/*++
Copyright (c) 2013 Microsoft Corporation

Module Name:

    ddnf.cpp

Abstract:

    DDNF based engine.

Author:

    Nikolaj Bjorner (nbjorner) 2014-08-21

Revision History:

   - inherits from Nuno Lopes Hassel utilities 
     and Garvit Juniwal's DDNF engine.

--*/

#include "muz/ddnf/ddnf.h"
#include "muz/base/dl_rule_set.h"
#include "muz/base/dl_context.h"
#include "ast/scoped_proof.h"
#include "ast/bv_decl_plugin.h"
#include "muz/rel/tbv.h"

namespace datalog {

    class ddnf_mgr;
    class ddnf_node;
    typedef ref_vector<ddnf_node, ddnf_mgr> ddnf_node_vector;

    class ddnf_node {
    public:

        struct eq {
            tbv_manager& m;
            eq(tbv_manager& m):m(m) {}
            bool operator()(ddnf_node* n1, ddnf_node* n2) const {
                return m.equals(n1->get_tbv(), n2->get_tbv());
            }
        };

        struct hash {
            tbv_manager& m;
            hash(tbv_manager& m):m(m) {}
            unsigned operator()(ddnf_node* n) const {
                return m.hash(n->get_tbv());
            }
        };

        typedef ptr_hashtable<ddnf_node, ddnf_node::hash, ddnf_node::eq> ddnf_nodes;
    private:
        tbv_manager&          tbvm;
        tbv const&            m_tbv;
        ddnf_node_vector      m_children;
        unsigned              m_refs;
        unsigned              m_id;
        ddnf_node::hash       m_hash;
        ddnf_node::eq         m_eq;
        ddnf_nodes            m_descendants;

        friend class ddnf_mgr;

    public:
        ddnf_node(ddnf_mgr& m, tbv_manager& tbvm, tbv const& tbv, unsigned id):
            tbvm(tbvm),
            m_tbv(tbv),
            m_children(m),
            m_refs(0),
            m_id(id),
            m_hash(tbvm),
            m_eq(tbvm),
            m_descendants(DEFAULT_HASHTABLE_INITIAL_CAPACITY, m_hash, m_eq) {
        }

        ~ddnf_node() {}

        unsigned inc_ref() {
            return ++m_refs;
        }

        void dec_ref() {
            SASSERT(m_refs > 0);
            --m_refs;
            if (m_refs == 0) {
                dealloc(this);
            }
        }

        ddnf_nodes& descendants() { return m_descendants; }

        unsigned get_id() const { return m_id; }
        
        unsigned num_children() const { return m_children.size(); }

        ddnf_node* operator[](unsigned index) { return m_children[index].get(); }

        tbv const& get_tbv() const { return m_tbv; }

        void add_child(ddnf_node* n);
        
        void remove_child(ddnf_node* n);
        
        bool contains_child(ddnf_node* n) const;

        void display(std::ostream& out) const {
            out << "node[" << get_id() << ": ";
            tbvm.display(out, m_tbv);
            for (unsigned i = 0; i < m_children.size(); ++i) {
                out << " " << m_children[i]->get_id();
            }
            out << "]";
        }
    };

    typedef ddnf_node::ddnf_nodes ddnf_nodes;


    class ddnf_mgr {        
        struct stats {
            unsigned           m_num_inserts;            
            unsigned           m_num_comparisons;
            stats() { reset(); }
            void reset() { memset(this, 0, sizeof(*this)); }
        };

        ddnf_node*             m_root;
        ddnf_node_vector       m_noderefs;
        bool                   m_internalized;
        tbv_manager            m_tbv;
        ddnf_node::hash        m_hash;
        ddnf_node::eq          m_eq;
        ddnf_nodes             m_nodes;
        svector<bool>          m_marked;
        stats                  m_stats;
    public:
        ddnf_mgr(unsigned n): m_noderefs(*this), m_internalized(false), m_tbv(n),
                              m_hash(m_tbv), m_eq(m_tbv),
                              m_nodes(DEFAULT_HASHTABLE_INITIAL_CAPACITY, m_hash, m_eq) {
            tbv* bX = m_tbv.allocateX();
            m_root = alloc(ddnf_node, *this, m_tbv, *bX, m_nodes.size());
            m_noderefs.push_back(m_root);
            m_nodes.insert(m_root);
        }

