feat(library/user_recursors): generalize acceptable use-defined recursors

see issue #492

src/emacs/lean-syntax.el

@@ -123,11 +123,12 @@
                "\[irreducible\]" "\[semireducible\]" "\[quasireducible\]" "\[wf\]"
                "\[whnf\]" "\[multiple-instances\]" "\[none\]"
                "\[decls\]" "\[declarations\]" "\[coercions\]" "\[classes\]"
-               "\[symm\]" "\[subst\]" "\[refl\]" "\[trans\]" "\[recursor\]"
+               "\[symm\]" "\[subst\]" "\[refl\]" "\[trans\]"
                "\[notations\]" "\[abbreviations\]" "\[begin-end-hints\]" "\[tactic-hints\]"
                "\[reduce-hints\]" "\[unfold-hints\]" "\[aliases\]" "\[eqv\]" "\[localrefinfo\]"))
       . 'font-lock-doc-face)
      (,(rx "\[priority" (zero-or-more (not (any "\]"))) "\]") . font-lock-doc-face)
+     (,(rx "\[recursor" (zero-or-more (not (any "\]"))) "\]") . font-lock-doc-face)
      (,(rx "\[unfold-c" (zero-or-more (not (any "\]"))) "\]") . font-lock-doc-face)
      ;; tactics
      ("cases[ \t\n]+[^ \t\n]+[ \t\n]+\\(with\\)" (1 'font-lock-constant-face))

src/frontends/lean/builtin_cmds.cpp

@@ -230,17 +230,30 @@ static void print_inductive(parser & p, name const & n, pos_info const & pos) {
 
 static void print_recursor_info(parser & p) {
     name c = p.check_constant_next("invalid 'print [recursor]', constant expected");
+    auto out = p.regular_stream();
     recursor_info info = get_recursor_info(p.env(), c);
-    p.regular_stream() << "recursor information\n"
+    out << "recursor information\n"
-                       << "  num. parameters:    " << info.get_num_params() << "\n"
+        << "  num. parameters:          " << info.get_num_params() << "\n"
-                       << "  num. indices:       " << info.get_num_indices() << "\n";
+        << "  num. indices:             " << info.get_num_indices() << "\n";
     if (auto r = info.get_motive_univ_pos())
-        p.regular_stream() << "  motive univ. pos. : " << *r << "\n";
+        out << "  motive univ. pos.:        " << *r << "\n";
     else
-        p.regular_stream() << "  recursor eliminate only to Prop\n";
+        out << "  recursor eliminate only to Prop\n";
-    p.regular_stream() << "  motive pos.:        " << info.get_motive_pos() << "\n"
+    out << "  motive pos.:              " << info.get_motive_pos() + 1 << "\n"
-                       << "  major premise pos.: " << info.get_major_pos() << "\n"
+        << "  major premise pos.:       " << info.get_major_pos() + 1 << "\n"
-                       << "  dep. elimination:   " << info.has_dep_elim() << "\n";
+        << "  dep. elimination:         " << info.has_dep_elim() << "\n";
+    if (info.get_num_params() > 0) {
+        out << "  parameters pos. at major:";
+        for (unsigned p : info.get_params_pos())
+            out << " " << p+1;
+        out << "\n";
+    }
+    if (info.get_num_indices() > 0) {
+        out << "  indices pos. at major:   ";
+        for (unsigned p : info.get_indices_pos())
+            out << " " << p+1;
+        out << "\n";
+    }
 }
 
 bool print_constant(parser & p, char const * kind, declaration const & d) {
@@ -406,6 +419,7 @@ environment print_cmd(parser & p) {
         print_inductive(p, c, pos);
     } else if (p.curr_is_token(get_recursor_tk())) {
         p.next();
+        p.check_token_next(get_rbracket_tk(), "invalid 'print [recursor]', ']' expected");
         print_recursor_info(p);
     } else if (print_polymorphic(p)) {
     } else {

src/frontends/lean/decl_cmds.cpp

@@ -361,6 +361,7 @@ struct decl_attributes {
     bool               m_refl;
     bool               m_subst;
     bool               m_recursor;
+    optional<unsigned> m_recursor_major_pos;
     optional<unsigned> m_priority;
     optional<unsigned> m_unfold_c_hint;
 
