/*++
Copyright (c) 2021 Microsoft Corporation

Module Name:

    Conflict explanation / resolution

Author:

    Nikolaj Bjorner (nbjorner) 2021-03-19
    Jakob Rath 2021-04-6

--*/
#include "math/polysat/explain.h"
#include "math/polysat/log.h"

namespace polysat {

    conflict_explainer::conflict_explainer(solver& s, constraints_and_clauses const& conflict):
        m_solver(s), m_conflict(conflict) {}

    clause_ref conflict_explainer::resolve(pvar v, ptr_vector<constraint> const& cjust) {
        LOG_H3("Attempting to explain conflict for v" << v);
        m_var = v;
        m_cjust_v = cjust;

        for (auto* c : cjust)
            m_conflict.push_back(c);

        for (auto* c : m_conflict.units())
            LOG("Constraint: " << show_deref(c));
        for (auto* c : m_conflict.clauses())
            LOG("Clause: " << show_deref(c));

        // TODO: this is a temporary workaround! we should not get any undef constraints at this point
        constraints_and_clauses confl = std::move(m_conflict);
        SASSERT(m_conflict.empty());
        for (auto* c : confl.units())
            if (!c->is_undef())
                m_conflict.push_back(c);
        for (auto* c : confl.clauses())
            m_conflict.push_back(c);

        // Collect unit constraints
        //
        // TODO: the distinction between units and unit clauses is a bit awkward; maybe it should be removed.
        //       We could then also remove the hybrid container 'constraints_and_clauses' by a clause_ref_vector
        SASSERT(m_conflict_units.empty());
        for (constraint* c : m_conflict.units())
            // if (c->is_eq())
                m_conflict_units.push_back(c);
        for (auto clause : m_conflict.clauses()) {
            if (clause->size() == 1) {                    
                sat::literal lit = (*clause)[0];
                constraint* c = m_solver.m_constraints.lookup(lit.var());                    
                LOG("unit clause: " << show_deref(c));
                // Morally, a derived unit clause is always asserted at the base level.
                // (Even if we don't want to keep this one around. But maybe we should? Do we want to reconstruct proofs?)
                c->set_unit_clause(clause);
                c->assign(!lit.sign());
                // this clause is really a unit.
                // if (c->is_eq()) {
                    m_conflict_units.push_back(c);
                // }
            }
        }

        // TODO: we should share work done for examining constraints between different resolution methods
        clause_ref lemma;
        if (!lemma) lemma = by_polynomial_superposition();
        if (!lemma) lemma = by_ugt_x();
        if (!lemma) lemma = by_ugt_y();
        if (!lemma) lemma = by_ugt_z();
        if (!lemma) lemma = y_ule_ax_and_x_ule_z();

        DEBUG_CODE({
            if (lemma) {
                LOG("New lemma: " << *lemma);
                for (auto* c : lemma->new_constraints()) {
                    LOG("New constraint: " << show_deref(c));
                }
                // All constraints in the lemma must be false in the conflict state
                for (auto lit : lemma->literals()) {
                    if (m_solver.m_bvars.value(lit) == l_false)
                        continue;
                    SASSERT(m_solver.m_bvars.value(lit) != l_true);
                    constraint* c = m_solver.m_constraints.lookup(lit.var());
                    SASSERT(c);
                    tmp_assign _t(c, lit);
                    // if (c->is_currently_true(m_solver)) {
                    //     LOG("ERROR: constraint is true: " << show_deref(c));
                    //     SASSERT(false);
                    // }
                    // SASSERT(!c->is_currently_true(m_solver));
                    // SASSERT(c->is_currently_false(m_solver));   // TODO: pvar v may not have a value at this point...
                }
            }
            else {
                LOG("No lemma");
            }
        });

        m_var = null_var;
        m_cjust_v.reset();
        return lemma;
    }

    /**
     *  Polynomial superposition.
     *  So far between two equalities.
     *  TODO: Also handle =, != superposition here?
     *  TODO: handle case when m_conflict.units().size() > 2
     *  TODO: handle super-position into a clause?
     */
    clause_ref conflict_explainer::by_polynomial_superposition() {
        LOG_H3("units-size: " << m_conflict.units().size() << " conflict-clauses " << m_conflict.clauses().size());

#if 0
        constraint* c1 = nullptr, *c2 = nullptr;

        if (m_conflict.units().size() == 2 && m_conflict.clauses().size() == 0) {
            c1 = m_conflict.units()[0];
            c2 = m_conflict.units()[1];
        }
        else {
            // other combinations?

