lean2/src/frontends/lean/frontend_elaborator.cpp

/*
Copyright (c) 2013 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.

Author: Leonardo de Moura
*/
#include <vector>
#include <utility>
#include <algorithm>
#include <limits>
#include "util/interrupt.h"
#include "kernel/type_checker.h"
#include "kernel/type_checker_justification.h"
#include "kernel/normalizer.h"
#include "kernel/replace_visitor.h"
#include "kernel/unification_constraint.h"
#include "kernel/instantiate.h"
#include "kernel/builtin.h"
#include "library/type_inferer.h"
#include "library/placeholder.h"
#include "library/elaborator/elaborator.h"
#include "frontends/lean/frontend.h"
#include "frontends/lean/frontend_elaborator.h"

namespace lean {
static name g_x_name("x");
static format g_assignment_fmt  = format(":=");
static format g_unification_u_fmt = format("\u2248");
static format g_unification_fmt = format("=?=");

/**
   \brief Internal value used to store choices for the elaborator.
   This is a transient value that is only used to setup a problem
   for the elaborator.
*/
struct choice_value : public value {
    std::vector<expr> m_choices;
    choice_value(unsigned num_fs, expr const * fs):m_choices(fs, fs + num_fs) {}
    virtual ~choice_value() {}
    virtual expr get_type() const { lean_unreachable(); } // LCOV_EXCL_LINE
    virtual name get_name() const { return name("Choice"); }
    virtual void display(std::ostream & out) const {
        out << "(Choice";
        for (auto c : m_choices) {
            out << " (" << c << ")";
        }
        out << ")";
    }
    // Remark: we don't implement the pp methods because the lean::pp_fn formatter
    // object has support for formatting choice internal values.
};

expr mk_choice(unsigned num_fs, expr const * fs) {
    lean_assert(num_fs >= 2);
    return mk_value(*(new choice_value(num_fs, fs)));
}

bool is_choice(expr const & e) {
    return is_value(e) && dynamic_cast<choice_value const *>(&to_value(e)) != nullptr;
}

choice_value const & to_choice_value(expr const & e) {
    lean_assert(is_choice(e));
    return static_cast<choice_value const &>(to_value(e));
}

unsigned get_num_choices(expr const & e) {
    return to_choice_value(e).m_choices.size();
}

expr const & get_choice(expr const & e, unsigned i) {
    return to_choice_value(e).m_choices[i];
}

class coercion_justification_cell : public justification_cell {
    context m_ctx;
    expr    m_src;
public:
    coercion_justification_cell(context const & c, expr const & src):m_ctx(c), m_src(src) {}
    virtual ~coercion_justification_cell() {}
    virtual format pp_header(formatter const & fmt, options const & opts) const {
        unsigned indent = get_pp_indent(opts);
        format expr_fmt = fmt(m_ctx, m_src, false, opts);
        format r;
        r += format("Coercion for");
        r += nest(indent, compose(line(), expr_fmt));
        return r;
    }
    virtual void get_children(buffer<justification_cell*> &) const {}
    virtual optional<expr> get_main_expr() const { return some_expr(m_src); }
    context const & get_context() const { return m_ctx; }
};

class overload_justification_cell : public justification_cell {
    context m_ctx;
    expr    m_app;
public:
    overload_justification_cell(context const & c, expr const & app):m_ctx(c), m_app(app) {}
    virtual ~overload_justification_cell() {}
    virtual format pp_header(formatter const & fmt, options const & opts) const {
        unsigned indent = get_pp_indent(opts);
        format expr_fmt = fmt(m_ctx, m_app, false, opts);
        format r;
        r += format("Overloading at");
        r += nest(indent, compose(line(), expr_fmt));
        return r;
    }
    virtual void get_children(buffer<justification_cell*> &) const {}
    virtual optional<expr> get_main_expr() const { return some_expr(m_app); }
    context const & get_context() const { return m_ctx; }
    expr const & get_app() const { return m_app; }
};


inline justification mk_coercion_justification(context const & ctx, expr const & e) {
    return justification(new coercion_justification_cell(ctx, e));
}

inline justification mk_overload_justification(context const & ctx, expr const & app) {
    return justification(new overload_justification_cell(ctx, app));
}

/**
    \brief Actual implementation of the frontend_elaborator.
*/
class frontend_elaborator::imp {
    frontend  const &                   m_frontend;
    environment const &                 m_env;
    type_checker                        m_type_checker;
    type_inferer                        m_type_inferer;
    normalizer                          m_normalizer;
    metavar_env                         m_menv;
    buffer<unification_constraint>      m_ucs;
    // The following mapping is used to store the relationship
    // between elaborated expressions and non-elaborated expressions.
    // We need that because a frontend may associate line number information
    // with the original non-elaborated expressions.
    expr_map<expr>                      m_trace;

