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working on quantifiers in interpolation

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Ken McMillan 2013-11-14 10:18:44 -08:00
parent d73310cfa1
commit 9cba5d7c85
4 changed files with 180 additions and 40 deletions
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2
src/interp/iz3base.h
View file

@ -153,8 +153,10 @@ class iz3base : public iz3mgr, public scopes {
int frames; // number of frames
protected:
void add_frame_range(int frame, ast t);
private:
void initialize(const std::vector<ast> &_parts, const std::vector<int> &_parents, const std::vector<ast> &_theory);
void initialize(const std::vector<std::vector<ast> > &_parts, const std::vector<int> &_parents, const std::vector<ast> &_theory);

8
src/interp/iz3mgr.cpp
View file

@ -240,7 +240,9 @@ iz3mgr::ast iz3mgr::clone(const ast &t, const std::vector<ast> &_args){
void iz3mgr::show(ast t){
std::cout << mk_pp(t.raw(), m()) << std::endl;
params_ref p;
p.set_bool("flat_assoc",false);
std::cout << mk_pp(t.raw(), m(), p) << std::endl;
}
void iz3mgr::show_symb(symb s){
@ -248,7 +250,9 @@ void iz3mgr::show_symb(symb s){
}
void iz3mgr::print_expr(std::ostream &s, const ast &e){
s << mk_pp(e.raw(), m());
params_ref p;
p.set_bool("flat_assoc",false);
s << mk_pp(e.raw(), m(), p);
}

90
src/interp/iz3proof_itp.cpp
View file

@ -417,7 +417,16 @@ class iz3proof_itp_impl : public iz3proof_itp {
std::pair<hash_map<ast,ast>::iterator,bool> bar = subst_memo.insert(foo);
ast &res = bar.first->second;
if(bar.second){
if(sym(e) == rotate_sum && var == get_placeholder(arg(e,0))){
symb g = sym(e);
if(g == rotate_sum){
if(var == get_placeholder(arg(e,0))){
res = e;
}
else
res = make(rotate_sum,arg(e,0),subst_term_and_simp_rec(var,t,arg(e,1)));
return res;
}
if(g == concat){
res = e;
return res;
}
@ -453,18 +462,26 @@ class iz3proof_itp_impl : public iz3proof_itp {
int nargs = num_args(e);
std::vector<ast> args(nargs);
bool placeholder_arg = false;
symb g = sym(e);
if(g == concat){
res = e;
return res;
}
for(int i = 0; i < nargs; i++){
args[i] = simplify_rec(arg(e,i));
if(i == 0 && g == rotate_sum)
args[i] = arg(e,i);
else
args[i] = simplify_rec(arg(e,i));
placeholder_arg |= is_placeholder(args[i]);
}
try {
opr f = op(e);
if(f == Equal && args[0] == args[1]) res = mk_true();
else if(f == And) res = my_and(args);
else if(f == Or) res = my_or(args);
else if(f == Or)
res = my_or(args);
else if(f == Idiv) res = mk_idiv(args[0],args[1]);
else if(f == Uninterpreted && !placeholder_arg){
symb g = sym(e);
if(g == rotate_sum) res = simplify_rotate(args);
