diff --git a/Library/Homebrew/utils/analytics.rb b/Library/Homebrew/utils/analytics.rb
index f7fb2e6564..52393ecd54 100644
--- a/Library/Homebrew/utils/analytics.rb
+++ b/Library/Homebrew/utils/analytics.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "context"
@@ -60,7 +60,7 @@ module Utils
           puts Utils.popen_read(curl, *args, url)
         else
           pid = spawn curl, *args, url
-          Process.detach T.must(pid)
+          Process.detach(pid)
         end
       end
 
@@ -161,52 +161,62 @@ module Utils
         report_influx(:test_bot_test, tags, fields)
       end
 
+      sig { returns(T::Boolean) }
       def influx_message_displayed?
         config_true?(:influxanalyticsmessage)
       end
 
+      sig { returns(T::Boolean) }
       def messages_displayed?
-        config_true?(:analyticsmessage) &&
+        !!(config_true?(:analyticsmessage) &&
           config_true?(:caskanalyticsmessage) &&
-          influx_message_displayed?
+          influx_message_displayed?)
       end
 
+      sig { returns(T::Boolean) }
       def disabled?
         return true if Homebrew::EnvConfig.no_analytics?
 
         config_true?(:analyticsdisabled)
       end
 
+      sig { returns(T::Boolean) }
       def not_this_run?
         ENV["HOMEBREW_NO_ANALYTICS_THIS_RUN"].present?
       end
 
+      sig { returns(T::Boolean) }
       def no_message_output?
         # Used by Homebrew/install
         ENV["HOMEBREW_NO_ANALYTICS_MESSAGE_OUTPUT"].present?
       end
 
+      sig { void }
       def messages_displayed!
         Homebrew::Settings.write :analyticsmessage, true
         Homebrew::Settings.write :caskanalyticsmessage, true
         Homebrew::Settings.write :influxanalyticsmessage, true
       end
 
+      sig { void }
       def enable!
         Homebrew::Settings.write :analyticsdisabled, false
         delete_uuid!
         messages_displayed!
       end
 
+      sig { void }
       def disable!
         Homebrew::Settings.write :analyticsdisabled, true
         delete_uuid!
       end
 
+      sig { void }
       def delete_uuid!
         Homebrew::Settings.delete :analyticsuuid
       end
 
+      sig { params(args: Homebrew::Cmd::Info::Args, filter: T.nilable(String)).void }
       def output(args:, filter: nil)
         require "api"
 
@@ -244,6 +254,7 @@ module Utils
         table_output(category, days, results, os_version:, cask_install:)
       end
 
+      sig { params(json: T::Hash[String, T.untyped], args: Homebrew::Cmd::Info::Args).void }
       def output_analytics(json, args:)
         full_analytics = args.analytics? || verbose?
 
@@ -273,6 +284,7 @@ module Utils
       # It relies on screen scraping some GitHub HTML that's not available as an API.
       # This seems very likely to break in the future.
       # That said, it's the only way to get the data we want right now.
+      sig { params(formula: Formula, args: Homebrew::Cmd::Info::Args).void }
       def output_github_packages_downloads(formula, args:)
         return unless args.github_packages_downloads?
         return unless formula.core_formula?
@@ -316,6 +328,7 @@ module Utils
         puts "#{number_readable(thirty_day_download_count)} (30 days)"
       end
 
+      sig { params(formula: Formula, args: Homebrew::Cmd::Info::Args).void }
       def formula_output(formula, args:)
         return if Homebrew::EnvConfig.no_analytics? || Homebrew::EnvConfig.no_github_api?
 
@@ -331,6 +344,7 @@ module Utils
         nil
       end
 
+      sig { params(cask: Cask::Cask, args: Homebrew::Cmd::Info::Args).void }
       def cask_output(cask, args:)
         return if Homebrew::EnvConfig.no_analytics? || Homebrew::EnvConfig.no_github_api?
 
