/*++
Copyright (c) 2022 Microsoft Corporation

Module Name:

    polysat_internalize.cpp

Abstract:

    PolySAT internalize
    
Author:

    Nikolaj Bjorner (nbjorner) 2022-01-26

--*/

#include "params/bv_rewriter_params.hpp"
#include "sat/smt/polysat_solver.h"
#include "sat/smt/euf_solver.h"

namespace polysat {

    euf::theory_var solver::mk_var(euf::enode* n) {
        theory_var v = euf::th_euf_solver::mk_var(n);
        ctx.attach_th_var(n, this, v);
        return v;
    }

    sat::literal solver::internalize(expr* e, bool sign, bool root) {
        force_push();
        SASSERT(m.is_bool(e));
        if (!visit_rec(m, e, sign, root))
            return sat::null_literal;
        sat::literal lit = expr2literal(e);
        if (sign)
            lit.neg();
        return lit;
    }

    void solver::internalize(expr* e) {
        force_push();
        visit_rec(m, e, false, false);
    }

    bool solver::visit(expr* e) {      
        force_push();
        if (!is_app(e) || to_app(e)->get_family_id() != get_id()) {
            ctx.internalize(e);
            return true;
        }
        m_stack.push_back(sat::eframe(e));
        return false;
    }

    bool solver::visited(expr* e) {
        euf::enode* n = expr2enode(e);
        return n && n->is_attached_to(get_id());        
    }

    bool solver::post_visit(expr* e, bool sign, bool root) {
        euf::enode* n = expr2enode(e);
        app* a = to_app(e);

        if (visited(e))
            return true;

        SASSERT(!n || !n->is_attached_to(get_id()));
        if (!n)
            n = mk_enode(e, false);

        SASSERT(!n->is_attached_to(get_id()));
        mk_var(n);
        SASSERT(n->is_attached_to(get_id()));
        internalize_polysat(a);
        return true;
    }
  
    void solver::internalize_polysat(app* a) {

#define if_unary(F) if (a->get_num_args() == 1) { internalize_unary(a, [&](pdd const& p) { return F(p); }); break; }

        switch (a->get_decl_kind()) {
        case OP_BMUL:             internalize_binary(a, [&](pdd const& p, pdd const& q) { return p * q; }); break;
        case OP_BADD:             internalize_binary(a, [&](pdd const& p, pdd const& q) { return p + q; }); break;
        case OP_BSUB:             internalize_binary(a, [&](pdd const& p, pdd const& q) { return p - q; }); break;
        case OP_BLSHR:            internalize_lshr(a); break;
        case OP_BSHL:             internalize_shl(a); break;
        case OP_BASHR:            internalize_ashr(a); break;
        case OP_BAND:             internalize_band(a); break;
        case OP_BOR:              internalize_bor(a); break;
        case OP_BXOR:             internalize_bxor(a); break;
        case OP_BNAND:            if_unary(m_core.bnot); internalize_bnand(a); break;
        case OP_BNOR:             if_unary(m_core.bnot); internalize_bnor(a); break;
        case OP_BXNOR:            if_unary(m_core.bnot); internalize_bxnor(a); break;
        case OP_BNOT:             internalize_unary(a, [&](pdd const& p) { return m_core.bnot(p); }); break;
        case OP_BNEG:             internalize_unary(a, [&](pdd const& p) { return -p; }); break;
        case OP_MKBV:             internalize_mkbv(a); break;
        case OP_BV_NUM:           internalize_num(a); break;
        case OP_ULEQ:             internalize_le<false, false, false>(a); break;
        case OP_SLEQ:             internalize_le<true,  false, false>(a); break;
        case OP_UGEQ:             internalize_le<false, true,  false>(a); break;
        case OP_SGEQ:             internalize_le<true,  true,  false>(a); break;
        case OP_ULT:              internalize_le<false, true,  true>(a); break;
        case OP_SLT:              internalize_le<true,  true,  true>(a); break;
        case OP_UGT:              internalize_le<false, false, true>(a); break;
        case OP_SGT:              internalize_le<true,  false, true>(a); break;