else if(g == symm) res = simplify_symm(args);
else if(g == modpon) res = simplify_modpon(args);
@ -1945,38 +1962,45 @@ class iz3proof_itp_impl : public iz3proof_itp {
hash_map<ast,ast>::iterator it = localization_map.find(e);
if(it != localization_map.end()){
pf = localization_pf_map[e];
return it->second;
e = it->second;
}
// if is is non-local, we must first localize the arguments to
// the range of its function symbol
int nargs = num_args(e);
if(nargs > 0 /* && (!is_local(e) || flo <= hi || fhi >= lo) */){
prover::range frng = rng;
if(op(e) == Uninterpreted){
symb f = sym(e);
prover::range srng = pv->sym_range(f);
if(pv->ranges_intersect(srng,rng)) // localize to desired range if possible
frng = pv->range_glb(srng,rng);
}
std::vector<ast> largs(nargs);
std::vector<ast> eqs;
std::vector<ast> pfs;
for(int i = 0; i < nargs; i++){
ast argpf;
largs[i] = localize_term(arg(e,i),frng,argpf);
frng = pv->range_glb(frng,pv->ast_scope(largs[i]));
if(largs[i] != arg(e,i)){
eqs.push_back(make_equiv(largs[i],arg(e,i)));
pfs.push_back(argpf);
else {
// if it is non-local, we must first localize the arguments to
// the range of its function symbol
int nargs = num_args(e);
if(nargs > 0 /* && (!is_local(e) || flo <= hi || fhi >= lo) */){
prover::range frng = rng;
if(op(e) == Uninterpreted){
symb f = sym(e);
prover::range srng = pv->sym_range(f);
if(pv->ranges_intersect(srng,rng)) // localize to desired range if possible
frng = pv->range_glb(srng,rng);
else
frng = srng; // this term will be localized
}
std::vector<ast> largs(nargs);
std::vector<ast> eqs;
std::vector<ast> pfs;
for(int i = 0; i < nargs; i++){
ast argpf;
largs[i] = localize_term(arg(e,i),frng,argpf);
frng = pv->range_glb(frng,pv->ast_scope(largs[i]));
if(largs[i] != arg(e,i)){
eqs.push_back(make_equiv(largs[i],arg(e,i)));
pfs.push_back(argpf);
}
}
e = clone(e,largs);
if(pfs.size())
pf = make_congruence(eqs,make_equiv(e,orig_e),pfs);
// assert(is_local(e));
}
e = clone(e,largs);
if(pfs.size())
pf = make_congruence(eqs,make_equiv(e,orig_e),pfs);
// assert(is_local(e));
localization_pf_map[orig_e] = pf;
localization_map[orig_e] = e;
}
if(pv->ranges_intersect(pv->ast_scope(e),rng))
@ -1986,7 +2010,7 @@ class iz3proof_itp_impl : public iz3proof_itp {
int frame = pv->range_near(pv->ast_scope(e),rng);
ast new_var = fresh_localization_var(e,frame);
localization_map[e] = new_var;
localization_map[orig_e] = new_var;
std::vector<ast> foo; foo.push_back(make_equiv(new_var,e));
ast bar = make_assumption(frame,foo);
pf = make_transitivity(new_var,e,orig_e,bar,pf);

