feat(library/coercion): new coercion manager

closes #668

library/data/int/div.lean

@@ -72,10 +72,12 @@ calc
   a div b = -((-a - 1) div b + 1) : div_of_neg_of_pos Ha Hb
       ... < 0                     : neg_neg_of_pos H2
 
+set_option pp.coercions true
+
 theorem zero_div (b : ℤ) : 0 div b = 0 :=
 calc
   0 div b = sign b * (#nat 0 div (nat_abs b)) : rfl
-      ... = sign b * 0 : nat.zero_div
+      ... = sign b * (0:nat) : nat.zero_div
       ... = 0                : mul_zero
 
 theorem div_zero (a : ℤ) : a div 0 = 0 :=
@@ -98,7 +100,7 @@ int.cases_on a
         assume H : m < n,
         calc
           m div n = #nat m div n : of_nat_div
-              ... = 0            : nat.div_eq_zero_of_lt (lt_of_of_nat_lt_of_nat H))
+              ... = (0:nat)      : nat.div_eq_zero_of_lt (lt_of_of_nat_lt_of_nat H))
       (take n,
         assume H : m < -[1+n],
         have H1 : ¬(m < -[1+n]), from dec_trivial,

src/frontends/lean/builtin_cmds.cpp

@@ -54,15 +54,15 @@ static void print_coercions(parser & p, optional<name> const & C) {
     opts = opts.update(get_pp_coercions_option_name(), true);
     io_state_stream out = p.regular_stream().update_options(opts);
     char const * arrow = get_pp_unicode(opts) ? "↣" : ">->";
-    for_each_coercion_user(env, [&](name const & C1, name const & D, expr const & c, level_param_names const &, unsigned) {
+    for_each_coercion_user(env, [&](name const & C1, name const & c, name const & D) {
             if (!C || *C == C1)
                 out << C1 << " " << arrow << " " << D << " : " << c << endl;
         });
-    for_each_coercion_sort(env, [&](name const & C1, expr const & c, level_param_names const &, unsigned) {
+    for_each_coercion_sort(env, [&](name const & C1, name const & c) {
             if (!C || *C == C1)
                 out << C1 << " " << arrow << " [sort-class] : " << c << endl;
         });
-    for_each_coercion_fun(env, [&](name const & C1, expr const & c, level_param_names const &, unsigned) {
+    for_each_coercion_fun(env, [&](name const & C1, name const & c) {
             if (!C || *C == C1)
                 out << C1 << " " << arrow << " [fun-class] : " << c << endl;
         });
@@ -960,20 +960,6 @@ static environment init_hits_cmd(parser & p) {
     return module::declare_hits(p.env());
 }
 
-static environment compose_cmd(parser & p) {
-    name g = p.check_constant_next("invalid #compose command, constant expected");
-    name f = p.check_constant_next("invalid #compose command, constant expected");
-    optional<name> gf;
-    if (p.curr_is_token(get_arrow_tk())) {
-        p.next();
-        name id = p.check_id_next("invalid #compose command, identifier expected");
-        gf = get_namespace(p.env()) + id;
-    }
-    auto r = compose(p.env(), g, f, gf);
-    p.regular_stream() << ">> " << r.second << "\n";
-    return r.first;
-}
-
 void init_cmd_table(cmd_table & r) {
     add_cmd(r, cmd_info("open",          "create aliases for declarations, and use objects defined in other namespaces",
                         open_cmd));
@@ -997,7 +983,6 @@ void init_cmd_table(cmd_table & r) {
     add_cmd(r, cmd_info("#erase_cache",  "erase cached definition (for debugging purposes)", erase_cache_cmd));
     add_cmd(r, cmd_info("#projections",  "generate projections for inductive datatype (for debugging purposes)", projections_cmd));
     add_cmd(r, cmd_info("#telescope_eq", "(for debugging purposes)", telescope_eq_cmd));
-    add_cmd(r, cmd_info("#compose",      "(for debugging purposes)", compose_cmd));
     register_decl_cmds(r);
     register_inductive_cmd(r);
     register_structure_cmd(r);

src/frontends/lean/decl_attributes.cpp

@@ -181,7 +181,7 @@ environment decl_attributes::apply(environment env, io_state const & ios, name c
         }
     }
     if (m_is_coercion)
-        env = add_coercion(env, d, ios, m_persistent);
+        env = add_coercion(env, ios, d, m_persistent);
     auto decl = env.find(d);
     if (decl && decl->is_definition()) {
         if (m_is_reducible)

