diff --git a/Library/Homebrew/cask/artifact/relocated.rb b/Library/Homebrew/cask/artifact/relocated.rb
index 0642db0e2b..97bc0e8dda 100644
--- a/Library/Homebrew/cask/artifact/relocated.rb
+++ b/Library/Homebrew/cask/artifact/relocated.rb
@@ -13,7 +13,7 @@ module Cask
         source_string, target_hash = args
 
         if target_hash
-          raise CaskInvalidError unless target_hash.respond_to?(:keys)
+          raise CaskInvalidError.new(cask) unless target_hash.respond_to?(:keys)
 
           target_hash.assert_valid_keys(:target)
         end
diff --git a/Library/Homebrew/cask/config.rb b/Library/Homebrew/cask/config.rb
index ae3533e7a8..b546a44f48 100644
--- a/Library/Homebrew/cask/config.rb
+++ b/Library/Homebrew/cask/config.rb
@@ -78,6 +78,8 @@ module Cask
         key = k.to_sym
 
         if DEFAULT_DIRS.key?(key)
+          raise TypeError, "Invalid path for default dir #{k}: #{v.inspect}" if v.is_a?(Array)
+
           [key, Pathname(v).expand_path]
         else
           [key, v]
diff --git a/Library/Homebrew/cask/url.rb b/Library/Homebrew/cask/url.rb
index db93901c5b..fd4865f313 100644
--- a/Library/Homebrew/cask/url.rb
+++ b/Library/Homebrew/cask/url.rb
@@ -236,7 +236,7 @@ module Cask
     def raw_url_line
       return @raw_url_line if defined?(@raw_url_line)
 
-      @raw_url_line = Pathname(@caller_location.path)
+      @raw_url_line = Pathname(T.must(@caller_location.path))
                       .each_line
                       .drop(@caller_location.lineno - 1)
                       .first
diff --git a/Library/Homebrew/cmd/update-report.rb b/Library/Homebrew/cmd/update-report.rb
index b5fd1544de..6eef639aa9 100644
--- a/Library/Homebrew/cmd/update-report.rb
+++ b/Library/Homebrew/cmd/update-report.rb
@@ -320,7 +320,7 @@ module Homebrew
         next unless tap.installed?
 
         if tap.git_branch == "master" &&
-           (Date.parse(tap.git_repo.last_commit_date) <= Date.today.prev_month)
+           (Date.parse(T.must(tap.git_repo.last_commit_date)) <= Date.today.prev_month)
           ohai "#{tap.name} is old and unneeded, untapping to save space..."
           tap.uninstall
         else
diff --git a/Library/Homebrew/dependencies.rb b/Library/Homebrew/dependencies.rb
index 625a874210..1e69bfecdf 100644
--- a/Library/Homebrew/dependencies.rb
+++ b/Library/Homebrew/dependencies.rb
@@ -59,6 +59,8 @@ class Requirements < SimpleDelegator
         __getobj__.delete(req)
       end
     end
+    # see https://sorbet.org/docs/faq#how-can-i-fix-type-errors-that-arise-from-super
+    T.bind(self, T.untyped)
     super
     self
   end
diff --git a/Library/Homebrew/dev-cmd/bump-cask-pr.rb b/Library/Homebrew/dev-cmd/bump-cask-pr.rb
index 23efb2850e..71f377afda 100644
--- a/Library/Homebrew/dev-cmd/bump-cask-pr.rb
+++ b/Library/Homebrew/dev-cmd/bump-cask-pr.rb
@@ -177,7 +177,7 @@ module Homebrew
   sig {
     params(
       cask:              Cask::Cask,
-      new_hash:          T.nilable(String),
+      new_hash:          T.any(NilClass, String, Symbol),
       new_version:       BumpVersionParser,
       replacement_pairs: T::Array[[T.any(Regexp, String), T.any(Regexp, String)]],
     ).returns(T::Array[[T.any(Regexp, String), T.any(Regexp, String)]])
@@ -234,7 +234,7 @@ module Homebrew
           end
         elsif new_hash
           opoo "Cask contains multiple hashes; only updating hash for current arch." if cask.on_system_blocks_exist?
-          replacement_pairs << [old_hash.to_s, new_hash]
+          replacement_pairs << [old_hash.to_s, new_hash.to_s]
         end
       end
     end
diff --git a/Library/Homebrew/extend/pathname.rb b/Library/Homebrew/extend/pathname.rb
index b169d984d0..c2b5a8a933 100644
--- a/Library/Homebrew/extend/pathname.rb
+++ b/Library/Homebrew/extend/pathname.rb
@@ -126,7 +126,7 @@ class Pathname
     #   https://bugs.ruby-lang.org/issues/7707
     # In that case, use the system "mv" command.
     if src.symlink?
-      raise unless Kernel.system "mv", src, dst
+      raise unless Kernel.system "mv", src.to_s, dst
     else
       FileUtils.mv src, dst
     end
diff --git a/Library/Homebrew/extend/predicable.rbi b/Library/Homebrew/extend/predicable.rbi
index cd5e165e4c..027500f579 100644
--- a/Library/Homebrew/extend/predicable.rbi
+++ b/Library/Homebrew/extend/predicable.rbi
@@ -1,5 +1,6 @@
 # typed: strict
 
