lean2/src/library/coercion.cpp

/*
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.

Author: Leonardo de Moura
*/
#include <utility>
#include <string>
#include "util/rb_map.h"
#include "util/sstream.h"
#include "kernel/instantiate.h"
#include "library/coercion.h"
#include "library/module.h"
#include "library/kernel_serializer.h"
#include "library/kernel_bindings.h"
#include "library/scoped_ext.h"

namespace lean {
coercion_class coercion_class::mk_user(name n) { return coercion_class(coercion_class_kind::User, n); }
coercion_class coercion_class::mk_sort() { return coercion_class(coercion_class_kind::Sort); }
coercion_class coercion_class::mk_fun() { return coercion_class(coercion_class_kind::Fun); }
bool operator==(coercion_class const & c1, coercion_class const & c2) {
    return c1.m_kind == c2.m_kind && c1.m_name == c2.m_name;
}
bool operator!=(coercion_class const & c1, coercion_class const & c2) {
    return !(c1 == c2);
}

std::ostream & operator<<(std::ostream & out, coercion_class const & cls) {
    switch (cls.kind()) {
    case coercion_class_kind::User: out << cls.get_name(); break;
    case coercion_class_kind::Sort: out << "Sort-class"; break;
    case coercion_class_kind::Fun:  out << "Function-class"; break;
    }
    return out;
}

struct coercion_class_cmp_fn {
    int operator()(coercion_class const & c1, coercion_class const & c2) const {
        if (c1.kind() != c2.kind())
            return c1.kind() < c2.kind() ? -1 : 1;
        else
            return quick_cmp(c1.get_name(), c2.get_name());
    }
};

struct coercion_info {
    expr              m_fun;
    expr              m_fun_type;
    level_param_names m_level_params;
    unsigned          m_num_args;
    coercion_class    m_to;
    coercion_info() {}
    coercion_info(expr const & f, expr const & f_type, level_param_names const & ls, unsigned num, coercion_class const & cls):
        m_fun(f), m_fun_type(f_type), m_level_params(ls), m_num_args(num), m_to(cls) {}
};

struct coercion_state {
    name_map<list<coercion_info>>                             m_coercion_info;
    // m_from and m_to contain "direct" coercions
    typedef std::tuple<coercion_class, expr, expr>            from_data;
    name_map<list<from_data>>                                 m_from; // map user-class -> list of (class, coercion-fun)
    rb_map<coercion_class, list<name>, coercion_class_cmp_fn> m_to;
    name_map<pair<name, unsigned>>                            m_coercions; // map coercion -> (from-class, num-args)

    template<typename F>
    void for_each_info(name const & from, coercion_class const & to, F && f) {
        auto it = m_coercion_info.find(from);
        lean_assert(it);
        for (coercion_info info : *it) {
            if (info.m_to == to) {
                f(info);
            }
        }
    }

    void update_from_to(type_checker & tc, name const & C, coercion_class const & D,
                        expr const & f, expr const & f_type, io_state const & ios) {
        auto it1 = m_from.find(C);
        if (!it1) {
            m_from.insert(C, to_list(from_data(D, f, f_type)));
        } else {
            coercion_class D_it; expr f_it, f_type_it;
            auto it  = it1->begin();
            auto end = it1->end();
            for (; it != end; ++it) {
                std::tie(D_it, f_it, f_type_it) = *it;
                if (D_it == D && tc.is_def_eq(f_type_it, f_type).first)
                    break;
            }
            if (it == end)
                m_from.insert(C, cons(from_data(D, f, f_type), *it1));
            else if (std::get<1>(*it) != f)
                ios.get_diagnostic_channel() << "replacing the coercion from '" << C << "' to '" << D << "'\n";
        }
        auto it2 = m_to.find(D);
        if (!it2)
            m_to.insert(D, to_list(C));
        else if (std::find(it2->begin(), it2->end(), C) == it2->end())
            m_to.insert(D, cons(C, *it2));
    }
};

static void check_pi(name const & f, expr const & t) {
    if (!is_pi(t))
        throw exception(sstream() << "invalid coercion, '" << f << "' is not function");
}