    /**
       \brief Replace placeholders and choices with metavariables.
       It also introduce metavariables where coercions are needed.
    */
    struct preprocessor : public replace_visitor {
        imp & m_ref;
        preprocessor(imp & r):m_ref(r) {}

        expr instantiate(expr const & e, expr const & v) {
            return ::lean::instantiate(e, v, m_ref.m_menv);
        }

        virtual expr visit_constant(expr const & e, context const & ctx) {
            if (is_placeholder(e)) {
                expr m = m_ref.m_menv->mk_metavar(ctx, visit(const_type(e), ctx));
                m_ref.m_trace[m] = e;
                return m;
            } else {
                return e;
            }
        }

        /**
           \brief Return the type of \c e if possible.
           The idea is to use the type to catch the easy cases where we can solve
           overloads (aka choices) and coercions during preprocessing.
        */
        optional<expr> get_type(expr const & e, context const & ctx) {
            try {
                return some_expr(m_ref.m_type_inferer(e, ctx));
            } catch (exception &) {
                return none_expr();
            }
        }

        /**
           \brief Make sure f_t is a Pi, if it is not, then return none_expr()
        */
        optional<expr> check_pi(optional<expr> const & f_t, context const & ctx) {
            if (!f_t || is_pi(*f_t)) {
                return f_t;
            } else {
                expr r = m_ref.m_normalizer(*f_t, ctx, m_ref.m_menv);
                if (is_pi(r))
                    return some_expr(r);
                else
                    return none_expr();
            }
        }

        expr add_coercion_mvar_app(list<expr_pair> const & l, expr const & a, expr const & a_t,
                                   context const & ctx, expr const & original_a) {
            buffer<expr> choices;
            expr mvar = m_ref.m_menv->mk_metavar(ctx);
            for (auto p : l) {
                choices.push_back(p.second);
            }
            choices.push_back(mk_lambda(g_x_name, a_t, mk_var(0))); // add indentity function
            std::reverse(choices.begin(), choices.end());
            m_ref.m_ucs.push_back(mk_choice_constraint(ctx, mvar, choices.size(), choices.data(),
                                                       mk_coercion_justification(ctx, original_a)));
            return mk_app(mvar, a);
        }

        optional<expr> find_coercion(list<expr_pair> const & l, expr const & to_type) {
            for (auto p : l) {
                if (p.first == to_type) {
                    return some_expr(p.second);
                }
            }
            return none_expr();
        }

        /**
           \brief Try to solve overload at preprocessing time.
        */
        void choose(buffer<expr> & f_choices,  buffer<optional<expr>> & f_choice_types,
                    buffer<expr> const & args, buffer<optional<expr>> const & arg_types,
                    context const & ctx) {
            unsigned best_num_coercions = std::numeric_limits<unsigned>::max();
            unsigned num_choices = f_choices.size();
            unsigned num_args    = args.size();
            buffer<unsigned> delayed;
            buffer<unsigned> matched;

            for (unsigned j = 0; j < num_choices; j++) {
                optional<expr> f_t = f_choice_types[j];
                unsigned num_coercions   = 0; // number of coercions needed by current choice
                unsigned num_skipped_args = 0;
                unsigned i = 1;
                for (; i < num_args; i++) {
                    f_t = check_pi(f_t, ctx);
                    if (!f_t) {
                        // can't process this choice at preprocessing time
                        delayed.push_back(j);
                        break;
                    } else {
                        expr expected        = abst_domain(*f_t);
                        optional<expr> given = arg_types[i];
                        if (!given) {
                            num_skipped_args++;
                        } else {
                            if (!has_metavar(expected) && !has_metavar(*given)) {
                                if (m_ref.m_type_checker.is_convertible(*given, expected, ctx)) {
                                    // compatible
                                } else if (m_ref.m_frontend.get_coercion(*given, expected)) {
                                    // compatible if using coercion
                                    num_coercions++;
                                } else {
                                    // failed, this choice does not work
                                    break;
                                }
                            } else {
                                num_skipped_args++;
                            }
                        }
                        f_t = some_expr(instantiate(abst_body(*f_t), args[i]));
                    }
                }
                if (i == num_args) {
                    if (num_skipped_args > 0) {
                        // should keep this choice because we could not check all arguments
                        delayed.push_back(j);
                    } else if (num_coercions < best_num_coercions) {
                        // found best choice
                        best_num_coercions = num_coercions;
                        matched.clear();
                        matched.push_back(j);
                    } else {
                        matched.push_back(j);
                    }
                }
            }

            matched.append(delayed);

            if (matched.size() == 0) {
                // TODO(Leo): must use another exception that stores the choices considered.
                // We currently do nothing, and let the elaborator to sign the error
            } else {
                buffer<expr> to_keep;
                buffer<optional<expr>> to_keep_types;
                std::sort(matched.begin(), matched.end()); // we must preserve the original order
                for (unsigned i : matched) {
                    to_keep.push_back(f_choices[i]);
                    to_keep_types.push_back(f_choice_types[i]);
                }
                f_choices.clear();
                f_choice_types.clear();
                f_choices.append(to_keep);
                f_choice_types.append(to_keep_types);
            }
        }

