diff --git a/src/math/dd/dd_bdd.h b/src/math/dd/dd_bdd.h
index ff7735b2a..1892c5317 100644
--- a/src/math/dd/dd_bdd.h
+++ b/src/math/dd/dd_bdd.h
@@ -233,8 +233,8 @@ namespace dd {
         bdd_manager* m;
         bdd(unsigned root, bdd_manager* m): root(root), m(m) { m->inc_ref(root); }
     public:
-        bdd(bdd & other): root(other.root), m(other.m) { m->inc_ref(root); }
-        bdd(bdd && other): root(0), m(other.m) { std::swap(root, other.root); }
+        bdd(bdd const & other): root(other.root), m(other.m) { m->inc_ref(root); }
+        bdd(bdd && other) noexcept : root(0), m(other.m) { std::swap(root, other.root); }
         bdd& operator=(bdd const& other);
         ~bdd() { m->dec_ref(root); }
         bdd lo() const { return bdd(m->lo(root), m); }
diff --git a/src/math/polysat/polysat.cpp b/src/math/polysat/polysat.cpp
index ed8244ff6..884888964 100644
--- a/src/math/polysat/polysat.cpp
+++ b/src/math/polysat/polysat.cpp
@@ -43,51 +43,157 @@ namespace polysat {
         return false;
     }
 
-    /*
-        struct del_var;
-        struct del_constraint;
-        struct var_unassign;
+    struct solver::del_var : public trail {
+        solver& s;
+        del_var(solver& s): s(s) {}
+        void undo() override { s.do_del_var(); }
+    };
 
-        void push();
-        void pop(unsigned n);
+    struct solver::del_constraint : public trail {
+        solver& s;
+        del_constraint(solver& s): s(s) {}
+        void undo() override { s.do_del_constraint(); }
+    };
 
-        solver(trail_stack& s);
-        ~solver() {}
+    struct solver::var_unassign : public trail {
+        solver& s;
+        var_unassign(solver& s): s(s) {}
+        void undo() override { s.do_var_unassign(); }
+    };
+    
+    solver::solver(trail_stack& s): 
+        m_trail(s),
+        m_region(s.get_region()),
+        m_pdd(1000),
+        m_bdd(1000),
+        m_free_vars(m_activity) {
+    }
 
-        lbool check_sat();
+    solver::~solver() {}
+    
+    lbool solver::check_sat() { 
+        return l_undef;
+    }
         
-        unsigned add_var(unsigned sz);
+    unsigned solver::add_var(unsigned sz) {
+        unsigned v = m_viable.size();
+        // TODO: set var size sz into m_pdd.
+        m_value.push_back(rational::zero());
+        m_justification.push_back(justification::unassigned());
+        m_viable.push_back(m_bdd.mk_true());
+        m_vdeps.push_back(m_dep_manager.mk_empty());
+        m_pdeps.push_back(vector<poly>());
+        m_watch.push_back(unsigned_vector());
+        m_activity.push_back(0);
+        m_vars.push_back(m_pdd.mk_var(v));
+        m_trail.push(del_var(*this));
+        return v;
+    }
 
-        poly var(unsigned v);
-        poly mul(rational cons& r, poly const& p);
-        poly num(rational const& r, unsigned sz);
-        poly add(poly const& p, poly const& q);
+    void solver::do_del_var() {
+        unsigned v = m_viable.size() - 1;
+        m_free_vars.del_var_eh(v);
+        m_viable.pop_back();
+        m_vdeps.pop_back();
+        m_pdeps.pop_back();
+        m_value.pop_back();
+        m_justification.pop_back();
+        m_watch.pop_back();
+        m_activity.pop_back();
+        m_vars.pop_back();
+    }
 
-        vector<mono> poly2monos(poly const& p) const;        
+    void solver::do_del_constraint() {
+        // TODO remove variables from watch lists
+        m_constraints.pop_back();
+        m_cdeps.pop_back();
+    }
 
-        void add_eq(poly const& p, unsigned dep);
-        void add_diseq(poly const& p, unsigned dep);
-        void add_ule(poly const& p, poly const& q, unsigned dep);
-        void add_sle(poly const& p, poly const& q, unsigned dep);
-        void assign(unsigned var, unsigned index, bool value, unsigned dep);        
+    void solver::do_var_unassign() {
 
