feat(frontends/lean): rename 'using' command to 'open'

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

doc/lean/calc.org

@@ -26,7 +26,7 @@ Here is an example
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
   variables a b c d e : nat.
   axiom Ax1 : a = b.
   axiom Ax2 : b = c + 1.
@@ -55,7 +55,7 @@ some form of transitivity. It can even combine different relations.
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
 
   theorem T2 (a b c : nat) (H1 : a = b) (H2 : b = c + 1) : a ≠ 0
   := calc  a = b      : H1

doc/lean/tutorial.org

@@ -30,7 +30,7 @@ the input value.
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
   -- defines the double function
   definition double (x : nat) := x + x
 #+END_SRC
@@ -62,7 +62,7 @@ The command =import= loads existing libraries and extensions.
 
 We say =nat.ge= is a hierarchical name comprised of two parts: =nat= and =ge=.
 
-The command =using= creates aliases based on a given prefix. The
+The command =open= creates aliases based on a given prefix. The
 command also imports notation, hints, and other features. We will
 discuss its other applications later. Regarding aliases,
 the following command creates aliases for all objects starting with
@@ -70,7 +70,7 @@ the following command creates aliases for all objects starting with
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
   check ge -- display the type of nat.ge
 #+END_SRC
 
@@ -79,11 +79,11 @@ that =n=, =m= and =o= have type =nat=.
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
   variable n : nat
   variable m : nat
   variable o : nat
-  -- The command 'using nat' also imported the notation defined at the namespace 'nat'
+  -- The command 'open nat' also imported the notation defined at the namespace 'nat'
   check n + m
   check n ≤ m
 #+END_SRC
@@ -96,7 +96,7 @@ for =n = n=. In Lean, =refl= is the reflexivity theorem.
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
   variable n : nat
   check refl n
 #+END_SRC
@@ -108,7 +108,7 @@ The following commands postulate two axioms =Ax1= and =Ax2= that state that =n =
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
   variables m n o : nat
   axiom Ax1 : n = m
   axiom Ax2 : m = o
@@ -146,7 +146,7 @@ example, =symm= is the symmetry theorem.
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
 
   theorem nat_trans3 (a b c d : nat) (H1 : a = b) (H2 : c = b) (H3 : c = d) : a = d :=
   trans (trans H1 (symm H2)) H3
@@ -175,7 +175,7 @@ implicit arguments.
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
 
   theorem nat_trans3i {a b c d : nat} (H1 : a = b) (H2 : c = b) (H3 : c = d) : a = d :=
   trans (trans H1 (symm H2)) H3
@@ -210,7 +210,7 @@ This is useful when debugging non-trivial problems.
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
 
   variables a b c : nat
   axiom H1 : a = b
@@ -361,7 +361,7 @@ examples.
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
 
   check fun x : nat, x + 1
   check fun x y : nat, x + 2 * y
@@ -375,7 +375,7 @@ In all examples above, the type can be inferred automatically.
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
 
   check fun x, x + 1
   check fun x y, x + 2 * y
@@ -392,7 +392,7 @@ function applications
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
   check (fun x y, x + 2 * y) 1
   check (fun x y, x + 2 * y) 1 2
   check (fun x y, not (x ∧ y)) true false
@@ -420,7 +420,7 @@ are equal using just =refl=. Here is a simple example.
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
 
   theorem def_eq_th (a : nat) : ((λ x : nat, x + 1) a) = a + 1 := refl (a+1)
 #+END_SRC
@@ -652,7 +652,7 @@ Then we instantiate the axiom using function application.
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
 
   variable f : nat → nat
   axiom fzero : ∀ x, f x = 0
@@ -668,7 +668,7 @@ abstraction. In the following example, we create a proof term showing that for a
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
 
   variable f : nat → nat
   axiom fzero : ∀ x, f x = 0
@@ -693,7 +693,7 @@ for =∃ a : nat, a = w= using
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
 
   theorem nat_trans3i {a b c d : nat} (H1 : a = b) (H2 : c = b) (H3 : c = d) : a = d :=
   trans (trans H1 (symm H2)) H3
@@ -720,7 +720,7 @@ has different values for the implicit argument =P=.
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
 
   check @exists_intro
   variable g : nat → nat → nat
@@ -751,7 +751,7 @@ of two even numbers is an even number.
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
 
   definition even (a : nat) := ∃ b, a = 2*b
   theorem EvenPlusEven {a b : nat} (H1 : even a) (H2 : even b) : even (a + b) :=
@@ -772,7 +772,7 @@ With this macro we can write the example above in a more natural way
 
 #+BEGIN_SRC lean
   import data.nat
-  using nat
+  open nat
   definition even (a : nat) := ∃ b, a = 2*b
   theorem EvenPlusEven {a b : nat} (H1 : even a) (H2 : even b) : even (a + b) :=
   obtain (w1 : nat) (Hw1 : a = 2*w1), from H1,

library/data/bool.lean

@@ -4,7 +4,7 @@
 
 import logic.core.connectives logic.classes.decidable logic.classes.inhabited
 
-using eq_ops decidable
+open eq_ops decidable
 
 inductive bool : Type :=
 ff : bool,

library/data/int/basic.lean

@@ -11,20 +11,13 @@ import ..nat.basic ..nat.order ..nat.sub ..prod ..quotient ..quotient tools.tact
 import struc.binary
 import tools.fake_simplifier
 