// similar to check_pi, but produces a more informative message
static void check_valid_coercion(name const & f, expr const & t) {
    if (!is_pi(t)) {
        throw exception(sstream() << "invalid coercion, type of '" << f
                        << "' does not match any of the allowed expected types for coercions\n"
                        << "  Pi (x_1 : A_1) ... (x_n : A_n) (y: C x_1 ... x_n), D t_1 ... t_m\n"
                        << "  Pi (x_1 : A_1) ... (x_n : A_n) (y: C x_1 ... x_n), Type\n"
                        << "  Pi (x_1 : A_1) ... (x_n : A_n) (y: C x_1 ... x_n), A -> B");
    }
}

/** \brief Return true iff args contains Var(0), Var(1), ..., Var(args.size() - 1) */
static bool check_var_args(buffer<expr> const & args) {
    for (unsigned i = 0; i < args.size(); i++) {
        if (!is_var(args[i]) || var_idx(args[i]) != i)
            return false;
    }
    return true;
}

/** \brief Return true iff param_id(levels[i]) == level_params[i] */
static bool check_levels(levels ls, level_param_names ps) {
    while (!is_nil(ls) && !is_nil(ps)) {
        if (!is_param(head(ls)))
            return false;
        if (param_id(head(ls)) != head(ps))
            return false;
        ls = tail(ls);
        ps = tail(ps);
    }
    return is_nil(ls) && is_nil(ps);
}

optional<coercion_class> type_to_coercion_class(expr const & t) {
    if (is_sort(t)) {
        return optional<coercion_class>(coercion_class::mk_sort());
    } else if (is_pi(t)) {
        return optional<coercion_class>(coercion_class::mk_fun());
    } else {
        expr const & C = get_app_fn(t);
        if (is_constant(C))
            return optional<coercion_class>(coercion_class::mk_user(const_name(C)));
        else
            return optional<coercion_class>();
    }
}

typedef std::tuple<name, coercion_class, expr> arrow;
typedef list<arrow> arrows;
static bool contains(type_checker & tc, arrows const & as, name const & C, coercion_class const & D, expr const & f_type) {
    name C_it; coercion_class D_it; expr f_type_it;
    for (arrow const & a : as) {
        std::tie(C_it, D_it, f_type_it) = a;
        if (C == C_it && D == D_it && tc.is_def_eq(f_type_it, f_type).first)
            return true;
    }
    return false;
}
static arrows insert(arrows const & a, name const & C, coercion_class const & D, expr const & f_type) {
    return arrows(arrow(C, D, f_type), a);
}

struct add_coercion_fn {
    type_checker        m_tc;
    coercion_state      m_state;
    arrows              m_visited;
    io_state const &    m_ios;

    void add_coercion_trans(name const & C,
                            level_param_names const & f_level_params, expr const & f, expr const & f_type, unsigned f_num_args,
                            level_param_names const & g_level_params, expr g, expr const & g_type, unsigned g_num_args,
                            coercion_class const & g_class) {
        expr t = f_type;
        buffer<expr> args;
        for (unsigned i = 0; i <= f_num_args; i++)
            args.push_back(mk_var(i));
        expr f_app = apply_beta(f, args.size(), args.data());
        buffer<name> f_arg_names;
        buffer<expr> f_arg_types;
        while (is_pi(t)) {
            f_arg_names.push_back(binding_name(t));
            f_arg_types.push_back(binding_domain(t));
            t = binding_body(t);
        }
        expr D_app = t;
        buffer<expr> gf_args;
        gf_args.push_back(f_app);
        expr D_cnst = get_app_rev_args(D_app, gf_args);
        if (gf_args.size() != g_num_args + 1)
            return;
        if (length(const_levels(D_cnst)) != length(g_level_params))
            return;
        // C >-> D >-> E
        g  = instantiate_univ_params(g, g_level_params, const_levels(D_cnst));
        expr gf = apply_beta(g, gf_args.size(), gf_args.data());
        expr gf_type = g_type;
        while (is_pi(gf_type))
            gf_type = binding_body(gf_type);
        gf_type = instantiate(instantiate_univ_params(gf_type, g_level_params,
                                                      const_levels(D_cnst)), gf_args.size(), gf_args.data());
        unsigned i = f_arg_types.size();
        while (i > 0) {
            --i;
            gf = mk_lambda(f_arg_names[i], f_arg_types[i], gf);
            gf_type = mk_pi(f_arg_names[i], f_arg_types[i], gf_type);
        }
        add_coercion(C, gf, gf_type, f_level_params, f_num_args, g_class);
    }

