diff --git a/Library/Homebrew/cask/info.rb b/Library/Homebrew/cask/info.rb
index acac2cbc29096..937d620c922be 100644
--- a/Library/Homebrew/cask/info.rb
+++ b/Library/Homebrew/cask/info.rb
@@ -1,10 +1,11 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "json"
 
 module Cask
   class Info
+    sig { params(cask: Cask).returns(String) }
     def self.get_info(cask)
       require "cask/installer"
 
@@ -25,6 +26,7 @@ def self.get_info(cask)
       output
     end
 
+    sig { params(cask: Cask).void }
     def self.info(cask)
       puts get_info(cask)
 
@@ -32,16 +34,19 @@ def self.info(cask)
       ::Utils::Analytics.cask_output(cask, args: Homebrew::CLI::Args.new)
     end
 
+    sig { params(cask: Cask).returns(String) }
     def self.title_info(cask)
       title = "#{oh1_title(cask.token)}: #{cask.version}"
       title += " (auto_updates)" if cask.auto_updates
       title
     end
 
+    sig { params(cask: Cask).returns(String) }
     def self.installation_info(cask)
       return "Not installed" unless cask.installed?
+      return "No installed version" unless (installed_version = cask.installed_version).present?
 
-      versioned_staged_path = cask.caskroom_path.join(cask.installed_version)
+      versioned_staged_path = cask.caskroom_path.join(installed_version)
 
       return "Installed\n#{versioned_staged_path} (#{Formatter.error("does not exist")})\n" unless versioned_staged_path.exist?
 
@@ -55,6 +60,7 @@ def self.installation_info(cask)
       info.join("\n")
     end
 
+    sig { params(cask: Cask).returns(String) }
     def self.name_info(cask)
       <<~EOS
         #{ohai_title((cask.name.size > 1) ? "Names" : "Name")}
@@ -62,6 +68,7 @@ def self.name_info(cask)
       EOS
     end
 
+    sig { params(cask: Cask).returns(String) }
     def self.desc_info(cask)
       <<~EOS
         #{ohai_title("Description")}
@@ -69,6 +76,7 @@ def self.desc_info(cask)
       EOS
     end
 
+    sig { params(cask: Cask).returns(T.nilable(String)) }
     def self.language_info(cask)
       return if cask.languages.empty?
 
@@ -78,6 +86,7 @@ def self.language_info(cask)
       EOS
     end
 
+    sig { params(cask: Cask).returns(T.nilable(String)) }
     def self.repo_info(cask)
       return if cask.tap.nil?
 
@@ -90,6 +99,7 @@ def self.repo_info(cask)
       "From: #{Formatter.url(url)}"
     end
 
+    sig { params(cask: Cask).returns(String) }
     def self.artifact_info(cask)
       artifact_output = ohai_title("Artifacts").dup
       cask.artifacts.each do |artifact|
diff --git a/Library/Homebrew/cmd/cleanup.rb b/Library/Homebrew/cmd/cleanup.rb
index 4430137479c72..4d75cfaa5ee34 100644
--- a/Library/Homebrew/cmd/cleanup.rb
+++ b/Library/Homebrew/cmd/cleanup.rb
@@ -8,7 +8,7 @@ module Homebrew
   module Cmd
     class CleanupCmd < AbstractCommand
       cmd_args do
-        days = Homebrew::EnvConfig::ENVS[:HOMEBREW_CLEANUP_MAX_AGE_DAYS][:default]
+        days = Homebrew::EnvConfig::ENVS[:HOMEBREW_CLEANUP_MAX_AGE_DAYS]&.dig(:default)
         description <<~EOS
           Remove stale lock files and outdated downloads for all formulae and casks,
           and remove old versions of installed formulae. If arguments are specified,
diff --git a/Library/Homebrew/env_config.rb b/Library/Homebrew/env_config.rb
index 68cdcef9abc86..58cff02330250 100644
--- a/Library/Homebrew/env_config.rb
+++ b/Library/Homebrew/env_config.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module Homebrew
@@ -8,7 +8,7 @@ module Homebrew
   module EnvConfig
     module_function
 