-using nat (hiding case)
-using quotient
-using subtype
-using prod
-using relation
-using decidable
-using binary
-using fake_simplifier
-using eq_ops
+open nat (hiding case)
+open quotient subtype prod relation
+open decidable binary fake_simplifier
+open eq_ops
+
 namespace int
-
-
 -- ## The defining equivalence relation on ℕ × ℕ
-
 abbreviation rel (a b : ℕ × ℕ) : Prop :=  pr1 a + pr2 b = pr2 a + pr1 b
 
 theorem rel_comp (n m k l : ℕ) : (rel (pair n m) (pair k l)) ↔ (n + l = m + k) :=

library/data/int/order.lean

@@ -9,10 +9,10 @@
 
 import .basic
 
-using nat (hiding case)
-using decidable
-using fake_simplifier
-using int eq_ops
+open nat (hiding case)
+open decidable
+open fake_simplifier
+open int eq_ops
 
 namespace int
 

library/data/list/basic.lean

@@ -14,9 +14,9 @@ import data.nat
 import logic tools.helper_tactics
 -- import if -- for find
 
-using nat
-using eq_ops
-using helper_tactics
+open nat
+open eq_ops
+open helper_tactics
 
 namespace list
 

library/data/nat/basic.lean

@@ -9,10 +9,10 @@
 
 import logic data.num tools.tactic struc.binary tools.helper_tactics
 
-using num tactic binary eq_ops
-using decidable (hiding induction_on rec_on)
-using relation -- for subst_iff
-using helper_tactics
+open num tactic binary eq_ops
+open decidable (hiding induction_on rec_on)
+open relation -- for subst_iff
+open helper_tactics
 
 -- Definition of the type
 -- ----------------------

library/data/nat/div.lean

@@ -11,9 +11,9 @@
 import logic .sub struc.relation data.prod
 import tools.fake_simplifier
 
-using nat relation relation.iff_ops prod
-using fake_simplifier decidable
-using eq_ops
+open nat relation relation.iff_ops prod
+open fake_simplifier decidable
+open eq_ops
 
 namespace nat
 

library/data/nat/order.lean

@@ -10,9 +10,9 @@
 import .basic logic.classes.decidable
 import tools.fake_simplifier
 
-using nat eq_ops tactic
-using fake_simplifier
-using decidable (decidable inl inr)
+open nat eq_ops tactic
+open fake_simplifier
+open decidable (decidable inl inr)
 
 namespace nat
 

library/data/nat/sub.lean

@@ -10,9 +10,9 @@
 import data.nat.order
 import tools.fake_simplifier
 
-using nat eq_ops tactic
-using helper_tactics
-using fake_simplifier
+open nat eq_ops tactic
+open helper_tactics
+open fake_simplifier
 
 namespace nat
 

library/data/option.lean

@@ -3,7 +3,7 @@
 -- Author: Leonardo de Moura
 
 import logic.core.eq logic.classes.inhabited logic.classes.decidable
-using eq_ops decidable
+open eq_ops decidable
 
 namespace option
 

library/data/prod.lean

@@ -9,7 +9,7 @@
 
 import logic.classes.inhabited logic.core.eq logic.classes.decidable
 
-using inhabited decidable
+open inhabited decidable
 
 inductive prod (A B : Type) : Type :=
 pair : A → B → prod A B

library/data/quotient/aux.lean

@@ -5,8 +5,8 @@
 import logic ..prod struc.relation
 import tools.fake_simplifier
 
-using prod eq_ops
-using fake_simplifier
+open prod eq_ops
+open fake_simplifier
 
 namespace quotient
 

library/data/quotient/basic.lean

@@ -9,8 +9,8 @@ import logic tools.tactic ..subtype logic.core.cast struc.relation data.prod
 import logic.core.instances
 import .aux
 
-using relation prod inhabited nonempty tactic eq_ops
-using subtype relation.iff_ops
+open relation prod inhabited nonempty tactic eq_ops
+open subtype relation.iff_ops
 
 namespace quotient
 

library/data/quotient/classical.lean

@@ -8,7 +8,7 @@ import logic.axioms.classical logic.axioms.hilbert logic.axioms.funext
 
 namespace quotient
 
-using relation nonempty subtype
+open relation nonempty subtype
 
 -- abstract quotient
 -- -----------------

library/data/set.lean

@@ -4,7 +4,7 @@
 --- Author: Jeremy Avigad, Leonardo de Moura
 ----------------------------------------------------------------------------------------------------
 import data.bool
-using eq_ops bool
+open eq_ops bool
 
 namespace set
 definition set (T : Type) :=

library/data/sigma.lean

@@ -4,7 +4,7 @@
 
 import logic.classes.inhabited logic.core.eq
 
-using inhabited
+open inhabited
 
 inductive sigma {A : Type} (B : A → Type) : Type :=
 dpair : Πx : A, B x → sigma B

library/data/string.lean

@@ -4,7 +4,7 @@
 
 import data.bool
 
-using bool inhabited
+open bool inhabited
 
 namespace string
 

library/data/subtype.lean

@@ -4,7 +4,7 @@
 
 import logic.classes.inhabited logic.core.eq logic.classes.decidable
 
-using decidable
+open decidable
 
 inductive subtype {A : Type} (P : A → Prop) : Type :=
 tag : Πx : A, P x → subtype P

library/data/sum.lean

@@ -9,7 +9,7 @@
 
 import logic.core.prop logic.classes.inhabited logic.classes.decidable
 
-using inhabited decidable
+open inhabited decidable
 
 namespace sum
 

library/data/unit.lean

@@ -4,7 +4,7 @@
 
 import logic.classes.decidable logic.classes.inhabited
 
-using decidable
+open decidable
 
 namespace unit
 

library/hott/fibrant.lean

@@ -5,7 +5,7 @@
 import data.unit data.bool data.nat
 import data.prod data.sum data.sigma
 
-using unit bool nat prod sum sigma
+open unit bool nat prod sum sigma
 
 inductive fibrant (T : Type) : Type :=
 fibrant_mk : fibrant T

library/hott/path.lean

@@ -10,7 +10,7 @@
 
 import general_notation struc.function
 
-using function
+open function
 
 -- Path
 -- ----
@@ -30,7 +30,7 @@ end path
 
 
 -- TODO: should all this be in namespace path?
-using path (induction_on)
+open path (induction_on)
 