        case OP_BUMUL_NO_OVFL:    internalize_binaryc(a, [&](pdd const& p, pdd const& q) { return m_core.umul_ovfl(p, q); }); break;
        case OP_BSMUL_NO_OVFL:    internalize_binaryc(a, [&](pdd const& p, pdd const& q) { return m_core.smul_ovfl(p, q); }); break;
        case OP_BSMUL_NO_UDFL:    internalize_binaryc(a, [&](pdd const& p, pdd const& q) { return m_core.smul_udfl(p, q); }); break;

        case OP_BUMUL_OVFL:       
        case OP_BSMUL_OVFL:
        case OP_BSDIV_OVFL:
        case OP_BNEG_OVFL:
        case OP_BUADD_OVFL:
        case OP_BSADD_OVFL:
        case OP_BUSUB_OVFL:
        case OP_BSSUB_OVFL:
            verbose_stream() << mk_pp(a, m) << "\n";
            // handled by bv_rewriter for now
            UNREACHABLE();
            break;

        case OP_BUDIV_I:          internalize_udiv_i(a); break;
        case OP_BUREM_I:          internalize_urem_i(a); break;

        case OP_BUDIV:            internalize_div_rem(a, true); break;
        case OP_BUREM:            internalize_div_rem(a, false); break;
        case OP_BSDIV0:           UNREACHABLE(); break;
        case OP_BUDIV0:           UNREACHABLE(); break;
        case OP_BSREM0:           UNREACHABLE(); break;
        case OP_BUREM0:           UNREACHABLE(); break;
        case OP_BSMOD0:           UNREACHABLE(); break;

        case OP_EXTRACT:          internalize_extract(a); break;
        case OP_CONCAT:           internalize_concat(a); break;
        case OP_ZERO_EXT:         internalize_zero_extend(a); break;
        case OP_SIGN_EXT:         internalize_sign_extend(a); break; 

        case OP_BSREM:          
        case OP_BSREM_I:          
        case OP_BSMOD:            
        case OP_BSMOD_I:         
        case OP_BSDIV:            
        case OP_BSDIV_I:
        case OP_BREDOR:  // x > 0               unary, return single bit, 1 if at least one input bit is set.
        case OP_BREDAND: // x == 2^K - 1        unary, return single bit, 1 if all input bits are set.
        case OP_BCOMP:   // x == y ? 1 : 0      binary, return single bit, 1 if the arguments are equal.
        case OP_ROTATE_LEFT:
        case OP_ROTATE_RIGHT:
        case OP_EXT_ROTATE_LEFT:
        case OP_EXT_ROTATE_RIGHT:
        case OP_INT2BV:
        case OP_BV2INT:           
            if (bv.is_bv(a))
                expr2pdd(a);
            m_delayed_axioms.push_back(a);            
            ctx.push(push_back_vector(m_delayed_axioms));
            break;

        default:
            IF_VERBOSE(0, verbose_stream() << mk_pp(a, m) << "\n");
            NOT_IMPLEMENTED_YET();
            return;
        }
#undef if_unary
    }

    class solver::mk_atom_trail : public trail {
        solver& th;
        sat::bool_var m_var;
    public:
        mk_atom_trail(sat::bool_var v, solver& th) : th(th), m_var(v) {}
        void undo() override {
            th.erase_bv2a(m_var);
        }
    };

    void solver::mk_atom(sat::bool_var bv, signed_constraint& sc) {
        if (get_bv2a(bv))
            return;
        auto index = m_core.register_constraint(sc, dependency(bv));
        auto a = new (get_region()) atom(bv, index);
        insert_bv2a(bv, a);
        ctx.push(mk_atom_trail(bv, *this));
    }

    void solver::internalize_binaryc(app* e, std::function<polysat::signed_constraint(pdd, pdd)> const& fn) {
        auto p = expr2pdd(e->get_arg(0));
        auto q = expr2pdd(e->get_arg(1));
        auto sc = ~fn(p, q);
        sat::literal lit = expr2literal(e);
        if (lit.sign())
            sc = ~sc;
        mk_atom(lit.var(), sc);
    }

    void solver::internalize_udiv_i(app* e) {
        expr* x, *y;
        expr_ref rm(m);
        if (bv.is_bv_udivi(e, x, y))
            rm = bv.mk_bv_urem_i(x, y);
        else if (bv.is_bv_udiv(e, x, y))
            rm = bv.mk_bv_urem(x, y);
        else
            UNREACHABLE();
        internalize(rm);
    }

