diff --git a/Library/Homebrew/env_config.rb b/Library/Homebrew/env_config.rb
index 713c460222..e6675f14f0 100644
--- a/Library/Homebrew/env_config.rb
+++ b/Library/Homebrew/env_config.rb
@@ -351,6 +351,7 @@ module Homebrew
     end
 
     # Needs a custom implementation.
+    sig { returns(String) }
     def make_jobs
       jobs = ENV["HOMEBREW_MAKE_JOBS"].to_i
       return jobs.to_s if jobs.positive?
diff --git a/Library/Homebrew/extend/ENV.rb b/Library/Homebrew/extend/ENV.rb
index 17a6fd1227..d83beea7dc 100644
--- a/Library/Homebrew/extend/ENV.rb
+++ b/Library/Homebrew/extend/ENV.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: strict
 # frozen_string_literal: true
 
 require "hardware"
@@ -7,11 +7,22 @@ require "extend/ENV/shared"
 require "extend/ENV/std"
 require "extend/ENV/super"
 
-def superenv?(env)
-  env != "std" && Superenv.bin
+module Kernel
+  extend T::Sig
+
+  sig { params(env: T.nilable(String)).returns(T::Boolean) }
+  def superenv?(env)
+    return false if env == "std"
+
+    !Superenv.bin.nil?
+  end
+  private :superenv?
 end
 
 module EnvActivation
+  extend T::Sig
+
+  sig { params(env: T.nilable(String)).void }
   def activate_extensions!(env: nil)
     if superenv?(env)
       extend(Superenv)
@@ -20,25 +31,41 @@ module EnvActivation
     end
   end
 
-  def with_build_environment(env: nil, cc: nil, build_bottle: false, bottle_arch: nil)
+  sig do
+    params(
+      env:          T.nilable(String),
+      cc:           T.nilable(String),
+      build_bottle: T.nilable(T::Boolean),
+      bottle_arch:  T.nilable(String),
+      _block:       T.proc.returns(T.untyped),
+    ).returns(T.untyped)
+  end
+  def with_build_environment(env: nil, cc: nil, build_bottle: false, bottle_arch: nil, &_block)
     old_env = to_hash.dup
     tmp_env = to_hash.dup.extend(EnvActivation)
-    tmp_env.activate_extensions!(env: env)
-    tmp_env.setup_build_environment(cc: cc, build_bottle: build_bottle, bottle_arch: bottle_arch)
+    T.cast(tmp_env, EnvActivation).activate_extensions!(env: env)
+    T.cast(tmp_env, T.any(Superenv, Stdenv))
+     .setup_build_environment(cc: cc, build_bottle: build_bottle, bottle_arch: bottle_arch)
     replace(tmp_env)
-    yield
-  ensure
-    replace(old_env)
+
+    begin
+      yield
+    ensure
+      replace(old_env)
+    end
   end
 
+  sig { params(key: T.any(String, Symbol)).returns(T::Boolean) }
   def sensitive?(key)
-    /(cookie|key|token|password)/i =~ key
+    key.match?(/(cookie|key|token|password)/i)
   end
 
+  sig { returns(T::Hash[String, String]) }
   def sensitive_environment
     select { |key, _| sensitive?(key) }
   end
 
+  sig { void }
   def clear_sensitive_environment!
     each_key { |key| delete key if sensitive?(key) }
   end
diff --git a/Library/Homebrew/extend/ENV.rbi b/Library/Homebrew/extend/ENV.rbi
new file mode 100644
index 0000000000..edee664dba
--- /dev/null
+++ b/Library/Homebrew/extend/ENV.rbi
@@ -0,0 +1,49 @@
+# typed: strict
+
+module EnvMethods
+  include Kernel
+
+  sig { params(key: String).returns(T::Boolean) }
+  def key?(key); end
+
+  sig { params(key: String).returns(T.nilable(String)) }
+  def [](key); end
+
+  sig { params(key: String).returns(String) }
+  def fetch(key); end
+
+  sig { params(key: String, value: T.nilable(T.any(String, PATH))).returns(T.nilable(String)) }
+  def []=(key, value); end
+
+  sig { params(block: T.proc.params(arg0: [String, String]).returns(T::Boolean)).returns(T::Hash[String, String]) }
+  def select(&block); end
+
+  sig { params(block: T.proc.params(arg0: String).void).void }
+  def each_key(&block); end
+
+  sig { params(key: String).returns(T.nilable(String)) }
+  def delete(key); end
+
+  sig do
+    params(other: T.any(T::Hash[String, String], Sorbet::Private::Static::ENVClass))
+      .returns(Sorbet::Private::Static::ENVClass)
+  end
+  def replace(other); end
+
+  sig { returns(T::Hash[String, String]) }
+  def to_hash; end
+end
+
+module EnvActivation
+  include EnvMethods
+end
+
+class Sorbet
+  module Private
+    module Static
+      class ENVClass
+        include EnvActivation
+      end
+    end
+  end
+end
diff --git a/Library/Homebrew/extend/ENV/shared.rb b/Library/Homebrew/extend/ENV/shared.rb
index ae49480479..eac0a305d4 100644
--- a/Library/Homebrew/extend/ENV/shared.rb
+++ b/Library/Homebrew/extend/ENV/shared.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "compilers"
@@ -11,13 +11,16 @@ require "development_tools"
 # @see Stdenv
 # @see https://www.rubydoc.info/stdlib/Env Ruby's ENV API
 module SharedEnvExtension
+  extend T::Sig
+
   include CompilerConstants
 
