diff --git a/Library/Homebrew/development_tools.rb b/Library/Homebrew/development_tools.rb
index fc78720816..89fd30e568 100644
--- a/Library/Homebrew/development_tools.rb
+++ b/Library/Homebrew/development_tools.rb
@@ -108,7 +108,7 @@ class DevelopmentTools
       true
     end
 
-    sig { returns(T::Hash[String, T.untyped]) }
+    sig { returns(T::Hash[String, T.nilable(String)]) }
     def build_system_info
       {
         "os"         => ENV["HOMEBREW_SYSTEM"],
diff --git a/Library/Homebrew/os/mac.rb b/Library/Homebrew/os/mac.rb
index 47aaaf722a..4f3b153c84 100644
--- a/Library/Homebrew/os/mac.rb
+++ b/Library/Homebrew/os/mac.rb
@@ -75,6 +75,7 @@ module OS
       languages.first
     end
 
+    sig { returns(String) }
     def active_developer_dir
       @active_developer_dir ||= Utils.popen_read("/usr/bin/xcode-select", "-print-path").strip
     end
diff --git a/Library/Homebrew/os/mac/xcode.rb b/Library/Homebrew/os/mac/xcode.rb
index fb36eabcf3..4e8851d858 100755
--- a/Library/Homebrew/os/mac/xcode.rb
+++ b/Library/Homebrew/os/mac/xcode.rb
@@ -91,6 +91,9 @@ module OS
       # directory or nil if Xcode.app is not installed.
       sig { returns(T.nilable(Pathname)) }
       def prefix
+        return @prefix if defined?(@prefix)
+
+        @prefix = T.let(@prefix, T.nilable(Pathname))
         @prefix ||=
           begin
             dir = MacOS.active_developer_dir
diff --git a/Library/Homebrew/sorbet/rbi/upstream.rbi b/Library/Homebrew/sorbet/rbi/upstream.rbi
index dbade1d0dc..28a1b9b5b6 100644
--- a/Library/Homebrew/sorbet/rbi/upstream.rbi
+++ b/Library/Homebrew/sorbet/rbi/upstream.rbi
@@ -21,3 +21,14 @@ class Module
   end
   def define_method(arg0, arg1=T.unsafe(nil), &blk); end
 end
+
+class Pathname
+  # https://github.com/sorbet/sorbet/pull/4660
+  sig do
+    params(
+        consider_symlink: T::Boolean,
+    )
+    .returns(Pathname)
+  end
+  def cleanpath(consider_symlink=T.unsafe(nil)); end
+end