z3/src/sat/smt/q_model_fixer.cpp

/*++
Copyright (c) 2020 Microsoft Corporation

Module Name:

    q_model_fixer.cpp

Abstract:

    Model-based quantifier instantiation model-finder plugin

Author:

    Nikolaj Bjorner (nbjorner) 2020-10-02

Notes:
   
    Derives from smt/smt_model_finder.cpp

--*/


#include "ast/for_each_expr.h"
#include "ast/ast_util.h"
#include "ast/arith_decl_plugin.h"
#include "ast/bv_decl_plugin.h"
#include "model/model_macro_solver.h"
#include "sat/smt/q_model_fixer.h"
#include "sat/smt/q_solver.h"
#include "sat/smt/euf_solver.h"


namespace q {

    template<typename U>
    static bool lt(U const& u, expr* x, expr* y) {
        rational v1, v2;
        if (u.is_numeral(x, v1) && u.is_numeral(y, v2))
            return v1 < v2;
        else
            return x->get_id() < y->get_id();
    }

    class arith_projection : public projection_function {
        arith_util   a;
    public:
        arith_projection(ast_manager& m) : projection_function(m), a(m) {}
        bool operator()(expr* e1, expr* e2) const override { return lt(a, e1, e2); }
        expr* mk_lt(expr* x, expr* y) override { return a.mk_lt(x, y); }
    };

    class ubv_projection : public projection_function {
        bv_util bvu;
    public:
        ubv_projection(ast_manager& m) : projection_function(m), bvu(m) {}
        bool operator()(expr* e1, expr* e2) const override { return lt(bvu, e1, e2); }
        expr* mk_lt(expr* x, expr* y) override { return m.mk_not(bvu.mk_ule(y, x)); }
    };

    model_fixer::model_fixer(euf::solver& ctx, q::solver& qs) :
        ctx(ctx), m_qs(qs), m(ctx.get_manager()), m_dependencies(m) {}

    void model_fixer::operator()(model& mdl) {
        ptr_vector<quantifier> univ;
        for (sat::literal lit : m_qs.universal()) {
            quantifier* q = to_quantifier(ctx.bool_var2expr(lit.var()));
            if (ctx.is_relevant(lit.var()))
                univ.push_back(q);
        }
        if (univ.empty())
            return;

        TRACE("q", tout << "start: " << mdl << "\n";);
        m_dependencies.reset();
        m_projection_data.reset();
        m_projection_pinned.reset();
        ptr_vector<quantifier> residue;

        simple_macro_solver sms(m, *this);
        sms(mdl, univ, residue);

        hint_macro_solver hms(m, *this);
        hms(mdl, univ, residue);

        non_auf_macro_solver nas(m, *this, m_dependencies);
        nas.set_mbqi_force_template(ctx.get_config().m_mbqi_force_template);
        nas(mdl, univ, residue);

        univ.append(residue);
        add_projection_functions(mdl, univ);
	for (unsigned i = mdl.get_num_functions(); i-- > 0; ) {
            func_decl* f = mdl.get_function(i);
            func_interp* fi = mdl.get_func_interp(f);
            if (fi->is_partial())
                fi->set_else(fi->get_max_occ_result());
            if (fi->is_partial())
                fi->set_else(mdl.get_some_value(f->get_range()));
	}
        TRACE("q", tout << "end: " << mdl << "\n";);
    }

    quantifier_macro_info* model_fixer::operator()(quantifier* q) {
        quantifier_macro_info* info = nullptr;
        if (!m_q2info.find(q, info)) {
            info = alloc(quantifier_macro_info, m, m_qs.flatten(q));
            m_q2info.insert(q, info);
            ctx.push(new_obj_trail<quantifier_macro_info>(info));
            ctx.push(insert_obj_map<quantifier, quantifier_macro_info*>(m_q2info, q));
        }
        return info;
    }

    void model_fixer::add_projection_functions(model& mdl, ptr_vector<quantifier> const& qs) {
        func_decl_set fns;
        collect_partial_functions(qs, fns);
        for (func_decl* f : fns)
            add_projection_functions(mdl, f);
    }