@@ -388,6 +402,12 @@ module Utils
         end
       end
 
+      sig {
+        params(
+          category: String, days: String, results: T::Hash[String, Integer], os_version: T::Boolean,
+          cask_install: T::Boolean
+        ).void
+      }
       def table_output(category, days, results, os_version: false, cask_install: false)
         oh1 "#{category} (#{days} days)"
         total_count = results.values.inject("+")
@@ -475,14 +495,17 @@ module Utils
              "#{formatted_total_count_footer} | #{formatted_total_percent_footer}%"
       end
 
+      sig { params(key: Symbol).returns(T::Boolean) }
       def config_true?(key)
         Homebrew::Settings.read(key) == "true"
       end
 
+      sig { params(count: Integer).returns(String) }
       def format_count(count)
         count.to_s.reverse.gsub(/(\d{3})(?=\d)/, '\\1,').reverse
       end
 
+      sig { params(percent: T.any(Integer, Float)).returns(String) }
       def format_percent(percent)
         format("%<percent>.2f", percent:)
       end
diff --git a/Library/Homebrew/utils/fork.rb b/Library/Homebrew/utils/fork.rb
index 8c19ac282f..5da2621622 100644
--- a/Library/Homebrew/utils/fork.rb
+++ b/Library/Homebrew/utils/fork.rb
@@ -1,10 +1,11 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "fcntl"
 require "utils/socket"
 
 module Utils
+  sig { params(child_error: T::Hash[String, T.untyped]).returns(Exception) }
   def self.rewrite_child_error(child_error)
     inner_class = Object.const_get(child_error["json_class"])
     error = if child_error["cmd"] && inner_class == ErrorDuringExecution
@@ -33,7 +34,11 @@ module Utils
   # When using this function, remember to call `exec` as soon as reasonably possible.
   # This function does not protect against the pitfalls of what you can do pre-exec in a fork.
   # See `man fork` for more information.
-  def self.safe_fork(directory: nil, yield_parent: false)
+  sig {
+    params(directory: T.nilable(String), yield_parent: T::Boolean,
+           _blk: T.proc.params(arg0: T.nilable(String)).void).void
+  }
+  def self.safe_fork(directory: nil, yield_parent: false, &_blk)
     require "json/add/exception"
 
     block = proc do |tmpdir|
@@ -80,8 +85,6 @@ module Utils
           exit!(true)
         end
 
-        pid = T.must(pid)
-
         begin
           yield(nil) if yield_parent
 
diff --git a/Library/Homebrew/utils/pypi.rb b/Library/Homebrew/utils/pypi.rb
index 6432d8b8c4..9b0940ef2a 100644
--- a/Library/Homebrew/utils/pypi.rb
+++ b/Library/Homebrew/utils/pypi.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "utils/inreplace"
@@ -14,20 +14,20 @@ module PyPI
   class Package
     sig { params(package_string: String, is_url: T::Boolean, python_name: String).void }
     def initialize(package_string, is_url: false, python_name: "python")
-      @pypi_info = nil
+      @pypi_info = T.let(nil, T.nilable(T::Array[String]))
       @package_string = package_string
       @is_url = is_url
-      @is_pypi_url = package_string.start_with? PYTHONHOSTED_URL_PREFIX
+      @is_pypi_url = T.let(package_string.start_with?(PYTHONHOSTED_URL_PREFIX), T::Boolean)
       @python_name = python_name
     end
 
-    sig { returns(String) }
+    sig { returns(T.nilable(String)) }
     def name
       basic_metadata if @name.blank?
       @name
     end
 
-    sig { returns(T::Array[T.nilable(String)]) }
+    sig { returns(T.nilable(T::Array[String])) }
     def extras
       basic_metadata if @extras.blank?
       @extras
@@ -43,7 +43,7 @@ module PyPI
     def version=(new_version)
       raise ArgumentError, "can't update version for non-PyPI packages" unless valid_pypi_package?
 
-      @version = new_version
+      @version = T.let(new_version, T.nilable(String))
     end
 
     sig { returns(T::Boolean) }
@@ -97,8 +97,8 @@ module PyPI
     sig { returns(String) }
     def to_s
       if valid_pypi_package?
-        out = name
-        out += "[#{extras.join(",")}]" if extras.present?
+        out = T.must(name)
+        out += "[#{extras&.join(",")}]" if extras.present?
         out += "==#{version}" if version.present?
         out
       else
@@ -132,14 +132,15 @@ module PyPI
     private
 
     # Returns [name, [extras], version] for this package.
+    sig { returns(T.nilable(T.any(String, T::Array[String]))) }
     def basic_metadata
       if @is_pypi_url
         match = File.basename(@package_string).match(/^(.+)-([a-z\d.]+?)(?:.tar.gz|.zip)$/)
         raise ArgumentError, "Package should be a valid PyPI URL" if match.blank?
 