    // From "Hacker's Delight", section 2-2. Addition Combined with Logical Operations;
    // found via Int-Blasting paper; see https://doi.org/10.1007/978-3-030-94583-1_24
    // (p + q) - band(p, q);
    void solver::internalize_bor(app* n) { 
        internalize_binary(n, [&](expr* const& x, expr* const& y) { return bv.mk_bv_sub(bv.mk_bv_add(x, y), bv.mk_bv_and(x, y)); });   
    }

    // From "Hacker's Delight", section 2-2. Addition Combined with Logical Operations;
    // found via Int-Blasting paper; see https://doi.org/10.1007/978-3-030-94583-1_24
    // (p + q) - 2*band(p, q);
    void solver::internalize_bxor(app* n) {
        internalize_binary(n, [&](expr* const& x, expr* const& y) { 
            return bv.mk_bv_sub(bv.mk_bv_add(x, y), bv.mk_bv_add(bv.mk_bv_and(x, y), bv.mk_bv_and(x, y))); 
            });
    }

    void solver::internalize_bnor(app* n) {
        internalize_binary(n, [&](expr* const& x, expr* const& y) { return bv.mk_bv_not(bv.mk_bv_or(x, y)); });
    }

    void solver::internalize_bnand(app* n) {
        internalize_binary(n, [&](expr* const& x, expr* const& y) { return bv.mk_bv_not(bv.mk_bv_and(x, y)); });
    }

    void solver::internalize_bxnor(app* n) {
        internalize_binary(n, [&](expr* const& x, expr* const& y) { return bv.mk_bv_not(bv.mk_bv_xor(x, y)); });
    }

    void solver::internalize_band(app* n) {
        if (n->get_num_args() == 2) {
            expr* x, * y;
            VERIFY(bv.is_bv_and(n, x, y));
            m_core.band(expr2pdd(x), expr2pdd(y), expr2pdd(n));
        }
        else {
            expr_ref z(n->get_arg(0), m);
            for (unsigned i = 1; i < n->get_num_args(); ++i) {
                z = bv.mk_bv_and(z, n->get_arg(i));
                ctx.internalize(z);
            }
            internalize_set(n, expr2pdd(z));
        }
    }

    void solver::internalize_lshr(app* n) {
        expr* x, * y;
        VERIFY(bv.is_bv_lshr(n, x, y));
        m_core.lshr(expr2pdd(x), expr2pdd(y), expr2pdd(n));
    }

    void solver::internalize_ashr(app* n) {
        expr* x, * y;
        VERIFY(bv.is_bv_ashr(n, x, y));
        m_core.ashr(expr2pdd(x), expr2pdd(y), expr2pdd(n));
    }

    void solver::internalize_shl(app* n) {
        expr* x, * y;
        VERIFY(bv.is_bv_shl(n, x, y));
        m_core.shl(expr2pdd(x), expr2pdd(y), expr2pdd(n));
    }