@@ -513,6 +514,13 @@ struct decl_attributes {
                 m_subst = true;
             } else if (p.curr_is_token(get_recursor_tk())) {
                 p.next();
+                if (!p.curr_is_token(get_rbracket_tk())) {
+                    unsigned r = p.parse_small_nat();
+                    if (r == 0)
+                        throw parser_error("invalid '[recursor]' attribute, value must be greater than 0", pos);
+                    m_recursor_major_pos = r - 1;
+                }
+                p.check_token_next(get_rbracket_tk(), "invalid 'recursor', ']' expected");
                 m_recursor = true;
             } else {
                 break;
@@ -570,7 +578,7 @@ struct decl_attributes {
         if (m_subst)
             env = add_subst(env, d, m_persistent);
         if (m_recursor)
-            env = add_user_recursor(env, d, m_persistent);
+            env = add_user_recursor(env, d, m_recursor_major_pos, m_persistent);
         if (m_is_class)
             env = add_class(env, d, m_persistent);
         if (m_has_multiple_instances)

src/frontends/lean/token_table.cpp

@@ -107,7 +107,7 @@ void init_token_table(token_table & t) {
          "definition", "example", "coercion", "abbreviation",
          "variables", "parameter", "parameters", "constant", "constants", "[persistent]", "[visible]", "[instance]",
          "[none]", "[class]", "[coercion]", "[reducible]", "[irreducible]", "[semireducible]", "[quasireducible]",
-         "[parsing-only]", "[multiple-instances]", "[symm]", "[trans]", "[refl]", "[subst]", "[recursor]",
+         "[parsing-only]", "[multiple-instances]", "[symm]", "[trans]", "[refl]", "[subst]", "[recursor",
          "evaluate", "check", "eval", "[wf]", "[whnf]", "[priority", "[unfold-f]",
          "[constructor]", "[unfold-c", "print",
          "end", "namespace", "section", "prelude", "help",
@@ -117,7 +117,8 @@ void init_token_table(token_table & t) {
          "exit", "set_option", "open", "export", "calc_subst", "calc_refl", "calc_trans", "calc_symm", "tactic_hint",
          "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", nullptr};
+         "include", "omit", "migrate", "init_quotient", "init_hits", "#erase_cache", "#projections", "#telescope_eq",
+         nullptr};
 
     pair<char const *, char const *> aliases[] =
         {{g_lambda_unicode, "fun"}, {"forall", "Pi"}, {g_forall_unicode, "Pi"}, {g_pi_unicode, "Pi"},

src/frontends/lean/tokens.cpp

@@ -244,7 +244,7 @@ void initialize_tokens() {
     g_trans_tk = new name{"[trans]"};
     g_refl_tk = new name{"[refl]"};
     g_subst_tk = new name{"[subst]"};
-    g_recursor_tk = new name{"[recursor]"};
+    g_recursor_tk = new name{"[recursor"};
     g_attribute_tk = new name{"attribute"};
     g_with_tk = new name{"with"};
     g_class_tk = new name{"[class]"};

src/frontends/lean/tokens.txt

@@ -106,7 +106,7 @@ symm         [symm]
 trans        [trans]
 refl         [refl]
 subst        [subst]
-recursor     [recursor]
+recursor     [recursor
 attribute    attribute
 with         with
 class        [class]

src/library/user_recursors.cpp

@@ -22,20 +22,25 @@ bool recursor_info::is_minor(unsigned pos) const {
     return true;
 }
 