-        @name ||= PyPI.normalize_python_package match[1]
-        @extras ||= []
-        @version ||= match[2]
+        @name ||= T.let(PyPI.normalize_python_package(T.must(match[1])), T.nilable(String))
+        @extras ||= T.let([], T.nilable(T::Array[String]))
+        @version ||= T.let(match[2], T.nilable(String))
       elsif @is_url
         ensure_formula_installed!(@python_name)
 
@@ -162,9 +163,9 @@ module PyPI
 
         metadata = JSON.parse(pip_output)["install"].first["metadata"]
 
-        @name ||= PyPI.normalize_python_package metadata["name"]
-        @extras ||= []
-        @version ||= metadata["version"]
+        @name ||= T.let(PyPI.normalize_python_package(metadata["name"]), T.nilable(String))
+        @extras ||= T.let([], T.nilable(T::Array[String]))
+        @version ||= T.let(metadata["version"], T.nilable(String))
       else
         if @package_string.include? "=="
           name, version = @package_string.split("==")
@@ -180,7 +181,7 @@ module PyPI
           extras = []
         end
 
-        @name ||= PyPI.normalize_python_package name
+        @name ||= T.let(PyPI.normalize_python_package(T.must(name)), T.nilable(String))
         @extras ||= extras
         @version ||= version
       end
@@ -248,7 +249,7 @@ module PyPI
       missing_msg = "formulae required to update \"#{formula.name}\" resources: #{missing_dependencies.join(", ")}"
       odie "Missing #{missing_msg}" unless install_dependencies
       ohai "Installing #{missing_msg}"
-      missing_dependencies.each(&method(:ensure_formula_installed!))
+      missing_dependencies.each(&:ensure_formula_installed!)
     end
 
     python_deps = formula.deps
@@ -327,12 +328,12 @@ module PyPI
     # Resolve the dependency tree of all input packages
     show_info = !print_only && !silent
     ohai "Retrieving PyPI dependencies for \"#{input_packages.join(" ")}\"..." if show_info
-    found_packages = pip_report(input_packages, python_name:, print_stderr: verbose && show_info)
+    found_packages = pip_report(input_packages, python_name:, print_stderr: !!(verbose && show_info))
     # Resolve the dependency tree of excluded packages to prune the above
     exclude_packages.delete_if { |package| found_packages.exclude? package }
     ohai "Retrieving PyPI dependencies for excluded \"#{exclude_packages.join(" ")}\"..." if show_info
-    exclude_packages = pip_report(exclude_packages, python_name:, print_stderr: verbose && show_info)
-    exclude_packages += [Package.new(main_package.name)] unless main_package.nil?
+    exclude_packages = pip_report(exclude_packages, python_name:, print_stderr: !!(verbose && show_info))
+    exclude_packages += [Package.new(T.must(main_package.name))] unless main_package.nil?
 
     new_resource_blocks = ""
     found_packages.sort.each do |package|
@@ -404,12 +405,18 @@ module PyPI
     true
   end
 
+  sig { params(name: String).returns(String) }
   def self.normalize_python_package(name)
     # This normalization is defined in the PyPA packaging specifications;
     # https://packaging.python.org/en/latest/specifications/name-normalization/#name-normalization
     name.gsub(/[-_.]+/, "-").downcase
   end
 
+  sig {
+    params(
+      packages: T::Array[Package], python_name: String, print_stderr: T::Boolean,
+    ).returns(T::Array[Package])
+  }
   def self.pip_report(packages, python_name: "python", print_stderr: false)
     return [] if packages.blank?
 