-    ENVS = {
+    ENVS = T.let({
       HOMEBREW_ALLOWED_TAPS:                     {
         description: "A space-separated list of taps. Homebrew will refuse to install a " \
                      "formula unless it and all of its dependencies are in an official tap " \
@@ -481,7 +481,7 @@ module EnvConfig
         description: "A comma-separated list of hostnames and domain names excluded " \
                      "from proxying by `curl`(1), `git`(1) and `svn`(1) when downloading through Homebrew.",
       },
-    }.freeze
+    }.freeze, T::Hash[Symbol, T::Hash[Symbol, T.untyped]])
 
     sig { params(env: Symbol, hash: T::Hash[Symbol, T.untyped]).returns(String) }
     def env_method_name(env, hash)
@@ -492,10 +492,10 @@ def env_method_name(env, hash)
       method_name
     end
 
-    CUSTOM_IMPLEMENTATIONS = Set.new([
+    CUSTOM_IMPLEMENTATIONS = T.let(Set.new([
       :HOMEBREW_MAKE_JOBS,
       :HOMEBREW_CASK_OPTS,
-    ]).freeze
+    ]).freeze, T::Set[Symbol])
 
     ENVS.each do |env, hash|
       # Needs a custom implementation.
diff --git a/Library/Homebrew/official_taps.rb b/Library/Homebrew/official_taps.rb
index 510c89ad23378..65c0473342280 100644
--- a/Library/Homebrew/official_taps.rb
+++ b/Library/Homebrew/official_taps.rb
@@ -1,17 +1,17 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 OFFICIAL_CASK_TAPS = %w[
   cask
 ].freeze
 
-OFFICIAL_CMD_TAPS = {
+OFFICIAL_CMD_TAPS = T.let({
   "homebrew/aliases"           => ["alias", "unalias"],
   "homebrew/bundle"            => ["bundle"],
   "homebrew/command-not-found" => ["command-not-found-init", "which-formula", "which-update"],
   "homebrew/test-bot"          => ["test-bot"],
   "homebrew/services"          => ["services"],
-}.freeze
+}.freeze, T::Hash[String, T::Array[String]])
 
 DEPRECATED_OFFICIAL_TAPS = %w[
   apache
diff --git a/Library/Homebrew/os.rb b/Library/Homebrew/os.rb
index 6dfeeb460faec..a22add846fd4a 100644
--- a/Library/Homebrew/os.rb
+++ b/Library/Homebrew/os.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "version"
@@ -31,7 +31,7 @@ def self.linux?
   sig { returns(Version) }
   def self.kernel_version
     require "utils/popen"
-    @kernel_version ||= Version.new(Utils.safe_popen_read("uname", "-r").chomp)
+    @kernel_version ||= T.let(Version.new(Utils.safe_popen_read("uname", "-r").chomp), T.nilable(Version))
   end
 
   # Get the kernel name.
@@ -40,10 +40,10 @@ def self.kernel_version
   sig { returns(String) }
   def self.kernel_name
     require "utils/popen"
-    @kernel_name ||= Utils.safe_popen_read("uname", "-s").chomp
+    @kernel_name ||= T.let(Utils.safe_popen_read("uname", "-s").chomp, T.nilable(String))
   end
 
-  ::OS_VERSION = ENV.fetch("HOMEBREW_OS_VERSION").freeze
+  ::OS_VERSION = T.let(ENV.fetch("HOMEBREW_OS_VERSION").freeze, String)
 