#if 1
            // A clause can also be a unit.
            // Even if a clause is not a unit, we could still resolve a propagation 
            // into some literal in the current conflict clause.
            // Selecting resolvents should not be specific to superposition.

            for (auto clause : m_conflict.clauses()) {
                LOG("clause " << *clause << "  size " << clause->size());
                if (clause->size() == 1) {                    
                    sat::literal lit = (*clause)[0];
                    // if (lit.sign())
                    //     continue;
                    constraint* c = m_solver.m_constraints.lookup(lit.var());                    
                    // Morally, a derived unit clause is always asserted at the base level.
                    // (Even if we don't want to keep this one around. But maybe we should? Do we want to reconstruct proofs?)
                    c->set_unit_clause(clause);
                    c->assign(!lit.sign());
                    // this clause is really a unit.
                    LOG("unit clause: " << *c);
                    if (c->is_eq()) { //  && c->is_positive()) {
                        c1 = c;
                        break;
                    }
                }
            }
            if (!c1)
                return nullptr;

            for (constraint* c : m_conflict.units()) {
                if (c->is_eq() && c->is_positive()) {
                    c2 = c;
                    break;
                }
            }
#endif
        }
        if (!c1 || !c2 || c1 == c2)
            return nullptr;
        LOG("c1: " << show_deref(c1));
        LOG("c2: " << show_deref(c2));
        if (c1->is_eq() && c2->is_eq() && c1->is_positive() && c2->is_positive()) {
            pdd a = c1->to_eq().p();
            pdd b = c2->to_eq().p();
            pdd r = a;
            if (!a.resolve(m_var, b, r) && !b.resolve(m_var, a, r))
                return nullptr;
            unsigned const lvl = std::max(c1->level(), c2->level());
            clause_builder clause(m_solver);
            clause.push_literal(~c1->blit());
            clause.push_literal(~c2->blit());
            clause.push_new_constraint(m_solver.m_constraints.eq(lvl, r));
            return clause.build();
        }
        if (c1->is_eq() && c2->is_eq() && c1->is_negative() && c2->is_positive()) {
            pdd a = c1->to_eq().p();
            pdd b = c2->to_eq().p();
            pdd r = a;
            // TODO: only holds if the factor for 'a' is non-zero
            if (!a.resolve(m_var, b, r))
                return nullptr;
            unsigned const lvl = std::max(c1->level(), c2->level());
            clause_builder clause(m_solver);
            clause.push_literal(~c1->blit());
            clause.push_literal(~c2->blit());
            clause.push_new_constraint(~m_solver.m_constraints.eq(lvl, r));
            SASSERT(false);  // TODO "breakpoint" for debugging
            return clause.build();
        }

#else
        for (constraint* c1 : m_conflict_units) {
            if (!c1->is_eq())
                continue;
            for (constraint* c2 : m_conflict_units) {  // TODO: can start iteration at index(c1)+1
                if (c1 == c2)
                    continue;
                if (!c2->is_eq())
                    continue;
                if (c1->is_negative() && c2->is_negative())
                    continue;
                LOG("c1: " << show_deref(c1));
                LOG("c2: " << show_deref(c2));
                if (c1->is_positive() && c2->is_negative()) {
                    std::swap(c1, c2);
                }
                pdd a = c1->to_eq().p();
                pdd b = c2->to_eq().p();
                pdd r = a;
                unsigned const lvl = std::max(c1->level(), c2->level());
                if (c1->is_positive() && c2->is_positive()) {
                    if (!a.resolve(m_var, b, r) && !b.resolve(m_var, a, r))
                        continue;
                    clause_builder clause(m_solver);
                    clause.push_literal(~c1->blit());
                    clause.push_literal(~c2->blit());
                    clause.push_new_constraint(m_solver.m_constraints.eq(lvl, r));
                    auto cl = clause.build();
                    LOG("r: " << show_deref(cl->new_constraints()[0]));
                    LOG("result: " << show_deref(cl));
                    // SASSERT(false);  // NOTE: this is a simple "breakpoint" for debugging
                    return cl;
                }
                if (c1->is_negative() && c2->is_positive()) {
                    // TODO: only holds if the factor for 'a' is non-zero
                    if (!a.resolve(m_var, b, r))
                        continue;
                    clause_builder clause(m_solver);
                    clause.push_literal(~c1->blit());
                    clause.push_literal(~c2->blit());
                    clause.push_new_constraint(~m_solver.m_constraints.eq(lvl, r));
                    auto cl = clause.build();
                    LOG("r: " << show_deref(cl->new_constraints()[0]));
                    LOG("result: " << show_deref(cl));
                    // SASSERT(false);  // NOTE: this is a simple "breakpoint" for debugging
                    return cl;
                }
            }
        }
#endif
        return nullptr;
    }