@@ -430,6 +437,7 @@ module PyPI
     pip_report_to_packages(JSON.parse(pip_output)).uniq
   end
 
+  sig { params(report: T::Hash[String, T.untyped]).returns(T::Array[Package]) }
   def self.pip_report_to_packages(report)
     return [] if report.blank?
 
diff --git a/Library/Homebrew/utils/shell.rb b/Library/Homebrew/utils/shell.rb
index a621fbff8d..f5b3424a49 100644
--- a/Library/Homebrew/utils/shell.rb
+++ b/Library/Homebrew/utils/shell.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 module Utils
@@ -98,17 +98,20 @@ module Utils
       end
     end
 
-    SHELL_PROFILE_MAP = {
-      bash: "~/.profile",
-      csh:  "~/.cshrc",
-      fish: "~/.config/fish/config.fish",
-      ksh:  "~/.kshrc",
-      mksh: "~/.kshrc",
-      rc:   "~/.rcrc",
-      sh:   "~/.profile",
-      tcsh: "~/.tcshrc",
-      zsh:  "~/.zshrc",
-    }.freeze
+    SHELL_PROFILE_MAP = T.let(
+      {
+        bash: "~/.profile",
+        csh:  "~/.cshrc",
+        fish: "~/.config/fish/config.fish",
+        ksh:  "~/.kshrc",
+        mksh: "~/.kshrc",
+        rc:   "~/.rcrc",
+        sh:   "~/.profile",
+        tcsh: "~/.tcshrc",
+        zsh:  "~/.zshrc",
+      }.freeze,
+      T::Hash[T.nilable(Symbol), String],
+    )
 
     UNSAFE_SHELL_CHAR = %r{([^A-Za-z0-9_\-.,:/@~+\n])}
 
diff --git a/Library/Homebrew/utils/spdx.rb b/Library/Homebrew/utils/spdx.rb
index 6ecf406573..bf45bf377c 100644
--- a/Library/Homebrew/utils/spdx.rb
+++ b/Library/Homebrew/utils/spdx.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "utils/curl"
@@ -8,7 +8,7 @@ require "utils/github"
 module SPDX
   module_function
 
-  DATA_PATH = (HOMEBREW_DATA_PATH/"spdx").freeze
+  DATA_PATH = T.let((HOMEBREW_DATA_PATH/"spdx").freeze, Pathname)
   API_URL = "https://api.github.com/repos/spdx/license-list-data/releases/latest"
   LICENSEREF_PREFIX = "LicenseRef-Homebrew-"
   ALLOWED_LICENSE_SYMBOLS = [
@@ -16,24 +16,43 @@ module SPDX
     :cannot_represent,
   ].freeze
 
+  sig { returns(T::Hash[String, T.untyped]) }
   def license_data
-    @license_data ||= JSON.parse (DATA_PATH/"spdx_licenses.json").read
+    @license_data ||= T.let(JSON.parse((DATA_PATH/"spdx_licenses.json").read), T.nilable(T::Hash[String, T.untyped]))
   end
 
+  sig { returns(T::Hash[String, T.untyped]) }
   def exception_data
-    @exception_data ||= JSON.parse (DATA_PATH/"spdx_exceptions.json").read
+    @exception_data ||= T.let(JSON.parse((DATA_PATH/"spdx_exceptions.json").read),
+                              T.nilable(T::Hash[String, T.untyped]))
   end
 
+  sig { returns(String) }
   def latest_tag
-    @latest_tag ||= GitHub::API.open_rest(API_URL)["tag_name"]
+    @latest_tag ||= T.let(GitHub::API.open_rest(API_URL)["tag_name"], T.nilable(String))
   end
 
+  sig { params(to: Pathname).void }
   def download_latest_license_data!(to: DATA_PATH)
     data_url = "https://raw.githubusercontent.com/spdx/license-list-data/#{latest_tag}/json/"
     Utils::Curl.curl_download("#{data_url}licenses.json", to: to/"spdx_licenses.json")
     Utils::Curl.curl_download("#{data_url}exceptions.json", to: to/"spdx_exceptions.json")
   end
 
+  sig {
+    params(
+      license_expression: T.any(
+        String,
+        Symbol,
+        T::Hash[T.any(Symbol, String), T.untyped],
+        T::Array[String],
+      ),
+    ).returns(
+      [
+        T::Array[T.any(String, Symbol)], T::Array[String]
+      ],
+    )
+  }
   def parse_license_expression(license_expression)
     licenses = T.let([], T::Array[T.any(String, Symbol)])
     exceptions = T.let([], T::Array[String])
@@ -63,6 +82,7 @@ module SPDX
     [licenses, exceptions]
   end
 