-        bool  can_propagate();
-        lbool propagate();
+    }
 
-        bool can_decide();
-        void decide(rational & val, unsigned& var);
-        void assign(unsigned var, rational const& val);
+    poly solver::var(unsigned v) {
+        return poly(*this, m_vars[v]);
+    }
+
+    vector<mono> solver::poly2monos(poly const& p) const {
+        return vector<mono>();
+    }
+
+    void solver::add_eq(poly const& p, unsigned dep) {
+        m_constraints.push_back(constraint::eq(p));
+        m_cdeps.push_back(m_dep_manager.mk_leaf(dep));
+        // TODO init watch list
+        m_trail.push(del_constraint(*this));
+    }
+
+    void solver::add_diseq(poly const& p, unsigned dep) {
+#if 0
+        // Basically: 
+        auto slack = add_var(p.size());
+        p = p + var(slack);
+        add_eq(p, dep);
+        m_viable[slack] &= slack != 0;
+#endif
+    }
+
+    void solver::add_ule(poly const& p, poly const& q, unsigned dep) {
+        // save for later
+    }
+
+    void solver::add_sle(poly const& p, poly const& q, unsigned dep) {
+        // save for later
+    }
+
+    void solver::assign(unsigned var, unsigned index, bool value, unsigned dep) {
+
+    }
+
+    bool  solver::can_propagate() {
+        return false;
+    }
+
+    lbool solver::propagate() {
+        return l_false;
+    }
+
+    bool solver::can_decide() {
+        return false;
+    }
+
+    void solver::decide(rational & val, unsigned& var) {
+
+    }
+
+    void solver::assign(unsigned var, rational const& val) {
+
+    }
         
-        bool is_conflict();
-        unsigned resolve_conflict(unsigned_vector& deps);            
+    bool solver::is_conflict() {
+        return false;
+    }
+
+    unsigned resolve_conflict(unsigned_vector& deps) {
+        return 0;
+    }
         
-        bool can_learn();
-        void learn(constraint& c, unsigned_vector& deps); 
-        void learn(vector<constraint>& cs, unsigned_vector& deps); 
+    bool solver::can_learn() {
+        return false;
+    }
 
-        std::ostream& display(std::ostream& out) const;
+    void solver::learn(constraint& c, unsigned_vector& deps) {
+
+    } 
+
+    void solver::learn(vector<constraint>& cs, unsigned_vector& deps) {
+
+    }
+
+    std::ostream& solver::display(std::ostream& out) const {
+        return out;
+    }
 
-        */
 
 }
 
diff --git a/src/math/polysat/polysat.h b/src/math/polysat/polysat.h
index e0f74fd33..d495077bf 100644
--- a/src/math/polysat/polysat.h
+++ b/src/math/polysat/polysat.h
@@ -19,6 +19,7 @@ Author:
 #include "util/dependency.h"
 #include "util/trail.h"
 #include "util/lbool.h"
+#include "util/var_queue.h"
 #include "math/dd/dd_pdd.h"
 #include "math/dd/dd_bdd.h"
 
@@ -29,13 +30,18 @@ namespace polysat {
     typedef dd::bdd bdd;
 
     class poly {
+        friend class solver;
         solver&  s;
         pdd      m_pdd;
-        unsigned m_lidx { UINT_MAX };
     public:
         poly(solver& s, pdd const& p): s(s), m_pdd(p) {}
-        poly(solver& s, pdd const& p, unsigned lidx): s(s), m_pdd(p), m_lidx(lidx) {}
+        poly(solver& s, rational const& r, unsigned sz);
         std::ostream& display(std::ostream& out) const;
+        unsigned size() const { throw default_exception("nyi query pdd for size"); }
+        
+        poly operator*(rational const& r);
+        poly operator+(poly const& other) { return poly(s, m_pdd + other.m_pdd); }
+        poly operator*(poly const& other) { return poly(s, m_pdd * other.m_pdd); }
     };
 
     inline std::ostream& operator<<(std::ostream& out, poly const& p) { return p.display(out); }
@@ -101,16 +107,20 @@ namespace polysat {
         static justification propagation(unsigned idx) { return justification(justification_k::propagation, idx); }
         justification_k kind() const { return m_kind; }
         unsigned constraint_index() const { return m_idx; }
+        std::ostream& display(std::ostream& out) const;
     };
 
+    inline std::ostream& operator<<(std::ostream& out, justification const& j) { return j.display(out); }
+
     class solver {
         friend class poly;
 