    bool solver::propagate_delayed_axioms() {
        if (m_delayed_axioms_qhead == m_delayed_axioms.size())
            return false;
        ctx.push(value_trail(m_delayed_axioms_qhead));
        for (; m_delayed_axioms_qhead < m_delayed_axioms.size() && !inconsistent(); ++m_delayed_axioms_qhead) {
            app* e = m_delayed_axioms[m_delayed_axioms_qhead];
            expr* x, *y;
            unsigned n = 0;
            if (bv.is_bv_sdiv(e, x, y))
                axiomatize_sdiv(e, x, y);
            else if (bv.is_bv_sdivi(e, x, y))
                axiomatize_sdiv(e, x, y);
            else if (bv.is_bv_srem(e, x, y))
                axiomatize_srem(e, x, y);
            else if (bv.is_bv_sremi(e, x, y))
                axiomatize_srem(e, x, y);
            else if (bv.is_bv_smod(e, x, y))
                axiomatize_smod(e, x, y);
            else if (bv.is_bv_smodi(e, x, y))
                axiomatize_smod(e, x, y);
            else if (bv.is_redand(e, x))
                axiomatize_redand(e, x);
            else if (bv.is_redor(e, x))
                axiomatize_redor(e, x);
            else if (bv.is_comp(e, x, y))
                axiomatize_comp(e, x, y);
            else if (bv.is_rotate_left(e, n, x))
                axiomatize_rotate_left(e, n, x);
            else if (bv.is_rotate_right(e, n, x))
                axiomatize_rotate_right(e, n, x);
            else if (bv.is_ext_rotate_left(e, x, y))
                axiomatize_ext_rotate_left(e, x, y);
            else if (bv.is_ext_rotate_right(e, x, y))
                axiomatize_ext_rotate_right(e, x, y);
            else if (bv.is_bv2int(e, x))
                axiomatize_bv2int(e, x);
            else if (bv.is_int2bv(e, n, x))
                axiomatize_int2bv(e, n, x);
            else if (bv.is_extract(e))
                axioms_for_extract(e);
            else
                UNREACHABLE();
        }
        return true;
    }

    void solver::axiomatize_int2bv(app* e, unsigned sz, expr* x) {
        // e = int2bv(x)
        // bv2int(int2bv(x)) = x mod N   
        rational N = rational::power_of_two(sz);
        add_unit(eq_internalize(bv.mk_bv2int(e), m_autil.mk_mod(x, m_autil.mk_int(N))));        
    }
    
    void solver::axiomatize_bv2int(app* e, expr* x) {
        // e := bv2int(x)
        // e = sum_bits(x)
        unsigned sz = bv.get_bv_size(x);
        expr* one = m_autil.mk_int(1);
        expr* zero = m_autil.mk_int(0);
        expr* r = zero;
        pdd p = expr2pdd(x);
        for (unsigned i = 0; i < sz; ++i)
            r = m_autil.mk_add(r, m.mk_ite(constraint2expr(m_core.bit(p, i)), one, zero));
        add_unit(eq_internalize(e, r));
    }


    expr* solver::rotate_left(app* e, unsigned n, expr* x) {
        unsigned sz = bv.get_bv_size(x);
        n = n % sz;
        if (n == 0 || sz == 1)
            return x;
        else
            return bv.mk_concat(bv.mk_extract(n, 0, x), bv.mk_extract(sz - 1, sz - n - 1, x));
    }    

    void solver::axiomatize_rotate_left(app* e, unsigned n, expr* x) {
        // e = x[n : 0] ++ x[sz - 1, sz - n - 1] 
        add_unit(eq_internalize(e, rotate_left(e, n, x)));              
    }

    void solver::axiomatize_rotate_right(app* e, unsigned n, expr* x) {
        unsigned sz = bv.get_bv_size(x);
        axiomatize_rotate_left(e, sz - n, x);
    }

    void solver::axiomatize_ext_rotate_left(app* e, expr* x, expr* y) {
        unsigned sz = bv.get_bv_size(x);
        for (unsigned i = 0; i < sz; ++i)
            add_clause(~eq_internalize(bv.mk_numeral(i, sz), y), eq_internalize(e, rotate_left(e, i, x)));
        add_clause(~mk_literal(bv.mk_ule(bv.mk_numeral(sz, sz), y)), eq_internalize(e, bv.mk_zero(sz)));
    }

    void solver::axiomatize_ext_rotate_right(app* e, expr* x, expr* y) {
        unsigned sz = bv.get_bv_size(x);
        for (unsigned i = 0; i < sz; ++i)
            add_clause(~eq_internalize(bv.mk_numeral(i, sz), y), eq_internalize(e, rotate_left(e, sz - i, x)));
        add_clause(~mk_literal(bv.mk_ule(bv.mk_numeral(sz, sz), y)), eq_internalize(e, bv.mk_zero(sz)));
    }