-recursor_info::recursor_info(name const & r, name const & I, unsigned num_params, unsigned num_indices, unsigned major,
+recursor_info::recursor_info(name const & r, name const & I, optional<unsigned> const & motive_univ_pos,
-                             optional<unsigned> const & motive_univ_pos, bool dep_elim):
+                             bool dep_elim, unsigned major_pos, list<unsigned> const & params_pos,
-    m_recursor(r), m_type_name(I), m_num_params(num_params), m_num_indices(num_indices), m_major_pos(major),
+                             list<unsigned> const & indices_pos):
-    m_motive_univ_pos(motive_univ_pos), m_dep_elim(dep_elim) {}
+    m_recursor(r), m_type_name(I), m_motive_univ_pos(motive_univ_pos), m_dep_elim(dep_elim),
+    m_major_pos(major_pos), m_params_pos(params_pos), m_indices_pos(indices_pos) {}
 recursor_info::recursor_info() {}
 
 void recursor_info::write(serializer & s) const {
-    s << m_recursor << m_type_name << m_num_params << m_num_indices << m_major_pos << m_motive_univ_pos << m_dep_elim;
+    s << m_recursor << m_type_name << m_motive_univ_pos << m_dep_elim << m_major_pos;
+    write_list(s, m_params_pos);
+    write_list(s, m_indices_pos);
 }
 
 recursor_info recursor_info::read(deserializer & d) {
     recursor_info info;
-    d >> info.m_recursor >> info.m_type_name >> info.m_num_params >> info.m_num_indices >> info.m_major_pos
+    d >> info.m_recursor >> info.m_type_name >> info.m_motive_univ_pos >> info.m_dep_elim
-      >> info.m_motive_univ_pos >> info.m_dep_elim;
+      >> info.m_major_pos;
+    info.m_params_pos  = read_list<unsigned>(d);
+    info.m_indices_pos = read_list<unsigned>(d);
     return info;
 }
 
@@ -47,30 +52,19 @@ static void throw_invalid_motive(expr const & C) {
                     "and I is a constant");
 }
 