    /**
    *  we are given f with interpretation:
    *      if x = v0 and y = w0 then f0
    *      else if x = v1 and y = w1 then f1
    *      ...
    * Create a new interpretation for f as follows:
    * f := f_aux(project1(x), project2(y))
    * f_aux uses the original interpretation of f
    * project1 sorts the values of v0, v1, ..., and maps arguments below v0 to v0, between v0, v1 to v1 etc.
    * project2 sorts values of w0, w1, ... and maps argument y to values w0, w1, ..
    * 
    */
    void model_fixer::add_projection_functions(model& mdl, func_decl* f) {
        // update interpretation of f so that the graph of f is fully determined by the
        // ground values of its arguments.

        func_interp* fi = mdl.get_func_interp(f);
        if (!fi)
            return;
        if (fi->is_constant())
            return;
        expr_ref_vector args(m);
        for (unsigned i = 0; i < f->get_arity(); ++i)
            args.push_back(add_projection_function(mdl, f, i));
        if (!fi->get_else() && fi->num_entries() > 0) {
            unsigned idx = ctx.s().rand()(fi->num_entries());
            func_entry const* e = fi->get_entry(idx);
            fi->set_else(e->get_result());
            fi->del_entry(idx);
        }
        bool has_projection = false;
        for (expr* arg : args)
            has_projection |= !is_var(arg);
        if (!has_projection)
            return;
        func_interp* new_fi = alloc(func_interp, m, f->get_arity());
        func_decl* f_new = m.mk_fresh_func_decl(f->get_name(), symbol("aux"), f->get_arity(), f->get_domain(), f->get_range());
        new_fi->set_else(m.mk_app(f_new, args));
        mdl.update_func_interp(f, new_fi);
        mdl.register_decl(f_new, fi);
    }

    /*
    * For function f(...,t_idx, ..) collect the values of terms at position idx of f 
    * as "values". 
    * Map t_idx |-> mdl(t_idx)
    * and mdl(t_idx) |-> t_idx
    * Sort the values as [v_1, v_2, ..., v_n] with corresponding terms
    * [t_1, t_2, ..., t_n]
    * 
    * Create the term if p(x) = if x <= v_1 then t_1 else if x <= v_2 then t_2 else ...  t_n
    * where p is a fresh function 
    * and return p(x)
    */

    expr_ref model_fixer::add_projection_function(model& mdl, func_decl* f, unsigned idx) {
        sort* srt = f->get_domain(idx);
        projection_function* proj = get_projection(srt);
        if (!proj)
            return expr_ref(m.mk_var(idx, srt), m);
        scoped_ptr<projection_meta_data> md = alloc(projection_meta_data, m);
        expr_ref_vector& values = md->values;
        for (euf::enode* n : ctx.get_egraph().enodes_of(f)) {
            expr* t = n->get_arg(idx)->get_expr();
            values.push_back(mdl(t));
            if (!m.is_value(values.back())) 
                return expr_ref(m.mk_var(idx, srt), m);
            md->v2t.insert(values.back(), t);
            md->t2v.insert(t, values.back());
        }
        if (values.empty())
            return expr_ref(m.mk_var(idx, srt), m);
        struct lt {
            projection_function* p;
            lt(projection_function* p) : p(p) {}
            bool operator()(expr* a, expr* b) const { return (*p)(a, b); }
        };
        lt _lt(proj);
        std::sort(values.data(), values.data() + values.size(), _lt);
        unsigned j = 0;
        for (unsigned i = 0; i < values.size(); ++i)
            if (i == 0 || values.get(i - 1) != values.get(i))
                values[j++] = values.get(i);
        values.shrink(j);

        m_projection_data.insert(indexed_decl(f, idx), md.get());
        m_projection_pinned.push_back(md.detach());

        unsigned sz = values.size();
        expr_ref var(m.mk_var(0, srt), m);
        expr_ref pi(values.get(sz - 1), m);
        for (unsigned i = sz - 1; i >= 1; i--) {
            expr* c = proj->mk_lt(var, values.get(i));
            pi = m.mk_ite(c, values.get(i - 1), pi);
        }
        func_interp* rpi = alloc(func_interp, m, 1);
        rpi->set_else(pi);
        func_decl* p = m.mk_fresh_func_decl(1, &srt, srt);
        mdl.register_decl(p, rpi);
        return expr_ref(m.mk_app(p, m.mk_var(idx, srt)), m);
    }