    // x = N - 1
    void solver::axiomatize_redand(app* e, expr* x) {
        unsigned sz = bv.get_bv_size(x);
        rational N = rational::power_of_two(sz);
        add_equiv(expr2literal(e), eq_internalize(x, bv.mk_numeral(N - 1, sz)));
    }

    void solver::axiomatize_redor(app* e, expr* x) {
        unsigned sz = bv.get_bv_size(x);
        add_equiv(expr2literal(e), ~eq_internalize(x, bv.mk_zero(sz)));
    }

    void solver::axiomatize_comp(app* e, expr* x, expr* y) {
        unsigned sz = bv.get_bv_size(x);
        auto eq = eq_internalize(x, y);
        add_clause(~eq, eq_internalize(e, bv.mk_numeral(1, sz)));
        add_clause(eq, eq_internalize(e, bv.mk_numeral(0, sz)));
    }

    // y = 0 -> x
    // else x - sdiv(x, y) * y
    void solver::axiomatize_srem(app* e, expr* x, expr* y) {
        unsigned sz = bv.get_bv_size(x);
        sat::literal y_eq0 = eq_internalize(y, bv.mk_zero(sz));
        add_clause(~y_eq0, eq_internalize(e, x));
        add_clause(y_eq0, eq_internalize(e, bv.mk_bv_mul(bv.mk_bv_sdiv(x, y), y)));
    }

    // u := umod(x, y)
    // u = 0 ->  0
    // y = 0 ->  x
    // x < 0, y < 0 ->  -u
    // x < 0, y >= 0 ->  y - u
    // x >= 0, y < 0 ->  y + u
    // x >= 0, y >= 0 ->  u
    void solver::axiomatize_smod(app* e, expr* x, expr* y) {
        unsigned sz = bv.get_bv_size(x);
        expr* u = bv.mk_bv_urem(x, y);
        rational N = rational::power_of_two(bv.get_bv_size(x));
        expr* signx = bv.mk_ule(bv.mk_numeral(N / 2, sz), x);
        expr* signy = bv.mk_ule(bv.mk_numeral(N / 2, sz), y);
        sat::literal lsignx = mk_literal(signx);
        sat::literal lsigny = mk_literal(signy);
        sat::literal u_eq0 = eq_internalize(u, bv.mk_zero(sz)); 
        sat::literal y_eq0 = eq_internalize(y, bv.mk_zero(sz)); 
        add_clause(~u_eq0, eq_internalize(e, bv.mk_zero(sz)));
        add_clause(u_eq0, ~y_eq0, eq_internalize(e, x));
        add_clause(~lsignx, ~lsigny, eq_internalize(e, bv.mk_bv_neg(u)));
        add_clause(y_eq0, ~lsignx, lsigny, eq_internalize(e, bv.mk_bv_sub(y, u)));
        add_clause(y_eq0, lsignx, ~lsigny, eq_internalize(e, bv.mk_bv_add(y, u)));
        add_clause(y_eq0, lsignx, lsigny, eq_internalize(e, u));
    }


    // d = udiv(abs(x), abs(y))
    // y = 0, x > 0 -> 1
    // y = 0, x <= 0 -> -1
    // x = 0, y != 0 -> 0
    // x > 0, y < 0 -> -d
    // x < 0, y > 0 -> -d
    // x > 0, y > 0 -> d
    // x < 0, y < 0 -> d
    void solver::axiomatize_sdiv(app* e, expr* x, expr* y) {
        unsigned sz = bv.get_bv_size(x);
        rational N = rational::power_of_two(bv.get_bv_size(x));
        expr* signx = bv.mk_ule(bv.mk_numeral(N/2, sz), x);
        expr* signy = bv.mk_ule(bv.mk_numeral(N/2, sz), y);
        expr* absx = m.mk_ite(signx, bv.mk_bv_sub(bv.mk_numeral(N-1, sz), x), x);
        expr* absy = m.mk_ite(signy, bv.mk_bv_sub(bv.mk_numeral(N-1, sz), y), y);
        expr* d = bv.mk_bv_udiv(absx, absy);
        sat::literal lsignx = mk_literal(signx);
        sat::literal lsigny = mk_literal(signy);
        sat::literal y_eq0 = eq_internalize(y, bv.mk_zero(sz));
        add_clause(~y_eq0, ~lsignx, eq_internalize(e, bv.mk_numeral(1, sz)));
        add_clause(~y_eq0, lsignx, eq_internalize(e, bv.mk_numeral(N-1, sz)));
        add_clause(y_eq0, lsignx, ~lsigny, eq_internalize(e, bv.mk_bv_neg(d)));
        add_clause(y_eq0, ~lsignx, lsigny, eq_internalize(e, bv.mk_bv_neg(d)));
        add_clause(y_eq0, lsignx, lsigny, eq_internalize(e, d));
        add_clause(y_eq0, ~lsignx, ~lsigny, eq_internalize(e, d));
    }    

