refactor(library): use "symbolic" precedences in the standard library

library/data/sigma/decl.lean

@@ -1,7 +1,7 @@
 -- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
 -- Released under Apache 2.0 license as described in the file LICENSE.
 -- Author: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
-import logic.eq logic.heq data.unit
+import logic.eq logic.heq data.unit data.num.ops
 
 structure sigma {A : Type} (B : A → Type) :=
 dpair :: (dpr1 : A) (dpr2 : B dpr1)
@@ -14,8 +14,8 @@ namespace sigma
   notation `dpr₂` := dpr2
 
   namespace ops
-  postfix `.1`:10000 := dpr1
+  postfix `.1`:(max+1) := dpr1
-  postfix `.2`:10000 := dpr2
+  postfix `.2`:(max+1) := dpr2
-  notation `⟨` t:(foldr `,`:0 (e r, sigma.dpair e r)) `⟩`:0 := t --input ⟨ ⟩ as \< \>
+  notation `⟨` t:(foldr `,` (e r, sigma.dpair e r)) `⟩`:0 := t --input ⟨ ⟩ as \< \>
   end ops
 end sigma

library/hott/trunc.lean

@@ -22,8 +22,8 @@ namespace truncation
   minus_two : trunc_index,
   trunc_S : trunc_index → trunc_index
 
-  postfix `.+1`:10000 := trunc_index.trunc_S
+  postfix `.+1`:(max+1) := trunc_index.trunc_S
-  postfix `.+2`:10000 := λn, (n .+1 .+1)
+  postfix `.+2`:(max+1) := λn, (n .+1 .+1)
   notation `-2` := trunc_index.minus_two
   notation `-1` := (-2.+1)
 

library/hott/types/sigma.lean

@@ -39,14 +39,14 @@ namespace sigma
   definition pr1_path (p : u ≈ v) : u.1 ≈ v.1 :=
   ap dpr1 p
 
-  postfix `..1`:10000 := pr1_path
+  postfix `..1`:(max+1) := pr1_path
 
   definition pr2_path (p : u ≈ v) : p..1 ▹ u.2 ≈ v.2 :=
   path.rec_on p idp
   --Coq uses the following proof, which only computes if u,v are dpairs AND p is idp
   --(transport_compose B dpr1 p u.2)⁻¹ ⬝ apD dpr2 p
 
-  postfix `..2`:10000 := pr2_path
+  postfix `..2`:(max+1) := pr2_path
 
   definition dpair_path_sigma (p : u.1 ≈ v.1) (q : p ▹ u.2 ≈ v.2)
       :  dpair (path_sigma p q)..1 (path_sigma p q)..2 ≈ ⟨p, q⟩ :=

src/frontends/lean/class.cpp

@@ -12,6 +12,7 @@ Author: Leonardo de Moura
 #include "library/kernel_serializer.h"
 #include "library/reducible.h"
 #include "library/num.h"
+#include "library/normalize.h"
 #include "library/aliases.h"
 #include "frontends/lean/parser.h"
 #include "frontends/lean/util.h"
@@ -181,20 +182,14 @@ list<name> get_class_instances(environment const & env, name const & c) {
     return ptr_to_list(s.m_instances.find(c));
 }
 
-static environment open_priority_namespace(parser & p) {
-    name prio("std", "priority");
-    environment env = using_namespace(p.env(), p.ios(), prio);
-    return overwrite_aliases(env, prio, name());
-}
-
 optional<unsigned> parse_instance_priority(parser & p) {
     if (p.curr_is_token(get_priority_tk())) {
         p.next();
         auto pos = p.pos();
-        environment env = open_priority_namespace(p);
+        environment env = open_priority_aliases(open_num_notation(p.env()));
         parser::local_scope scope(p, env);
         expr val = p.parse_expr();
-        val = type_checker(p.env()).whnf(val).first;
+        val = normalize(p.env(), val);
         if (optional<mpz> mpz_val = to_num(val)) {
             if (!mpz_val->is_unsigned_int())
                 throw parser_error("invalid 'priority', argument does not fit in a machine integer", pos);

src/frontends/lean/notation_cmd.cpp

@@ -14,9 +14,11 @@ Author: Leonardo de Moura
 #include "library/scoped_ext.h"
 #include "library/explicit.h"
 #include "library/num.h"
+#include "library/normalize.h"
 #include "library/aliases.h"
 #include "frontends/lean/parser.h"
 #include "frontends/lean/tokens.h"
+#include "frontends/lean/util.h"
 
 namespace lean {
 static std::string parse_symbol(parser & p, char const * msg) {
@@ -32,21 +34,15 @@ static std::string parse_symbol(parser & p, char const * msg) {
     return n.to_string();
 }
 
-static environment open_prec_namespace(parser & p) {
-    name prec("std", "prec");
-    environment env = using_namespace(p.env(), p.ios(), prec);
-    return overwrite_aliases(env, prec, name());
-}
-
 static unsigned parse_precedence_core(parser & p) {
     auto pos = p.pos();
     if (p.curr_is_numeral()) {
         return p.parse_small_nat();
     } else {
-        environment env = open_prec_namespace(p);
+        environment env = open_prec_aliases(open_num_notation(p.env()));
         parser::local_scope scope(p, env);
         expr val = p.parse_expr(get_max_prec());
-        val = type_checker(p.env()).whnf(val).first;
+        val = normalize(p.env(), val);
         if (optional<mpz> mpz_val = to_num(val)) {
             if (!mpz_val->is_unsigned_int())
                 throw parser_error("invalid 'precedence', argument does not fit in a machine integer", pos);

src/frontends/lean/util.cpp

@@ -415,4 +415,25 @@ name get_decl_short_name(name const & d, environment const & env) {
     else
         return d;
 }
+
+environment open_num_notation(environment const & env) {
+    name num("num");
+    try {
+        environment new_env = overwrite_notation(env, num);
+        return overwrite_aliases(new_env, num, name());
+    } catch (exception &) {
+        // num namespace is not available, then use only the aliases
+        return overwrite_aliases(env, num, name());
+    }
+}
+
+environment open_prec_aliases(environment const & env) {
+    name prec("std", "prec");
+    return overwrite_aliases(env, prec, name());
+}
+
+environment open_priority_aliases(environment const & env) {
+    name prio("std", "priority");
+    return overwrite_aliases(env, prio, name());
+}
 }

src/frontends/lean/util.h

@@ -107,4 +107,11 @@ optional<name> is_uniquely_aliased(environment const & env, name const & n);
 
 /** \brief Get declaration 'short-name' that can uniquely identify it. */
 name get_decl_short_name(name const & d, environment const & env);
+
+/** \brief Open 'num' notation and aliases. */
+environment open_num_notation(environment const & env);
+/** \brief Open 'std.prec' aliases */
+environment open_prec_aliases(environment const & env);
+/** \brief Open 'std.priority' aliases */
+environment open_priority_aliases(environment const & env);
 }