ante,eq0pf);
return res;
}
// translate all the premises
std::vector<Iproof::node> args(nprems);
for(unsigned i = 0; i < nprems; i++)
@ -1578,9 +1618,13 @@ public:
throw unsupported();
}
break;
case ArrayTheory: // nothing fancy for this
res = iproof->make_axiom(lits);
case ArrayTheory: {// nothing fancy for this
ast store_array;
if(!get_store_array(con,store_array))
throw unsupported();
res = iproof->make_axiom(lits,ast_scope(store_array));
break;
}
default:
throw unsupported();
}

18
src/interp/iz3translate_direct.cpp
View file

@ -38,6 +38,24 @@ Revision History:
using namespace stl_ext;
#endif
#ifndef WIN32
/* This can introduce an address dependency if the range type of hash_map has
a destructor. Since the code in this file is not used and only here for
historical comparisons, we allow this non-determinism.
*/
namespace stl_ext {
template <class T>
class hash<T *> {
public:
size_t operator()(const T *p) const {
return (size_t) p;
}
};
}
#endif
static int lemma_count = 0;
static int nll_lemma_count = 0;

2
src/muz/duality/duality_dl_interface.cpp
View file

@ -472,7 +472,7 @@ static proof_ref extract_proof(dl_interface *d, Solver::Counterexample &cex) {
expr conc = f(args);
::vector<proof *> pprems;
::vector< ::proof *> pprems;
for(unsigned i = 0; i < prems.size(); i++)
pprems.push_back(prems[i].get());

1
src/smt/params/qi_params.cpp
View file

@ -27,6 +27,7 @@ void qi_params::updt_params(params_ref const & _p) {
m_mbqi_max_iterations = p.mbqi_max_iterations();
m_mbqi_trace = p.mbqi_trace();
m_mbqi_force_template = p.mbqi_force_template();
m_mbqi_id = p.mbqi_id();
m_qi_profile = p.qi_profile();
m_qi_profile_freq = p.qi_profile_freq();
m_qi_max_instances = p.qi_max_instances();

5
src/smt/params/qi_params.h
View file

@ -51,6 +51,7 @@ struct qi_params {
unsigned m_mbqi_max_iterations;
bool m_mbqi_trace;
unsigned m_mbqi_force_template;
const char * m_mbqi_id;
qi_params(params_ref const & p = params_ref()):
/*
@ -97,7 +98,9 @@ struct qi_params {
m_mbqi_max_cexs_incr(1),
m_mbqi_max_iterations(1000),
m_mbqi_trace(false),
m_mbqi_force_template(10) {
m_mbqi_force_template(10),
m_mbqi_id(0)
{
updt_params(p);
}

1
src/smt/params/smt_params_helper.pyg
View file

@ -21,6 +21,7 @@ def_module_params(module_name='smt',
('mbqi.max_iterations', UINT, 1000, 'maximum number of rounds of MBQI'),
('mbqi.trace', BOOL, False, 'generate tracing messages for Model Based Quantifier Instantiation (MBQI). It will display a message before every round of MBQI, and the quantifiers that were not satisfied'),
('mbqi.force_template', UINT, 10, 'some quantifiers can be used as templates for building interpretations for functions. Z3 uses heuristics to decide whether a quantifier will be used as a template or not. Quantifiers with weight >= mbqi.force_template are forced to be used as a template'),
('mbqi.id', STRING, '', 'Only use model-based instantiation for quantifiers with id\'s beginning with string'),
('qi.profile', BOOL, False, 'profile quantifier instantiation'),
('qi.profile_freq', UINT, UINT_MAX, 'how frequent results are reported by qi.profile'),
('qi.max_instances', UINT, UINT_MAX, 'maximum number of quantifier instantiations'),

1
src/smt/smt_model_checker.cpp
View file

@ -322,6 +322,7 @@ namespace smt {
for (; it != end; ++it) {
quantifier * q = *it;
if(!m_qm->mbqi_enabled(q)) continue;
if (m_context->is_relevant(q) && m_context->get_assignment(q) == l_true) {
if (m_params.m_mbqi_trace && q->get_qid() != symbol::null) {
verbose_stream() << "(smt.mbqi :checking " << q->get_qid() << ")\n";

24
src/smt/smt_quantifier.cpp
View file

@ -335,6 +335,10 @@ namespace smt {
return m_imp->m_plugin->model_based();
}
bool quantifier_manager::mbqi_enabled(quantifier *q) const {
return m_imp->m_plugin->mbqi_enabled(q);
}
void quantifier_manager::adjust_model(proto_model * m) {
m_imp->m_plugin->adjust_model(m);
}
@ -434,10 +438,24 @@ namespace smt {
virtual bool model_based() const { return m_fparams->m_mbqi; }
virtual bool mbqi_enabled(quantifier *q) const {
if(!m_fparams->m_mbqi_id) return true;
const symbol &s = q->get_qid();
unsigned len = strlen(m_fparams->m_mbqi_id);
if(s == symbol::null || s.is_numerical())
return len == 0;
return strncmp(s.bare_str(),m_fparams->m_mbqi_id,len) == 0;
}
/* Quantifier id's must begin with the prefix specified by
parameter mbqi.id to be instantiated with MBQI. The default
value is the empty string, so all quantifiers are
instantiated.
*/
virtual void add(quantifier * q) {
if (m_fparams->m_mbqi) {
m_model_finder->register_quantifier(q);
}
if (m_fparams->m_mbqi && mbqi_enabled(q)) {
m_model_finder->register_quantifier(q);
}
}
virtual void del(quantifier * q) {

6
src/smt/smt_quantifier.h
View file

@ -75,6 +75,7 @@ namespace smt {
};
bool model_based() const;
bool mbqi_enabled(quantifier *q) const; // can mbqi instantiate this quantifier?
void adjust_model(proto_model * m);
check_model_result check_model(proto_model * m, obj_map<enode, app *> const & root2value);
@ -144,6 +145,11 @@ namespace smt {
*/
virtual bool model_based() const = 0;
/**
\brief Is "model based" instantiate allowed to instantiate this quantifier?
*/
virtual bool mbqi_enabled(quantifier *q) const {return true;}
/**
\brief Give a change to the plugin to adjust the interpretation of unintepreted functions.
It can basically change the "else" of each uninterpreted function.

5
src/smt/theory_arith_aux.h
View file

@ -475,10 +475,11 @@ namespace smt {
bool theory_arith<Ext>::all_coeff_int(row const & r) const {
typename vector<row_entry>::const_iterator it = r.begin_entries();
typename vector<row_entry>::const_iterator end = r.end_entries();
for (; it != end; ++it) {
if (!it->is_dead() && !it->m_coeff.is_int())
for (; it != end; ++it) {
if (!it->is_dead() && !it->m_coeff.is_int()) {
TRACE("gomory_cut", display_row(tout, r, true););
return false;
}
}
return true;
}

5
src/util/id_gen.h
View file

@ -57,6 +57,11 @@ public:
m_free_ids.finalize();
}
unsigned show_hash(){
unsigned h = string_hash((char *)&m_free_ids[0],m_free_ids.size()*sizeof(unsigned),17);
return hash_u_u(h,m_next_id);
}
/**
\brief Return N if the range of ids generated by this module is in the set [0..N)
*/