diff --git a/Library/Homebrew/metafiles.rb b/Library/Homebrew/metafiles.rb
index 9f3a74239f..a321874cf2 100644
--- a/Library/Homebrew/metafiles.rb
+++ b/Library/Homebrew/metafiles.rb
@@ -1,27 +1,33 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 # Helper for checking if a file is considered a metadata file.
 module Metafiles
-  LICENSES = Set.new(%w[copying copyright license licence]).freeze
+  LICENSES = T.let(Set.new(%w[copying copyright license licence]).freeze, T::Set[String])
   # {https://github.com/github/markup#markups}
-  EXTENSIONS = Set.new(%w[
+  EXTENSIONS = T.let(Set.new(%w[
     .adoc .asc .asciidoc .creole .html .markdown .md .mdown .mediawiki .mkdn
     .org .pod .rdoc .rst .rtf .textile .txt .wiki
-  ]).freeze
-  BASENAMES = Set.new(%w[about authors changelog changes history news notes notice readme todo]).freeze
+  ]).freeze, T::Set[String])
+  BASENAMES = T.let(Set.new(%w[
+    about authors changelog changes history news notes notice readme todo
+  ]).freeze, T::Set[String])
 
   module_function
 
+  sig { params(file: String).returns(T::Boolean) }
   def list?(file)
     return false if %w[.DS_Store INSTALL_RECEIPT.json].include?(file)
 
     !copy?(file)
   end
 
+  sig { params(file: String).returns(T::Boolean) }
   def copy?(file)
     file = file.downcase
-    return true if LICENSES.include? file.split(/\.|-/).first
+    license = file.split(/\.|-/).first
+    return false unless license
+    return true if LICENSES.include?(license)
 
     ext  = File.extname(file)
     file = File.basename(file, ext) if EXTENSIONS.include?(ext)