+  sig { params(license: T.any(String, Symbol)).returns(T::Boolean) }
   def valid_license?(license)
     return ALLOWED_LICENSE_SYMBOLS.include? license if license.is_a? Symbol
 
@@ -70,22 +90,31 @@ module SPDX
     license_data["licenses"].any? { |spdx_license| spdx_license["licenseId"] == license }
   end
 
+  sig { params(license: T.any(String, Symbol)).returns(T::Boolean) }
   def deprecated_license?(license)
     return false if ALLOWED_LICENSE_SYMBOLS.include? license
     return false unless valid_license?(license)
 
-    license = license.delete_suffix "+"
+    license = license.to_s.delete_suffix "+"
     license_data["licenses"].none? do |spdx_license|
       spdx_license["licenseId"] == license && !spdx_license["isDeprecatedLicenseId"]
     end
   end
 
+  sig { params(exception: String).returns(T::Boolean) }
   def valid_license_exception?(exception)
     exception_data["exceptions"].any? do |spdx_exception|
       spdx_exception["licenseExceptionId"] == exception && !spdx_exception["isDeprecatedLicenseId"]
     end
   end
 
+  sig {
+    params(
+      license_expression: T.any(String, Symbol, T::Hash[T.nilable(T.any(Symbol, String)), T.untyped]),
+      bracket:            T::Boolean,
+      hash_type:          T.nilable(T.any(String, Symbol)),
+    ).returns(T.nilable(String))
+  }
   def license_expression_to_string(license_expression, bracket: false, hash_type: nil)
     case license_expression
     when String
@@ -125,6 +154,19 @@ module SPDX
     end
   end
 
+  sig {
+    params(
+      string: T.nilable(String),
+    ).returns(
+      T.nilable(
+        T.any(
+          String,
+          Symbol,
+          T::Hash[T.any(String, Symbol), T.untyped],
+        ),
+      ),
+    )
+  }
   def string_to_license_expression(string)
     return if string.blank?
 
@@ -162,13 +204,23 @@ module SPDX
     end
   end
 
+  sig {
+    params(
+      license: T.any(String, Symbol),
+    ).returns(
+      T.any(
+        [T.any(String, Symbol)],
+        [String, T.nilable(String), T::Boolean],
+      ),
+    )
+  }
   def license_version_info(license)
     return [license] if ALLOWED_LICENSE_SYMBOLS.include? license
 
     match = license.match(/-(?<version>[0-9.]+)(?:-.*?)??(?<or_later>\+|-only|-or-later)?$/)
     return [license] if match.blank?
 
-    license_name = license.split(match[0]).first
+    license_name = license.to_s.split(match[0].to_s).first
     or_later = match["or_later"].present? && %w[+ -or-later].include?(match["or_later"])
 
     # [name, version, later versions allowed?]
@@ -176,12 +228,18 @@ module SPDX
     [license_name, match["version"], or_later]
   end
 
+  sig {
+    params(license_expression: T.any(String, Symbol, T::Hash[Symbol, T.untyped]),
+           forbidden_licenses: T::Hash[Symbol, T.untyped]).returns(T::Boolean)
+  }
   def licenses_forbid_installation?(license_expression, forbidden_licenses)
     case license_expression
     when String, Symbol
       forbidden_licenses_include? license_expression.to_s, forbidden_licenses
     when Hash
       key = license_expression.keys.first
+      return false if key.nil?
+
       case key
       when :any_of
         license_expression[key].all? { |license| licenses_forbid_installation? license, forbidden_licenses }
@@ -193,6 +251,12 @@ module SPDX
     end
   end
 
+  sig {
+    params(
+      license:            T.any(Symbol, String),
+      forbidden_licenses: T::Hash[T.any(Symbol, String), T.untyped],
+    ).returns(T::Boolean)
+  }
   def forbidden_licenses_include?(license, forbidden_licenses)
     return true if forbidden_licenses.key? license
 
diff --git a/Library/Homebrew/utils/tty.rb b/Library/Homebrew/utils/tty.rb
index a539e37b5b..e033f85111 100644
--- a/Library/Homebrew/utils/tty.rb
+++ b/Library/Homebrew/utils/tty.rb
@@ -1,49 +1,58 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 # Various helper functions for interacting with TTYs.
 module Tty
-  @stream = $stdout
+  @stream = T.let($stdout, T.nilable(T.any(IO, StringIO)))
 