        /**
           \brief Create a metavariable for representing the choice.
        */
        expr mk_overload_mvar(buffer<expr> & f_choices, context const & ctx, expr const & src) {
            std::reverse(f_choices.begin(), f_choices.end());
            expr mvar = m_ref.m_menv->mk_metavar(ctx);
            m_ref.m_ucs.push_back(mk_choice_constraint(ctx, mvar, f_choices.size(), f_choices.data(),
                                                       mk_overload_justification(ctx, src)));
            return mvar;
        }

        virtual expr visit_app(expr const & e, context const & ctx) {
            expr f = arg(e, 0);
            optional<expr> f_t;
            buffer<expr>   args;
            buffer<optional<expr>> arg_types;
            args.push_back(expr());      // placeholder
            arg_types.push_back(none_expr()); // placeholder
            for (unsigned i = 1; i < num_args(e); i++) {
                expr a = arg(e, i);
                expr new_a   = visit(a, ctx);
                optional<expr> new_a_t = get_type(new_a, ctx);
                args.push_back(new_a);
                arg_types.push_back(new_a_t);
            }

            if (is_choice(f)) {
                buffer<expr> f_choices;
                buffer<optional<expr>> f_choice_types;
                unsigned num_alts = get_num_choices(f);
                for (unsigned i = 0; i < num_alts; i++) {
                    expr c       = get_choice(f, i);
                    expr new_c   = visit(c, ctx);
                    optional<expr> new_c_t = get_type(new_c, ctx);
                    f_choices.push_back(new_c);
                    f_choice_types.push_back(new_c_t);
                }
                choose(f_choices, f_choice_types, args, arg_types, ctx);
                if (f_choices.size() > 1) {
                    args[0] = mk_overload_mvar(f_choices, ctx, e);
                    for (unsigned i = 1; i < args.size(); i++) {
                        if (arg_types[i]) {
                            list<expr_pair> coercions = m_ref.m_frontend.get_coercions(*(arg_types[i]));
                            if (coercions)
                                args[i] = add_coercion_mvar_app(coercions, args[i], *(arg_types[i]), ctx, arg(e, i));
                        }
                    }
                    return mk_app(args);
                } else {
                    // managed to solve overload at preprocessing time
                    f   = f_choices[0];
                    f_t = f_choice_types[0];
                }
            } else {
                f   = visit(f, ctx);
                f_t = get_type(f, ctx);
            }

            buffer<expr> new_args;
            new_args.push_back(f);
            for (unsigned i = 1; i < num_args(e); i++) {
                f_t = check_pi(f_t, ctx);
                expr a       = arg(e, i);
                expr new_a   = args[i];
                optional<expr> new_a_t = arg_types[i];
                if (new_a_t) {
                    list<expr_pair> coercions = m_ref.m_frontend.get_coercions(*new_a_t);
                    if (coercions) {
                        if (!f_t) {
                            new_a = add_coercion_mvar_app(coercions, new_a, *new_a_t, ctx, a);
                        } else {
                            expr expected = abst_domain(*f_t);
                            if (expected != *new_a_t) {
                                optional<expr> c = find_coercion(coercions, expected);
                                if (c) {
                                    new_a = mk_app(*c, new_a); // apply coercion
                                } else {
                                    new_a = add_coercion_mvar_app(coercions, new_a, *new_a_t, ctx, a);
                                }
                            }
                        }
                    }
                }
                new_args.push_back(new_a);
                if (f_t)
                    f_t = some_expr(instantiate(abst_body(*f_t), new_a));
            }
            return mk_app(new_args);
        }