        ~ddnf_mgr() {
            m_noderefs.reset();
            m_tbv.reset();
        }

        void inc_ref(ddnf_node* n) {
            n->inc_ref();
        }

        void dec_ref(ddnf_node* n) {
            n->dec_ref();
        }

        void reset_accumulate() {
            m_marked.resize(m_nodes.size());
            for (unsigned i = 0; i < m_marked.size(); ++i) {
                m_marked[i] = false;
            }
        }

        void accumulate(tbv const& t, unsigned_vector& acc) {
            ddnf_node* n = find(t);
            ptr_vector<ddnf_node> todo;
            todo.push_back(n);
            while (!todo.empty()) {
                n = todo.back();
                todo.pop_back();
                unsigned id = n->get_id();
                if (m_marked[id]) continue;
                acc.push_back(id);
                m_marked[id] = true;
                unsigned sz = n->num_children();
                for (unsigned i = 0; i < sz; ++i) {
                    todo.push_back((*n)[i]);
                }
            }
        }

        ddnf_node* insert(tbv const& t) {
            SASSERT(!m_internalized);
            ptr_vector<tbv const> new_tbvs;
            new_tbvs.push_back(&t);
            for (unsigned i = 0; i < new_tbvs.size(); ++i) {
                tbv const& nt = *new_tbvs[i];
                IF_VERBOSE(10, m_tbv.display(verbose_stream() << "insert: ", nt); verbose_stream() << "\n";);
                ddnf_node* n;
                if (contains(nt)) {
                    n = find(nt);
                }
                else {
                    n = alloc(ddnf_node, *this, m_tbv, nt, m_noderefs.size());
                    m_noderefs.push_back(n);
                    m_nodes.insert(n);
                }
                insert(*m_root, n, new_tbvs);
            }
            return find(t);
        }

        tbv* allocate(uint64_t v, unsigned hi, unsigned lo) {
            return m_tbv.allocate(v, hi, lo);
        }

        tbv_manager& get_tbv_manager() {
            return m_tbv;
        }

        unsigned size() const { 
            return m_noderefs.size(); 
        }

        ddnf_nodes const& lookup(tbv const& t)  {
            internalize();
            return find(t)->descendants();
        }

        void display_statistics(std::ostream& out) const {            
            std::cout << "Number of insertions:  " << m_stats.m_num_inserts << "\n";
            std::cout << "Number of comparisons: " << m_stats.m_num_comparisons << "\n";
            std::cout << "Number of nodes:       " << size() << "\n";
        }

        void display(std::ostream& out) const {            
            for (unsigned i = 0; i < m_noderefs.size(); ++i) {
                m_noderefs[i]->display(out);
                out << "\n";
            }
        }

        bool contains(tbv const& t) {
            ddnf_node dummy(*this, m_tbv, t, 0);
            return m_nodes.contains(&dummy);
        }    

        bool well_formed() {
            ptr_vector<ddnf_node> todo;
            todo.push_back(m_root);
            reset_accumulate();
            while (!todo.empty()) {
                ddnf_node* n = todo.back();
                todo.pop_back();
                if (m_marked[n->get_id()]) continue;
                m_marked[n->get_id()] = true;
                unsigned sz = n->num_children();
                for (unsigned i = 0; i < sz; ++i) {
                    ddnf_node* child = (*n)[i];
                    if (!m_tbv.contains(n->get_tbv(), child->get_tbv())) {
                        IF_VERBOSE(0, 
                                   m_tbv.display(verbose_stream() << "parent ", n->get_tbv());
                                   m_tbv.display(verbose_stream() << " does not contains child: ", child->get_tbv());
                                   display(verbose_stream());
                                   );
                        return false;
                    }
                    todo.push_back(child);
                }

            }
            return true;
        }
   

    private:

        ddnf_node* find(tbv const& t) {
            ddnf_node dummy(*this, m_tbv, t, 0);
            return *(m_nodes.find(&dummy));
        }
    

        void insert(ddnf_node& root, ddnf_node* new_n, ptr_vector<tbv const>& new_intersections) {
            tbv const& new_tbv = new_n->get_tbv();
            