 -- Concatenation and inverse
 -- -------------------------

library/logic/axioms/classical.lean

@@ -7,7 +7,7 @@
 
 import logic.core.quantifiers logic.core.cast struc.relation
 
-using eq_ops
+open eq_ops
 
 axiom prop_complete (a : Prop) : a = true ∨ a = false
 
@@ -48,7 +48,7 @@ propext
   (assume H, iff_to_eq H)
   (assume H, eq_to_iff H)
 
-using relation
+open relation
 theorem iff_congruence [instance] (P : Prop → Prop) : congruence iff iff P :=
 congruence_mk
   (take (a b : Prop),

library/logic/axioms/examples/diaconescu.lean

@@ -3,7 +3,7 @@
 -- Author: Leonardo de Moura
 
 import logic.axioms.hilbert logic.axioms.funext
-using eq_ops nonempty inhabited
+open eq_ops nonempty inhabited
 
 -- Diaconescu’s theorem
 -- Show that Excluded middle follows from

library/logic/axioms/funext.lean

@@ -5,7 +5,7 @@
 ----------------------------------------------------------------------------------------------------
 
 import logic.core.eq struc.function
-using function
+open function
 
 -- Function extensionality
 axiom funext : ∀ {A : Type} {B : A → Type} {f g : Π x, B x} (H : ∀ x, f x = g x), f = g

library/logic/axioms/hilbert.lean

@@ -12,7 +12,7 @@ import logic.core.quantifiers
 import logic.classes.inhabited logic.classes.nonempty
 import data.subtype data.sum
 
-using subtype inhabited nonempty
+open subtype inhabited nonempty
 
 
 -- the axiom

library/logic/axioms/piext.lean

@@ -6,7 +6,7 @@
 
 import logic.classes.inhabited logic.core.cast
 
-using inhabited
+open inhabited
 
 -- Pi extensionality
 axiom piext {A : Type} {B B' : A → Type} {H : inhabited (Π x, B x)} :

library/logic/axioms/prop_decidable.lean

@@ -6,7 +6,7 @@
 -- ===========================
 
 import logic.axioms.classical logic.axioms.hilbert logic.classes.decidable
-using decidable inhabited nonempty
+open decidable inhabited nonempty
 
 -- Excluded middle + Hilbert implies every proposition is decidable
 

library/logic/classes/nonempty.lean

@@ -4,7 +4,7 @@
 
 import .inhabited
 
-using inhabited
+open inhabited
 
 namespace nonempty
 

library/logic/core/cast.lean

@@ -6,7 +6,7 @@
 
 import .eq .quantifiers
 
-using eq_ops
+open eq_ops
 
 definition cast {A B : Type} (H : A = B) (a : A) : B :=
 eq_rec a H

library/logic/core/eq.lean

@@ -40,7 +40,7 @@ namespace eq_ops
   infixr `⬝`   := trans
   infixr `▸`   := subst
 end eq_ops
-using eq_ops
+open eq_ops
 
 theorem true_ne_false : ¬true = false :=
 assume H : true = false,

library/logic/core/examples/instances_test.lean

@@ -4,11 +4,10 @@
 
 import ..instances
 
-using relation
-
-using relation.general_operations
-using relation.iff_ops
-using eq_ops
+open relation
+open relation.general_operations
+open relation.iff_ops
+open eq_ops
 
 section
 

library/logic/core/identities.lean

@@ -10,7 +10,7 @@
 
 import logic.core.instances logic.classes.decidable logic.core.quantifiers logic.core.cast
 
-using relation decidable relation.iff_ops
+open relation decidable relation.iff_ops
 
 theorem or_right_comm (a b c : Prop) : (a ∨ b) ∨ c ↔ (a ∨ c) ∨ b :=
 calc

library/logic/core/if.lean

@@ -5,7 +5,7 @@
 ----------------------------------------------------------------------------------------------------
 
 import logic.classes.decidable tools.tactic
-using decidable tactic eq_ops
+open decidable tactic eq_ops
 
 definition ite (c : Prop) {H : decidable c} {A : Type} (t e : A) : A :=
 decidable.rec_on H (assume Hc,  t) (assume Hnc, e)

library/logic/core/instances.lean

@@ -9,7 +9,7 @@ import logic.core.connectives struc.relation
 
 namespace relation
 
-using relation
+open relation
 
 -- Congruences for logic
 -- ---------------------

library/logic/core/quantifiers.lean

@@ -4,7 +4,7 @@
 
 import .connectives ..classes.nonempty
 
-using inhabited nonempty
+open inhabited nonempty
 
 inductive Exists {A : Type} (P : A → Prop) : Prop :=
 exists_intro : ∀ (a : A), P a → Exists P

library/struc/binary.lean

@@ -1,9 +1,8 @@
 -- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
 -- Released under Apache 2.0 license as described in the file LICENSE.
 -- Author: Leonardo de Moura
-
 import logic.core.eq
-using eq_ops
+open eq_ops
 
 namespace binary
 section

library/struc/wf.lean

@@ -5,7 +5,7 @@
 import logic.axioms.classical logic.axioms.prop_decidable logic.classes.decidable
 import logic.core.identities
 
