diff --git a/Library/Homebrew/api/cask.rb b/Library/Homebrew/api/cask.rb
index baaf2f0d8e..17ca86b716 100644
--- a/Library/Homebrew/api/cask.rb
+++ b/Library/Homebrew/api/cask.rb
@@ -60,7 +60,7 @@ module Homebrew
         end
         private :download_and_cache_data!
 
-        sig { returns(Hash) }
+        sig { returns(T::Hash[String, Hash]) }
         def all_casks
           unless cache.key?("casks")
             json_updated = download_and_cache_data!
diff --git a/Library/Homebrew/cask/cask_loader.rb b/Library/Homebrew/cask/cask_loader.rb
index 4aa25a9bf0..3eb99e2dd9 100644
--- a/Library/Homebrew/cask/cask_loader.rb
+++ b/Library/Homebrew/cask/cask_loader.rb
@@ -281,7 +281,11 @@ module Cask
     class FromAPILoader
       include ILoader
 
-      attr_reader :token, :path
+      sig { returns(String) }
+      attr_reader :token
+
+      sig { returns(Pathname) }
+      attr_reader :path
 
       sig { returns(T.nilable(Hash)) }
       attr_reader :from_json
@@ -296,7 +300,7 @@ module Cask
 
         return unless (match = ref.match(HOMEBREW_MAIN_TAP_CASK_REGEX))
 
-        token = match[:token]
+        token = T.cast(match[:token], String)
         return if !Homebrew::API::Cask.all_casks.key?(token) && !Homebrew::API::Cask.all_renames.key?(token)
 
         ref = "#{CoreCaskTap.instance}/#{token}"
@@ -313,7 +317,7 @@ module Cask
       end
 
       def load(config:)
-        json_cask = from_json || Homebrew::API::Cask.all_casks[token]
+        json_cask = from_json || Homebrew::API::Cask.all_casks.fetch(token)
 
         cask_options = {
           loaded_from_api: true,
diff --git a/Library/Homebrew/cli/named_args.rb b/Library/Homebrew/cli/named_args.rb
index 04f81687ba..9b470f4f2e 100644
--- a/Library/Homebrew/cli/named_args.rb
+++ b/Library/Homebrew/cli/named_args.rb
@@ -256,11 +256,11 @@ module Homebrew
               paths = []
 
               if formula_path.exist? ||
-                 (!CoreTap.instance.installed? && Homebrew::API::Formula.all_formulae.key?(path.basename))
+                 (!CoreTap.instance.installed? && Homebrew::API::Formula.all_formulae.key?(path.basename.to_s))
                 paths << formula_path
               end
               if cask_path.exist? ||
-                 (!CoreCaskTap.instance.installed? && Homebrew::API::Cask.all_casks.key?(path.basename))
+                 (!CoreCaskTap.instance.installed? && Homebrew::API::Cask.all_casks.key?(path.basename.to_s))
                 paths << cask_path
               end