-        trail_stack&         m_trail;
-        region&              m_region;
-        dd::pdd_manager      m_pdd;
-        dd::bdd_manager      m_bdd;
-        u_dependency_manager m_dep_manager;
+        trail_stack&             m_trail;
+        region&                  m_region;
+        dd::pdd_manager          m_pdd;
+        dd::bdd_manager          m_bdd;
+        u_dependency_manager     m_dep_manager;
+        var_queue                m_free_vars;
 
         /**
          * store of linear polynomials. The l_idx points to linear monomials.
@@ -119,16 +129,22 @@ namespace polysat {
         vector<linear>           m_linear; 
 
         // Per constraint state
-        vector<u_dependency>     m_cdeps;   // each constraint has set of dependencies
+        ptr_vector<u_dependency> m_cdeps;   // each constraint has set of dependencies
         vector<constraint>       m_constraints;
 
         // Per variable information
         vector<bdd>              m_viable;   // set of viable values.
-        vector<u_dependency>     m_vdeps;    // dependencies for viable values
+        ptr_vector<u_dependency> m_vdeps;    // dependencies for viable values
         vector<vector<poly>>     m_pdeps;    // dependencies in polynomial form
         vector<rational>         m_value;    // assigned value
         vector<justification>    m_justification; // justification for variable assignment
         vector<unsigned_vector>  m_watch;    // watch list datastructure into constraints.
+        unsigned_vector          m_activity; 
+        vector<pdd>              m_vars;
+
+        // search state that lists assigned variables
+        unsigned_vector          m_search;
+        unsigned                 m_qhead { 0 };
 
         /**
          * retrieve bit-size associated with polynomial.
@@ -148,11 +164,15 @@ namespace polysat {
         struct del_constraint;
         struct var_unassign;
 
+        void do_del_var();
+        void do_del_constraint();
+        void do_var_unassign();
+
         /**
          * push / pop are used only in self-contained mode from check_sat.
          */
-        void push();
-        void pop(unsigned n);
+        void push() { m_trail.push_scope(); }
+        void pop(unsigned n) { m_trail.pop_scope(n); }
 
     public:
 
@@ -162,7 +182,7 @@ namespace polysat {
          * by pushing an undo action on the trail stack.
          */
         solver(trail_stack& s);
-        ~solver() {}
+        ~solver();
 
         /**
          * Self-contained satisfiability checker.
@@ -179,9 +199,6 @@ namespace polysat {
          * Create polynomial terms
          */
         poly var(unsigned v);
-        poly mul(rational const& r, poly const& p);
-        poly num(rational const& r, unsigned sz);
-        poly add(poly const& p, poly const& q);
 
         /**
          * deconstruct polynomials into sum of monomials.
diff --git a/src/sat/sat_solver.h b/src/sat/sat_solver.h
index cc06ad1b3..bcb2c0e77 100644
--- a/src/sat/sat_solver.h
+++ b/src/sat/sat_solver.h
@@ -19,11 +19,19 @@ Revision History:
 #pragma once
 
 #include <cmath>
+#include "util/var_queue.h"
+#include "util/params.h"
+#include "util/statistics.h"
+#include "util/stopwatch.h"
+#include "util/ema.h"
+#include "util/trace.h"
+#include "util/rlimit.h"
+#include "util/scoped_ptr_vector.h"
+#include "util/scoped_limit_trail.h"
 #include "sat/sat_types.h"
 #include "sat/sat_clause.h"
 #include "sat/sat_watched.h"
 #include "sat/sat_justification.h"
-#include "sat/sat_var_queue.h"
 #include "sat/sat_extension.h"
 #include "sat/sat_config.h"
 #include "sat/sat_cleaner.h"
@@ -38,14 +46,6 @@ Revision History:
 #include "sat/sat_parallel.h"
 #include "sat/sat_local_search.h"
 #include "sat/sat_solver_core.h"
-#include "util/params.h"
-#include "util/statistics.h"
-#include "util/stopwatch.h"
-#include "util/ema.h"
-#include "util/trace.h"
-#include "util/rlimit.h"
-#include "util/scoped_ptr_vector.h"
-#include "util/scoped_limit_trail.h"
 