-using decidable
+open decidable
 
 -- Well-founded relation definition
 -- We are essentially saying that a relation R is well-founded

library/tools/fake_simplifier.lean

@@ -1,5 +1,5 @@
 import .tactic
-using tactic
+open tactic
 
 namespace fake_simplifier
 

library/tools/helper_tactics.lean

@@ -9,7 +9,7 @@
 
 import .tactic
 
-using tactic
+open tactic
 
 namespace helper_tactics
   definition apply_refl := apply @refl

library/tools/tactic.lean

@@ -5,8 +5,8 @@
 ----------------------------------------------------------------------------------------------------
 
 import data.string data.num
-using string
-using num
+open string
+open num
 
 namespace tactic
 -- This is just a trick to embed the 'tactic language' as a

src/emacs/lean-syntax.el

@@ -11,7 +11,7 @@
   '("import" "abbreviation" "opaque_hint" "tactic_hint" "definition" "renaming"
     "inline" "hiding" "exposing" "parameter" "parameters" "begin" "proof" "qed" "conjecture"
     "hypothesis" "lemma" "corollary" "variable" "variables" "print" "theorem"
-    "axiom" "inductive" "with" "structure" "universe" "alias" "help" "environment"
+    "context" "open" "axiom" "inductive" "with" "structure" "universe" "alias" "help" "environment"
     "options" "precedence" "postfix" "prefix" "calc_trans" "calc_subst" "calc_refl"
     "infix" "infixl" "infixr" "notation" "eval" "check" "exit" "coercion" "end"
     "private" "using" "namespace" "builtin" "including" "instance" "class" "section"
@@ -60,10 +60,6 @@
      ;; Constants
      (,(rx (or "#" "@" "->" "∼" "↔" "/" "==" "=" ":=" "<->" "/\\" "\\/" "∧" "∨" "≠" "<" ">" "≤" "≥" "¬" "<=" ">=" "⁻¹" "⬝" "▸" "+" "*" "-" "/")) . 'font-lock-constant-face)
      (,(rx (or "λ" "→" "∃" "∀" ":=")) . 'font-lock-constant-face )
-     (,(rx symbol-start
-           (or "\\b.*_tac" "Cond" "or_else" "then" "try" "when" "assumption" "apply" "back" "beta" "done" "exact")
-           symbol-end)
-      . 'font-lock-constant-face)
      ;; universe/inductive/theorem... "names"
      (,(rx symbol-start
            (group (or "universe" "inductive" "theorem" "axiom" "lemma" "hypothesis"
@@ -76,7 +72,12 @@
      ;; place holder
      (,(rx symbol-start "_" symbol-end) . 'font-lock-preprocessor-face)
      ;; modifiers
-     (,(rx (or "\[protected\]" "\[private\]" "\[instance\]" "\[coercion\]" "\[inline\]")) . 'font-lock-doc-face)
+     (,(rx (or "\[notation\]" "\[protected\]" "\[private\]" "\[instance\]" "\[coercion\]" "\[inline\]")) . 'font-lock-doc-face)
+     ;; tactics
+     (,(rx symbol-start
+           (or "\\b.*_tac" "Cond" "or_else" "then" "try" "when" "assumption" "apply" "back" "beta" "done" "exact" "repeat")
+           symbol-end)
+      . 'font-lock-constant-face)
      ;; sorry
      (,(rx symbol-start "sorry" symbol-end) . 'font-lock-warning-face)
      ;; ? query

src/frontends/lean/builtin_cmds.cpp

@@ -166,9 +166,9 @@ static name parse_class(parser & p) {
         else if (p.curr_is_keyword() || p.curr_is_command())
             n = p.get_token_info().value();
         else
-            throw parser_error("invalid 'using' command, identifier or symbol expected", p.pos());
+            throw parser_error("invalid 'open' command, identifier or symbol expected", p.pos());
         p.next();
-        p.check_token_next(g_rbracket, "invalid 'using' command, ']' expected");
+        p.check_token_next(g_rbracket, "invalid 'open' command, ']' expected");
         return n;
     } else {
         return name();
@@ -178,17 +178,17 @@ static name parse_class(parser & p) {
 static void check_identifier(parser & p, environment const & env, name const & ns, name const & id) {
     name full_id = ns + id;
     if (!env.find(full_id))
-        throw parser_error(sstream() << "invalid 'using' command, unknown declaration '" << full_id << "'", p.pos());
+        throw parser_error(sstream() << "invalid 'open' command, unknown declaration '" << full_id << "'", p.pos());
 }
 
-// using [class] id (id ...) (renaming id->id id->id) (hiding id ... id)
-environment using_cmd(parser & p) {
+// open [class] id (id ...) (renaming id->id id->id) (hiding id ... id)
+environment open_cmd(parser & p) {
     environment env = p.env();
     while (true) {
         name cls = parse_class(p);
         bool decls = cls.is_anonymous() || cls == g_decls || cls == g_declarations;
         auto pos   = p.pos();
-        name ns    = p.check_id_next("invalid 'using' command, identifier expected");
+        name ns    = p.check_id_next("invalid 'open' command, identifier expected");
         optional<name> real_ns = to_valid_namespace_name(env, ns);
         if (!real_ns)
             throw parser_error(sstream() << "invalid namespace name '" << ns << "'", pos);
@@ -205,8 +205,8 @@ environment using_cmd(parser & p) {
                     while (p.curr_is_identifier()) {
                         name from_id = p.get_name_val();
                         p.next();
-                        p.check_token_next(g_arrow, "invalid 'using' command renaming, '->' expected");
-                        name to_id = p.check_id_next("invalid 'using' command renaming, identifier expected");
+                        p.check_token_next(g_arrow, "invalid 'open' command renaming, '->' expected");
+                        name to_id = p.check_id_next("invalid 'open' command renaming, identifier expected");
                         check_identifier(p, env, ns, from_id);
                         exceptions.push_back(from_id);
                         env = add_expr_alias(env, to_id, ns+from_id);
@@ -228,11 +228,11 @@ environment using_cmd(parser & p) {
                         env = add_expr_alias(env, id, ns+id);
                     }
                 } else {
-                    throw parser_error("invalid 'using' command option, identifier, 'hiding' or 'renaming' expected", p.pos());
+                    throw parser_error("invalid 'open' command option, identifier, 'hiding' or 'renaming' expected", p.pos());
                 }
                 if (found_explicit && !exceptions.empty())
-                    throw parser_error("invalid 'using' command option, mixing explicit and implicit 'using' options", p.pos());
-                p.check_token_next(g_rparen, "invalid 'using' command option, ')' expected");
+                    throw parser_error("invalid 'open' command option, mixing explicit and implicit 'open' options", p.pos());
+                p.check_token_next(g_rparen, "invalid 'open' command option, ')' expected");
             }
             if (!found_explicit)
                 env = add_aliases(env, ns, name(), exceptions.size(), exceptions.data());
@@ -303,7 +303,7 @@ environment erase_cache_cmd(parser & p) {
 