src/frontends/lean/structure_cmd.cpp

@@ -818,7 +818,7 @@ struct structure_cmd_fn {
             save_def_info(coercion_name);
             add_alias(coercion_name);
             if (!m_private_parents[i]) {
-                m_env = add_coercion(m_env, coercion_name, m_p.ios());
+                m_env = add_coercion(m_env, m_p.ios(), coercion_name);
                 if (m_modifiers.is_class() && is_class(m_env, parent_name)) {
                     // if both are classes, then we also mark coercion_name as an instance
                     m_env = add_trans_instance(m_env, coercion_name);

src/frontends/lean/token_table.cpp

@@ -120,7 +120,7 @@ void init_token_table(token_table & t) {
          "add_begin_end_tactic", "set_begin_end_tactic", "instance", "class",
          "multiple_instances", "find_decl", "attribute", "persistent",
          "include", "omit", "migrate", "init_quotient", "init_hits", "#erase_cache", "#projections", "#telescope_eq",
-         "#compose", nullptr};
+         nullptr};
 
     pair<char const *, char const *> aliases[] =
         {{g_lambda_unicode, "fun"}, {"forall", "Pi"}, {g_forall_unicode, "Pi"}, {g_pi_unicode, "Pi"},

src/library/coercion.cpp

@@ -9,121 +9,219 @@ Author: Leonardo de Moura
 #include "util/rb_map.h"
 #include "util/sstream.h"
 #include "kernel/instantiate.h"
+#include "library/tc_multigraph.h"
 #include "library/coercion.h"
+#include "library/reducible.h"
+#include "library/protected.h"
 #include "library/module.h"
 #include "library/kernel_serializer.h"
-#include "library/kernel_bindings.h"
 #include "library/scoped_ext.h"
 
 namespace lean {
-enum class coercion_class_kind { User, Sort, Fun };
-/**
-   \brief A coercion is a mapping between classes.
-   We support three kinds of classes: User, Sort, Function.
-*/
-class coercion_class {
-    name                m_name; // relevant only if m_kind == User
-    coercion_class(name const & n): m_name(n) {}
-public:
-    coercion_class();
-    static coercion_class mk_user(name n);
-    static coercion_class mk_sort();
-    static coercion_class mk_fun();
-    friend bool operator==(coercion_class const & c1, coercion_class const & c2) { return c1.m_name == c2.m_name; }
-    friend bool operator!=(coercion_class const & c1, coercion_class const & c2) { return c1.m_name != c2.m_name; }
-    coercion_class_kind kind() const;
-    name get_name() const { return m_name; }
-};
-
 static name * g_fun  = nullptr;
 static name * g_sort = nullptr;
 
-coercion_class::coercion_class():m_name(*g_sort) {}
-
-coercion_class coercion_class::mk_user(name n) { return coercion_class(n); }
-coercion_class coercion_class::mk_sort() { return coercion_class(*g_sort); }
-coercion_class coercion_class::mk_fun() { return coercion_class(*g_fun); }
-
-coercion_class_kind coercion_class::kind() const {
-    if (m_name == *g_sort) return coercion_class_kind::Sort;
-    else if (m_name == *g_fun) return coercion_class_kind::Fun;
-    else return coercion_class_kind::User;
-}
-
-
-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 {
-        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;
+struct coercion_entry {
+    name     m_from;
+    name     m_coe;
     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) {}
+    name     m_to;
+    coercion_entry() {}
+    coercion_entry(name const & from, name const & coe, unsigned num, name const & to):
+        m_from(from), m_coe(coe), m_num_args(num), m_to(to) {}
 };
 
 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;
-
+    tc_multigraph                   m_graph;
     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 add1(environment const & env, name const & from, name const & coe, unsigned num, name const & to) {
+        m_coercions.insert(coe, mk_pair(from, num));
+        m_graph.add1(env, from, coe, to);
     }
 
-    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;
+    coercion_state():m_graph("coercion") {}
+};
+
+static name * g_class_name = nullptr;
+static std::string * g_key = nullptr;
+
+struct coercion_config {
+    typedef coercion_state  state;
+    typedef coercion_entry  entry;
+    static void add_entry(environment const & env, io_state const &, state & s, entry const & e) {
+        s.add1(env, e.m_from, e.m_coe, e.m_num_args, e.m_to);
     }
-            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";
+    static name const & get_class_name() {
+        return *g_class_name;
     }
-        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 std::string const & get_serialization_key() {
+        return *g_key;
+    }
+    static void  write_entry(serializer & s, entry const & e) {
+        s << e.m_from << e.m_coe << e.m_num_args << e.m_to;
+    }
+    static entry read_entry(deserializer & d) {
+        entry e;
+        d >> e.m_from >> e.m_coe >> e.m_num_args >> e.m_to;
+        return e;
+    }
+    static optional<unsigned> get_fingerprint(entry const & e) {
+        return some(e.m_coe.hash());
     }
 };
 
