diff --git a/Library/Homebrew/checksum.rb b/Library/Homebrew/checksum.rb
index 30d0d2f22e..b79cc30127 100644
--- a/Library/Homebrew/checksum.rb
+++ b/Library/Homebrew/checksum.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 # A formula's checksum.
@@ -7,14 +7,17 @@
 class Checksum
   extend Forwardable
 
+  sig { returns(String) }
   attr_reader :hexdigest
 
+  sig { params(hexdigest: String).void }
   def initialize(hexdigest)
-    @hexdigest = hexdigest.downcase
+    @hexdigest = T.let(hexdigest.downcase, String)
   end
 
   delegate [:empty?, :to_s, :length, :[]] => :@hexdigest
 
+  sig { params(other: T.any(String, Checksum, Symbol)).returns(T::Boolean) }
   def ==(other)
     case other
     when String