refactor(*): normalize metaclass names

@avigad and @fpvandoorn, I changed the metaclasses names. They
were not uniform:
- The plural was used in some cases (e.g., [coercions]).
- In other cases a cryptic name was used (e.g., [brs]).

Now, I tried to use the attribute name as the metaclass name whenever
possible. For example, we write

   definition foo [coercion] ...
   definition bla [forward] ...

and

  open [coercion] nat
  open [forward] nat

It is easier to remember and is uniform.

hott/init/default.hlean

@@ -17,11 +17,11 @@ namespace core
   export empty (hiding elim)
   export sum (hiding elim)
   export sigma (hiding pr1 pr2)
-  export [notations] prod
+  export [notation] prod
-  export [notations] nat
+  export [notation] nat
   export eq (idp idpath concat inverse transport ap ap10 cast tr_inv homotopy ap11 apd refl)
-  export [declarations] function
+  export [declaration] function
   export equiv (to_inv to_right_inv to_left_inv)
   export is_equiv (inv right_inv left_inv adjointify)
-  export [abbreviations] [declarations] is_trunc (trunctype hprop.mk hset.mk)
+  export [abbreviation] [declaration] is_trunc (trunctype hprop.mk hset.mk)
 end core

hott/init/equiv.hlean

@@ -373,5 +373,5 @@ namespace is_equiv
 
 end is_equiv
 
-export [unfold_hints] equiv
+export [unfold] equiv
-export [unfold_hints] is_equiv
+export [unfold] is_equiv

hott/init/function.hlean

@@ -60,4 +60,4 @@ notation f ` -[` op `]- ` g  := combine f op g
 end function
 
 -- copy reducible annotations to top-level
-export [reduce_hints] [unfold_hints] function
+export [reducible] [unfold] function

library/data/bag.lean

@@ -7,7 +7,7 @@ Finite bags.
 -/
 import data.nat data.list.perm algebra.binary
 open nat quot list subtype binary function eq.ops
-open [declarations] perm
+open [decl] perm
 
 variable {A : Type}
 

library/data/finset/basic.lean

@@ -7,7 +7,7 @@ Finite sets.
 -/
 import data.fintype.basic data.nat data.list.perm algebra.binary
 open nat quot list subtype binary function eq.ops
-open [declarations] perm
+open [decl] perm
 
 definition nodup_list (A : Type) := {l : list A | nodup l}
 

library/data/hf.lean

@@ -11,7 +11,7 @@ this bijection is implemeted using the Ackermann coding.
 -/
 import data.nat data.finset.equiv data.list
 open nat binary
-open - [notations] finset
+open - [notation] finset
 
 definition hf := nat
 
@@ -479,7 +479,7 @@ theorem empty_mem_powerset (s : hf) : ∅ ∈ 𝒫 s :=
 mem_powerset_of_subset (empty_subset s)
 
 /- hf as lists -/
-open - [notations] list
+open - [notation] list
 
 definition of_list (s : list hf) : hf :=
 @equiv.to_fun _ _ list_nat_equiv_nat s

library/data/int/div.lean

@@ -8,8 +8,8 @@ Definitions and properties of div and mod, following the SSReflect library.
 Following SSReflect and the SMTlib standard, we define a % b so that 0 ≤ a % b < |b| when b ≠ 0.
 -/
 import data.int.order data.nat.div
-open [coercions] [reduce_hints] nat
+open [coercion] [reducible] nat
-open [declarations] [classes] nat (succ)
+open [declaration] [class] nat (succ)
 open eq.ops
 
 namespace int

library/data/real/basic.lean

@@ -22,7 +22,7 @@ The construction of the reals is arranged in four files.
 -/
 import data.nat data.rat.order data.pnat
 open nat eq pnat
-open - [coercions] rat
+open - [coercion] rat
 
 local postfix `⁻¹` := pnat.inv
 

library/data/real/complete.lean

@@ -163,7 +163,7 @@ theorem r_equiv_neg_abs_of_le_zero {s : reg_seq} (Hz : r_le s r_zero) : requiv (
 end rat_seq
 
 namespace real
-open [classes] rat_seq
+open [class] rat_seq
 
 private theorem rewrite_helper9 (a b c : ℝ) : b - c = (b - a) - (c - a) :=
   by rewrite [-sub_add_eq_sub_sub_swap, sub_add_cancel]