+template class scoped_ext<coercion_config>;
+typedef scoped_ext<coercion_config> coercion_ext;
+
+void initialize_coercion() {
+    name p       = name::mk_internal_unique_name();
+    g_fun        = new name(p, "Fun");
+    g_sort       = new name(p, "Sort");
+    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;
+    delete g_fun;
+    delete g_sort;
+}
+
+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);
+    return !is_nil(ext.m_graph.get_predecessors(D));
+}
+
+bool has_coercions_to_sort(environment const & env) {
+    coercion_state const & ext = coercion_ext::get_state(env);
+    return !is_nil(ext.m_graph.get_predecessors(*g_sort));
+}
+
+bool has_coercions_to_fun(environment const & env) {
+    coercion_state const & ext = coercion_ext::get_state(env);
+    return !is_nil(ext.m_graph.get_predecessors(*g_fun));
+}
+
+bool has_coercions_from(environment const & env, name const & C) {
+    coercion_state const & ext = coercion_ext::get_state(env);
+    return !is_nil(ext.m_graph.get_successors(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);
+    for (pair<name, name> const & coe_to : ext.m_graph.get_successors(const_name(C_fn))) {
+        name const & coe = coe_to.first;
+        if (auto it = ext.m_coercions.find(coe)) {
+            if (it->second == get_app_num_args(C))
+                return true;
+        }
+    }
+    return false;
+}
+
+static list<expr> get_coercions_core(environment const & env, expr const & C, name 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);
+    buffer<expr> r;
+    for (pair<name, name> const & coe_to : ext.m_graph.get_successors(const_name(C_fn))) {
+        name const & coe = coe_to.first;
+        name const & to  = coe_to.second;
+        if (to != D)
+            continue;
+        if (auto it = ext.m_coercions.find(coe)) {
+            if (it->second != args.size())
+                continue;
+        }
+        declaration const & coe_decl = env.get(coe);
+        if (coe_decl.get_num_univ_params() != length(const_levels(C_fn)))
+            continue;
+        expr f = mk_constant(coe, const_levels(C_fn));
+        r.push_back(mk_rev_app(f, args.size(), args.data()));
+    }
+    return to_list(r);
+}
+
+
+list<expr> get_coercions(environment const & env, expr const & C, name const & D) {
+    return get_coercions_core(env, C, D);
+}
+
+list<expr> get_coercions_to_sort(environment const & env, expr const & C) {
+    return get_coercions_core(env, C, *g_sort);
+}
+
+list<expr> get_coercions_to_fun(environment const & env, expr const & C) {
+    return get_coercions_core(env, C, *g_fun);
+}
+
+bool get_coercions_from(environment const & env, expr const & C, buffer<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);
+    bool r = false;
+    for (pair<name, name> const & coe_to : ext.m_graph.get_successors(const_name(C_fn))) {
+        name const & coe = coe_to.first;
+        if (auto it = ext.m_coercions.find(coe)) {
+            if (it->second != args.size())
+                continue;
+        }
+        declaration const & coe_decl = env.get(coe);
+        if (coe_decl.get_num_univ_params() != length(const_levels(C_fn)))
+            continue;
+        expr f = mk_constant(coe, const_levels(C_fn));
+        result.push_back(mk_rev_app(f, args.size(), args.data()));
+        r = true;
+    }
+    return r;
+}
+
+void for_each_coercion_user(environment const & env, coercion_user_fn const & f) {
+    tc_multigraph const & g = coercion_ext::get_state(env).m_graph;
+    g.for_each(f);
+}
+
+void for_each_coercion_sort(environment const & env, coercion_sort_fn const & f) {
+    tc_multigraph const & g = coercion_ext::get_state(env).m_graph;
+    g.for_each([&](name const & from, name const & coe, name const & to) {
+            if (to == *g_sort)
+                f(from, coe);
+        });
+}
+
+void for_each_coercion_fun(environment const & env, coercion_fun_fn const & f) {
+    tc_multigraph const & g = coercion_ext::get_state(env).m_graph;
+    g.for_each([&](name const & from, name const & coe, name const & to) {
+            if (to == *g_fun)
+                f(from, coe);
+        });
+}
+
 static void check_pi(name const & f, expr const & t) {
     if (!is_pi(t))
         throw exception(sstream() << "invalid coercion, '" << f << "' is not function");
@@ -162,160 +260,59 @@ static bool check_levels(levels ls, level_param_names ps) {
     return is_nil(ls) && is_nil(ps);
 }
 
