diff --git a/spec/compiler/parser/parser_spec.cr b/spec/compiler/parser/parser_spec.cr
index 05b572acea27..f637577c20a5 100644
--- a/spec/compiler/parser/parser_spec.cr
+++ b/spec/compiler/parser/parser_spec.cr
@@ -705,7 +705,10 @@ describe "Parser" do
   it_parses "lib LibC\nalias Foo = Bar\nend", LibDef.new("LibC", [Alias.new("Foo", "Bar".path)] of ASTNode)
   it_parses "lib LibC; struct Foo; include Bar; end; end", LibDef.new("LibC", [CStructOrUnionDef.new("Foo", Include.new("Bar".path))] of ASTNode)
 
+  it_parses "lib LibC\nfun SomeFun\nend", LibDef.new("LibC", [FunDef.new("SomeFun")] of ASTNode)
+
   it_parses "fun foo(x : Int32) : Int64\nx\nend", FunDef.new("foo", [Arg.new("x", restriction: "Int32".path)], "Int64".path, body: "x".var)
+  assert_syntax_error "fun Foo : Int64\nend"
 
   it_parses "lib LibC; {{ 1 }}; end", LibDef.new("LibC", body: [MacroExpression.new(1.int32)] of ASTNode)
   it_parses "lib LibC; {% if 1 %}2{% end %}; end", LibDef.new("LibC", body: [MacroIf.new(1.int32, MacroLiteral.new("2"))] of ASTNode)
@@ -1297,6 +1300,8 @@ describe "Parser" do
 
   it_parses "1 ** -x", Call.new(1.int32, "**", Call.new("x".call, "-"))
 
+  it_parses "foo.Bar", Call.new("foo".call, "Bar")
+
   assert_syntax_error "return do\nend", "unexpected token: do"
 
   %w(def macro class struct module fun alias abstract include extend lib).each do |keyword|
diff --git a/src/compiler/crystal/syntax/parser.cr b/src/compiler/crystal/syntax/parser.cr
index bdf7057cd542..87d481d57fc0 100644
--- a/src/compiler/crystal/syntax/parser.cr
+++ b/src/compiler/crystal/syntax/parser.cr
@@ -550,7 +550,7 @@ module Crystal
       end
     end
 
-    AtomicWithMethodCheck = [:IDENT, :"+", :"-", :"*", :"/", :"%", :"|", :"&", :"^", :"**", :"<<", :"<", :"<=", :"==", :"!=", :"=~", :"!~", :">>", :">", :">=", :"<=>", :"===", :"[]", :"[]=", :"[]?", :"["]
+    AtomicWithMethodCheck = [:IDENT, :CONST, :"+", :"-", :"*", :"/", :"%", :"|", :"&", :"^", :"**", :"<<", :"<", :"<=", :"==", :"!=", :"=~", :"!~", :">>", :">", :">=", :"<=>", :"===", :"[]", :"[]=", :"[]?", :"["]
 
     def parse_atomic_with_method
       location = @token.location
@@ -619,7 +619,12 @@ module Crystal
           elsif @token.type == :"["
             return parse_atomic_method_suffix(atomic, location)
           else
-            name = @token.type == :IDENT ? @token.value.to_s : @token.type.to_s
+            name = case @token.type
+                   when :IDENT, :CONST
+                     @token.value.to_s
+                   else
+                     @token.type.to_s
+                   end
             end_location = token_end_location
 
             @wants_regex = false
@@ -1026,7 +1031,7 @@ module Crystal
         when :fun
           check_type_declaration do
             check_not_inside_def("can't define fun inside def") do
-              parse_fun_def require_body: true
+              parse_fun_def top_level: true, require_body: true
             end
           end
         when :alias
@@ -4864,7 +4869,7 @@ module Crystal
         when :alias
           parse_alias
         when :fun
-          parse_fun_def
+          parse_fun_def(top_level: false)
         when :type
           parse_type_def
         when :struct
@@ -4918,14 +4923,21 @@ module Crystal
 
     IdentOrConst = [:IDENT, :CONST]
 
-    def parse_fun_def(require_body = false)
+    def parse_fun_def(top_level, require_body = false)
       location = @token.location
       doc = @token.doc
 
       push_def if require_body
 
       next_token_skip_space_or_newline
-      name = check_ident
+
+      name = if top_level
+               check_ident
+             else
+               check IdentOrConst
+               @token.value.to_s
+             end
+
       next_token_skip_space_or_newline
 
       if @token.type == :"="