library/data/real/division.lean

@@ -581,7 +581,7 @@ theorem r_abs_well_defined {s t : reg_seq} (H : requiv s t) : requiv (r_abs s) (
 end rat_seq
 
 namespace real
-open [classes] rat_seq
+open [class] rat_seq
 
 noncomputable protected definition inv (x : ℝ) : ℝ :=
   quot.lift_on x (λ a, quot.mk (rat_seq.r_inv a))

library/data/real/order.lean

@@ -1015,7 +1015,7 @@ theorem r_le_of_reprs_le (s t : reg_seq) (Hle : ∀ n : ℕ+, r_le (r_const (reg
 end rat_seq
 
 open real
-open [classes] rat_seq
+open [class] rat_seq
 namespace real
 
 protected definition lt (x y : ℝ) :=

library/init/function.lean

@@ -156,4 +156,4 @@ theorem bijective_id : bijective (@id A) := and.intro injective_id surjective_id
 end function
 
 -- copy reducible annotations to top-level
-export [reduce_hints] [unfold_hints] function
+export [reducible] [unfold] function

library/theories/analysis/real_limit.lean

@@ -38,7 +38,7 @@ protected definition metric_space [instance] : metric_space ℝ :=
 ⦄
 
 open nat
-open [classes] rat
+open [class] rat
 
 definition converges_to_seq (X : ℕ → ℝ) (y : ℝ) : Prop :=
 ∀ ⦃ε : ℝ⦄, ε > 0 → ∃ N : ℕ, ∀ {n}, n ≥ N → abs (X n - y) < ε

src/emacs/lean-syntax.el

@@ -54,10 +54,10 @@
          '("persistent" "notation" "visible" "instance" "trans_instance"
            "class" "parsing_only" "coercion" "unfold_full" "constructor"
            "reducible" "irreducible" "semireducible" "quasireducible" "wf"
-           "whnf" "multiple_instances" "none" "decls" "declarations"
+           "whnf" "multiple_instances" "none" "decl" "declaration"
-           "coercions" "classes" "symm" "subst" "refl" "trans" "simp" "simps" "congr"
+           "relation" "symm" "subst" "refl" "trans" "simp" "congr"
-           "forward" "no_pattern" "notations" "abbreviations" "begin_end_hints" "tactic_hints"
+           "backward" "forward" "no_pattern" "begin_end" "tactic" "abbreviation"
-           "reduce_hints" "unfold_hints" "aliases" "eqv" "intro" "intro!" "elim"
+           "reducible" "unfold" "alias" "eqv" "intro" "intro!" "elim" "grinder"
            "localrefinfo" "recursor"))
   "lean modifiers")
 (defconst lean-modifiers-regexp

src/frontends/lean/begin_end_ext.cpp

@@ -78,8 +78,8 @@ bool is_begin_end_annotation(expr const & e) { return is_annotation(e, *g_begin_
 bool is_begin_end_element_annotation(expr const & e) { return is_annotation(e, *g_begin_end_element); }
 
 void initialize_begin_end_ext() {
-    g_class_name = new name("begin_end_hints");
+    g_class_name = new name("begin_end");
-    g_key        = new std::string("bepretac");
+    g_key        = new std::string("BEPRETAC");
     begin_end_ext::initialize();
     g_begin_end  = new name("begin_end");
     g_begin_end_element = new name("begin_end_element");