        virtual expr visit_let(expr const & e, context const & ctx) {
            lean_assert(is_let(e));
            return update_let(e, [&](optional<expr> const & t, expr const & v, expr const & b) {
                    optional<expr> new_t = visit(t, ctx);
                    expr new_v = visit(v, ctx);
                    if (new_t) {
                        optional<expr> new_v_t = get_type(new_v, ctx);
                        if (new_v_t && *new_t != *new_v_t) {
                            list<expr_pair> coercions = m_ref.m_frontend.get_coercions(*new_v_t);
                            if (coercions) {
                                new_v = add_coercion_mvar_app(coercions, new_v, *new_v_t, ctx, v);
                            }
                        }
                    }
                    {
                        cache::mk_scope sc(m_cache);
                        expr new_b = visit(b, extend(ctx, let_name(e), new_t, new_v));
                        return std::make_tuple(new_t, new_v, new_b);
                    }
                });
        }

        optional<expr> visit(optional<expr> const & e, context const & ctx) {
            return replace_visitor::visit(e, ctx);
        }

        virtual expr visit(expr const & e, context const & ctx) {
            check_interrupted();
            expr r = replace_visitor::visit(e, ctx);
            if (!is_eqp(r, e))
                m_ref.m_trace[r] = e;
            return r;
        }
    };

    metavar_env elaborate_core() {
        // std::stable_sort(m_ucs.begin(), m_ucs.end(),
        //                 [](unification_constraint const & c1, unification_constraint const & c2) {
        //                     return !is_choice(c1) && is_choice(c2);
        //                 });
        elaborator elb(m_env, m_menv, m_ucs.size(), m_ucs.data());
        return elb.next();
    }

public:
    imp(frontend const & fe):
        m_frontend(fe),
        m_env(fe.get_environment()),
        m_type_checker(m_env),
        m_type_inferer(m_env),
        m_normalizer(m_env) {
    }

    expr elaborate(expr const & e) {
        // std::cout << "Elaborate " << e << "\n";
        clear();
        expr new_e = preprocessor(*this)(e);
        // std::cout << "After preprocessing\n" << new_e << "\n";
        if (has_metavar(new_e)) {
            m_type_checker.infer_type(new_e, context(), m_menv, m_ucs);
            // for (auto c : m_ucs) {
            //     formatter fmt = mk_simple_formatter();
            //     std::cout << c.pp(fmt, options(), nullptr, false) << "\n";
            // }
            metavar_env new_menv = elaborate_core();
            return new_menv->instantiate_metavars(new_e);
        } else {
            return new_e;
        }
    }

    std::tuple<expr, expr, metavar_env> elaborate(name const & n, expr const & t, expr const & e) {
        // std::cout << "Elaborate " << t << " : " << e << "\n";
        clear();
        expr new_t = preprocessor(*this)(t);
        expr new_e = preprocessor(*this)(e);
        // std::cout << "After preprocessing\n" << new_t << "\n" << new_e << "\n";
        if (has_metavar(new_e) || has_metavar(new_t)) {
            m_type_checker.infer_type(new_t, context(), m_menv, m_ucs);
            expr new_e_t = m_type_checker.infer_type(new_e, context(), m_menv, m_ucs);
            m_ucs.push_back(mk_convertible_constraint(context(), new_e_t, new_t,
                                                      mk_def_type_match_justification(context(), n, e)));
            // for (auto c : m_ucs) {
            //    formatter fmt = mk_simple_formatter();
            //    std::cout << c.pp(fmt, options(), nullptr, false) << "\n";
            // }
            metavar_env new_menv = elaborate_core();
            return std::make_tuple(new_menv->instantiate_metavars(new_t),
                                   new_menv->instantiate_metavars(new_e),
                                   new_menv);
        } else {
            return std::make_tuple(new_t, new_e, metavar_env());
        }
    }

    expr const & get_original(expr const & e) {
        expr const * r = &e;
        while (true) {
            auto it = m_trace.find(*r);
            if (it == m_trace.end()) {
                return *r;
            } else {
                r = &(it->second);
            }
        }
    }

    void clear() {
        m_menv = metavar_env();
        m_ucs.clear();
        m_trace.clear();
        m_type_checker.clear();
        m_type_inferer.clear();
        m_normalizer.clear();
    }

    environment const & get_environment() const {
        return m_env;
    }
};

frontend_elaborator::frontend_elaborator(frontend const & fe):m_ptr(new imp(fe)) {}
frontend_elaborator::~frontend_elaborator() {}
expr frontend_elaborator::operator()(expr const & e) { return m_ptr->elaborate(e); }
std::tuple<expr, expr, metavar_env> frontend_elaborator::operator()(name const & n, expr const & t, expr const & e) {
    return m_ptr->elaborate(n, t, e);
}
expr const & frontend_elaborator::get_original(expr const & e) const { return m_ptr->get_original(e); }
void frontend_elaborator::clear() { m_ptr->clear(); }
environment const & frontend_elaborator::get_environment() const { return m_ptr->get_environment(); }
}