-optional<coercion_class> type_to_coercion_class(expr const & t) {
+static optional<name> type_to_coercion_class(expr const & t) {
     if (is_sort(t)) {
-        return optional<coercion_class>(coercion_class::mk_sort());
+        return optional<name>(*g_sort);
     } else if (is_pi(t)) {
-        return optional<coercion_class>(coercion_class::mk_fun());
+        return optional<name>(*g_fun);
     } else {
         expr const & C = get_app_fn(t);
         if (is_constant(C))
-            return optional<coercion_class>(coercion_class::mk_user(const_name(C)));
+            return optional<name>(const_name(C));
         else
-            return optional<coercion_class>();
+            return optional<name>();
     }
 }
 
-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);
+static bool is_user_class(name const & cls) {
+    return cls != *g_fun && cls != *g_sort;
 }
 
-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;
+static unsigned get_num_args(environment const & env, tc_edge const & new_coe) {
+    declaration const & d = env.get(new_coe.m_cnst);
+    unsigned num = 0;
     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));
+    expr t = d.get_type();
+    while (true) {
+        if (!is_pi(t))
+            return num;
+        expr fn = get_app_fn(binding_domain(t));
+        if (is_constant(fn) && const_name(fn) == new_coe.m_from)
+            return num;
         t = binding_body(t);
+        num++;
     }
-        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);
-                });
-        }
+static environment add_coercion_core(environment const & env,
+                                     name const & from, name const & coe, unsigned num_args, name const & to,
+                                     bool persistent) {
+    coercion_state st = coercion_ext::get_state(env);
+    pair<environment, list<tc_edge>> new_env_coes = st.m_graph.add(env, from, coe, to);
+    environment new_env = new_env_coes.first;
+    new_env = coercion_ext::add_entry(new_env, get_dummy_ios(), coercion_entry(from, coe, num_args, to), persistent);
+    for (tc_edge const & new_coe : new_env_coes.second) {
+        unsigned nargs = get_num_args(new_env, new_coe);
+        new_env = coercion_ext::add_entry(new_env, get_dummy_ios(),
+                                          coercion_entry(new_coe.m_from, new_coe.m_cnst, nargs, new_coe.m_to), persistent);
+        new_env = set_reducible(new_env, new_coe.m_cnst, reducible_status::Reducible, persistent);
+        new_env = add_protected(new_env, new_coe.m_cnst);
     }
+    return new_env;
+}
 
-    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) {
+static environment add_coercion(environment const & env, io_state const & ios,
+                                name const & f, name const & C, bool persistent) {
     declaration d = env.get(f);
     unsigned num = 0;
     buffer<expr> args;
@@ -329,13 +326,13 @@ coercion_state add_coercion(environment const & env, io_state const & ios, coerc
             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));
+            optional<name> 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 << "' cannot be used as a coercion from '"
+                                << C << "'");
+            else if (is_user_class(*cls) && *cls == 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);
+            return add_coercion_core(env, C, f, num, *cls, persistent);
         }
         t = binding_body(t);
         num++;
@@ -343,60 +340,7 @@ coercion_state add_coercion(environment const & env, io_state const & ios, coerc
     }
 }
 
-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() {
-    name p       = name::mk_internal_unique_name();
-    g_fun        = new name(p, "Fun");
-    g_sort       = new name(p, "Sort");
-    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;
-    delete g_fun;
-    delete g_sort;
-}
-
-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) {
+environment add_coercion(environment const & env, io_state const & ios, name const & f, bool persistent) {
     declaration d = env.get(f);
     expr t = d.get_type();
     check_pi(f, t);
@@ -414,10 +358,10 @@ environment add_coercion(environment const & env, name const & f, io_state const
         --i;
         if (i == 0) {
             // last alternative
-            return add_coercion(env, f, Cs[i], ios, persistent);
+            return add_coercion(env, ios, f, Cs[i], persistent);
         } else {
             try {
-                return add_coercion(env, f, Cs[i], ios, persistent);
+                return add_coercion(env, ios, f, Cs[i], persistent);
             } catch (exception &) {
                 // failed, keep trying...
             }
@@ -425,142 +369,4 @@ environment add_coercion(environment const & env, name const & f, io_state const
     }
     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<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.push_back(c);
-            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);
-        });
-}
 }

src/library/coercion.h

@@ -38,7 +38,7 @@ namespace lean {
 
    \remark if persistent == true, then coercion is saved in .olean files
 */
-environment add_coercion(environment const & env, name const & f, io_state const & ios, bool persistent = true);
+environment add_coercion(environment const & env, io_state const & ios, name const & f, bool persistent = true);
 /** \brief If \c f is a coercion, then return the name of the 'from-class' and the number of
     class parameters.
 */
@@ -67,9 +67,9 @@ list<expr> get_coercions_to_fun(environment const & env, expr const & C);
 */
 bool get_coercions_from(environment const & env, expr const & C, buffer<expr> & result);
 