    void add_coercion_trans_to(name const & C, expr const & f, expr const & f_type,
                               level_param_names const & ls, unsigned num_args, coercion_class const & cls) {
        // apply transitivity using ext.m_to
        coercion_class C_cls = coercion_class::mk_user(C);
        auto it1 = m_state.m_to.find(C_cls);
        if (!it1)
            return;
        for (name const & B : *it1) {
            m_state.for_each_info(B, C_cls, [&](coercion_info const & info) {
                    // B >-> C >-> D
                    add_coercion_trans(B, info.m_level_params, info.m_fun, info.m_fun_type, info.m_num_args,
                                       ls, f, f_type, num_args, cls);
                });
        }
    }

    void add_coercion_trans_from(name const & C, expr const & f, expr const & f_type,
                                 level_param_names const & ls, unsigned num_args, coercion_class const & cls) {
        // apply transitivity using ext.m_from
        if (cls.kind() != coercion_class_kind::User)
            return; // nothing to do Sort and Fun classes are terminal
        name const & D = cls.get_name();
        auto it = m_state.m_from.find(D);
        if (!it)
            return;
        for (auto const & p : *it) {
            coercion_class E   = std::get<0>(p);
            m_state.for_each_info(D, E, [&](coercion_info const & info) {
                    // C >-> D >-> E
                    add_coercion_trans(C, ls, f, f_type, num_args,
                                       info.m_level_params, info.m_fun, info.m_fun_type, info.m_num_args, info.m_to);
                });
        }
    }

    void add_coercion_core(name const & C, expr const & f, expr const & f_type,
                           level_param_names const & ls, unsigned num_args, coercion_class const & cls) {
        auto it = m_state.m_coercion_info.find(C);
        if (!it) {
            list<coercion_info> infos(coercion_info(f, f_type, ls, num_args, cls));
            m_state.m_coercion_info.insert(C, infos);
        } else {
            list<coercion_info> infos = *it;
            infos = filter(infos, [&](coercion_info const & info) {
                    return info.m_to != cls || !m_tc.is_def_eq(info.m_fun_type, f_type).first;
                });
            infos = cons(coercion_info(f, f_type, ls, num_args, cls), infos);
            m_state.m_coercion_info.insert(C, infos);
        }
        if (is_constant(f))
            m_state.m_coercions.insert(const_name(f), mk_pair(C, num_args));
    }

    void add_coercion(name const & C, expr const & f, expr const & f_type,
                      level_param_names const & ls, unsigned num_args, coercion_class const & cls) {
        if (contains(m_tc, m_visited, C, cls, f_type))
            return;
        if (cls.kind() == coercion_class_kind::User && cls.get_name() == C)
            return;
        m_visited = insert(m_visited, C, cls, f_type);
        add_coercion_core(C, f, f_type, ls, num_args, cls);
        add_coercion_trans_to(C, f, f_type, ls, num_args, cls);
        add_coercion_trans_from(C, f, f_type, ls, num_args, cls);
    }

    add_coercion_fn(environment const & env, coercion_state const & s, io_state const & ios):
        m_tc(env), m_state(s), m_ios(ios) {}

    coercion_state operator()(name const & C, expr const & f, expr const & f_type,
                              level_param_names const & ls, unsigned num_args, coercion_class const & cls) {
        add_coercion(C, f, f_type, ls, num_args, cls);
        m_state.update_from_to(m_tc, C, cls, f, f_type, m_ios);
        return m_state;
    }
};

coercion_state add_coercion(environment const & env, io_state const & ios, coercion_state const & st,
                            name const & f, name const & C) {
    declaration d = env.get(f);
    unsigned num = 0;
    buffer<expr> args;
    expr t = d.get_type();
    check_pi(f, t);
    while (true) {
        args.clear();
        expr const & C_fn = get_app_rev_args(binding_domain(t), args);
        if (is_constant(C_fn) &&
            const_name(C_fn) == C &&
            num == args.size() &&
            check_var_args(args) &&
            check_levels(const_levels(C_fn), d.get_univ_params())) {
            expr fn = mk_constant(f, const_levels(C_fn));
            optional<coercion_class> cls = type_to_coercion_class(binding_body(t));
            if (!cls)
                throw exception(sstream() << "invalid coercion, '" << f << "' cannot be used as a coercion from '" << C << "'");
            else if (cls->kind() == coercion_class_kind::User && cls->get_name() == C)
                throw exception(sstream() << "invalid coercion, '" << f << "' is a coercion from '" << C << "' to itself");
            return add_coercion_fn(env, st, ios)(C, fn, d.get_type(), d.get_univ_params(), num, *cls);
        }
        t = binding_body(t);
        num++;
        check_valid_coercion(f, t);
    }
}