            IF_VERBOSE(10, m_tbv.display(verbose_stream() << "root: ", root.get_tbv()); 
                       m_tbv.display(verbose_stream() << " new node ", new_tbv); verbose_stream() << "\n";);
            SASSERT(m_tbv.contains(root.get_tbv(), new_tbv));
            if (m_eq(&root, new_n)) return;
            ++m_stats.m_num_inserts;
            bool inserted = false;
            for (unsigned i = 0; i < root.num_children(); ++i) {
                ddnf_node& child = *(root[i]);
                ++m_stats.m_num_comparisons;
                IF_VERBOSE(10, m_tbv.display(verbose_stream() << "child ", child.get_tbv()); 
                           verbose_stream() << " contains: " << m_tbv.contains(child.get_tbv(), new_tbv) << "\n";);
                if (m_tbv.contains(child.get_tbv(), new_tbv)) {
                    inserted = true;
                    insert(child, new_n, new_intersections);
                }
            }
            if (inserted) {
                return;
            }
            ddnf_node_vector subset_children(*this);
            tbv* intr = m_tbv.allocate();
            for (unsigned i = 0; i < root.num_children(); ++i) {
                ddnf_node& child = *(root[i]);
                // cannot be superset
                SASSERT(!m_tbv.contains(child.get_tbv(),new_tbv));
                // checking for subset
                if (m_tbv.contains(new_tbv, child.get_tbv())) {
                    subset_children.push_back(&child);
                    IF_VERBOSE(10, m_tbv.display(verbose_stream() << "contains child", child.get_tbv()); verbose_stream() << "\n";);
                    ++m_stats.m_num_comparisons;
                }
                else if (m_tbv.intersect(child.get_tbv(), new_tbv, *intr)) {
                    // this means there is a non-full intersection
                    new_intersections.push_back(intr);
                    IF_VERBOSE(10, m_tbv.display(verbose_stream() << "intersect child ", child.get_tbv()); verbose_stream() << "\n";);
                    intr = m_tbv.allocate();
                    m_stats.m_num_comparisons += 2;
                }
                else {
                    m_stats.m_num_comparisons += 2;
                }
            }
            m_tbv.deallocate(intr);
            for (unsigned i = 0; i < subset_children.size(); ++i) {
                root.remove_child(subset_children[i].get());
                new_n->add_child(subset_children[i].get());
            }
            root.add_child(new_n);           
        }


        void internalize() {
            // populate maps (should be bit-sets) of decendants.
            if (m_internalized) {                
                return;
            }
            ptr_vector<ddnf_node> todo;
            todo.push_back(m_root);
            svector<bool> done(m_noderefs.size(), false);
            while (!todo.empty()) {
                ddnf_node& n = *todo.back();
                if (done[n.get_id()]) {
                    todo.pop_back();
                    continue;
                }
                unsigned sz = n.num_children();
                bool all_done = true;
                for (unsigned i = 0; i < sz; ++i) {
                    ddnf_node* child = n[i];
                    if (!done[child->get_id()]) {
                        all_done = false;
                        todo.push_back(child);
                    }
                }
                if (all_done) {
                    n.descendants().insert(&n);
                    for (unsigned i = 0; i < sz; ++i) {
                        ddnf_node* child = n[i];
                        add_table(n.descendants(), child->descendants());
                    }
                    done[n.get_id()] = true;
                    todo.pop_back();
                }                
            }
            m_internalized = true;            
        }

        void add_table(ddnf_nodes& dst, ddnf_nodes const& src) {
            ddnf_nodes::iterator it = src.begin(), end = src.end();
            for (; it != end; ++it) {
                dst.insert(*it);
            }
        }        
    };

    ddnf_core::ddnf_core(unsigned n) {
        m_imp = alloc(ddnf_mgr, n);
    }
    ddnf_core::~ddnf_core() {
        dealloc(m_imp);
    }
    ddnf_node* ddnf_core::insert(tbv const& t) {
        return m_imp->insert(t);
    }
    tbv_manager& ddnf_core::get_tbv_manager() {
        return m_imp->get_tbv_manager();
    }
    unsigned ddnf_core::size() const {
        return m_imp->size();
    }
    bool ddnf_core::contains(tbv const& t) {
        return m_imp->contains(t);
    }
    bool ddnf_core::well_formed()  {
        return m_imp->well_formed();
    }