-static void throw_invalid_major(buffer<expr> const & tele, expr const & I, unsigned num_params,
+recursor_info mk_recursor_info(environment const & env, name const & r, optional<unsigned> const & given_major_pos) {
-                                unsigned num_indices, unsigned major_pos) {
-    sstream msg;
-    msg << "invalid user defined recursor, major premise '" << tele[major_pos] << "' is expected to have type " << I;
-    for (unsigned i = 0; i < num_params; i++)
-        msg << " " << tele[i];
-    for (unsigned i = major_pos - num_indices; i < major_pos; i++)
-        msg << " " << tele[i];
-    throw exception(msg);
-}
-
-recursor_info mk_recursor_info(environment const & env, name const & r) {
     if (auto I = inductive::is_elim_rule(env, r)) {
         if (*inductive::get_num_type_formers(env, *I) > 1)
             throw exception(sstream() << "unsupported recursor '" << r << "', it has multiple motives");
         optional<unsigned> motive_univ_pos;
         if (env.get(name(*I, "rec")).get_num_univ_params() != env.get(name(*I)).get_num_univ_params())
             motive_univ_pos = 0;
-        return recursor_info(r, *I,
+        unsigned major_pos         = *inductive::get_elim_major_idx(env, r);
-                             *inductive::get_num_params(env, *I),
+        unsigned num_indices       = *inductive::get_num_indices(env, *I);
-                             *inductive::get_num_indices(env, *I),
+        list<unsigned> params_pos  = mk_list_range(0, *inductive::get_num_params(env, *I));
-                             *inductive::get_elim_major_idx(env, r),
+        list<unsigned> indices_pos = mk_list_range(major_pos - num_indices, major_pos);
-                             motive_univ_pos,
+        return recursor_info(r, *I, motive_univ_pos, inductive::has_dep_elim(env, *I),
-                             inductive::has_dep_elim(env, *I));
+                             major_pos, params_pos, indices_pos);
     }
     declaration d = env.get(r);
     type_checker tc(env);
@@ -78,22 +72,99 @@ recursor_info mk_recursor_info(environment const & env, name const & r) {
     expr rtype    = to_telescope(tc, d.get_type(), tele);
     buffer<expr> C_args;
     expr C        = get_app_args(rtype, C_args);
-    if (!is_local(C) || !std::all_of(C_args.begin(), C_args.end(), is_local) || C_args.empty()) {
+    if (!is_local(C) || !std::all_of(C_args.begin(), C_args.end(), is_local)) {
-        throw exception("invalid user defined recursor, result type must be of the form (C i t), "
+        throw exception("invalid user defined recursor, result type must be of the form (C t), "
-                        "where C and t are bound variables, and i is a (possibly empty) sequence of bound variables");
+                        "where C is a bound variable, and t is a (possibly empty) sequence of bound variables");
     }
-    unsigned num_indices = C_args.size() - 1;
+
+    // Compute number of parameters.
+    // We assume a parameter is anything that occurs before the motive.
     unsigned num_params  = 0;
     for (expr const & x : tele) {
         if (mlocal_name(x) == mlocal_name(C))
             break;
         num_params++;
     }
+
+    // Locate major premise, and check whether the recursor supports dependent elimination or not.
+    expr major;
+    unsigned major_pos = 0;
+    bool dep_elim;
+    if (given_major_pos) {
+        if (*given_major_pos >= tele.size())
+            throw exception(sstream() << "invalid user defined recursor, invalid major premise position, "
+                            "recursor has only " << tele.size() << "arguments");
+        major     = tele[*given_major_pos];
+        major_pos = *given_major_pos;
+        if (!C_args.empty() && tc.is_def_eq(C_args.back(), major).first)
+            dep_elim = true;
+        else
+            dep_elim = false;
+    } else {
+        major    = C_args.back();
+        dep_elim = true;
+        for (expr const & x : tele) {
+            if (tc.is_def_eq(x, major).first)
+                break;
+            major_pos++;
+        }
+    }
+
+    // Number of indices
+    unsigned num_indices = C_args.size();
+    if (dep_elim)
+        num_indices--; // when we have dependent elimination, the last element is the major premise.
+    if (major_pos < num_indices)
+        throw exception(sstream() << "invalid user defined recursor, indices must occur before major premise '"
+                        << major << "'");
+
+    buffer<expr> I_args;
+    expr I = get_app_args(mlocal_type(major), I_args);
+    if (!is_constant(I)) {
+        throw exception(sstream() << "invalid user defined recursor, type of the major premise '" << major
+                        << "' must be for the form (I ...), where I is a constant");
+    }
+
+    // Store position of the recursor parameters in the major premise.
+    buffer<unsigned> params_pos;
+    for (unsigned i = 0; i < num_params; i++) {
+        expr const & A = tele[i];
+        unsigned j = 0;
+        for (; j < I_args.size(); j++) {
+            if (tc.is_def_eq(I_args[j], A).first)
+                break;
+        }
+        if (j == I_args.size()) {
+            throw exception(sstream() << "invalid user defined recursor, type of the major premise '" << major
+                            << "' does not contain the recursor parameter '" << A << "'");
+        }
+        params_pos.push_back(j);
+    }
+
+    // Store position of the recursor indices in the major premise
+    buffer<unsigned> indices_pos;
+    for (unsigned i = major_pos - num_indices; i < major_pos; i++) {
+        expr const & idx = tele[i];
+        unsigned j = 0;
+        for (; j < I_args.size(); j++) {
+            if (tc.is_def_eq(I_args[j], idx).first)
+                break;
+        }
+        if (j == I_args.size()) {
+            throw exception(sstream() << "invalid user defined recursor, type of the major premise '" << major
+                            << "' does not contain the recursor index '" << idx << "'");
+        }
+        indices_pos.push_back(j);
+    }
+
+
     buffer<expr> C_tele;
     expr C_rtype  = to_telescope(tc, mlocal_type(C), C_tele);
     if (!is_sort(C_rtype) || C_tele.size() != C_args.size()) {
         throw_invalid_motive(C);
     }
+    // Calculate position of the motive's universe.
+    // Remark: if we are in the standard environment, then the motive may be a proposition, and be fixed at 0.
     // The following pragma is for avoiding gcc bogus warning
     #if defined(__GNUC__) && !defined(__CLANG__)
     #pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
@@ -120,52 +191,8 @@ recursor_info mk_recursor_info(environment const & env, name const & r) {
         lean_assert(*C_univ_pos < length(d.get_univ_params()));
     }
 