 cmd_table init_cmd_table() {
     cmd_table r;
-    add_cmd(r, cmd_info("using",        "create aliases for declarations, and use objects defined in other namespaces", using_cmd));
+    add_cmd(r, cmd_info("open",         "create aliases for declarations, and use objects defined in other namespaces", open_cmd));
     add_cmd(r, cmd_info("set_option",   "set configuration option", set_option_cmd));
     add_cmd(r, cmd_info("exit",         "exit", exit_cmd));
     add_cmd(r, cmd_info("print",        "print a string", print_cmd));

src/frontends/lean/token_table.cpp

@@ -68,7 +68,7 @@ token_table init_token_table() {
     pair<char const *, unsigned> builtin[] =
         {{"fun", 0}, {"Pi", 0}, {"let", 0}, {"in", 0}, {"have", 0}, {"show", 0}, {"obtain", 0}, {"by", 0}, {"then", 0},
          {"from", 0}, {"(", g_max_prec}, {")", 0}, {"{", g_max_prec}, {"}", 0}, {"_", g_max_prec},
-         {"[", g_max_prec}, {"]", 0}, {"⦃", g_max_prec}, {"⦄", 0}, {".{", 0}, {"Type", g_max_prec}, {"Type'", g_max_prec},
+         {"[", g_max_prec}, {"]", 0}, {"⦃", g_max_prec}, {"⦄", 0}, {".{", 0}, {"Type", g_max_prec}, {"Type'", g_max_prec}, {"using", 0},
          {"|", 0}, {"!", 0}, {"?", 0}, {"with", 0}, {"...", 0}, {",", 0}, {".", 0}, {":", 0}, {"::", 0}, {"calc", 0}, {":=", 0}, {"--", 0}, {"#", 0},
          {"(*", 0}, {"/-", 0}, {"begin", g_max_prec}, {"proof", g_max_prec}, {"qed", 0}, {"@", g_max_prec}, {"including", 0}, {"sorry", g_max_prec},
          {"+", g_plus_prec}, {g_cup, g_cup_prec}, {"->", g_arrow_prec}, {nullptr, 0}};
@@ -78,7 +78,7 @@ token_table init_token_table() {
                                "abbreviation", "opaque_hint", "evaluate", "check", "print", "end", "namespace", "section", "import",
                                "abbreviation", "inductive", "record", "renaming", "extends", "structure", "module", "universe",
                                "precedence", "infixl", "infixr", "infix", "postfix", "prefix", "notation", "context",
-                               "exit", "set_option", "using", "calc_subst", "calc_refl", "calc_trans", "tactic_hint",
+                               "exit", "set_option", "open", "calc_subst", "calc_refl", "calc_trans", "tactic_hint",
                                "add_begin_end_tactic", "set_begin_end_tactic", "instance", "class", "#erase_cache", nullptr};
 
     pair<char const *, char const *> aliases[] =

tests/lean/alias.lean

@@ -10,16 +10,15 @@ namespace N2
   variable foo : val → val → val
 end N2
 
-using N2
-using N1
+open N2
+open N1
 variables a b : num
 print raw foo a b
-using N2
+open N2
 print raw foo a b
-using N1
+open N1
 print raw foo a b
-using N1
+open N1
 print raw foo a b
-using N2
+open N2
 print raw foo a b
-

tests/lean/choice_expl.lean

@@ -6,7 +6,7 @@ namespace N2
   definition pr {A : Type} (a b : A) := b
 end N2
 
-using N1 N2
+open N1 N2
 variable N : Type.{1}
 variables a b : N
 check @pr

tests/lean/empty.lean

@@ -1,5 +1,5 @@
 import logic logic.axioms.hilbert
-using inhabited nonempty
+open inhabited nonempty
 
 definition v1 : Prop := epsilon (λ x, true)
 inductive Empty : Type

tests/lean/empty_thm.lean

@@ -1,5 +1,5 @@
 import logic tools.tactic
-using tactic
+open tactic
 
 definition simple := apply trivial
 

tests/lean/have1.lean

@@ -1,5 +1,5 @@
 import logic
-using bool eq_ops tactic
+open bool eq_ops tactic
 
 variables a b c : bool
 axiom H1 : a = b

tests/lean/interactive/class_bug.lean

@@ -1,5 +1,5 @@
 import logic.axioms.hilbert data.nat.basic
-using nonempty inhabited nat
+open nonempty inhabited nat
 
 theorem int_inhabited [instance] : inhabited nat := inhabited_mk zero
 

tests/lean/let3.lean

@@ -1,5 +1,5 @@
 import data.num
-using num
+open num
 
 variable f : num → num → num → num
 

tests/lean/let4.lean

@@ -1,5 +1,5 @@
 import data.num
-using num
+open num
 
 variable f : num → num → num → num
 
@@ -15,5 +15,3 @@ check
       d := 10,
       e := f (f 10 10 d) (f d 10 10) a
   in f a b (f e d 10)
-
-

tests/lean/num.lean

@@ -1,5 +1,5 @@
 import data.num
-using num
+open num
 
 check 10
 check 20

tests/lean/protected.lean

@@ -5,6 +5,6 @@ namespace foo
   definition D := true
 end foo
 
-using foo
+open foo
 check C
 check D

tests/lean/run/algebra1.lean

@@ -1,5 +1,5 @@
 import logic
-using num
+open num
 
 abbreviation Type1 := Type.{1}
 
@@ -88,7 +88,7 @@ namespace monoid
   definition assoc [inline] {A : Type} (s : monoid_struct A) : is_assoc (mul s)
   := monoid_struct_rec (fun mul id a i, a) s
 