    void ddnf_core::reset_accumulate() {
        return m_imp->reset_accumulate();
    }
    void ddnf_core::accumulate(tbv const& t, unsigned_vector& acc) {
        return m_imp->accumulate(t, acc);
    }
    void ddnf_core::display(std::ostream& out) const {
        m_imp->display(out);
    }
    void ddnf_core::display_statistics(std::ostream& out) const {
        m_imp->display_statistics(out);
    }
    

    void ddnf_node::add_child(ddnf_node* n) {
        //SASSERT(!m_tbv.is_subset(n->m_tbv));
        m_children.push_back(n);
    }
    
    void ddnf_node::remove_child(ddnf_node* n) {
        m_children.erase(n);
    }
    
    bool ddnf_node::contains_child(ddnf_node* n) const {
        return m_children.contains(n);
    }        


    class ddnfs {
        u_map<ddnf_mgr*> m_mgrs;
    public:
        ddnfs() {}

        ~ddnfs() {
            u_map<ddnf_mgr*>::iterator it = m_mgrs.begin(), end = m_mgrs.end();
            for (; it != end; ++it) {
                dealloc(it->m_value);
            }
        }
        
        tbv* allocate(unsigned num_bits, uint64_t v, unsigned hi, unsigned lo) {
            return get(num_bits).allocate(v, hi, lo);
        }
        void insert(unsigned num_bits, tbv const& t) {
            get(num_bits).insert(t);
        }
        
        ddnf_mgr& get(unsigned num_bits) {
            return *insert(num_bits);
        }

        ddnf_nodes const& lookup(unsigned n, tbv const& t) const {
            return m_mgrs.find(n)->lookup(t);
        }

        void display(std::ostream& out) const {
            u_map<ddnf_mgr*>::iterator it = m_mgrs.begin(), end = m_mgrs.end();
            for (; it != end; ++it) {
                it->m_value->display(out);
            }
        }

    private:

        ddnf_mgr* insert(unsigned n) {
            ddnf_mgr* m = nullptr;
            if (!m_mgrs.find(n, m)) {
                m = alloc(ddnf_mgr, n);
                m_mgrs.insert(n, m);
            }
            return m;
        }
    };

    class ddnf::imp {
        struct stats {
            stats() { reset(); }
            void reset() { memset(this, 0, sizeof(*this)); }
        };

        context&               m_ctx;
        ast_manager&           m;
        rule_manager&          rm;
        bv_util                bv;
        ptr_vector<expr>       m_todo;
        ast_mark               m_visited1, m_visited2;
        ddnfs                  m_ddnfs;
        stats                  m_stats;
        obj_map<expr, tbv*>    m_expr2tbv;
        obj_map<expr, expr*>   m_cache;
        expr_ref_vector        m_trail;
        context                m_inner_ctx;

    public:
        imp(context& ctx):
            m_ctx(ctx), 
            m(ctx.get_manager()),
            rm(ctx.get_rule_manager()),
            bv(m),
            m_trail(m),
            m_inner_ctx(m, m_ctx.get_register_engine(), m_ctx.get_fparams())
        {
            params_ref params;
            params.set_sym("engine", symbol("datalog"));
            m_inner_ctx.updt_params(params);
        }

        ~imp() {}        

        lbool query(expr* query) {
            m_ctx.ensure_opened();
            rule_set& old_rules = m_ctx.get_rules();
            rm.mk_query(query, old_rules);
            rule_set new_rules(m_ctx);
            IF_VERBOSE(10, verbose_stream() << "(ddnf.preprocess)\n";);
            if (!pre_process_rules(old_rules)) {
                return l_undef;
            }
            IF_VERBOSE(10, verbose_stream() << "(ddnf.compile)\n";);
            if (!compile_rules1(old_rules, new_rules)) {
                return l_undef;
            }
            IF_VERBOSE(15, m_ddnfs.display(verbose_stream()););

            dump_rules(new_rules);
            return l_undef;

