/*++
Copyright (c) 2021 Microsoft Corporation

Module Name:

    polysat conflict

Author:

    Nikolaj Bjorner (nbjorner) 2021-03-19
    Jakob Rath 2021-04-06

Notes:

    A conflict state is of the form <Vars, Constraints, Lemmas>
    Where Vars are shorthand for the constraints v = value(v) for v in Vars and value(v) is the assignment.
    Lemmas provide justifications for newly created constraints.

    The conflict state is unsatisfiable under background clauses F.
    Dually, the negation is a consequence of F.

    Conflict resolution resolves an assignment in the search stack against the conflict state.

    Assignments are of the form:

    lit <- D => lit              - lit is propagated by the clause D => lit
    lit <- asserted              - lit is asserted
    lit <- Vars                  - lit is propagated from variable evaluation.

    v = value <- D               - v is assigned value by constraints D
    v = value <- ?               - v is a decision literal.

    - All literals should be assigned in the stack prior to their use;
      or justified by one of the side lemmas.
      (thus: all literals in the core must have bvalue == l_true)

    l <- D => l,       < Vars, { l } u C >   ===>   < Vars, C u D >
    l <- ?,            < Vars, { l } u C >   ===>   ~l <- (C & Vars = value(Vars) => ~l)
    l <- asserted,     < Vars, { l } u C >   ===>   < Vars, { l } u C >
    l <- Vars',        < Vars, { l } u C >   ===>   < Vars u Vars', C >          if all Vars' are propagated
    l <- Vars',        < Vars, { l } u C >   ===>   Mark < Vars, { l } u C > as bailout

    v = value <- D,  < Vars u { v }, C >     ===>   < Vars, D u C >
    v = value <- ?,  < Vars u { v }, C >     ===>   v != value <- (C & Vars = value(Vars) => v != value)


Example derivations:

Trail:       z <= y  <- asserted
             xz > xy <- asserted
             x = a   <- ?
             y = b   <- ?
             z = c   <- ?
Conflict:    < {x, y, z}, xz > xy > when ~O(a,b) and c <= b
Append       x <= a <- { x }
Append       y <= b <- { y }
Conflict:    < {}, y >= z, xz > xy, x <= a, y <= b >
Based on:    z <= y & x <= a & y <= b => xz <= xy
Resolve:     y <= b <- { y }, y is a decision variable.
Bailout:     lemma ~(y >= z & xz > xy & x <= a & y <= b) at decision level of lemma

With overflow predicate:
Append       ~O(x, y) <- { x, y }
Conflict:    < {}, y >= z, xz > xy, ~O(x,y) >
Based on     z <= y & ~O(x,y) => xz <= xy
Resolve:     ~O(x, y) <- { x, y } both x, y are decision variables
Lemma:       y < z or xz <= xy or O(x,y)

--*/
#pragma once
#include "math/polysat/types.h"
#include "math/polysat/constraint.h"
#include "math/polysat/inference_logger.h"
#include <optional>

namespace polysat {

    class solver;
    class conflict_iterator;
    class conflict_resolver;

    enum class conflict_kind_t {
        // standard conflict resolution
        ok,
        // bailout lemma because no appropriate conflict resolution method applies
        bailout,
        // conflict contains the final lemma;
        // backtrack to and revert the last relevant decision
        // NOTE: this is currently used for the forbidden intervals lemmas.
        //       we should find a way to use resolve_value with these lemmas,
        //       to properly eliminate value propagations. (see todo notes above)
        backtrack,
        // conflict contains the final lemma;
        // force backjumping without further conflict resolution because a good lemma has been found
        backjump,
    };

    class conflict {
        solver& s;
        scoped_ptr<inference_logger> m_logger;
        scoped_ptr<conflict_resolver> m_resolver;

        // current conflict core consists of m_literals and m_vars
        indexed_uint_set m_literals;        // set of boolean literals in the conflict
        uint_set m_vars;                    // variable assignments used as premises, shorthand for literals (x := v)
        uint_set m_bail_vars;               // decision variables that are only used to evaluate a constraint; see resolve_with_assignment.
        uint_set m_relevant_vars;           // tracked for cone of influence but not directly involved in conflict resolution

        unsigned_vector m_var_occurrences;  // for each variable, the number of constraints in m_literals that contain it