-  using semigroup
+  open semigroup
   definition is_semigroup_struct [inline] [instance] (A : Type) (s : monoid_struct A) : semigroup_struct A
   := mk_semigroup_struct (mul s) (assoc s)
 
@@ -104,7 +104,7 @@ end monoid
 end algebra
 
 section
-  using algebra algebra.semigroup algebra.monoid
+  open algebra algebra.semigroup algebra.monoid
   variable M : monoid
   variables a b c : M
   check a*b*c*a*b*c*a*b*a*b*c*a

tests/lean/run/alias1.lean

@@ -10,8 +10,8 @@ namespace N2
   variable foo : val → val → val
 end N2
 
-using N1
-using N2
+open N1
+open N2
 variables a b : num
 variables x y : val
 
@@ -35,7 +35,7 @@ definition aux1 := foo a b  -- System elaborated it to N1.foo a b
 theorem T2 : aux1 = N1.foo a b
 := refl _
 
-using N1
+open N1
 definition aux2 := foo a b  -- Now N1 is in the end of the queue, this is elaborated to N2.foo (f a) (f b)
 check aux2
 

tests/lean/run/alias2.lean

@@ -10,8 +10,8 @@ namespace N2
   variable foo : val → val → val
 end N2
 
-using N1
-using N2
+open N1
+open N2
 variables a b : num
 variable f : num → val
 coercion f
@@ -20,4 +20,3 @@ definition aux2 := foo a b
 check aux2
 theorem T3 : aux2 = N1.foo a b
 := refl _
-

tests/lean/run/booltst.lean

@@ -1,4 +1,4 @@
 import data.bool
-using bool
+open bool
 
 check ff

tests/lean/run/calc.lean

@@ -1,5 +1,5 @@
 import data.num
-using num
+open num
 
 namespace foo
   variable le : num → num → Prop

tests/lean/run/choice_ctx.lean

@@ -1,5 +1,5 @@
 import data.nat.basic
-using nat
+open nat
 
 set_option pp.coercion true
 
@@ -8,7 +8,7 @@ theorem trans {a b c : nat} (H1 : a = b) (H2 : b = c) : a = c :=
 trans H1 H2
 end foo
 
-using foo
+open foo
 
 theorem tst (a b : nat) (H0 : b = a) (H : b = 0) : a = 0
 := have H1 : a = b, from symm H0,
@@ -17,4 +17,3 @@ theorem tst (a b : nat) (H0 : b = a) (H : b = 0) : a = 0
 definition f (a b : nat) :=
 let x := 3 in
 a + x
-

tests/lean/run/class1.lean

@@ -1,5 +1,5 @@
 import logic data.prod
-using num prod inhabited
+open num prod inhabited
 
 definition H : inhabited (Prop × num × (num → num)) := _
 

tests/lean/run/class2.lean

@@ -1,5 +1,5 @@
 import logic data.prod
-using num prod nonempty inhabited
+open num prod nonempty inhabited
 
 theorem H {A B : Type} (H1 : inhabited A) : inhabited (Prop × A × (B → num))
 := _

tests/lean/run/class3.lean

@@ -1,5 +1,5 @@
 import logic data.prod
-using num prod inhabited
+open num prod inhabited
 
 section
   parameter {A : Type}

tests/lean/run/class5.lean

@@ -23,36 +23,36 @@ namespace nat
 end nat
 
 section
-  using algebra nat
+  open algebra nat
   variables a b c : nat
   check a * b * c
   definition tst1 : nat := a * b * c
 end
 
 section
-  using [notation] algebra
-  using nat
-  -- check mul_struct nat  << This is an error, we are using only the notation from algebra
+  open [notation] algebra
+  open nat
+  -- check mul_struct nat  << This is an error, we are open only the notation from algebra
   variables a b c : nat
   check a * b * c
   definition tst2 : nat := a * b * c
 end
 
 section
-  using nat
-  -- check mul_struct nat  << This is an error, we are using only the notation from algebra
+  open nat
+  -- check mul_struct nat  << This is an error, we are open only the notation from algebra
   variables a b c : nat
   check #algebra a*b*c
   definition tst3 : nat := #algebra a*b*c
 end
 
 section
-  using nat
+  open nat
   set_option pp.implicit true
   definition add_struct [instance] : algebra.mul_struct nat
   := algebra.mk_mul_struct add
 
   variables a b c : nat
-  check #algebra a*b*c  -- << is using add instead of mul
+  check #algebra a*b*c  -- << is open add instead of mul
   definition tst4 : nat := #algebra a*b*c
 end

tests/lean/run/class6.lean

@@ -1,5 +1,5 @@
 import logic data.prod
-using prod
+open prod
 
 inductive t1 : Type :=
 mk1 : t1

tests/lean/run/class7.lean

@@ -1,5 +1,5 @@
 import logic
-using num tactic
+open num tactic
 
 inductive inh (A : Type) : Type :=
 inh_intro : A -> inh A

tests/lean/run/class8.lean

@@ -1,5 +1,5 @@
 import logic data.prod
-using num tactic prod
+open num tactic prod
 