            // return execute_rules(new_rules);
        }
    
       
        void reset_statistics() {
            m_stats.reset();
        }

        void collect_statistics(statistics& st) const {
        }

        void display_certificate(std::ostream& out) const {
            expr_ref ans = get_answer();
            out << mk_pp(ans, m) << "\n";
        }

        expr_ref get_answer() const {
            UNREACHABLE();
            return expr_ref(m.mk_true(), m);
        }

    private:
    
        proof_ref get_proof() const {
            scoped_proof sp(m);
            proof_ref pr(m);
            return pr;
        }
   
        bool pre_process_rules(rule_set const& rules)  {
            m_visited1.reset();
            m_todo.reset();
            m_cache.reset();
            m_expr2tbv.reset();
            datalog::rule_set::iterator it  = rules.begin();
            datalog::rule_set::iterator end = rules.end();
            for (; it != end; ++it) {
                if (!pre_process_rule(**it)) {
                    return false;
                }
            }
            return true;
        }

        bool pre_process_rule(rule const& r) {
            // all predicates are monadic.
            unsigned utsz = r.get_uninterpreted_tail_size();
            unsigned sz = r.get_tail_size();
            for (unsigned i = utsz; i < sz; ++i) {
                m_todo.push_back(r.get_tail(i));
            }
            if (process_todo()) {
                return true;
            }
            else {
                r.display(m_ctx, std::cout);
                return false;
            }
        }

        bool process_todo() {
            while (!m_todo.empty()) {
                expr* e = m_todo.back();
                m_todo.pop_back();
                if (m_visited1.is_marked(e)) {
                    continue;
                }
                m_visited1.mark(e, true);
                if (is_var(e)) {
                    continue;
                }
                if (is_quantifier(e)) {
                    return false;
                }
                if (m.is_and(e) ||
                    m.is_or(e) ||
                    m.is_iff(e) ||
                    m.is_not(e) ||
                    m.is_implies(e)) {
                    m_todo.append(to_app(e)->get_num_args(), to_app(e)->get_args());
                    continue;
                }
                if (is_ground(e)) {
                    continue;
                }
                if (process_atomic(e)) {
                    continue;
                }
                IF_VERBOSE(0, verbose_stream() << "Could not handle: " << mk_pp(e, m) << "\n";);
                return false;
            }
            return true;
        }        

        bool process_atomic(expr* e) {
            expr* e1, *e2, *e3;
            unsigned lo, hi;            
            
            if (m.is_eq(e, e1, e2) && bv.is_bv(e1)) {
                if (is_var(e1) && is_ground(e2)) {
                    return process_eq(e, to_var(e1), bv.get_bv_size(e1)-1, 0, e2); 
                }
                if (is_var(e2) && is_ground(e1)) {
                    return process_eq(e, to_var(e2), bv.get_bv_size(e2)-1, 0, e1); 
                }
                if (bv.is_extract(e1, lo, hi, e3) && is_var(e3) && is_ground(e2)) {
                    return process_eq(e, to_var(e3), hi, lo, e2);
                }
                if (bv.is_extract(e2, lo, hi, e3) && is_var(e3) && is_ground(e1)) {
                    return process_eq(e, to_var(e3), hi, lo, e1);
                }
                if (is_var(e1) && is_var(e2)) {
                    return true;
                }                
            }
            return false;
        }

        bool process_eq(expr* e, var* v, unsigned hi, unsigned lo, expr* c) {
            rational val;
            unsigned sz_c;
            unsigned sz_v = bv.get_bv_size(v);
            if (!bv.is_numeral(c, val, sz_c)) {
                return false;
            }
            if (!val.is_uint64()) {
                return false;
            }
            // v[hi:lo] = val
            tbv* tv = m_ddnfs.allocate(sz_v, val.get_uint64(), hi, lo);
            m_ddnfs.insert(sz_v, *tv);
            m_expr2tbv.insert(e, tv);
            // std::cout << mk_pp(v, m) << " " << lo << " " << hi << " " << v << " " << tbv << "\n";
            return true;
        }