    void solver::internalize_urem_i(app* rem) {
        expr* x, *y;
        euf::enode* n = expr2enode(rem);
        SASSERT(n && n->is_attached_to(get_id()));
        theory_var v = n->get_th_var(get_id());
        if (m_var2pdd_valid.get(v, false))
            return;
        expr_ref quot(m);
        if (bv.is_bv_uremi(rem, x, y))
            quot = bv.mk_bv_udiv_i(x, y);
        else if (bv.is_bv_urem(rem, x, y))
            quot = bv.mk_bv_udiv(x, y);
        else
            UNREACHABLE();
        m_var2pdd_valid.setx(v, true, false);
        ctx.internalize(quot);
        m_var2pdd_valid.setx(v, false, false);
        quot_rem(quot, rem, x, y);
    }
    
    void solver::quot_rem(expr* quot, expr* rem, expr* x, expr* y) {
        pdd a = expr2pdd(x);
        pdd b = expr2pdd(y);
        euf::enode* qn = expr2enode(quot);
        euf::enode* rn = expr2enode(rem);
        auto& m = a.manager();
        unsigned sz = m.power_of_2();
        if (b.is_zero()) {
            // By SMT-LIB specification, b = 0 ==> q = -1, r = a.
            internalize_set(quot, m.mk_val(m.max_value()));
            internalize_set(rem, a);
            return;
        }
        if (b.is_one()) {
            internalize_set(quot, a);
            internalize_set(rem, m.zero());
            return;
        }

        if (a.is_val() && b.is_val()) {
            rational const av = a.val();
            rational const bv = b.val();
            SASSERT(!bv.is_zero());
            rational rv;
            rational qv = machine_div_rem(av, bv, rv);
            pdd q = m.mk_val(qv);
            pdd r = m.mk_val(rv);
            SASSERT_EQ(a, b * q + r);
            SASSERT(b.val() * q.val() + r.val() <= m.max_value());
            SASSERT(r.val() <= (b * q + r).val());
            SASSERT(r.val() < b.val());
            internalize_set(quot, q);
            internalize_set(rem, r);
            return;
        }       
        
        pdd r = var2pdd(rn->get_th_var(get_id()));
        pdd q = var2pdd(qn->get_th_var(get_id()));

        // Axioms for quotient/remainder
        // 
        //      a = b*q + r
        //      multiplication does not overflow in b*q
        //      addition does not overflow in (b*q) + r; for now expressed as: r <= bq+r
        //      b ≠ 0  ==>  r < b
        //      b = 0  ==>  q = -1
        // TODO: when a,b become evaluable, can we actually propagate q,r? doesn't seem like it.
        //       Maybe we need something like an op_constraint for better propagation.
        add_axiom("[axiom] quot_rem 1", { m_core.eq(b * q + r - a) }, false);
        add_axiom("[axiom] quot_rem 2", { ~m_core.umul_ovfl(b, q) }, false);
        // r <= b*q+r
        //  { apply equivalence:  p <= q  <=>  q-p <= -p-1 }
        // b*q <= -r-1
        add_axiom("[axiom] quot_rem 3", { m_core.ule(b * q, -r - 1) }, false);

        auto c_eq = m_core.eq(b);
        if (!c_eq.is_always_true())
            add_axiom("[axiom] quot_rem 4", { c_eq, ~m_core.ule(b, r) }, false);
        if (!c_eq.is_always_false())
            add_axiom("[axiom] quot_rem 5", { ~c_eq, m_core.eq(q + 1) }, false);
    }