 inductive inh (A : Type) : Prop :=
 inh_intro : A -> inh A

tests/lean/run/class_coe.lean

@@ -1,5 +1,5 @@
 import data.num
-using num
+open num
 
 variables int nat real : Type.{1}
 variable nat_add  : nat → nat → nat

tests/lean/run/coercion_bug.lean

@@ -1,5 +1,5 @@
 import data.nat
-using nat
+open nat
 
 definition tst1  : Prop := zero = 0
 definition tst2  : nat  := 0

tests/lean/run/coercion_bug2.lean

@@ -1,5 +1,5 @@
 import data.nat
-using nat
+open nat
 
 inductive list (T : Type) : Type :=
 nil {} : list T,

tests/lean/run/congr_imp_bug.lean

@@ -4,7 +4,7 @@
 --- Author: Jeremy Avigad
 ----------------------------------------------------------------------------------------------------
 import logic.core.connectives struc.function
-using function
+open function
 
 namespace congr
 

tests/lean/run/decidable.lean

@@ -1,5 +1,5 @@
 import logic data.unit
-using bool unit decidable
+open bool unit decidable
 
 variables a b c : bool
 variables u v : unit

tests/lean/run/e10.lean

@@ -1,4 +1,3 @@
-
 precedence `+`:65
 
 namespace nat
@@ -8,7 +7,7 @@ namespace nat
 end nat
 
 namespace int
-  using nat (nat)
+  open nat (nat)
   variable int : Type.{1}
   variable add : int → int → int
   infixl + := add
@@ -17,8 +16,8 @@ namespace int
 end int
 
 section
-  using nat
-  using int
+  open nat
+  open int
 
   variables n m : nat
   variables i j : int
@@ -36,7 +35,7 @@ section
 
   -- Moving 'nat' to the 'front'
   print ">>> Moving nat notation to the 'front'"
-  using nat
+  open nat
   print raw i + n
   check n + m
 end

tests/lean/run/e11.lean

@@ -7,7 +7,7 @@ namespace nat
 end nat
 
 namespace int
-  using nat (nat)
+  open nat (nat)
   variable int : Type.{1}
   variable add : int → int → int
   infixl + := add
@@ -16,18 +16,18 @@ namespace int
 end int
 
 section
-  -- Using "only" the notation and declarations from the namespaces nat and int
-  using [notation] nat
-  using [notation] int
-  using [decls] nat
-  using [decls] int
+  -- Open "only" the notation and declarations from the namespaces nat and int
+  open [notation] nat
+  open [notation] int
+  open [decls] nat
+  open [decls] int
 
   variables n m : nat
   variables i j : int
   check n + m
   check i + j
 
-  -- The following check does not work, since we are not using the coercions
+  -- The following check does not work, since we are not open the coercions
   -- check n + i
 
   -- Here is a possible trick for this kind of configuration

tests/lean/run/e12.lean

@@ -7,7 +7,7 @@ namespace nat
 end nat
 
 namespace int
-  using nat (nat)
+  open nat (nat)
   variable int : Type.{1}
   variable add : int → int → int
   infixl + := add
@@ -19,17 +19,17 @@ variables n m : nat.nat
 variables i j : int.int
 
 section
-  using [notation] nat
-  using [notation] int
-  using [decls] nat
-  using [decls] int
+  open [notation] nat
+  open [notation] int
+  open [decls] nat
+  open [decls] int
   check n+m
   check i+j
   --  check i+n -- Error
 end
 
 namespace int
-  using [decls] nat (nat)
+  open [decls] 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)
@@ -38,18 +38,18 @@ namespace int
 end int
 
 section
-  using [notation] nat
-  using [notation] int
-  using [declarations] nat
-  using [declarations] int
+  open [notation] nat
+  open [notation] int
+  open [declarations] nat
+  open [declarations] int
   check n+m
   check i+n
   check n+i
 end
 
 section
-  using nat
-  using int
+  open nat
+  open int
   check n+m
   check i+n
 end

tests/lean/run/e13.lean

@@ -7,7 +7,7 @@ namespace nat
 end nat
 
 namespace int
-  using nat (nat)
+  open nat (nat)
   variable int : Type.{1}
   variable add : int → int → int
   infixl + := add
@@ -17,10 +17,9 @@ namespace int
   end coercions
 end int
 
-using nat
-using int
+open nat
+open int
 variables n m : nat
 check n+m -- coercion nat -> int is not available
-using int.coercions
+open int.coercions
 check n+m -- coercion nat -> int is available
-

tests/lean/run/e6.lean

@@ -1,4 +1,3 @@
-
 precedence `+`:65
 
 namespace nat
@@ -8,7 +7,7 @@ namespace nat
 end nat
 
 namespace int
-  using nat (nat)
+  open nat (nat)
   variable int : Type.{1}
   variable add : int → int → int
   infixl + := add
@@ -16,8 +15,8 @@ namespace int
   coercion of_nat
 end int
 
-using int
-using nat
+open int
+open nat
 
 variables n m : nat
 variables i j : int
@@ -29,5 +28,3 @@ check i + n + n + n + n + n + n + n + n + n + n + n +
       n + n + n + n + n + n + n + n + n + n + n + n +
       n + n + n + n + n + n + n + n + n + n + n + n +
       n + n + n + n + n + n + n + n + n + n + n + n
-
-

tests/lean/run/e7.lean

@@ -1,4 +1,3 @@
-
 precedence `+`:65
 
 namespace nat
@@ -8,7 +7,7 @@ namespace nat
 end nat
 
 namespace int
-  using nat (nat)
+  open nat (nat)
   variable int : Type.{1}
   variable add : int → int → int
   infixl + := add
@@ -16,8 +15,8 @@ namespace int
   coercion of_nat
 end int
 
