feat(frontends/lean): max precedence used by Lean is not max_uint anymore

The motivation is to allow users to define notation with higher
precedence than function application.

src/frontends/lean/notation_cmd.cpp

@@ -35,7 +35,7 @@ static optional<unsigned> parse_optional_precedence(parser & p) {
         return optional<unsigned>(p.parse_small_nat());
     } else if (p.curr_is_token_or_id(get_max_tk())) {
         p.next();
-        return optional<unsigned>(std::numeric_limits<unsigned>::max());
+        return optional<unsigned>(get_max_prec());
     } else {
         return optional<unsigned>();
     }

src/frontends/lean/parser.cpp

@@ -1022,10 +1022,11 @@ expr parser::parse_nud_notation() {
 }
 
 expr parser::parse_led_notation(expr left) {
-    if (led().find(get_token_info().value()))
+    if (led().find(get_token_info().value())) {
         return parse_notation(led(), &left);
-    else
-        return mk_app(left, parse_nud_notation(), pos_of(left));
+    } else {
+        return mk_app(left, parse_expr(get_max_prec()), pos_of(left));
+    }
 }
 
 expr parser::id_to_expr(name const & id, pos_info const & p) {
@@ -1188,12 +1189,8 @@ expr parser::parse_nud() {
 
 expr parser::parse_led(expr left) {
     switch (curr()) {
-    case scanner::token_kind::Keyword:     return parse_led_notation(left);
-    case scanner::token_kind::Identifier:  return mk_app(left, parse_id(), pos_of(left));
-    case scanner::token_kind::Numeral:     return mk_app(left, parse_numeral_expr(), pos_of(left));
-    case scanner::token_kind::Decimal:     return mk_app(left, parse_decimal_expr(), pos_of(left));
-    case scanner::token_kind::String:      return mk_app(left, parse_string_expr(), pos_of(left));
-    default:                               return left;
+    case scanner::token_kind::Keyword: return parse_led_notation(left);
+    default:                           return mk_app(left, parse_expr(get_max_prec()), pos_of(left));
     }
 }
 
@@ -1206,7 +1203,7 @@ unsigned parser::curr_lbp() const {
         return 0;
     case scanner::token_kind::Identifier:     case scanner::token_kind::Numeral:
     case scanner::token_kind::Decimal:        case scanner::token_kind::String:
-        return std::numeric_limits<unsigned>::max();
+        return get_max_prec();
     }
     lean_unreachable(); // LCOV_EXCL_LINE
 }

src/frontends/lean/pp.cpp

@@ -766,7 +766,7 @@ auto pretty_fn::pp_notation(notation_entry const & entry, buffer<optional<expr>>
         to_buffer(entry.get_transitions(), ts);
         format fmt;
         unsigned i         = ts.size();
-        unsigned last_rbp  = max_bp()-1;
+        unsigned last_rbp  = inf_bp()-1;
         unsigned token_lbp = 0;
         bool extra_space   = false;
         bool last          = true;
@@ -779,7 +779,7 @@ auto pretty_fn::pp_notation(notation_entry const & entry, buffer<optional<expr>>
             case notation::action_kind::Skip:
                 curr = format(tk);
                 if (last)
-                    last_rbp = max_bp();
+                    last_rbp = inf_bp();
                 break;
             case notation::action_kind::Expr:
                 if (args.empty() || !args.back()) {
@@ -915,7 +915,7 @@ auto pretty_fn::pp_notation(notation_entry const & entry, buffer<optional<expr>>
             }
             extra_space = add_extra_space(tk);
         }
-        unsigned first_lbp = max_bp();
+        unsigned first_lbp = inf_bp();
         if (!entry.is_nud()) {
             first_lbp = token_lbp;
             lean_assert(!last);

src/frontends/lean/pp.h

@@ -21,14 +21,15 @@ class notation_entry;
 
 class pretty_fn {
 public:
-    static unsigned max_bp() { return std::numeric_limits<unsigned>::max(); }
+    static unsigned max_bp() { return get_max_prec(); }
+    static unsigned inf_bp() { return std::numeric_limits<unsigned>::max(); }
     class result {
         unsigned m_lbp;
         unsigned m_rbp;
         format   m_fmt;
     public:
         result():m_lbp(max_bp()), m_rbp(max_bp()) {}
-        result(format const & fmt):m_lbp(max_bp()), m_rbp(max_bp()), m_fmt(fmt) {}
+        result(format const & fmt):m_lbp(inf_bp()), m_rbp(inf_bp()), m_fmt(fmt) {}
         result(unsigned rbp, format const & fmt):m_lbp(max_bp()), m_rbp(rbp), m_fmt(fmt) {}
         result(unsigned lbp, unsigned rbp, format const & fmt):m_lbp(lbp), m_rbp(rbp), m_fmt(fmt) {}
         unsigned lbp() const { return m_lbp; }

src/frontends/lean/token_table.cpp

@@ -11,7 +11,7 @@ Author: Leonardo de Moura
 
 namespace lean {
 static unsigned g_arrow_prec = 25;
-static unsigned g_max_prec   = std::numeric_limits<unsigned>::max();
+static unsigned g_max_prec   = 1024;
 static unsigned g_plus_prec  = 65;
 static unsigned g_cup_prec   = 60;
 unsigned get_max_prec() { return g_max_prec; }

tests/lean/notation7.lean

@@ -0,0 +1,13 @@
+import logic
+open num
+
+constant f : num → num
+constant g : num → num → num
+
+notation A `:+1`:100000 := f A
+
+check g 0:+1:+1 (1:+1 + 2:+1):+1
+
+set_option pp.notation false
+
+check g 0:+1:+1 (1:+1 + 2:+1):+1

tests/lean/notation7.lean.expected.out

@@ -0,0 +1,2 @@
+g 0 :+1 :+1 (1 :+1 + 2 :+1) :+1 : num
+g (f (f 0)) (f (add (f 1) (f 2))) : num