 module Predicable
-  requires_ancestor { Class }
+  include Kernel
+  requires_ancestor { Module }
 end
diff --git a/Library/Homebrew/formula.rb b/Library/Homebrew/formula.rb
index e7b757c5e8..631c47fbc2 100644
--- a/Library/Homebrew/formula.rb
+++ b/Library/Homebrew/formula.rb
@@ -343,7 +343,7 @@ class Formula
 
   # The path that was specified to find this formula.
   def specified_path
-    default_specified_path = Pathname(alias_path) if alias_path.present?
+    default_specified_path = Pathname(T.must(alias_path)) if alias_path.present?
     default_specified_path ||= @unresolved_path
 
     return default_specified_path if default_specified_path.presence&.exist?
diff --git a/Library/Homebrew/language/node.rb b/Library/Homebrew/language/node.rb
index 5974e3bc25..3e90e2fe94 100644
--- a/Library/Homebrew/language/node.rb
+++ b/Library/Homebrew/language/node.rb
@@ -17,7 +17,8 @@ module Language
       # fed to `npm install` only symlinks are created linking back to that
       # directory, consequently breaking that assumption. We require a tarball
       # because npm install creates a "real" installation when fed a tarball.
-      if (package = Pathname("package.json")) && package.exist?
+      package = Pathname("package.json")
+      if package.exist?
         begin
           pkg_json = JSON.parse(package.read)
         rescue JSON::ParserError
diff --git a/Library/Homebrew/lazy_object.rb b/Library/Homebrew/lazy_object.rb
index 4dfcbdb4e6..831fb9fe74 100644
--- a/Library/Homebrew/lazy_object.rb
+++ b/Library/Homebrew/lazy_object.rb
@@ -23,6 +23,8 @@ class LazyObject < Delegator
 
   # Forward to the inner object to make lazy objects type-checkable.
   def is_a?(klass)
+    # see https://sorbet.org/docs/faq#how-can-i-fix-type-errors-that-arise-from-super
+    T.bind(self, T.untyped)
     __getobj__.is_a?(klass) || super
   end
 end
diff --git a/Library/Homebrew/macos_version.rb b/Library/Homebrew/macos_version.rb
index f728b610ca..b871c3d0c7 100644
--- a/Library/Homebrew/macos_version.rb
+++ b/Library/Homebrew/macos_version.rb
@@ -42,7 +42,7 @@ class MacOSVersion < Version
   def initialize(version)
     raise MacOSVersion::Error, version unless /\A1\d+(?:\.\d+){0,2}\Z/.match?(version)
 
-    super(version)
+    super(T.must(version))
 
     @comparison_cache = {}
   end
diff --git a/Library/Homebrew/software_spec.rb b/Library/Homebrew/software_spec.rb
index 016c80382e..4af61b3d72 100644
--- a/Library/Homebrew/software_spec.rb
+++ b/Library/Homebrew/software_spec.rb
@@ -541,11 +541,11 @@ class BottleSpecification
   end
   alias eql? ==
 