src/frontends/lean/builtin_cmds.cpp

@@ -221,19 +221,26 @@ static optional<name> parse_metaclass(parser & p) {
             p.next();
         }
         p.check_token_next(get_rbracket_tk(), "invalid 'open' command, ']' expected");
-        if (!is_metaclass(n) && n != get_decls_tk() && n != get_declarations_tk())
+        if (!is_metaclass(n) && n != get_decl_tk() && n != get_declaration_tk())
             throw parser_error(sstream() << "invalid metaclass name '[" << n << "]'", pos);
         return optional<name>(n);
     } else if (p.curr() == scanner::token_kind::CommandKeyword) {
+        // Meta-classes whose name conflict with tokens of the form `[<id>]` `[<id>`
+        // Example: [class] and [unfold
         name v = p.get_token_info().value();
-        if (v.is_atomic() && v.is_string() && v.size() > 2 && v.get_string()[0] == '[' && v.get_string()[v.size()-1] == ']') {
+        if (v.is_atomic() && v.is_string() && v.size() > 1 && v.get_string()[0] == '[') {
             auto pos = p.pos();
             p.next();
             std::string s(v.get_string() + 1);
-            s.pop_back();
+            if (v.get_string()[v.size()-1] == ']')
+                s.pop_back();
             name n(s);
-            if (!is_metaclass(n) && n != get_decls_tk() && n != get_declarations_tk())
+            if (!is_metaclass(n) && n != get_decl_tk() && n != get_declaration_tk())
                 throw parser_error(sstream() << "invalid metaclass name '[" << n << "]'", pos);
+            if (v.get_string()[v.size()-1] != ']') {
+                // Consume ']' for tokens such as `[unfold`
+                p.check_token_next(get_rbracket_tk(), "invalid 'open' command, ']' expected");
+            }
             return optional<name>(n);
         }
     }
@@ -245,12 +252,12 @@ static void parse_metaclasses(parser & p, buffer<name> & r) {
         p.next();
         buffer<name> tmp;
         get_metaclasses(tmp);
-        tmp.push_back(get_decls_tk());
+        tmp.push_back(get_decl_tk());
         while (true) {
             if (optional<name> m = parse_metaclass(p)) {
                 tmp.erase_elem(*m);
-                if (*m == get_declarations_tk())
+                if (*m == get_declaration_tk())
-                    tmp.erase_elem(get_decls_tk());
+                    tmp.erase_elem(get_decl_tk());
             } else {
                 break;
             }
@@ -299,8 +306,8 @@ environment open_export_cmd(parser & p, bool open) {
         parse_metaclasses(p, metacls);
         bool decls = false;
         if (metacls.empty() ||
-            std::find(metacls.begin(), metacls.end(), get_decls_tk()) != metacls.end() ||
+            std::find(metacls.begin(), metacls.end(), get_decl_tk()) != metacls.end() ||
-            std::find(metacls.begin(), metacls.end(), get_declarations_tk()) != metacls.end())
+            std::find(metacls.begin(), metacls.end(), get_declaration_tk()) != metacls.end())
             decls = true;
         for (name const & n : metacls)
             fingerprint = hash(fingerprint, n.hash());

src/frontends/lean/parser_config.cpp

@@ -437,11 +437,11 @@ cmd_table const & get_cmd_table(environment const & env) {
 }
 
 void initialize_parser_config() {
-    token_config::g_class_name = new name("notations");
+    token_config::g_class_name = new name("notation");
-    token_config::g_key        = new std::string("tk");
+    token_config::g_key        = new std::string("TK");
     token_ext::initialize();
-    notation_config::g_class_name = new name("notations");
+    notation_config::g_class_name = new name("notation");
-    notation_config::g_key        = new std::string("nota");
+    notation_config::g_key        = new std::string("NOTA");
     notation_ext::initialize();
     g_ext = new cmd_ext_reg();
 }

src/frontends/lean/tactic_hint.cpp

@@ -57,8 +57,8 @@ template class scoped_ext<tactic_hint_config>;
 typedef scoped_ext<tactic_hint_config> tactic_hint_ext;
 
 void initialize_tactic_hint() {
-    g_class_name = new name("tactic_hints");
+    g_class_name = new name("tactic");
-    g_key        = new std::string("tachint");
+    g_key        = new std::string("TACHINT");
     tactic_hint_ext::initialize();
 }
 