static name * g_class_name = nullptr;
static std::string * g_key = nullptr;

typedef pair<name, name> coercion_entry;
struct coercion_config {
    typedef coercion_state  state;
    typedef coercion_entry  entry;
    static void add_entry(environment const & env, io_state const & ios, state & s, entry const & e) {
        s = add_coercion(env, ios, s, e.first, e.second);
    }
    static name const & get_class_name() {
        return *g_class_name;
    }
    static std::string const & get_serialization_key() {
        return *g_key;
    }
    static void  write_entry(serializer & s, entry const & e) {
        s << e.first << e.second;
    }
    static entry read_entry(deserializer & d) {
        entry e;
        d >> e.first >> e.second;
        return e;
    }
    static optional<unsigned> get_fingerprint(entry const & e) {
        return some(hash(e.first.hash(), e.second.hash()));
    }
};

template class scoped_ext<coercion_config>;
typedef scoped_ext<coercion_config> coercion_ext;

void initialize_coercion() {
    g_class_name = new name("coercions");
    g_key        = new std::string("coerce");
    coercion_ext::initialize();
}

void finalize_coercion() {
    coercion_ext::finalize();
    delete g_key;
    delete g_class_name;
}

environment add_coercion(environment const & env, name const & f, name const & C, io_state const & ios, bool persistent) {
    return coercion_ext::add_entry(env, ios, coercion_entry(f, C), persistent);
}

environment add_coercion(environment const & env, name const & f, io_state const & ios, bool persistent) {
    declaration d = env.get(f);
    expr t = d.get_type();
    check_pi(f, t);
    buffer<name> Cs; // possible Cs
    while (is_pi(t)) {
        expr d = get_app_fn(binding_domain(t));
        if (is_constant(d))
            Cs.push_back(const_name(d));
        t = binding_body(t);
    }
    if (Cs.empty())
        throw exception(sstream() << "invalid coercion, '" << f << "' cannot be used as a coercion");
    unsigned i = Cs.size();
    while (i > 0) {
        --i;
        if (i == 0) {
            // last alternative
            return add_coercion(env, f, Cs[i], ios, persistent);
        } else {
            try {
                return add_coercion(env, f, Cs[i], ios, persistent);
            } catch (exception &) {
                // failed, keep trying...
            }
        }
    }
    lean_unreachable(); // LCOV_EXCL_LINE
}

optional<pair<name, unsigned>> is_coercion(environment const & env, name const & f) {
    coercion_state const & ext = coercion_ext::get_state(env);
    if (auto it = ext.m_coercions.find(f))
        return optional<pair<name, unsigned>>(*it);
    else
        return optional<pair<name, unsigned>>();
}

optional<pair<name, unsigned>> is_coercion(environment const & env, expr const & f) {
    if (!is_constant(f))
        return optional<pair<name, unsigned>>();
    return is_coercion(env, const_name(f));
}

bool has_coercions_to(environment const & env, name const & D) {
    coercion_state const & ext = coercion_ext::get_state(env);
    auto it = ext.m_to.find(coercion_class::mk_user(D));
    return it && !is_nil(*it);
}

bool has_coercions_to_sort(environment const & env) {
    coercion_state const & ext = coercion_ext::get_state(env);
    auto it = ext.m_to.find(coercion_class::mk_sort());
    return it && !is_nil(*it);
}

bool has_coercions_to_fun(environment const & env) {
    coercion_state const & ext = coercion_ext::get_state(env);
    auto it = ext.m_to.find(coercion_class::mk_fun());
    return it && !is_nil(*it);
}

bool has_coercions_from(environment const & env, name const & C) {
    coercion_state const & ext = coercion_ext::get_state(env);
    return ext.m_coercion_info.contains(C);
}

bool has_coercions_from(environment const & env, expr const & C) {
    expr const & C_fn = get_app_fn(C);
    if (!is_constant(C_fn))
        return false;
    coercion_state const & ext = coercion_ext::get_state(env);
    auto it = ext.m_coercion_info.find(const_name(C_fn));
    if (!it)
        return false;
    list<coercion_info> const & cs = *it;
    return
        head(cs).m_num_args == get_app_num_args(C) &&
        length(head(cs).m_level_params) == length(const_levels(C_fn));
}