-  COLOR_CODES = {
-    red:     31,
-    green:   32,
-    yellow:  33,
-    blue:    34,
-    magenta: 35,
-    cyan:    36,
-    default: 39,
-  }.freeze
+  COLOR_CODES = T.let(
+    {
+      red:     31,
+      green:   32,
+      yellow:  33,
+      blue:    34,
+      magenta: 35,
+      cyan:    36,
+      default: 39,
+    }.freeze,
+    T::Hash[Symbol, Integer],
+  )
 
-  STYLE_CODES = {
-    reset:         0,
-    bold:          1,
-    italic:        3,
-    underline:     4,
-    strikethrough: 9,
-    no_underline:  24,
-  }.freeze
+  STYLE_CODES = T.let(
+    {
+      reset:         0,
+      bold:          1,
+      italic:        3,
+      underline:     4,
+      strikethrough: 9,
+      no_underline:  24,
+    }.freeze,
+    T::Hash[Symbol, Integer],
+  )
 
-  SPECIAL_CODES = {
-    up:         "1A",
-    down:       "1B",
-    right:      "1C",
-    left:       "1D",
-    erase_line: "K",
-    erase_char: "P",
-  }.freeze
+  SPECIAL_CODES = T.let(
+    {
+      up:         "1A",
+      down:       "1B",
+      right:      "1C",
+      left:       "1D",
+      erase_line: "K",
+      erase_char: "P",
+    }.freeze,
+    T::Hash[Symbol, String],
+  )
 
-  CODES = COLOR_CODES.merge(STYLE_CODES).freeze
+  CODES = T.let(COLOR_CODES.merge(STYLE_CODES).freeze, T::Hash[Symbol, Integer])
 
   class << self
     sig { params(stream: T.any(IO, StringIO), _block: T.proc.params(arg0: T.any(IO, StringIO)).void).void }
     def with(stream, &_block)
       previous_stream = @stream
-      @stream = stream
+      @stream = T.let(stream, T.nilable(T.any(IO, StringIO)))
 
       yield stream
     ensure
-      @stream = previous_stream
+      @stream = T.let(previous_stream, T.nilable(T.any(IO, StringIO)))
     end
 
     sig { params(string: String).returns(String) }
@@ -88,17 +97,17 @@ module Tty
       height, width = `/bin/stty size 2>/dev/null`.presence&.split&.map(&:to_i)
       return if height.nil? || width.nil?
 
-      @size = [height, width]
+      @size = T.let([height, width], T.nilable([Integer, Integer]))
     end
 
     sig { returns(Integer) }
     def height
-      @height ||= size&.first || `/usr/bin/tput lines 2>/dev/null`.presence&.to_i || 40
+      @height ||= T.let(size&.first || `/usr/bin/tput lines 2>/dev/null`.presence&.to_i || 40, T.nilable(Integer))
     end
 
     sig { returns(Integer) }
     def width
-      @width ||= size&.second || `/usr/bin/tput cols 2>/dev/null`.presence&.to_i || 80
+      @width ||= T.let(size&.second || `/usr/bin/tput cols 2>/dev/null`.presence&.to_i || 80, T.nilable(Integer))
     end
 
     sig { params(string: String).returns(String) }
@@ -115,12 +124,12 @@ module Tty
 
     sig { void }
     def reset_escape_sequence!
-      @escape_sequence = nil
+      @escape_sequence = T.let(nil, T.nilable(T::Array[Integer]))
     end
 
     CODES.each do |name, code|
       define_method(name) do
-        @escape_sequence ||= []
+        @escape_sequence ||= T.let([], T.nilable(T::Array[Integer]))
         @escape_sequence << code
         self
       end
@@ -128,7 +137,8 @@ module Tty
 
     SPECIAL_CODES.each do |name, code|
       define_method(name) do
-        if @stream.tty?
+        @stream = T.let($stdout, T.nilable(T.any(IO, StringIO)))
+        if @stream&.tty?
           "\033[#{code}"
         else
           ""
@@ -152,7 +162,7 @@ module Tty
       return false if Homebrew::EnvConfig.no_color?
       return true if Homebrew::EnvConfig.color?
 
-      @stream.tty?
+      !!@stream&.tty?
     end
   end
 end