diff --git a/Library/Homebrew/extend/os/linux/dev-cmd/update-test.rb b/Library/Homebrew/extend/os/linux/dev-cmd/update-test.rb
index ebdbbd8f88..0f711eeafd 100644
--- a/Library/Homebrew/extend/os/linux/dev-cmd/update-test.rb
+++ b/Library/Homebrew/extend/os/linux/dev-cmd/update-test.rb
@@ -1,18 +1,16 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 module Homebrew
   extend T::Sig
 
-  module_function
-
   class << self
     alias generic_git_tags git_tags
-  end
 
-  def git_tags
-    tags = generic_git_tags
-    tags = Utils.popen_read("git tag --list | sort -rV") if tags.blank?
-    tags
+    def git_tags
+      tags = generic_git_tags
+      tags = Utils.popen_read("git tag --list | sort -rV") if tags.blank?
+      tags
+    end
   end
 end
diff --git a/Library/Homebrew/extend/os/linux/diagnostic.rb b/Library/Homebrew/extend/os/linux/diagnostic.rb
index a4d69332d2..c68dbcc802 100644
--- a/Library/Homebrew/extend/os/linux/diagnostic.rb
+++ b/Library/Homebrew/extend/os/linux/diagnostic.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "tempfile"
@@ -46,7 +46,7 @@ module Homebrew
         f.write "#!/bin/sh\n"
         f.chmod 0700
         f.close
-        return if system f.path
+        return if system T.must(f.path)
 
         <<~EOS
           The directory #{HOMEBREW_TEMP} does not permit executing
@@ -56,12 +56,12 @@ module Homebrew
             echo 'export HOMEBREW_TEMP=~/tmp' >> #{shell_profile}
         EOS
       ensure
-        f.unlink
+        f&.unlink
       end
 
       def check_xdg_data_dirs
-        return if ENV["XDG_DATA_DIRS"].blank?
-        return if ENV["XDG_DATA_DIRS"].split("/").include?(HOMEBREW_PREFIX/"share")
+        xdg_data_dirs = ENV["XDG_DATA_DIRS"]
+        return if xdg_data_dirs.blank? || xdg_data_dirs.split("/").include?(HOMEBREW_PREFIX/"share")
 
         <<~EOS
           Homebrew's share was not found in your XDG_DATA_DIRS but you have
diff --git a/Library/Homebrew/extend/os/linux/hardware/cpu.rb b/Library/Homebrew/extend/os/linux/hardware/cpu.rb
index 0e6805a6e0..253b7571ec 100644
--- a/Library/Homebrew/extend/os/linux/hardware/cpu.rb
+++ b/Library/Homebrew/extend/os/linux/hardware/cpu.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 module Hardware
@@ -111,6 +111,7 @@ module Hardware
       end
 
       %w[aes altivec avx avx2 lm ssse3 sse4_2].each do |flag|
+        T.bind(self, T.class_of(Hardware::CPU))
         define_method("#{flag}?") { flags.include? flag }
       end
 
diff --git a/Library/Homebrew/extend/os/mac/diagnostic.rb b/Library/Homebrew/extend/os/mac/diagnostic.rb
index 97350b4a89..1cbc907f33 100644
--- a/Library/Homebrew/extend/os/mac/diagnostic.rb
+++ b/Library/Homebrew/extend/os/mac/diagnostic.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 module Homebrew
@@ -379,7 +379,7 @@ module Homebrew
             real_tmp = tmp.realpath.parent
             where_tmp = volumes.which real_tmp
           ensure
-            Dir.delete tmp
+            Dir.delete tmp.to_s
           end
         rescue
           return