 namespace pb {
     class solver;
diff --git a/src/sat/sat_var_queue.h b/src/sat/sat_var_queue.h
deleted file mode 100644
index e73a440ce..000000000
--- a/src/sat/sat_var_queue.h
+++ /dev/null
@@ -1,78 +0,0 @@
-/*++
-Copyright (c) 2011 Microsoft Corporation
-
-Module Name:
-
-    sat_var_queue.h
-
-Abstract:
-
-    SAT variable priority queue.
-
-Author:
-
-    Leonardo de Moura (leonardo) 2011-05-21.
-
-Revision History:
-
---*/
-#pragma once
-
-#include "util/heap.h"
-#include "sat/sat_types.h"
-
-namespace sat {
-    
-    class var_queue {
-        struct lt {
-            svector<unsigned> & m_activity;
-            lt(svector<unsigned> & act):m_activity(act) {}
-            bool operator()(bool_var v1, bool_var v2) const { return m_activity[v1] > m_activity[v2]; }
-        };
-        heap<lt>  m_queue;
-    public:
-        var_queue(svector<unsigned> & act):m_queue(128, lt(act)) {}
-        
-        void activity_increased_eh(bool_var v) {
-            if (m_queue.contains(v))
-                m_queue.decreased(v);
-        }
-
-        void activity_changed_eh(bool_var v, bool up) {
-            if (m_queue.contains(v)) {
-                if (up) 
-                    m_queue.decreased(v);
-                else 
-                    m_queue.increased(v);
-            }
-        }
-
-        void mk_var_eh(bool_var v) {
-            m_queue.reserve(v+1);
-            m_queue.insert(v);
-        }
-
-        void del_var_eh(bool_var v) {
-            if (m_queue.contains(v))
-                m_queue.erase(v);
-        }
-
-        void unassign_var_eh(bool_var v) {
-            if (!m_queue.contains(v))
-                m_queue.insert(v);
-        }
-
-        void reset() {
-            m_queue.reset();
-        }
-
-        bool empty() const { return m_queue.empty(); }
-
-        bool_var next_var() { SASSERT(!empty()); return m_queue.erase_min(); }
-
-        bool_var min_var() { SASSERT(!empty()); return m_queue.min_value(); }
-
-        bool more_active(bool_var v1, bool_var v2) const { return m_queue.less_than(v1, v2); }
-    };
-};
-
diff --git a/src/util/var_queue.h b/src/util/var_queue.h
new file mode 100644
index 000000000..e5a21d9a4
--- /dev/null
+++ b/src/util/var_queue.h
@@ -0,0 +1,80 @@
+/*++
+Copyright (c) 2011 Microsoft Corporation
+
+Module Name:
+
+    var_queue.h
+
+Abstract:
+
+    SAT variable priority queue.
+
+Author:
+
+    Leonardo de Moura (leonardo) 2011-05-21.
+
+Revision History:
+
+--*/
+#pragma once
+
+#include "util/heap.h"
+
+
+    
+class var_queue {
+    typedef unsigned var;
+
+    struct lt {
+        svector<unsigned> & m_activity;
+    lt(svector<unsigned> & act):m_activity(act) {}
+        bool operator()(var v1, var v2) const { return m_activity[v1] > m_activity[v2]; }
+    };
+    heap<lt>  m_queue;
+public:
+
+    
+    var_queue(svector<unsigned> & act):m_queue(128, lt(act)) {}
+    
+    void activity_increased_eh(var v) {
+        if (m_queue.contains(v))
+            m_queue.decreased(v);
+    }
+    
+    void activity_changed_eh(var v, bool up) {
+        if (m_queue.contains(v)) {
+            if (up) 
+                m_queue.decreased(v);
+            else 
+                m_queue.increased(v);
+        }
+    }
+    
+    void mk_var_eh(var v) {
+        m_queue.reserve(v+1);
+        m_queue.insert(v);
+    }
+    
+    void del_var_eh(var v) {
+        if (m_queue.contains(v))
+            m_queue.erase(v);
+    }
+    
+    void unassign_var_eh(var v) {
+        if (!m_queue.contains(v))
+            m_queue.insert(v);
+    }
+    
+    void reset() {
+        m_queue.reset();
+    }
+    
+    bool empty() const { return m_queue.empty(); }
+    
+    var next_var() { SASSERT(!empty()); return m_queue.erase_min(); }
+    
+    var min_var() { SASSERT(!empty()); return m_queue.min_value(); }
+    
+    bool more_active(var v1, var v2) const { return m_queue.less_than(v1, v2); }
+};
+