    /// [x] zx > yx  ==>  Ω*(x,y) \/ z > y
    /// [x] yx <= zx  ==>  Ω*(x,y) \/ y <= z
    clause_ref conflict_explainer::by_ugt_x() {
        LOG_H3("Try zx > yx where x := v" << m_var);

        pdd const x = m_solver.var(m_var);
        unsigned const sz = m_solver.size(m_var);
        pdd const zero = m_solver.sz2pdd(sz).zero();

        // Find constraint of shape: yx <= zx
        for (auto* c1 : m_conflict.units()) {
            auto c = c1->as_inequality();
            if (c.lhs.degree(m_var) != 1)
                continue;
            if (c.rhs.degree(m_var) != 1)
                continue;
            pdd y = zero;
            pdd rest = zero;
            c.lhs.factor(m_var, 1, y, rest);
            if (!rest.is_zero())
                continue;
            pdd z = zero;
            c.rhs.factor(m_var, 1, z, rest);
            if (!rest.is_zero())
                continue;

            unsigned const lvl = c.src->level();

            clause_builder clause(m_solver);
            clause.push_literal(~c.src->blit());
            // Omega^*(x, y)
            if (!push_omega_mul(clause, lvl, sz, x, y))
                continue;
            constraint_literal y_le_z;
            if (c.is_strict)
                y_le_z = m_solver.m_constraints.ult(lvl, y, z);
            else
                y_le_z = m_solver.m_constraints.ule(lvl, y, z);
            LOG("z>y: " << show_deref(y_le_z));
            clause.push_new_constraint(std::move(y_le_z));

            return clause.build();
        }
        return nullptr;
    }

    /// [y] z' <= y /\ zx > yx  ==>  Ω*(x,y) \/ zx > z'x
    /// [y] z' <= y /\ yx <= zx  ==>  Ω*(x,y) \/ z'x <= zx
    clause_ref conflict_explainer::by_ugt_y() {
        LOG_H3("Try z' <= y && zx > yx where y := v" << m_var);

        pdd const y = m_solver.var(m_var);
        unsigned const sz = m_solver.size(m_var);
        pdd const zero = m_solver.sz2pdd(sz).zero();

        // Collect constraints of shape "_ <= y"
        vector<inequality> ds;
        for (auto* d1 : m_conflict.units()) {
            auto d = d1->as_inequality();
            // TODO: a*y where 'a' divides 'x' should also be easy to handle (assuming for now they're numbers)
            // TODO: also z' < y should follow the same pattern.
            if (d.rhs != y)
                continue;
            LOG("z' <= y candidate: " << show_deref(d.src));
            ds.push_back(std::move(d));
        }
        if (ds.empty())
            return nullptr;

        // Find constraint of shape: yx <= zx
        for (auto* c1 : m_conflict.units()) {
            auto c = c1->as_inequality();
            if (c.lhs.degree(m_var) != 1)
                continue;
            pdd x = zero;
            pdd rest = zero;
            c.lhs.factor(m_var, 1, x, rest);
            if (!rest.is_zero())
                continue;
            // TODO: in principle, 'x' could be any polynomial. However, we need to divide the lhs by x, and we don't have general polynomial division yet.
            //       so for now we just allow the form 'value*variable'.
            //       (extension to arbitrary monomials for 'x' should be fairly easy too)
            if (!x.is_unary())
                continue;
            unsigned x_var = x.var();
            rational x_coeff = x.hi().val();
            pdd xz = zero;
            if (!c.rhs.try_div(x_coeff, xz))
                continue;
            pdd z = zero;
            xz.factor(x_var, 1, z, rest);
            if (!rest.is_zero())
                continue;