    projection_function* model_fixer::get_projection(sort* srt) {
        projection_function* proj = nullptr;
        if (m_projections.find(srt, proj))
            return proj;
        arith_util autil(m);
        bv_util butil(m);
        if (autil.is_real(srt) || autil.is_int(srt))
            proj = alloc(arith_projection, m);
        else if (butil.is_bv_sort(srt))
            proj = alloc(ubv_projection, m);
        // TBD: sbv_projection? FP, ADT projection?
        if (!proj)
            return nullptr;
        m_projections.insert(srt, proj);
        ctx.push(new_obj_trail<projection_function>(proj));
        ctx.push(insert_obj_map<sort, projection_function*>(m_projections, srt));
        return proj;
    }

    void model_fixer::collect_partial_functions(ptr_vector<quantifier> const& qs, func_decl_set& fns) {
        for (quantifier* q : qs) {
            auto* info = (*this)(q);
            quantifier* flat_q = info->get_flat_q();
            expr_ref body(flat_q->get_expr(), m);
            for (expr* t : subterms::ground(body))
                if (is_uninterp(t) && !to_app(t)->is_ground())
                    fns.insert(to_app(t)->get_decl());
        }
    }

    expr* model_fixer::invert_app(app* t, expr* value) {
        euf::enode* r = nullptr;
        auto& v2r = ctx.values2root();
        TRACE("q",
              tout << "invert-app " << mk_pp(t, m) << " = " << mk_pp(value, m) << "\n";
              if (v2r.find(value, r)) 
                  tout << "inverse " << mk_pp(r->get_expr(), m) << "\n";
              /*ctx.display(tout); */
              );
        if (v2r.find(value, r)) 
            return r->get_expr();
        return value;
    }

    /**
    * We are given a term f(...,arg_i,..) and value = mdl(arg_i)
    * Create 
    * 1 the bounds t_j <= arg_i < t_{j+1} where 
    *   v_j <= value < v_{j+1} for the corresponding values of t_j, t_{j+1}
    * 2 or the bound arg_i < t_0     if value < v_0
    * 3 or the bound arg_i >= t_last if value > v_last
    */

    void model_fixer::invert_arg(app* t, unsigned i, expr* value, expr_ref_vector& lits) {
        TRACE("q", tout << "invert-arg " << mk_pp(t, m) << " " << i << " " << mk_pp(value, m) << "\n";);
        auto const* md = get_projection_data(t->get_decl(), i);
        if (!md)
            return;
        auto* proj = get_projection(t->get_decl()->get_domain(i));
        if (!proj)
            return;

        unsigned sz = md->values.size();
        if (sz <= 1)
            return;

        //
        // md->values are sorted
        // v1, v2, v3
        // x < v2       => f(x) = f(v1), so x < t2, where M(v2) = t2
        // v2 <= x < v3 => f(x) = f(v2), so t2 <= x < t3, where M(v3) = t3
        // v3 <= x      => f(x) = f(v3)
        // 
        auto is_lt = [&](expr* val) {
            return (*proj)(value, val);
        };

        auto term = [&](unsigned j) {
            return md->v2t[md->values[j]];
        };
        
#if 0
        for (unsigned j = 0; j < sz; ++j)
            std::cout << mk_pp(md->values[j], m) << "\n";
#endif

        expr* arg = t->get_arg(i);

        if (is_lt(md->values[1])) {
            lits.push_back(proj->mk_lt(arg, term(1)));
            return;
        }

        for (unsigned j = 2; j < sz; ++j)
            if (is_lt(md->values[j])) {
                lits.push_back(proj->mk_le(term(j - 1), arg));
                lits.push_back(proj->mk_lt(arg, term(j)));
                return;
            }

        lits.push_back(proj->mk_le(term(sz - 1), arg));
    }

    /*
    * restrict arg_i of t := f(...,arg_i,...) to be one of terms from the ground instantiations of f.
    */
    expr_ref model_fixer::restrict_arg(app* t, unsigned i) {
        TRACE("q", tout << "restrict-arg " << mk_pp(t, m) << " " << i << "\n";);
        auto const* md = get_projection_data(t->get_decl(), i);
        if (!md)
            return expr_ref(m.mk_true(), m);

        expr* arg = t->get_arg(i);
        expr_ref_vector eqs(m);
        for (expr* v : md->values)
            eqs.push_back(m.mk_eq(arg, md->v2t[v]));
        if (eqs.empty())
            return expr_ref(m.mk_true(), m);
        return mk_or(eqs);
    }
}