        // Additional lemmas that justify new constraints generated during conflict resolution
        u_map<clause_ref> m_lemmas;

        conflict_kind_t m_kind = conflict_kind_t::ok;

        // Level at which the conflict was discovered
        unsigned m_level = UINT_MAX;

        void set_impl(signed_constraint c);
        bool minimize_vars(signed_constraint c);

    public:
        conflict(solver& s);
        ~conflict();

        inference_logger& logger();

        bool empty() const;
        void reset();

        using const_iterator = conflict_iterator;
        const_iterator begin() const;
        const_iterator end() const;

        uint_set const& vars() const { return m_vars; }
        uint_set const& bail_vars() const { return m_bail_vars; }

        unsigned level() const { return m_level; }

        conflict_kind_t kind() const { return m_kind; }
        bool is_bailout() const { return m_kind == conflict_kind_t::bailout; }
        bool is_backtracking() const { return m_kind == conflict_kind_t::backtrack; }
        bool is_backjumping() const { return m_kind == conflict_kind_t::backjump; }
        void set_bailout();
        void set_backtrack();
        void set_backjump();

        bool is_relevant_pvar(pvar v) const;
        bool is_relevant(sat::literal lit) const;

        /** conflict due to obvious input inconsistency */
        void init_at_base_level();
        /** conflict because the constraint c is false under current variable assignment */
        void init(signed_constraint c);
        /** boolean conflict with the given clause */
        void init(clause const& cl);
        /** conflict because there is no viable value for the variable v */
        void init(pvar v, bool by_viable_fallback);

        /** replace the current conflict by a single constraint */
        void set(signed_constraint c);

        bool contains(signed_constraint c) const { SASSERT(c); return contains(c.blit()); }
        bool contains(sat::literal lit) const;
        bool contains_pvar(pvar v) const { return m_vars.contains(v) || m_bail_vars.contains(v); }
        bool pvar_occurs_in_constraints(pvar v) const { return v < m_var_occurrences.size() && m_var_occurrences[v] > 0; }

        clause* side_lemma(signed_constraint c) const { SASSERT(c); return side_lemma(c.blit()); }
        clause* side_lemma(sat::literal lit) const;

        /**
         * Insert constraint c into conflict state.
         *
         * Skips trivial constraints:
         *  - e.g., constant constraints such as "4 > 1"
         */
        void insert(signed_constraint c);

        /**
         * Insert constraint c that is justified by the given lemma.
         */
        void insert(signed_constraint c, clause_ref lemma);

        /** Insert assigned variables of c */
        void insert_vars(signed_constraint c);

        /** Evaluate constraint under assignment and insert it into conflict state. */
        void insert_eval(signed_constraint c);

        /** Remove c from core */
        void remove(signed_constraint c);

        /** Perform boolean resolution with the clause upon the given literal. */
        void resolve_bool(sat::literal lit, clause const& cl);

        /** lit was fully evaluated under the assignment.  */
        void resolve_with_assignment(sat::literal lit);

        /** Perform resolution with "v = value <- ..." */
        bool resolve_value(pvar v);

        /** Convert the core into a lemma to be learned. */
        clause_ref build_lemma();

        std::ostream& display(std::ostream& out) const;
    };

    inline std::ostream& operator<<(std::ostream& out, conflict const& c) { return c.display(out); }

    class conflict_iterator {
        friend class conflict;

        using inner_t = indexed_uint_set::iterator;

        constraint_manager* m_cm;
        inner_t m_inner;

        conflict_iterator(constraint_manager& cm, inner_t inner):
            m_cm(&cm), m_inner(inner) {}

        static conflict_iterator begin(constraint_manager& cm, indexed_uint_set const& lits) {
            return {cm, lits.begin()};
        }

        static conflict_iterator end(constraint_manager& cm, indexed_uint_set const& lits) {
            return {cm, lits.end()};
        }

    public:
        using value_type = signed_constraint;
        using difference_type = unsigned;
        using pointer = signed_constraint const*;
        using reference = signed_constraint const&;
        using iterator_category = std::input_iterator_tag;

        conflict_iterator& operator++() {
            ++m_inner;
            return *this;
        }

        signed_constraint operator*() const {
            return m_cm->lookup(sat::to_literal(*m_inner));
        }

        bool operator==(conflict_iterator const& other) const {
            return m_inner == other.m_inner;
        }

        bool operator!=(conflict_iterator const& other) const { return !operator==(other); }
    };
}