   # See Linux-CI.md
   LINUX_CI_OS_VERSION = "Ubuntu 22.04"
diff --git a/Library/Homebrew/utils/github/actions.rb b/Library/Homebrew/utils/github/actions.rb
index 3d6e57cc47db1..9be540dc58b28 100644
--- a/Library/Homebrew/utils/github/actions.rb
+++ b/Library/Homebrew/utils/github/actions.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "securerandom"
@@ -85,13 +85,13 @@ def initialize(type, message, file: nil, title: nil, line: nil, end_line: nil, c
         raise ArgumentError, "Unsupported type: #{type.inspect}" if ANNOTATION_TYPES.exclude?(type)
 
         @type = type
-        @message = Tty.strip_ansi(message)
-        @file = self.class.path_relative_to_workspace(file) if file.present?
-        @title = Tty.strip_ansi(title) if title
-        @line = Integer(line) if line
-        @end_line = Integer(end_line) if end_line
-        @column = Integer(column) if column
-        @end_column = Integer(end_column) if end_column
+        @message = T.let(Tty.strip_ansi(message), String)
+        @file = T.let(self.class.path_relative_to_workspace(file), T.nilable(Pathname)) if file.present?
+        @title = T.let(Tty.strip_ansi(title), String) if title
+        @line = T.let(Integer(line), Integer) if line
+        @end_line = T.let(Integer(end_line), Integer) if end_line
+        @column = T.let(Integer(column), Integer) if column
+        @end_column = T.let(Integer(end_column), Integer) if end_column
       end
 
       sig { returns(String) }
diff --git a/Library/Homebrew/utils/github/artifacts.rb b/Library/Homebrew/utils/github/artifacts.rb
index 9e0756a5f1a8f..607ee521f9bc6 100644
--- a/Library/Homebrew/utils/github/artifacts.rb
+++ b/Library/Homebrew/utils/github/artifacts.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "download_strategy"
@@ -24,12 +24,14 @@ def self.download_artifact(url, artifact_id)
 
 # Strategy for downloading an artifact from GitHub Actions.
 class GitHubArtifactDownloadStrategy < AbstractFileDownloadStrategy
+  sig { params(url: String, artifact_id: String, token: String).void }
   def initialize(url, artifact_id, token:)
     super(url, "artifact", artifact_id)
-    @cache = HOMEBREW_CACHE/"gh-actions-artifact"
-    @token = token
+    @cache = T.let(HOMEBREW_CACHE/"gh-actions-artifact", Pathname)
+    @token = T.let(token, String)
   end
 
+  sig { params(timeout: T.nilable(Integer)).void }
   def fetch(timeout: nil)
     ohai "Downloading #{url}"
     if cached_location.exist?
diff --git a/Library/Homebrew/utils/tar.rb b/Library/Homebrew/utils/tar.rb
index bf4df5e664943..dd1dca89dcce4 100644
--- a/Library/Homebrew/utils/tar.rb
+++ b/Library/Homebrew/utils/tar.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "system_command"
@@ -11,18 +11,21 @@ class << self
 
       TAR_FILE_EXTENSIONS = %w[.tar .tb2 .tbz .tbz2 .tgz .tlz .txz .tZ].freeze
 
+      sig { returns(T::Boolean) }
       def available?
         executable.present?
       end
 
+      sig { returns(T.nilable(Pathname)) }
       def executable
         return @executable if defined?(@executable)
 
         gnu_tar_gtar_path = HOMEBREW_PREFIX/"opt/gnu-tar/bin/gtar"
         gnu_tar_gtar = gnu_tar_gtar_path if gnu_tar_gtar_path.executable?
-        @executable = which("gtar") || gnu_tar_gtar || which("tar")
+        @executable = T.let((which("gtar") || gnu_tar_gtar || which("tar")), T.nilable(Pathname))
       end
 
+      sig { params(path: T.any(Pathname, String)).void }
       def validate_file(path)
         return unless available?
 
@@ -33,6 +36,7 @@ def validate_file(path)
         odie "#{path} is not a valid tar file!" if !status.success? || stdout.blank?
       end
 
+      sig { void }
       def clear_executable_cache
         remove_instance_variable(:@executable) if defined?(@executable)
       end