list<expr> get_coercions(environment const & env, expr const & C, coercion_class const & D) {
    buffer<expr> args;
    expr const & C_fn = get_app_rev_args(C, args);
    if (!is_constant(C_fn))
        return list<expr>();
    coercion_state const & ext = coercion_ext::get_state(env);
    auto it = ext.m_coercion_info.find(const_name(C_fn));
    if (!it)
        return list<expr>();
    buffer<expr> r;
    for (coercion_info const & info : *it) {
        if (info.m_to == D && info.m_num_args == args.size() && length(info.m_level_params) == length(const_levels(C_fn))) {
            expr f = instantiate_univ_params(info.m_fun, info.m_level_params, const_levels(C_fn));
            r.push_back(apply_beta(f, args.size(), args.data()));
        }
    }
    return to_list(r.begin(), r.end());
}

list<expr> get_coercions(environment const & env, expr const & C, name const & D) {
    return get_coercions(env, C, coercion_class::mk_user(D));
}

list<expr> get_coercions_to_sort(environment const & env, expr const & C) {
    return get_coercions(env, C, coercion_class::mk_sort());
}

list<expr> get_coercions_to_fun(environment const & env, expr const & C) {
    return get_coercions(env, C, coercion_class::mk_fun());
}

bool get_coercions_from(environment const & env, expr const & C, buffer<std::tuple<coercion_class, expr, expr>> & result) {
    buffer<expr> args;
    expr const & C_fn = get_app_rev_args(C, args);
    if (!is_constant(C_fn))
        return false;
    coercion_state const & ext = coercion_ext::get_state(env);
    auto it = ext.m_coercion_info.find(const_name(C_fn));
    if (!it)
        return false;
    bool r = false;
    for (coercion_info const & info : *it) {
        if (info.m_num_args == args.size() &&
            length(info.m_level_params) == length(const_levels(C_fn))) {
            expr f = instantiate_univ_params(info.m_fun, info.m_level_params, const_levels(C_fn));
            expr c = apply_beta(f, args.size(), args.data());
            expr t = instantiate_univ_params(info.m_fun_type, info.m_level_params, const_levels(C_fn));
            for (unsigned i = 0; i < args.size(); i++) t = binding_body(t);
            t = instantiate(t, args.size(), args.data());
            result.emplace_back(info.m_to, c, t);
            r = true;
        }
    }
    return r;
}

template<typename F>
void for_each_coercion(environment const & env, F && f) {
    coercion_state const & ext = coercion_ext::get_state(env);
    ext.m_coercion_info.for_each([&](name const & C, list<coercion_info> const & infos) {
            for (auto const & info : infos) {
                f(C, info);
            }
        });
}

void for_each_coercion_user(environment const & env, coercion_user_fn const & f) {
    for_each_coercion(env, [&](name const & C, coercion_info const & info) {
            if (info.m_to.kind() == coercion_class_kind::User)
                f(C, info.m_to.get_name(), info.m_fun, info.m_level_params, info.m_num_args);
        });
}

void for_each_coercion_sort(environment const & env, coercion_sort_fn const & f) {
    for_each_coercion(env, [&](name const & C, coercion_info const & info) {
            if (info.m_to.kind() == coercion_class_kind::Sort)
                f(C, info.m_fun, info.m_level_params, info.m_num_args);
        });
}

void for_each_coercion_fun(environment const & env, coercion_fun_fn const & f) {
    for_each_coercion(env, [&](name const & C, coercion_info const & info) {
            if (info.m_to.kind() == coercion_class_kind::Fun)
                f(C, info.m_fun, info.m_level_params, info.m_num_args);
        });
}

static int add_coercion(lua_State * L) {
    int nargs = lua_gettop(L);
    if (nargs == 2)
        return push_environment(L, add_coercion(to_environment(L, 1), to_name_ext(L, 2), get_io_state(L)));
    else if (nargs == 3 && is_io_state(L, 3))
        return push_environment(L, add_coercion(to_environment(L, 1), to_name_ext(L, 2), to_io_state(L, 3)));
    else if (nargs == 3)
        return push_environment(L, add_coercion(to_environment(L, 1), to_name_ext(L, 2), to_name_ext(L, 3), get_io_state(L)));
    else
        return push_environment(L, add_coercion(to_environment(L, 1), to_name_ext(L, 2), to_name_ext(L, 3), to_io_state(L, 4)));
}