            LOG("zx > yx: " << show_deref(c.src));

            // TODO: for now, we just try all ds
            for (auto const& d : ds) {
                unsigned const lvl = std::max(c.src->level(), d.src->level());
                pdd const& z_prime = d.lhs;

                clause_builder clause(m_solver);
                clause.push_literal(~c.src->blit());
                clause.push_literal(~d.src->blit());
                // Omega^*(x, y)
                if (!push_omega_mul(clause, lvl, sz, x, y))
                    continue;
                // z'x <= zx
                constraint_literal zpx_le_zx;
                if (c.is_strict || d.is_strict)
                    zpx_le_zx = m_solver.m_constraints.ult(lvl, z_prime*x, z*x);
                else
                    zpx_le_zx = m_solver.m_constraints.ule(lvl, z_prime*x, z*x);
                LOG("zx>z'x: " << show_deref(zpx_le_zx));
                clause.push_new_constraint(std::move(zpx_le_zx));

                return clause.build();
            }
        }
        return nullptr;
    }

    /// [z] z <= y' /\ zx > yx  ==>  Ω*(x,y') \/ y'x > yx
    /// [z] z <= y' /\ yx <= zx  ==>  Ω*(x,y') \/ yx <= y'x
    clause_ref conflict_explainer::by_ugt_z() {
        LOG_H3("Try z <= y' && zx > yx where z := v" << m_var);

        pdd const z = m_solver.var(m_var);
        unsigned const sz = m_solver.size(m_var);
        pdd const zero = m_solver.sz2pdd(sz).zero();

        // Collect constraints of shape "z <= _"
        vector<inequality> ds;
        for (auto* d1 : m_conflict.units()) {
            auto d = d1->as_inequality();
            // TODO: a*y where 'a' divides 'x' should also be easy to handle (assuming for now they're numbers)
            // TODO: also z < y' should follow the same pattern.
            if (d.lhs != z)
                continue;
            LOG("z <= y' candidate: " << show_deref(d.src));
            ds.push_back(std::move(d));
        }
        if (ds.empty())
            return nullptr;

        // Find constraint of shape: yx <= zx
        for (auto* c1 : m_conflict.units()) {
            auto c = c1->as_inequality();
            if (c.rhs.degree(m_var) != 1)
                continue;
            pdd x = zero;
            pdd rest = zero;
            c.rhs.factor(m_var, 1, x, rest);
            if (!rest.is_zero())
                continue;
            // TODO: in principle, 'x' could be any polynomial. However, we need to divide the lhs by x, and we don't have general polynomial division yet.
            //       so for now we just allow the form 'value*variable'.
            //       (extension to arbitrary monomials for 'x' should be fairly easy too)
            if (!x.is_unary())
                continue;
            unsigned x_var = x.var();
            rational x_coeff = x.hi().val();
            pdd xy = zero;
            if (!c.lhs.try_div(x_coeff, xy))
                continue;
            pdd y = zero;
            xy.factor(x_var, 1, y, rest);
            if (!rest.is_zero())
                continue;

            LOG("zx > yx: " << show_deref(c.src));

            // TODO: for now, we just try all ds
            for (auto const& d : ds) {
                unsigned const lvl = std::max(c.src->level(), d.src->level());
                pdd const& y_prime = d.rhs;

                clause_builder clause(m_solver);
                clause.push_literal(~c.src->blit());
                clause.push_literal(~d.src->blit());
                // Omega^*(x, y')
                if (!push_omega_mul(clause, lvl, sz, x, y_prime))
                    continue;
                // yx <= y'x
                constraint_literal yx_le_ypx;
                if (c.is_strict || d.is_strict)
                    yx_le_ypx = m_solver.m_constraints.ult(lvl, y*x, y_prime*x);
                else
                    yx_le_ypx = m_solver.m_constraints.ule(lvl, y*x, y_prime*x);
                LOG("y'x>yx: " << show_deref(yx_le_ypx));
                clause.push_new_constraint(std::move(yx_le_ypx));

                return clause.build();
            }
        }
        return nullptr;
    }

    /// [x]  y <= ax /\ x <= z  (non-overflow case)
    ///     ==>   Ω*(a, z)  \/  y <= az
    clause_ref conflict_explainer::y_ule_ax_and_x_ule_z() {
        LOG_H3("Try y <= ax && x <= z where x := v" << m_var);

        pdd const x = m_solver.var(m_var);
        unsigned const sz = m_solver.size(m_var);
        pdd const zero = m_solver.sz2pdd(sz).zero();