-  sig { params(tag: Utils::Bottles::Tag).returns(T.any(Symbol, String)) }
+  sig { params(tag: Utils::Bottles::Tag).returns(String) }
   def tag_to_cellar(tag = Utils::Bottles.tag)
     spec = collector.specification_for(tag)
     if spec.present?
-      spec.cellar
+      spec.cellar.to_s
     else
       tag.default_cellar
     end
diff --git a/Library/Homebrew/sorbet/parlour.rb b/Library/Homebrew/sorbet/parlour.rb
index 6c64b82b53..66ca7aa820 100644
--- a/Library/Homebrew/sorbet/parlour.rb
+++ b/Library/Homebrew/sorbet/parlour.rb
@@ -10,7 +10,7 @@ end
 module Homebrew
   # Parlour type signature generator helper class for Homebrew.
   module Parlour
-    ROOT_DIR = T.let(Pathname(__dir__).parent.realpath.freeze, Pathname).freeze
+    ROOT_DIR = T.let(Pathname(T.must(__dir__)).parent.realpath.freeze, Pathname).freeze
 
     sig { returns(T::Array[Parser::AST::Node]) }
     def self.ast_list
diff --git a/Library/Homebrew/unpack_strategy.rb b/Library/Homebrew/unpack_strategy.rb
index 3f6f93d61f..d52d633db8 100644
--- a/Library/Homebrew/unpack_strategy.rb
+++ b/Library/Homebrew/unpack_strategy.rb
@@ -132,7 +132,7 @@ module UnpackStrategy
 
       children = tmp_unpack_dir.children
 
-      if children.count == 1 && !children.first.directory?
+      if children.size == 1 && !children.fetch(0).directory?
         s = UnpackStrategy.detect(children.first, prioritize_extension: prioritize_extension)
 
         s.extract_nestedly(to: to, verbose: verbose, prioritize_extension: prioritize_extension)
diff --git a/Library/Homebrew/unversioned_cask_checker.rb b/Library/Homebrew/unversioned_cask_checker.rb
index fb3d02d040..842181365e 100644
--- a/Library/Homebrew/unversioned_cask_checker.rb
+++ b/Library/Homebrew/unversioned_cask_checker.rb
@@ -158,7 +158,7 @@ module Homebrew
             top_level_info_plist_paths.each(&parse_info_plist)
           ensure
             Cask::Utils.gain_permissions_remove(extract_dir)
-            extract_dir.mkpath
+            Pathname(extract_dir).mkpath
           end
         end
 
@@ -252,7 +252,7 @@ module Homebrew
                                  }.uniq
           ensure
             Cask::Utils.gain_permissions_remove(extract_dir)
-            extract_dir.mkpath
+            Pathname(extract_dir).mkpath
           end
         end
 
diff --git a/Library/Homebrew/utils/bottles.rb b/Library/Homebrew/utils/bottles.rb
index 1c11ecf630..a4ee5d9e7f 100644
--- a/Library/Homebrew/utils/bottles.rb
+++ b/Library/Homebrew/utils/bottles.rb
@@ -65,12 +65,14 @@ module Utils
           receipt_file = file_from_bottle(bottle_file, receipt_file_path)
           tap = Tab.from_file_content(receipt_file, "#{bottle_file}/#{receipt_file_path}").tap
           "#{tap}/#{name}" if tap.present? && !tap.core_tap?
-        elsif (bottle_json_path = Pathname(bottle_file.sub(/\.(\d+\.)?tar\.gz$/, ".json"))) &&
-              bottle_json_path.exist? &&
+        else
+          bottle_json_path = Pathname(bottle_file.sub(/\.(\d+\.)?tar\.gz$/, ".json"))
+          if bottle_json_path.exist? &&
               (bottle_json_path_contents = bottle_json_path.read.presence) &&
               (bottle_json = JSON.parse(bottle_json_path_contents).presence) &&
               bottle_json.is_a?(Hash)
-          bottle_json.keys.first.presence
+            bottle_json.keys.first.presence
+          end
         end
         full_name ||= name
 
diff --git a/Library/Homebrew/yard/templates/default/docstring/html/setup.rb b/Library/Homebrew/yard/templates/default/docstring/html/setup.rb
index 27272f9ff6..860f921ef5 100644
--- a/Library/Homebrew/yard/templates/default/docstring/html/setup.rb
+++ b/Library/Homebrew/yard/templates/default/docstring/html/setup.rb
@@ -4,7 +4,7 @@
 def init
   # `sorbet` is available transitively through the `yard-sorbet` plugin, but we're
   # outside of the standalone sorbet config, so `checked` is enabled by default
-  T.bind(self, YARD::Templates::Template, checked: false)
+  T.bind(self, T.all(Class, YARD::Templates::Template), checked: false)
   super
 
   return if sections.empty?