static int is_coercion(lua_State * L) {
    optional<pair<name, unsigned>> r;
    if (is_expr(L, 2))
        r = is_coercion(to_environment(L, 1), to_expr(L, 2));
    else
        r = is_coercion(to_environment(L, 1), to_name_ext(L, 2));
    if (r) {
        push_name(L, r->first);
        push_integer(L, r->second);
        return 2;
    } else {
        return 0;
    }
}

static int has_coercions_from(lua_State * L) {
    if (is_expr(L, 2))
        return push_boolean(L, has_coercions_from(to_environment(L, 1), to_expr(L, 2)));
    else
        return push_boolean(L, has_coercions_from(to_environment(L, 1), to_name_ext(L, 2)));
}

static int get_coercions(lua_State * L) {
    return push_list_expr(L, get_coercions(to_environment(L, 1), to_expr(L, 2), to_name_ext(L, 3)));
}

static int get_coercions_to_sort(lua_State * L) {
    return push_list_expr(L, get_coercions_to_sort(to_environment(L, 1), to_expr(L, 2)));
}

static int get_coercions_to_fun(lua_State * L) {
    return push_list_expr(L, get_coercions_to_fun(to_environment(L, 1), to_expr(L, 2)));
}

static int get_coercions_from(lua_State * L) {
    buffer<std::tuple<coercion_class, expr, expr>> r;
    get_coercions_from(to_environment(L, 1), to_expr(L, 2), r);
    lua_newtable(L);
    int i = 1;
    for (auto p : r) {
        lua_newtable(L);
        coercion_class c = std::get<0>(p);
        push_integer(L, static_cast<unsigned>(c.kind()));
        lua_rawseti(L, -2, 1);
        if (c.kind() == coercion_class_kind::User) {
            push_name(L, c.get_name());
        } else {
            push_nil(L);
        }
        lua_rawseti(L, -2, 2);
        push_expr(L, std::get<1>(p));
        lua_rawseti(L, -2, 3);
        push_expr(L, std::get<2>(p));
        lua_rawseti(L, -2, 4);
        lua_rawseti(L, -2, i);
        i = i + 1;
    }
    return 1;
}

static int for_each_coercion(lua_State * L, coercion_class_kind k) {
    environment env = to_environment(L, 1);
    luaL_checktype(L, 2, LUA_TFUNCTION); // user-fun
    for_each_coercion(env, [&](name const & C, coercion_info const & info) {
            if (info.m_to.kind() != k)
                return;
            lua_pushvalue(L, 2); // push user-fun
            push_name(L, C);
            int nargs = 4;
            if (info.m_to.kind() == coercion_class_kind::User) {
                push_name(L, info.m_to.get_name());
                nargs++;
            }
            push_expr(L, info.m_fun);
            push_list_name(L, info.m_level_params);
            push_integer(L, info.m_num_args);
            pcall(L, nargs, 0, 0);
        });
    return 0;
}

static int for_each_coercion_user(lua_State * L) { return for_each_coercion(L, coercion_class_kind::User); }
static int for_each_coercion_sort(lua_State * L) { return for_each_coercion(L, coercion_class_kind::Sort); }
static int for_each_coercion_fun(lua_State * L) { return for_each_coercion(L, coercion_class_kind::Fun); }

void open_coercion(lua_State * L) {
    SET_GLOBAL_FUN(add_coercion,           "add_coercion");
    SET_GLOBAL_FUN(is_coercion,            "is_coercion");
    SET_GLOBAL_FUN(has_coercions_from,     "has_coercions_from");
    SET_GLOBAL_FUN(get_coercions,          "get_coercions");
    SET_GLOBAL_FUN(get_coercions_to_sort,  "get_coercions_to_sort");
    SET_GLOBAL_FUN(get_coercions_to_fun,   "get_coercions_to_fun");
    SET_GLOBAL_FUN(get_coercions_from,     "get_coercions_from");
    SET_GLOBAL_FUN(for_each_coercion_user, "for_each_coercion_user");
    SET_GLOBAL_FUN(for_each_coercion_sort, "for_each_coercion_sort");
    SET_GLOBAL_FUN(for_each_coercion_fun,  "for_each_coercion_fun");
}
}