    void solver::internalize_sign_extend(app* e) {
        expr* arg = e->get_arg(0);        
        unsigned sz = bv.get_bv_size(e);
        unsigned arg_sz = bv.get_bv_size(arg);
        unsigned sz2 = sz - arg_sz;
        var2pdd(expr2enode(e)->get_th_var(get_id()));
        if (arg_sz == sz) 
            add_clause(eq_internalize(e, arg), nullptr);
        else {
            sat::literal lt0 = ctx.mk_literal(bv.mk_slt(arg, bv.mk_numeral(0, arg_sz)));
            // arg < 0 ==> e = concat(arg, 1...1)
            // arg >= 0 ==> e = concat(arg, 0...0)
            add_clause(lt0, eq_internalize(e, bv.mk_concat(arg, bv.mk_numeral(rational::power_of_two(sz2) - 1, sz2))), nullptr);
            add_clause(~lt0, eq_internalize(e, bv.mk_concat(arg, bv.mk_numeral(0, sz2))), nullptr);
        }
    }

    void solver::internalize_zero_extend(app* e) {
        expr* arg = e->get_arg(0);
        unsigned sz = bv.get_bv_size(e);
        unsigned arg_sz = bv.get_bv_size(arg);
        unsigned sz2 = sz - arg_sz;
        var2pdd(expr2enode(e)->get_th_var(get_id()));
        if (arg_sz == sz)
            add_clause(eq_internalize(e, arg), nullptr);
        else 
            // e = concat(arg, 0...0)
            add_clause(eq_internalize(e, bv.mk_concat(arg, bv.mk_numeral(0, sz2))), nullptr);
    }

    void solver::internalize_div_rem(app* e, bool is_div) {
        bv_rewriter_params p(s().params());
        if (p.hi_div0()) {
            if (is_div)
                internalize_udiv_i(e);
            else
                internalize_urem_i(e);
            return;
        }
        expr* arg1 = e->get_arg(0);
        expr* arg2 = e->get_arg(1);
        unsigned sz = bv.get_bv_size(e);
        expr_ref zero(bv.mk_numeral(0, sz), m);
        sat::literal eqZ = eq_internalize(arg2, zero);
        sat::literal eqU = eq_internalize(e, is_div ? bv.mk_bv_udiv0(arg1) : bv.mk_bv_urem0(arg1));
        sat::literal eqI = eq_internalize(e, is_div ? bv.mk_bv_udiv_i(arg1, arg2) : bv.mk_bv_urem_i(arg1, arg2));
        add_clause(~eqZ, eqU);
        add_clause(eqZ, eqI);
        ctx.add_aux(~eqZ, eqU);
        ctx.add_aux(eqZ, eqI);        
    }

    void solver::internalize_num(app* a) {
        rational val;
        unsigned sz = 0;
        VERIFY(bv.is_numeral(a, val, sz));        
        auto p = m_core.value(val, sz);
        internalize_set(a, p);
    }

    // TODO - test that internalize works with recursive call on bit2bool
    void solver::internalize_mkbv(app* a) {
        unsigned i = 0;
        for (expr* arg : *a) {
            expr_ref b2b(m);
            b2b = bv.mk_bit2bool(a, i);            
            sat::literal bit_i = ctx.internalize(b2b, false, false);
            sat::literal lit = expr2literal(arg);
            add_equiv(lit, bit_i);
#if 0
            ctx.add_aux_equiv(lit, bit_i);
#endif
            ++i;
        }
    }

    void solver::internalize_extract(app* e) {
        m_delayed_axioms.push_back(e);
        ctx.push(push_back_vector(m_delayed_axioms));
        var2pdd(expr2enode(e)->get_th_var(get_id()));
    }