        void init_ctx(rule_set& rules) {
            m_inner_ctx.reset();
            func_decl_set const& predicates = m_ctx.get_predicates();
            for (func_decl_set::iterator fit = predicates.begin(); fit != predicates.end(); ++fit) {
                m_inner_ctx.register_predicate(*fit, false);
            }
            m_inner_ctx.ensure_opened();
            m_inner_ctx.replace_rules(rules);
            m_inner_ctx.close();
        }

        void dump_rules(rule_set& rules) {
            init_ctx(rules);
            m_inner_ctx.display_smt2(0, nullptr, std::cout);
        }

        lbool execute_rules(rule_set& rules) {
            init_ctx(rules);

            ptr_vector<func_decl> heads;
            rule_set::decl2rules::iterator dit  = rules.begin_grouped_rules();
            rule_set::decl2rules::iterator dend = rules.end_grouped_rules();
            for (; dit != dend; ++dit) {
                heads.push_back(dit->m_key);
            }
            return m_inner_ctx.rel_query(heads.size(), heads.c_ptr());
        }

        bool compile_rules1(rule_set const& rules, rule_set& new_rules) {
            datalog::rule_set::iterator it  = rules.begin();
            datalog::rule_set::iterator end = rules.end();
            unsigned idx = 0;
            for (; it != end; ++idx, ++it) {
                if (!compile_rule1(**it, rules, new_rules)) {
                    return false;
                }
            }
            return true;            
        }

        bool compile_rule1(rule& r, rule_set const& old_rules, rule_set& new_rules) {
            app_ref head(m), pred(m);
            app_ref_vector body(m);
            expr_ref tmp(m);
            compile_predicate(r.get_head(), head);
            unsigned utsz = r.get_uninterpreted_tail_size();
            unsigned sz = r.get_tail_size();
            for (unsigned i = 0; i < utsz; ++i) {
                compile_predicate(r.get_tail(i), pred);
                body.push_back(pred);
            }
            for (unsigned i = utsz; i < sz; ++i) {
                compile_expr(r.get_tail(i), tmp);
                body.push_back(to_app(tmp));
            }
            rule* r_new = rm.mk(head, body.size(), body.c_ptr(), nullptr, r.name(), false);
            new_rules.add_rule(r_new);
            IF_VERBOSE(20, r_new->display(m_ctx, verbose_stream()););
            if (old_rules.is_output_predicate(r.get_decl())) {
                new_rules.set_output_predicate(r_new->get_decl());
            }
            return true;
        }

        void compile_predicate(app* p, app_ref& result) {
            sort_ref_vector domain(m);
            func_decl* d = p->get_decl();
            SASSERT(d->get_family_id() == null_family_id);
            for (unsigned i = 0; i < p->get_num_args(); ++i) {
                domain.push_back(compile_sort(m.get_sort(p->get_arg(i))));
            }
            func_decl_ref fn(m);
            fn = m.mk_func_decl(d->get_name(), domain.size(), domain.c_ptr(), m.mk_bool_sort());
            m_ctx.register_predicate(fn, false);
            expr_ref_vector args(m);
            expr_ref tmp(m);
            for (unsigned i = 0; i < p->get_num_args(); ++i) {
                compile_expr(p->get_arg(i), tmp);
                args.push_back(tmp);
            }
            result = m.mk_app(fn, args.size(), args.c_ptr());
        }

        void insert_cache(expr* e, expr* r) {
            m_trail.push_back(r);
            m_cache.insert(e, r);
        }

        void compile_var(var* v, var_ref& result) {
            expr* r;
            if (m_cache.find(v, r)) {
                result = to_var(r);
            }
            else {
                unsigned idx = v->get_idx();
                result = m.mk_var(idx, compile_sort(v->get_sort()));
                insert_cache(v, result);
            }
        }

        sort* compile_sort(sort* s) {
            if (m.is_bool(s)) {
                return s;
            }
            if (bv.is_bv_sort(s)) {
                unsigned sz = bv.get_bv_size(s);
                ddnf_mgr const& mgr = m_ddnfs.get(sz);
                unsigned num_elems = mgr.size();
                unsigned nb = 1;
                while ((1UL << nb) <= num_elems) {
                    ++nb;                    
                }
                return bv.mk_sort(nb);
            }
            UNREACHABLE();
            return nullptr;
        }