-    buffer<expr> I_args;
+    return recursor_info(r, const_name(I), C_univ_pos, dep_elim, major_pos,
-    expr I = get_app_args(mlocal_type(C_tele.back()), I_args);
+                         to_list(params_pos), to_list(indices_pos));
-    if (!is_constant(I) || I_args.size() != num_params + num_indices) {
-        throw_invalid_motive(C);
-    }
-    for (unsigned i = 0; i < num_params; i++) {
-        if (!tc.is_def_eq(I_args[i], tele[i]).first)
-            throw_invalid_motive(C);
-    }
-    for (unsigned i = 0; i < num_indices; i++) {
-        if (!tc.is_def_eq(I_args[num_params + i], C_tele[i]).first) {
-            throw_invalid_motive(C);
-        }
-    }
-    expr const & major  = C_args.back();
-    unsigned major_pos  = 0;
-    for (expr const & x : tele) {
-        if (mlocal_name(x) == mlocal_name(major))
-            break;
-        major_pos++;
-    }
-    lean_assert(major_pos < tele.size());
-    if (major_pos < num_indices)
-        throw exception(sstream() << "invalid user defined recursor, indices must occur before major premise '"
-                        << major << "'");
-    recursor_info info(r, const_name(I), num_params, num_indices, major_pos, C_univ_pos, true);
-    unsigned first_index_pos = info.get_first_index_pos();
-    for (unsigned i = 0; i < num_indices; i++) {
-        if (!tc.is_def_eq(tele[first_index_pos+i], C_args[i]).first) {
-            throw exception(sstream() << "invalid user defined recursor, index '" << C_args[i]
-                            << "' expected, but got '" << tele[i] << "'");
-        }
-    }
-    buffer<expr> I_args_major;
-    expr I_major = get_app_args(mlocal_type(tele[major_pos]), I_args_major);
-    if (I != I_major)
-        throw_invalid_major(tele, I, num_params, num_indices, major_pos);
-    for (unsigned i = 0; i < num_params; i++) {
-        if (!tc.is_def_eq(I_args_major[i], tele[i]).first)
-            throw_invalid_major(tele, I, num_params, num_indices, major_pos);
-    }
-    for (unsigned i = 0; i < num_indices; i++) {
-        if (!tc.is_def_eq(I_args_major[num_params + i], tele[first_index_pos + i]).first)
-            throw_invalid_major(tele, I, num_params, num_indices, major_pos);
-    }
-    return info;
 }
 
 struct recursor_state {
@@ -214,17 +241,18 @@ struct recursor_config {
 template class scoped_ext<recursor_config>;
 typedef scoped_ext<recursor_config> recursor_ext;
 
-environment add_user_recursor(environment const & env, name const & r, bool persistent) {
+environment add_user_recursor(environment const & env, name const & r, optional<unsigned> const & major_pos,
+                              bool persistent) {
     if (inductive::is_elim_rule(env, r))
         throw exception(sstream() << "invalid user defined recursor, '" << r << "' is a builtin recursor");
-    recursor_info info = mk_recursor_info(env, r);
+    recursor_info info = mk_recursor_info(env, r, major_pos);
     return recursor_ext::add_entry(env, get_dummy_ios(), info, persistent);
 }
 
 recursor_info get_recursor_info(environment const & env, name const & r) {
     if (auto info = recursor_ext::get_state(env).m_recursors.find(r))
         return *info;
-    return mk_recursor_info(env, r);
+    return mk_recursor_info(env, r, optional<unsigned>());
 }
 
 list<name> get_recursors_for(environment const & env, name const & I) {

src/library/user_recursors.h

@@ -11,25 +11,33 @@ namespace lean {
 class recursor_info {
     name               m_recursor;
     name               m_type_name;
-    unsigned           m_num_params;
-    unsigned           m_num_indices;
-    unsigned           m_major_pos;
     optional<unsigned> m_motive_univ_pos; // if none, then recursor can only eliminate to Prop
     bool               m_dep_elim;
+    unsigned           m_major_pos;
+    list<unsigned>     m_params_pos; // position of the recursor parameters in the major premise
+    list<unsigned>     m_indices_pos; // position of the recursor indices in the major premise
 