    // x[hi:lo] = 0 or x >= 2^lo
    // x[w-1:lo] = 0 => x < 2^lo
    void solver::axioms_for_extract(app* e) {
        unsigned hi, lo;
        expr* x;
        VERIFY(bv.is_extract(e, lo, hi, x));
        auto sz_e = hi - lo + 1;
        auto sz_x = bv.get_bv_size(x);
        auto eq0 = eq_internalize(e, bv.mk_numeral(0, sz_e));
        auto gelo = mk_literal(bv.mk_ule(bv.mk_numeral(rational::power_of_two(lo), sz_x), x));
        add_clause(eq0, gelo);
        if (hi + 1 == sz_e) 
            add_clause(~eq0, ~gelo);        
    }

    void solver::internalize_concat(app* e) {
        SASSERT(bv.is_concat(e));
        var2pdd(expr2enode(e)->get_th_var(get_id()));
    }

    void solver::internalize_par_unary(app* e, std::function<pdd(pdd,unsigned)> const& fn) {
        pdd const p = expr2pdd(e->get_arg(0));
        unsigned const par = e->get_parameter(0).get_int();
        internalize_set(e, fn(p, par));
    }

    void solver::internalize_binary(app* e, std::function<pdd(pdd, pdd)> const& fn) {
        SASSERT(e->get_num_args() >= 1);
        auto p = expr2pdd(e->get_arg(0));
        for (unsigned i = 1; i < e->get_num_args(); ++i) 
            p = fn(p, expr2pdd(e->get_arg(i)));
        internalize_set(e, p);
    }

    void solver::internalize_binary(app* e, std::function<expr* (expr*, expr*)> const& fn) {
        SASSERT(e->get_num_args() >= 1);
        expr* r = e->get_arg(0);
        for (unsigned i = 1; i < e->get_num_args(); ++i)
            r = fn(r, e->get_arg(i));
        ctx.internalize(r);
        internalize_set(e, var2pdd(expr2enode(r)->get_th_var(get_id())));
    }

    void solver::internalize_unary(app* e, std::function<pdd(pdd)> const& fn) {
        SASSERT(e->get_num_args() == 1);
        auto p = expr2pdd(e->get_arg(0));
        internalize_set(e, fn(p));
    }

    template<bool Signed, bool Rev, bool Negated>
    void solver::internalize_le(app* e) {
        SASSERT(e->get_num_args() == 2);
        auto p = expr2pdd(e->get_arg(0));
        auto q = expr2pdd(e->get_arg(1));
        if (Rev)
            std::swap(p, q);
        auto sc = Signed ? m_core.sle(p, q) : m_core.ule(p, q);
        if (Negated)
            sc = ~sc;
        
        sat::literal lit = expr2literal(e);
        if (lit.sign())
            sc = ~sc;
        mk_atom(lit.var(), sc);
    }

    dd::pdd solver::expr2pdd(expr* e) {
        return var2pdd(get_th_var(e));
    }

    dd::pdd solver::var2pdd(euf::theory_var v) {
        if (!m_var2pdd_valid.get(v, false)) {
            unsigned bv_size = get_bv_size(v);
            pvar pv = m_core.add_var(bv_size);
            m_pddvar2var.setx(pv, v, UINT_MAX);
            pdd p = m_core.var(pv);
            internalize_set(v, p);
            return p;
        }
        return m_var2pdd[v];
    }

    void solver::apply_sort_cnstr(euf::enode* n, sort* s) {
        if (!bv.is_bv(n->get_expr()))
            return;
        theory_var v = n->get_th_var(get_id());
        if (v == euf::null_theory_var) 
            v = mk_var(n);
        var2pdd(v);
    }

    void solver::internalize_set(expr* e, pdd const& p) {
        internalize_set(get_th_var(e), p);
    }

    void solver::internalize_set(euf::theory_var v, pdd const& p) {
        SASSERT_EQ(get_bv_size(v), p.power_of_2());
        m_var2pdd.reserve(get_num_vars(), p);
        m_var2pdd_valid.reserve(get_num_vars(), false);
        ctx.push(set_bitvector_trail(m_var2pdd_valid, v));
        m_var2pdd[v].reset(p.manager());
        m_var2pdd[v] = p;
    }

    void solver::eq_internalized(euf::enode* n) {
        SASSERT(m.is_eq(n->get_expr()));
    }


}