        void compile_expr(expr* e, expr_ref& result) {
            expr* r = nullptr;
            if (m_cache.find(e, r)) {
                result = r;
                return;
            }

            if (is_ground(e)) {
                result = e;
                m_cache.insert(e, result);
                return;
            }

            if (is_var(e)) {
                var_ref w(m);
                compile_var(to_var(e), w);
                result = w;
                return;
            }
            
            if (m.is_and(e) ||
                m.is_or(e)  ||
                m.is_iff(e) ||
                m.is_not(e) ||
                m.is_implies(e)) {
                app* a = to_app(e);
                expr_ref tmp(m);
                expr_ref_vector args(m);
                for (unsigned i = 0; i < a->get_num_args(); ++i) {
                    compile_expr(a->get_arg(i), tmp);
                    args.push_back(tmp);
                } 
                result = m.mk_app(a->get_decl(), args.size(), args.c_ptr());
                insert_cache(e, result);
                return;
            }
            
            expr* e1, *e2, *e3;
            unsigned lo, hi; 
            if (m.is_eq(e, e1, e2) && bv.is_bv(e1)) {
                if (is_var(e1) && is_ground(e2)) {
                    compile_eq(e, result, to_var(e1), bv.get_bv_size(e1)-1, 0, e2); 
                }
                else if (is_var(e2) && is_ground(e1)) {
                    compile_eq(e, result, to_var(e2), bv.get_bv_size(e2)-1, 0, e1); 
                }
                else if (bv.is_extract(e1, lo, hi, e3) && is_var(e3) && is_ground(e2)) {
                    compile_eq(e, result, to_var(e3), hi, lo, e2);
                }
                else if (bv.is_extract(e2, lo, hi, e3) && is_var(e3) && is_ground(e1)) {
                    compile_eq(e, result, to_var(e3), hi, lo, e1);
                }
                else if (is_var(e1) && is_var(e2)) {
                    var_ref v1(m), v2(m);
                    compile_var(to_var(e1), v1);
                    compile_var(to_var(e2), v2);
                    result = m.mk_eq(v1, v2);
                }                
                else {
                    UNREACHABLE();
                }
                insert_cache(e, result);
                return;
            }         
            std::cout << mk_pp(e, m) << "\n";
            UNREACHABLE();
        }

        void compile_eq(expr* e, expr_ref& result, var* v, unsigned hi, unsigned lo, expr* c) {
            tbv* t = nullptr;
            // TBD: hi, lo are ignored.
            VERIFY(m_expr2tbv.find(e, t));            
            var_ref w(m);
            compile_var(v, w);
            unsigned num_bits = bv.get_bv_size(c);
            ddnf_nodes const& ns = m_ddnfs.lookup(num_bits, *t);
            ddnf_nodes::iterator it = ns.begin(), end = ns.end();
            expr_ref_vector eqs(m);
            sort* s = m.get_sort(w);
            for (; it != end; ++it) {
                eqs.push_back(m.mk_eq(w, bv.mk_numeral(rational((*it)->get_id()), s)));
            }
            switch (eqs.size()) {
            case 0:
                UNREACHABLE();
                result = m.mk_false();
                break;
            case 1:
                result = eqs[0].get();
                break;
            default:
                result = m.mk_or(eqs.size(), eqs.c_ptr());
                break;
            }
        }
    };

    ddnf::ddnf(context& ctx):
        datalog::engine_base(ctx.get_manager(),"tabulation"),
        m_imp(alloc(imp, ctx)) {        
    }
    ddnf::~ddnf() {
        dealloc(m_imp);
    }    
    lbool ddnf::query(expr* query) {
        return m_imp->query(query);
    }
    void ddnf::reset_statistics() {
        m_imp->reset_statistics();
    }
    void ddnf::collect_statistics(statistics& st) const {
        m_imp->collect_statistics(st);
    }
    void ddnf::display_certificate(std::ostream& out) const {
        m_imp->display_certificate(out);
    }
    expr_ref ddnf::get_answer() {
        return m_imp->get_answer();
    }
};