 public:
-    recursor_info(name const & r, name const & I, unsigned num_params, unsigned num_indices, unsigned major,
+    recursor_info(name const & r, name const & I,
-                  optional<unsigned> const & motive_univ_pos, bool dep_elim);
+                  optional<unsigned> const & motive_univ_pos,
+                  bool dep_elim,
+                  unsigned major_pos,
+                  list<unsigned> const & params_pos,
+                  list<unsigned> const & indices_pos);
     recursor_info();
 
     name const & get_name() const { return m_recursor; }
     name const & get_type_name() const { return m_type_name; }
-    unsigned get_num_params() const { return m_num_params; }
+    unsigned get_num_params() const { return length(m_params_pos); }
-    unsigned get_num_indices() const { return m_num_indices; }
+    unsigned get_num_indices() const { return length(m_indices_pos); }
-    unsigned get_motive_pos() const { return m_num_params; }
+    unsigned get_motive_pos() const { return get_num_params(); }
-    unsigned get_first_index_pos() const { return m_major_pos - m_num_indices; }
+    unsigned get_first_index_pos() const { return m_major_pos - get_num_indices(); }
     unsigned get_major_pos() const { return m_major_pos; }
-    optional<unsigned> get_motive_univ_pos() const { return m_motive_univ_pos; }
+    optional<unsigned> const & get_motive_univ_pos() const { return m_motive_univ_pos; }
+    /** \brief Return position of the recursor parameters in the major premise. */
+    list<unsigned> const & get_params_pos() const { return m_params_pos; }
+    /** \brief Return position of the recursor indices in the major premise. */
+    list<unsigned> const & get_indices_pos() const { return m_indices_pos; }
     bool has_dep_elim() const { return m_dep_elim; }
     bool is_minor(unsigned pos) const;
 
@@ -37,7 +45,7 @@ public:
     static recursor_info read(deserializer & d);
 };
 
-environment add_user_recursor(environment const & env, name const & r, bool persistent);
+environment add_user_recursor(environment const & env, name const & r, optional<unsigned> const & major_pos, bool persistent);
 recursor_info get_recursor_info(environment const & env, name const & r);
 list<name> get_recursors_for(environment const & env, name const & I);
 

src/util/CMakeLists.txt

@@ -4,6 +4,6 @@ add_library(util trace.cpp debug.cpp name.cpp name_set.cpp
   realpath.cpp script_state.cpp script_exception.cpp rb_map.cpp
   lua.cpp luaref.cpp lua_named_param.cpp stackinfo.cpp lean_path.cpp
   serializer.cpp lbool.cpp thread_script_state.cpp bitap_fuzzy_search.cpp
-  init_module.cpp thread.cpp memory_pool.cpp utf8.cpp name_map.cpp)
+  init_module.cpp thread.cpp memory_pool.cpp utf8.cpp name_map.cpp list_fn.cpp)
 
 target_link_libraries(util ${LEAN_LIBS})

src/util/list_fn.h

@@ -302,4 +302,6 @@ template<typename T>
 T const & get_ith(list<T> const & l, unsigned idx) {
     return idx == 0 ? head(l) : get_ith(tail(l), idx - 1);
 }
+
+list<unsigned> mk_list_range(unsigned from, unsigned to);
 }

tests/lean/hott/id_tac5.hlean

@@ -0,0 +1,14 @@
+open equiv
+
+constant rec_on_ua {A B : Type} {P : A ≃ B → Type}
+  (f : A ≃ B) (H : Π(q : A = B), P (equiv_of_eq q)) : P f
+
+set_option pp.universes true
+set_option pp.implicit true
+set_option pp.notation false
+
+check @rec_on_ua
+
+attribute rec_on_ua [recursor]
+
+print [recursor] rec_on_ua

tests/lean/hott/ind_tac3.hlean

@@ -0,0 +1,12 @@
+import cubical.pathover
+open cubical
+
+set_option pp.implicit true
+set_option pp.universes true
+set_option pp.notation false
+
+check @idp_rec_on
+
+attribute idp_rec_on [recursor]
+
+print [recursor] idp_rec_on