src/frontends/lean/tokens.cpp

@@ -63,8 +63,8 @@ static name const * g_instances_tk = nullptr;
 static name const * g_classes_tk = nullptr;
 static name const * g_coercions_tk = nullptr;
 static name const * g_arrow_tk = nullptr;
-static name const * g_declarations_tk = nullptr;
+static name const * g_declaration_tk = nullptr;
-static name const * g_decls_tk = nullptr;
+static name const * g_decl_tk = nullptr;
 static name const * g_hiding_tk = nullptr;
 static name const * g_exposing_tk = nullptr;
 static name const * g_renaming_tk = nullptr;
@@ -213,8 +213,8 @@ void initialize_tokens() {
     g_classes_tk = new name{"classes"};
     g_coercions_tk = new name{"coercions"};
     g_arrow_tk = new name{"->"};
-    g_declarations_tk = new name{"declarations"};
+    g_declaration_tk = new name{"declaration"};
-    g_decls_tk = new name{"decls"};
+    g_decl_tk = new name{"decl"};
     g_hiding_tk = new name{"hiding"};
     g_exposing_tk = new name{"exposing"};
     g_renaming_tk = new name{"renaming"};
@@ -364,8 +364,8 @@ void finalize_tokens() {
     delete g_classes_tk;
     delete g_coercions_tk;
     delete g_arrow_tk;
-    delete g_declarations_tk;
+    delete g_declaration_tk;
-    delete g_decls_tk;
+    delete g_decl_tk;
     delete g_hiding_tk;
     delete g_exposing_tk;
     delete g_renaming_tk;
@@ -514,8 +514,8 @@ name const & get_instances_tk() { return *g_instances_tk; }
 name const & get_classes_tk() { return *g_classes_tk; }
 name const & get_coercions_tk() { return *g_coercions_tk; }
 name const & get_arrow_tk() { return *g_arrow_tk; }
-name const & get_declarations_tk() { return *g_declarations_tk; }
+name const & get_declaration_tk() { return *g_declaration_tk; }
-name const & get_decls_tk() { return *g_decls_tk; }
+name const & get_decl_tk() { return *g_decl_tk; }
 name const & get_hiding_tk() { return *g_hiding_tk; }
 name const & get_exposing_tk() { return *g_exposing_tk; }
 name const & get_renaming_tk() { return *g_renaming_tk; }

src/frontends/lean/tokens.h

@@ -65,8 +65,8 @@ name const & get_instances_tk();
 name const & get_classes_tk();
 name const & get_coercions_tk();
 name const & get_arrow_tk();
-name const & get_declarations_tk();
+name const & get_declaration_tk();
-name const & get_decls_tk();
+name const & get_decl_tk();
 name const & get_hiding_tk();
 name const & get_exposing_tk();
 name const & get_renaming_tk();

src/frontends/lean/tokens.txt

@@ -58,8 +58,8 @@ instances    instances
 classes      classes
 coercions    coercions
 arrow        ->
-declarations declarations
+declaration  declaration
-decls        decls
+decl         decl
 hiding       hiding
 exposing     exposing
 renaming     renaming

src/library/abbreviation.cpp

@@ -119,8 +119,8 @@ expr expand_abbreviations(environment const & env, expr const & e) {
 }
 
 void initialize_abbreviation() {
-    g_class_name = new name("abbreviations");
+    g_class_name = new name("abbreviation");
-    g_key        = new std::string("abbrev");
+    g_key        = new std::string("ABBREV");
     abbrev_ext::initialize();
 }
 

src/library/aliases.cpp

@@ -264,7 +264,7 @@ void open_aliases(lua_State * L) {
 }
 
 void initialize_aliases() {
-    g_aliases = new name("aliases");
+    g_aliases = new name("alias");
     g_ext     = new aliases_ext_reg();
 }
 

src/library/blast/backward/backward_rule_set.cpp

@@ -148,8 +148,8 @@ list<gexpr> backward_rule_set::find(head_index const & h) const {
 }
 
 void initialize_backward_rule_set() {
-    g_class_name = new name("brs");
+    g_class_name = new name("backward");
-    g_key        = new std::string("brs");
+    g_key        = new std::string("BWD");
     brs_ext::initialize();
     register_prio_attribute("intro", "backward chaining",
                             [](environment const & env, io_state const &, name const & d, unsigned prio, name const & ns, bool persistent) {

src/library/blast/grinder/intro_elim_lemmas.cpp

@@ -114,7 +114,7 @@ void get_intro_lemmas(environment const & env, buffer<name> & r) {
 
 void initialize_intro_elim_lemmas() {
     g_class_name = new name("grinder");
-    g_key        = new std::string("grinder");
+    g_key        = new std::string("GRD");
     intro_elim_ext::initialize();
 
     register_prio_attribute("elim", "elimination rule that is eagerly applied by blast grinder",

src/library/blast/simplifier/simp_rule_set.cpp

@@ -579,8 +579,8 @@ io_state_stream const & operator<<(io_state_stream const & out, simp_rule_sets c
 