-typedef std::function<void(name const &, name const &, expr const &, level_param_names const &, unsigned)> coercion_user_fn;
-typedef std::function<void(name const &, expr const &, level_param_names const &, unsigned)> coercion_sort_fn;
-typedef std::function<void(name const &, expr const &, level_param_names const &, unsigned)> coercion_fun_fn;
+typedef std::function<void(name const &, name const &, name const &)> coercion_user_fn;
+typedef std::function<void(name const &, name const &)> coercion_sort_fn;
+typedef std::function<void(name const &, name const &)> coercion_fun_fn;
 void for_each_coercion_user(environment const & env, coercion_user_fn const & f);
 void for_each_coercion_sort(environment const & env, coercion_sort_fn const & f);
 void for_each_coercion_fun(environment const & env, coercion_fun_fn const & f);

src/library/tc_multigraph.cpp

@@ -186,4 +186,12 @@ list<name> tc_multigraph::get_predecessors(name const & c) const {
     else
         return list<name>();
 }
+
+void tc_multigraph::for_each(std::function<void(name const &, name const &, name const &)> const & fn) const {
+    m_successors.for_each([&](name const & from, list<pair<name, name>> const & succs) {
+            for (pair<name, name> const & p : succs) {
+                fn(from, p.first, p.second);
+            }
+        });
+}
 }

src/library/tc_multigraph.h

@@ -33,5 +33,6 @@ public:
     bool is_node(name const & c) const;
     list<pair<name, name>> get_successors(name const & c) const;
     list<name> get_predecessors(name const & c) const;
+    void for_each(std::function<void(name const &, name const &, name const &)> const & fn) const;
 };
 }

tests/lean/comp1.lean

@@ -1,24 +0,0 @@
-import data.real data.vector data.list
-open nat int rat
-
-#compose int.of_nat nat.of_num → num_to_int
-#compose int.of_nat nat.of_num → num_to_int_2
-set_option pp.all true
-
-print num_to_int
-
-check num_to_int
-check num_to_int_2 -- Error
-
-constant to_list {A : Type} {n : nat} : vector A n → list A
-constant to_vector {A : Type} (l : list A) : vector A (list.length l)
-constant matrix.{l} : Type.{l} → nat → nat → Type.{l}
-constant to_matrix {A : Type} {n : nat} : vector A n → matrix A n 1
-
-#compose list.length to_list → vec_len
-#compose to_matrix to_vector → list_to_matrix
-#compose to_matrix to_vector → list_to_matrix_2
-
-print vec_len
-print list_to_matrix
-check list_to_matrix_2 -- Error

tests/lean/comp1.lean.expected.out

@@ -1,14 +0,0 @@
->> num_to_int
->> num_to_int
-definition num_to_int : num → int :=
-λ (n : num), int.of_nat (nat.of_num n)
-num_to_int : num → int
-comp1.lean:11:6: error: unknown identifier 'num_to_int_2'
->> vec_len
->> list_to_matrix
->> list_to_matrix
-definition vec_len : Π {A : Type.{l_1}} {n : nat}, vector.{l_1} A n → nat :=
-λ {A : Type.{l_1}} {n : nat} (a : vector.{l_1} A n), @list.length.{l_1} A (@to_list.{l_1} A n a)
-definition list_to_matrix : Π {A : Type.{l_1}} (l : list.{l_1} A), matrix.{l_1} A (@list.length.{l_1} A l) (nat.of_num 1) :=
-λ {A : Type.{l_1}} (l : list.{l_1} A), @to_matrix.{l_1} A (@list.length.{l_1} A l) (@to_vector.{l_1} A l)
-comp1.lean:24:6: error: unknown identifier 'list_to_matrix_2'

tests/lean/local_notation_bug.lean.expected.out

@@ -3,4 +3,4 @@ f a b : A
 nat ↣ bool : foo
 bla : num
 local_notation_bug.lean:22:8: error: invalid expression
-num ↣ nat : of_num
+num ↣ nat : nat.of_num