        // Collect constraints of shape "x <= _"
        vector<inequality> ds;
        for (auto* d1 : m_conflict.units()) {
            inequality d = d1->as_inequality();
            if (d.lhs != x)
                continue;
            LOG("x <= z' candidate: " << show_deref(d.src));
            ds.push_back(std::move(d));
        }
        if (ds.empty())
            return nullptr;

        // Find constraint of shape: y <= ax
        for (auto* c1 : m_conflict.units()) {
            inequality c = c1->as_inequality();
            if (c.rhs.degree(m_var) != 1)
                continue;
            pdd a = zero;
            pdd rest = zero;
            c.rhs.factor(m_var, 1, a, rest);
            if (!rest.is_zero())
                continue;
            pdd const& y = c.lhs;

            LOG("y <= ax: " << show_deref(c1));

            // TODO: for now, we just try all of the other constraints in order
            for (auto const& d : ds) {
                unsigned const lvl = std::max(c1->level(), d.src->level());
                pdd const& z = d.rhs;

                clause_builder clause(m_solver);
                clause.push_literal(~c.src->blit());
                clause.push_literal(~d.src->blit());
                // Omega^*(a, z)
                if (!push_omega_mul(clause, lvl, sz, a, z))
                    continue;
                // y'x > yx
                constraint_literal y_ule_az;
                if (c.is_strict || d.is_strict)
                    y_ule_az = m_solver.m_constraints.ult(lvl, y, a*z);
                else
                    y_ule_az = m_solver.m_constraints.ule(lvl, y, a*z);
                LOG("y<=az: " << show_deref(y_ule_az));
                clause.push_new_constraint(std::move(y_ule_az));

                return clause.build();
            }
        }
        return nullptr;
    }

    /// Add Ω*(x, y) to the clause.
    ///
    /// @param[in] p    bit width
    bool conflict_explainer::push_omega_mul(clause_builder& clause, unsigned level, unsigned p, pdd const& x, pdd const& y) {
        LOG_H3("Omega^*(x, y)");
        LOG("x = " << x);
        LOG("y = " << y);
        auto& pddm = m_solver.sz2pdd(p);
        unsigned min_k = 0;
        unsigned max_k = p - 1;
        unsigned k = p/2;

        rational x_val;
        if (m_solver.try_eval(x, x_val)) {
            unsigned x_bits = x_val.bitsize();
            LOG("eval x: " << x << " := " << x_val << " (x_bits: " << x_bits << ")");
            SASSERT(x_val < rational::power_of_two(x_bits));
            min_k = x_bits;
        }

        rational y_val;
        if (m_solver.try_eval(y, y_val)) {
            unsigned y_bits = y_val.bitsize();
            LOG("eval y: " << y << " := " << y_val << " (y_bits: " << y_bits << ")");
            SASSERT(y_val < rational::power_of_two(y_bits));
            max_k = p - y_bits;
        }

        if (min_k > max_k) {
            // In this case, we cannot choose k such that both literals are false.
            // This means x*y overflows in the current model and the chosen rule is not applicable.
            // (or maybe we are in the case where we need the msb-encoding for overflow).
            return false;
        }

        SASSERT(min_k <= max_k);  // if this assertion fails, we cannot choose k s.t. both literals are false

        // TODO: could also choose other value for k (but between the bounds)
        if (min_k == 0)
            k = max_k;
        else
            k = min_k;

        LOG("k = " << k << "; min_k = " << min_k << "; max_k = " << max_k << "; p = " << p);
        SASSERT(min_k <= k && k <= max_k);

        // x >= 2^k
        auto c1 = m_solver.m_constraints.ule(level, pddm.mk_val(rational::power_of_two(k)), x);
        // y > 2^{p-k}
        auto c2 = m_solver.m_constraints.ult(level, pddm.mk_val(rational::power_of_two(p-k)), y);
        clause.push_new_constraint(std::move(c1));
        clause.push_new_constraint(std::move(c2));
        return true;
    }
}