 void initialize_simplifier_rule_set() {
     g_prefix     = new name(name::mk_internal_unique_name());
-    g_class_name = new name("simps");
+    g_class_name = new name("simp");
-    g_key        = new std::string("simp");
+    g_key        = new std::string("SIMP");
     rrs_ext::initialize();
     register_prio_attribute("simp", "simplification rule",
                             [](environment const & env, io_state const &, name const & d, unsigned prio, name const & ns, bool persistent) {

src/library/class.cpp

@@ -483,7 +483,7 @@ list<expr> get_local_instances(type_checker & tc, list<expr> const & ctx, name c
 void initialize_class() {
     g_tmp_prefix = new name(name::mk_internal_unique_name());
     g_source     = new name("_source");
-    g_class_name = new name("classes");
+    g_class_name = new name("class");
     g_key = new std::string("class");
     class_ext::initialize();
 

src/library/coercion.cpp

@@ -373,8 +373,8 @@ environment add_coercion(environment const & env, io_state const &, name const &
 void initialize_coercion() {
     g_fun        = new name("_Fun");
     g_sort       = new name("_Sort");
-    g_class_name = new name("coercions");
+    g_class_name = new name("coercion");
-    g_key        = new std::string("coerce");
+    g_key        = new std::string("COERCE");
     coercion_ext::initialize();
     register_attribute("coercion", "coercion",
                        [](environment const & env, io_state const & ios, name const & d, name const & ns, bool persistent) {

src/library/light_lt_manager.cpp

@@ -191,8 +191,8 @@ io_state_stream const & operator<<(io_state_stream const & out, light_rule_set c
 }
 
 void initialize_light_rule_set() {
-    g_class_name = new name("lrs");
+    g_class_name = new name("light");
-    g_key        = new std::string("lrs");
+    g_key        = new std::string("LIGHT");
     lrs_ext::initialize();
     register_param_attribute("light", "hint for simplifier",
                              [](environment const & env, io_state const &, name const & d, unsigned idx, name const & ns, bool persistent) {

src/library/normalize.cpp

@@ -163,8 +163,8 @@ environment erase_constructor_hint(environment const & env, name const & n, name
 }
 
 void initialize_normalize() {
-    g_unfold_hint_name = new name("unfold_hints");
+    g_unfold_hint_name = new name("unfold");
-    g_key = new std::string("unfoldh");
+    g_key = new std::string("UNFOLDH");
     unfold_hint_ext::initialize();
     register_params_attribute("unfold", "unfold definition when the given positions are constructors",
                               [](environment const & env, io_state const &, name const & d, list<unsigned> const & idxs, name const & ns, bool persistent) {

src/library/reducible.cpp

@@ -66,8 +66,8 @@ typedef scoped_ext<reducible_config> reducible_ext;
 static name * g_tmp_prefix = nullptr;
 
 void initialize_reducible() {
-    g_class_name = new name("reduce_hints");
+    g_class_name = new name("reducible");
-    g_key        = new std::string("redu");
+    g_key        = new std::string("REDU");
     g_tmp_prefix = new name(name::mk_internal_unique_name());
     reducible_ext::initialize();
 

src/library/relation_manager.cpp

@@ -327,8 +327,8 @@ is_relation_pred mk_is_relation_pred(environment const & env) {
 }
 
 void initialize_relation_manager() {
-    g_rel_name = new name("rel");
+    g_rel_name = new name("relation");
-    g_key       = new std::string("rel");
+    g_key       = new std::string("REL");
     rel_ext::initialize();
     register_attribute("refl", "reflexive relation",
                        [](environment const & env, io_state const &, name const & d, name const & ns, bool persistent) {

src/library/user_recursors.cpp

@@ -345,7 +345,7 @@ has_recursors_pred::has_recursors_pred(environment const & env):
 
 void initialize_user_recursors() {
     g_class_name = new name("recursor");
-    g_key        = new std::string("urec");
+    g_key        = new std::string("UREC");
     recursor_ext::initialize();
     register_opt_param_attribute("recursor", "user defined recursor",
                                  [](environment const & env, io_state const &, name const & d, optional<unsigned> const & major, name const & ns, bool persistent) {

tests/lean/bad_open.lean

@@ -1,3 +1,3 @@
 open "nat"
 