-using nat
-using int
+open nat
+open int
 
 variables n m : nat
 variables i j : int
@@ -34,6 +33,6 @@ check #nat n + m
 
 -- Moving 'nat' to the 'front'
 print ">>> Moving nat notation to the 'front'"
-using nat
+open nat
 print raw i + n
 check n + m

tests/lean/run/e8.lean

@@ -7,7 +7,7 @@ namespace nat
 end nat
 
 namespace int
-  using nat (nat)
+  open nat (nat)
   variable int : Type.{1}
   variable add : int → int → int
   infixl + := add
@@ -15,18 +15,18 @@ namespace int
   coercion of_nat
 end int
 
--- Using "only" the notation and declarations from the namespaces nat and int
-using [notation] nat
-using [notation] int
-using [decls] nat
-using [decls] int
+-- Open "only" the notation and declarations from the namespaces nat and int
+open [notation] nat
+open [notation] int
+open [decls] nat
+open [decls] int
 
 variables n m : nat
 variables i j : int
 check n + m
 check i + j
 
--- The following check does not work, since we are not using the coercions
+-- The following check does not work, since we are not open the coercions
 -- check n + i
 
 -- Here is a possible trick for this kind of configuration

tests/lean/run/e9.lean

@@ -7,7 +7,7 @@ namespace nat
 end nat
 
 namespace int
-  using nat (nat)
+  open nat (nat)
   variable int : Type.{1}
   variable add : int → int → int
   infixl + := add
@@ -18,9 +18,9 @@ namespace int_coercions
   coercion int.of_nat
 end int_coercions
 
--- Using "only" the notation and declarations from the namespaces nat and int
-using nat
-using int
+-- Open "only" the notation and declarations from the namespaces nat and int
+open nat
+open int
 
 variables n m : nat
 variables i j : int
@@ -29,10 +29,9 @@ check i + j
 
 section
   -- Temporarily use the int_coercions
-  using int_coercions
+  open int_coercions
   check n + i
 end
 
 -- The following one is an error
 -- check n + i
-

tests/lean/run/elab_bug1.lean

@@ -6,7 +6,7 @@
 
 import logic struc.function
 
-using function
+open function
 
 namespace congruence
 

tests/lean/run/elim.lean

@@ -1,5 +1,5 @@
 import logic
-using num
+open num
 variable p : num → num → num → Prop
 axiom H1 : ∃ x y z, p x y z
 axiom H2 : ∀ {x y z : num}, p x y z → p x x x

tests/lean/run/elim2.lean

@@ -1,5 +1,5 @@
 import logic
-using num tactic
+open num tactic
 variable p : num → num → num → Prop
 axiom H1 : ∃ x y z, p x y z
 axiom H2 : ∀ {x y z : num}, p x y z → p x x x

tests/lean/run/full.lean

@@ -2,7 +2,7 @@ import logic
 namespace foo
   variable x : num.num
   check x
-  using num
+  open num
   check x
   set_option pp.full_names true
   check x

tests/lean/run/fun.lean

@@ -1,5 +1,5 @@
 import logic struc.function
-using function num bool
+open function num bool
 
 
 variable f : num → bool

tests/lean/run/goal.lean

@@ -1,5 +1,5 @@
 import logic
-using tactic
+open tactic
 
 theorem T {a b c d : Prop} (H : a) (H : b) (H : c) (H : d) : a
 := by state; assumption

tests/lean/run/group.lean

@@ -1,5 +1,5 @@
 import logic
-using num
+open num
 
 section
   parameter {A  : Type}

tests/lean/run/group2.lean

@@ -1,5 +1,5 @@
 import logic
-using num
+open num
 
 section
   parameter {A  : Type}

tests/lean/run/have5.lean

@@ -1,5 +1,5 @@
 import logic
-using tactic
+open tactic
 variables a b c d : Prop
 axiom Ha : a
 axiom Hb : b

tests/lean/run/is_nil.lean

@@ -1,5 +1,5 @@
 import logic
-using tactic
+open tactic
 
 inductive list (A : Type) : Type :=
 nil {} : list A,

tests/lean/run/list_elab1.lean

@@ -10,7 +10,7 @@
 -- Basic properties of lists.
 
 import data.nat
-using nat eq_ops
+open nat eq_ops
 inductive list (T : Type) : Type :=
 nil {} : list T,
 cons : T → list T → list T

tests/lean/run/local_using.lean

@@ -15,10 +15,8 @@ end bla
 
 variable g : N → N → N
 
-using foo
-using bla
+open foo
+open bla
 print raw a + b -- + is overloaded, it creates a choice
 print raw #foo a + b   -- + is not overloaded, we are parsing inside #foo
 print raw g (#foo a + b) (#bla a + b) -- mixing both
-
-

tests/lean/run/match1.lean

@@ -1,5 +1,5 @@
 import data.nat
-using nat
+open nat
 
 definition two1 : nat := 2
 definition two2 : nat := succ (succ (zero))

tests/lean/run/match2.lean

@@ -1,5 +1,5 @@
 import data.nat
-using nat
+open nat
 
 definition two1 : nat := 2
 definition two2 : nat := succ (succ (zero))

tests/lean/run/nat_bug.lean

@@ -1,5 +1,5 @@
 import logic
-using decidable
+open decidable
 
 inductive nat : Type :=
 zero : nat,

tests/lean/run/nat_bug2.lean

@@ -1,5 +1,5 @@
 import logic
-using num eq_ops
+open num eq_ops
 
 inductive nat : Type :=
 zero : nat,

tests/lean/run/nat_bug3.lean

@@ -1,5 +1,5 @@
 import logic
-using num eq_ops
+open num eq_ops
 
 inductive nat : Type :=
 zero : nat,

tests/lean/run/nat_bug4.lean

@@ -1,5 +1,5 @@
 import logic
-using num eq_ops
+open num eq_ops
 
 inductive nat : Type :=
 zero : nat,

tests/lean/run/nat_bug5.lean

@@ -1,5 +1,5 @@
 import logic
-using num eq_ops
+open num eq_ops
 
 inductive nat : Type :=
 zero : nat,