tests/lean/hott/ind_tac4.hlean

@@ -0,0 +1,6 @@
+import hit.circle
+open circle
+
+attribute circle.elim_on [recursor 2]
+
+print [recursor] circle.elim_on

tests/lean/run/ind_tac1.lean

@@ -0,0 +1,5 @@
+check @heq.rec_on
+
+attribute heq.rec_on [recursor 6]
+
+print [recursor] heq.rec_on

tests/lean/urec.lean.expected.out

@@ -1,43 +1,46 @@
-urec.lean:3:0: error: invalid user defined recursor, result type must be of the form (C i t), where C and t are bound variables, and i is a (possibly empty) sequence of bound variables
+urec.lean:3:0: error: invalid user defined recursor, result type must be of the form (C t), where C is a bound variable, and t is a (possibly empty) sequence of bound variables
 urec.lean:5:0: error: invalid user defined recursor, 'nat.rec' is a builtin recursor
-urec.lean:19:0: error: invalid user defined recursor, motive 'C' must have a type of the form (C : Pi (i : B A), I A i -> Type), where A is (possibly empty) sequence of bound variables (aka parameters), (i : B A) is a (possibly empty) telescope (aka indices), and I is a constant
+urec.lean:19:0: error: invalid user defined recursor, type of the major premise 'a' must be for the form (I ...), where I is a constant
-urec.lean:23:0: error: invalid user defined recursor, resultant type of minor premise 'a' must be of the form (M ...)
 myrec.{l_1 l_2} :
   Π (A : Type.{l_1}) (M : list.{l_1} A → Type.{l_2}) (l : list.{l_1} A),
     M (@nil.{l_1} A) → (Π (a : A), M [a]) → (Π (a₁ a₂ : A), M [a₁, a₂]) → M l
 recursor information
-  num. parameters:    1
+  num. parameters:          1
-  num. indices:       0
+  num. indices:             0
-  motive univ. pos. : 1
+  motive univ. pos.:        1
-  motive pos.:        1
+  motive pos.:              2
-  major premise pos.: 2
+  major premise pos.:       3
-  dep. elimination:   1
+  dep. elimination:         1
+  parameters pos. at major: 1
 recursor information
-  num. parameters:    0
+  num. parameters:          0
-  num. indices:       0
+  num. indices:             0
   recursor eliminate only to Prop
-  motive pos.:        0
+  motive pos.:              1
-  major premise pos.: 1
+  major premise pos.:       2
-  dep. elimination:   1
+  dep. elimination:         1
 vector.induction_on.{l_1} :
   ∀ {A : Type.{l_1}} {C : Π (a : nat), vector.{l_1} A a → Prop} {a : nat} (n : vector.{l_1} A a),
     C nat.zero (@vector.nil.{l_1} A) →
     (∀ {n : nat} (a : A) (a_1 : vector.{l_1} A n), C n a_1 → C (nat.succ n) (@vector.cons.{l_1} A n a a_1)) →
     C a n
 recursor information
-  num. parameters:    1
+  num. parameters:          1
-  num. indices:       1
+  num. indices:             1
   recursor eliminate only to Prop
-  motive pos.:        1
+  motive pos.:              2
-  major premise pos.: 3
+  major premise pos.:       4
-  dep. elimination:   1
+  dep. elimination:         1
+  parameters pos. at major: 1
+  indices pos. at major:    2
 Exists.rec.{l_1} :
   ∀ {A : Type.{l_1}} {P : A → Prop} {C : Prop},
     (∀ (a : A), P a → C) → @Exists.{l_1} A P → C
 recursor information
-  num. parameters:    2
+  num. parameters:          2
-  num. indices:       0
+  num. indices:             0
   recursor eliminate only to Prop
-  motive pos.:        2
+  motive pos.:              3
-  major premise pos.: 4
+  major premise pos.:       5
-  dep. elimination:   0
+  dep. elimination:         0
+  parameters pos. at major: 1 2