-open [classes] "nat"
+open [class] "nat"

tests/lean/bad_open.lean.expected.out

@@ -1,2 +1,2 @@
 bad_open.lean:1:5: error: invalid 'open/export' command, identifier expected
-bad_open.lean:3:15: error: invalid 'open/export' command, identifier expected
+bad_open.lean:3:13: error: invalid 'open/export' command, identifier expected

tests/lean/extra/bag.lean

@@ -7,7 +7,7 @@ Finite bags.
 -/
 import data.nat data.list.perm algebra.binary
 open nat quot list subtype binary function eq.ops algebra
-open [declarations] perm
+open [decl] perm
 
 variable {A : Type}
 

tests/lean/open_tst.lean

@@ -11,7 +11,7 @@ section
 end
 
 section
-  open - [classes] nat
+  open - [class] nat
   variable a : nat
   check a + a
   check add a a
@@ -21,7 +21,7 @@ section
 end
 
 section
-  open - [classes] [decls] nat
+  open - [class] [decl] nat
   variable a : nat
   check a + a
   check a + 1
@@ -30,7 +30,7 @@ section
 end
 
 section
-  open [classes] nat
+  open [class] nat
   definition foo3 : inhabited nat :=
   _
 

tests/lean/run/568.lean

@@ -7,9 +7,9 @@ namespace f2
 end f2
 
 namespace f3
-  export [declarations] f1
+  export [declaration] f1
-  export - [declarations] f2
+  export - [declaration] f2
 end f3
 
-export [declarations] f1
+export [declaration] f1
-export - [declarations] f2
+export - [declaration] f2

tests/lean/run/blast_simp_sum.lean

@@ -1,5 +1,5 @@
 import data.nat
-open - [simps] nat
+open - [simp] nat
 
 definition Sum : nat → (nat → nat) → nat :=
 sorry

tests/lean/run/class5.lean

@@ -31,7 +31,7 @@ section
 end
 
 section
-  open [notations] algebra
+  open [notation] algebra
   open nat
   -- check mul_struct nat  << This is an error, we opened only the notation from algebra
   variables a b c : nat

tests/lean/run/e11.lean

@@ -18,10 +18,10 @@ end int
 
 section
   -- Open "only" the notation and declarations from the namespaces nat and int
-  open [notations] nat
+  open [notation] nat
-  open [notations] int
+  open [notation] int
-  open [decls] nat
+  open [decl] nat
-  open [decls] int
+  open [decl] int
 
   variables n m : nat
   variables i j : int

tests/lean/run/e12.lean

@@ -20,17 +20,17 @@ constants n m : nat.nat
 constants i j : int.int
 
 section
-  open [notations] nat
+  open [notation] nat
-  open [notations] int
+  open [notation] int
-  open [decls] nat
+  open [decl] nat
-  open [decls] int
+  open [decl] int
   check n+m
   check i+j
   --  check i+n -- Error
 end
 
 namespace int
-  open [decls] nat (nat)
+  open [decl] nat (nat)
   -- Here is a possible trick for this kind of configuration
   definition add_ni (a : nat) (b : int) := (of_nat a) + b
   definition add_in (a : int) (b : nat) := a + (of_nat b)
@@ -39,10 +39,10 @@ namespace int
 end int
 
 section
-  open [notations] nat
+  open [notation] nat
-  open [notations] int
+  open [notation] int
-  open [declarations] nat
+  open [declaration] nat
-  open [declarations] int
+  open [declaration] int
   check n+m
   check i+n
   check n+i

tests/lean/run/e8.lean

@@ -17,10 +17,10 @@ attribute of_nat [coercion]
 end int
 
 -- Open "only" the notation and declarations from the namespaces nat and int
-open [notations] nat
+open [notation] nat
-open [notations] int
+open [notation] int
-open [decls] nat
+open [decl] nat
-open [decls] int
+open [decl] int
 
 constants n m : nat
 constants i j : int

tests/lean/run/ppbeta.lean

@@ -1,6 +1,6 @@
 import data.int
-open [coercions] [classes] int
+open [coercion] [class] int
-open [coercions] nat
+open [coercion] nat
 
 definition lt1 (a b : int) := int.le (int.add a 1) b
 infix `<`     := lt1

tests/lean/t14.lean

@@ -41,13 +41,13 @@ section
 end
 
 section
-  open [notations] foo -- use only the notation
+  open [notation] foo -- use only the notation
   check foo.a * foo.c
   check a * c -- Error
 end
 
 section
-  open [decls] foo -- use only the declarations
+  open [decl] foo -- use only the declarations
   check f a c
   check a*c -- Error
 end