120
src/interp/iz3translate.cpp
View file

@ -105,6 +105,42 @@ public:
range rng; // the range of frames in the "A" part of the interpolant
#endif
/* To handle skolemization, we have to scan the proof for skolem
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;
pfrule dk = pr(proof);
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);
if(range_is_empty(r))
throw "can't skolemize";
int frame = range_max(r);
if(frame >= frames) frame = frames - 1;
add_frame_range(frame,arg(conc(proof),1));
r = ast_scope(arg(conc(proof),1));
}
else {
unsigned nprems = num_prems(proof);
for(unsigned i = 0; i < nprems; i++){
scan_skolems_rec(memo,prem(proof,i));
}
}
}
void scan_skolems(const ast &proof){
hash_set<ast> memo;
scan_skolems_rec(memo,proof);
}
// determine locality of a proof term
// return frame of derivation if local, or -1 if not
// result INT_MAX means the proof term is a tautology
@ -115,7 +151,8 @@ public:
std::pair<AstToInt::iterator, bool> bar = locality.insert(foo);
int &res = bar.first->second;
if(!bar.second) return res;
if(pr(proof) == PR_ASSERTED){
pfrule dk = pr(proof);
if(dk == PR_ASSERTED){
ast ass = conc(proof);
res = frame_of_assertion(ass);
#ifdef NEW_LOCALITY
@ -125,6 +162,12 @@ public:
res = frames-1;
#endif
}
else if(dk == PR_QUANT_INST){
std::vector<ast> lits;
ast con = conc(proof);
get_Z3_lits(con, lits);
iproof->make_axiom(lits);
}
else {
unsigned nprems = num_prems(proof);
for(unsigned i = 0; i < nprems; i++){
@ -563,6 +606,33 @@ public:
return 1;
}
void symbols_out_of_scope_rec(hash_set<ast> &memo, hash_set<symb> &symb_memo, int frame, const ast &t){
if(memo.find(t) != memo.end())
return;
memo.insert(t);
if(op(t) == Uninterpreted){
symb s = sym(t);
range r = sym_range(s);
if(!in_range(frame,r) && symb_memo.find(s) == symb_memo.end()){
std::cout << string_of_symbol(s) << "\n";
symb_memo.insert(s);
}
}
int nargs = num_args(t);
for(int i = 0; i < nargs; i++)
symbols_out_of_scope_rec(memo,symb_memo,frame,arg(t,i));
}
void symbols_out_of_scope(int frame, const ast &t){
hash_set<ast> memo;
hash_set<symb> symb_memo;
symbols_out_of_scope_rec(memo,symb_memo,frame,t);
}
void conc_symbols_out_of_scope(int frame, const ast &t){
symbols_out_of_scope(frame,conc(t));
}
std::vector<ast> lit_trace;
hash_set<ast> marked_proofs;
@ -634,18 +704,36 @@ public:
return !(f == And || f == Or || f == Iff);
}
hash_map<int,ast> asts_by_id;
void print_lit(const ast &lit){
ast abslit = is_not(lit) ? arg(lit,0) : lit;
if(!is_literal_or_lit_iff(lit)){
if(is_not(lit)) std::cout << "~";
std::cout << "[";
// print_expr(std::cout,abslit);
std::cout << "]";
int id = ast_id(abslit);
asts_by_id[id] = abslit;
std::cout << "[" << id << "]";
}
else
print_expr(std::cout,lit);
}
void expand(int id){
if(asts_by_id.find(id) == asts_by_id.end())
std::cout << "undefined\n";
else {
ast lit = asts_by_id[id];
std::string s = string_of_symbol(sym(lit));
std::cout << "(" << s;
unsigned nargs = num_args(lit);
for(unsigned i = 0; i < nargs; i++){
std::cout << " ";
print_lit(arg(lit,i));
}
std::cout << ")\n";;
}
}
void show_lit(const ast &lit){
print_lit(lit);
std::cout << "\n";
@ -682,6 +770,8 @@ public:
print_lit(lits[i]);
std::cout << " ";
}
range r = ast_scope(con);
std::cout << " {" << r.lo << "," << r.hi << "}";
std::cout << "\n";
}
@ -753,8 +843,12 @@ public:
ast prem0 = prem(proof,0);
Iproof::node itp = translate_main(prem0,true);
std::vector<ast> clause;
get_Z3_lits(conc(prem0),clause);
ast conc0 = conc(prem0);
int nprems = num_prems(proof);
if(nprems == 2 && conc0 == mk_not(conc(prem(proof,1))))
clause.push_back(conc0);
else
get_Z3_lits(conc0,clause);
for(int position = 1; position < nprems; position++){
ast ante = prem(proof,position);
ast pnode = conc(ante);
@ -1500,6 +1594,10 @@ public:
res = iproof->make_axiom(lits);
break;
}
case PR_DEF_AXIOM: { // this should only happen for formulas resulting from quantifier instantiation
res = iproof->make_axiom(lits);
break;
}
default:
assert(0 && "translate_main: unsupported proof rule");
throw unsupported();
@ -1518,6 +1616,7 @@ public:
iz3proof::node translate(ast proof, iz3proof &dst){
std::vector<ast> itps;
scan_skolems(proof);
for(int i = 0; i < frames -1; i++){
#ifdef NEW_LOCALITY
rng = range_downward(i);
@ -1609,6 +1708,17 @@ void iz3translation_full_pfprem(iz3translation_full *p, int i){
p->pfprem(i);
}
void iz3translation_full_expand(iz3translation_full *p, int i){
p->expand(i);
}
void iz3translation_full_symbols_out_of_scope(iz3translation_full *p, int i, const iz3mgr::ast &t){
p->symbols_out_of_scope(i,t);
}
void iz3translation_full_conc_symbols_out_of_scope(iz3translation_full *p, int i, const iz3mgr::ast &t){
p->conc_symbols_out_of_scope(i,t);
}
struct stdio_fixer {
stdio_fixer(){