-  # @private
   CC_FLAG_VARS = %w[CFLAGS CXXFLAGS OBJCFLAGS OBJCXXFLAGS].freeze
-  # @private
+  private_constant :CC_FLAG_VARS
+
   FC_FLAG_VARS = %w[FCFLAGS FFLAGS].freeze
-  # @private
+  private_constant :FC_FLAG_VARS
+
   SANITIZED_VARS = %w[
     CDPATH CLICOLOR_FORCE
     CPATH C_INCLUDE_PATH CPLUS_INCLUDE_PATH OBJC_INCLUDE_PATH
@@ -28,8 +31,16 @@ module SharedEnvExtension
     GOBIN GOPATH GOROOT PERL_MB_OPT PERL_MM_OPT
     LIBRARY_PATH LD_LIBRARY_PATH LD_PRELOAD LD_RUN_PATH
   ].freeze
+  private_constant :SANITIZED_VARS
 
-  # @private
+  sig do
+    params(
+      formula:      T.nilable(Formula),
+      cc:           T.nilable(String),
+      build_bottle: T.nilable(T::Boolean),
+      bottle_arch:  T.nilable(T::Boolean),
+    ).void
+  end
   def setup_build_environment(formula: nil, cc: nil, build_bottle: false, bottle_arch: nil)
     @formula = formula
     @cc = cc
@@ -37,57 +48,62 @@ module SharedEnvExtension
     @bottle_arch = bottle_arch
     reset
   end
+  private :setup_build_environment
 
-  # @private
+  sig { void }
   def reset
     SANITIZED_VARS.each { |k| delete(k) }
   end
+  private :reset
 
+  sig { returns(T::Hash[String, String]) }
   def remove_cc_etc
     keys = %w[CC CXX OBJC OBJCXX LD CPP CFLAGS CXXFLAGS OBJCFLAGS OBJCXXFLAGS LDFLAGS CPPFLAGS]
-    removed = Hash[*keys.flat_map { |key| [key, self[key]] }]
-    keys.each do |key|
-      delete(key)
-    end
-    removed
+    keys.map { |key| [key, delete(key)] }.to_h
   end
 
+  sig { params(newflags: String).void }
   def append_to_cflags(newflags)
     append(CC_FLAG_VARS, newflags)
   end
 
+  sig { params(val: T.any(Regexp, String)).void }
   def remove_from_cflags(val)
     remove CC_FLAG_VARS, val
   end
 
+  sig { params(value: String).void }
   def append_to_cccfg(value)
     append("HOMEBREW_CCCFG", value, "")
   end
 
+  sig { params(keys: T.any(String, T::Array[String]), value: T.untyped, separator: String).void }
   def append(keys, value, separator = " ")
     value = value.to_s
     Array(keys).each do |key|
-      old = self[key]
-      if old.nil? || old.empty?
-        self[key] = value
+      old_value = self[key]
+      self[key] = if old_value.nil? || old_value.empty?
+        value
       else
-        self[key] += separator + value
+        old_value + separator + value
       end
     end
   end
 
+  sig { params(keys: T.any(String, T::Array[String]), value: T.untyped, separator: String).void }
   def prepend(keys, value, separator = " ")
     value = value.to_s
     Array(keys).each do |key|
-      old = self[key]
-      self[key] = if old.nil? || old.empty?
+      old_value = self[key]
+      self[key] = if old_value.nil? || old_value.empty?
         value
       else
-        value + separator + old
+        value + separator + old_value
       end
     end
   end
 
+  sig { params(key: String, path: String).void }
   def append_path(key, path)
     self[key] = PATH.new(self[key]).append(path)
   end
@@ -99,61 +115,78 @@ module SharedEnvExtension
   # Prepending a system path such as /usr/bin is a no-op so that requirements
   # don't accidentally override superenv shims or formulae's `bin` directories.
   # <pre>ENV.prepend_path "PATH", which("emacs").dirname</pre>
+  sig { params(key: String, path: String).void }
   def prepend_path(key, path)
     return if %w[/usr/bin /bin /usr/sbin /sbin].include? path.to_s
 
     self[key] = PATH.new(self[key]).prepend(path)
   end
 
+  sig { params(key: String, path: T.any(String, Pathname)).void }
   def prepend_create_path(key, path)
-    path = Pathname.new(path) unless path.is_a? Pathname
+    path = Pathname(path)
     path.mkpath
     prepend_path key, path
   end
 
+  sig { params(keys: T.any(String, T::Array[String]), value: T.untyped).void }
   def remove(keys, value)
     return if value.nil?
 
     Array(keys).each do |key|
-      next unless self[key]
+      old_value = self[key]
+      next if old_value.nil?
 
-      self[key] = self[key].sub(value, "")
-      delete(key) if self[key].empty?
+      new_value = old_value.sub(value, "")
+      if new_value.empty?
+        delete(key)
+      else
+        self[key] = new_value
+      end
     end
   end
 
+  sig { returns(T.nilable(String)) }
   def cc
     self["CC"]
   end
 
+  sig { returns(T.nilable(String)) }
   def cxx
     self["CXX"]
   end
 
+  sig { returns(T.nilable(String)) }
   def cflags
     self["CFLAGS"]
   end
 
+  sig { returns(T.nilable(String)) }
   def cxxflags
     self["CXXFLAGS"]
   end
 
+  sig { returns(T.nilable(String)) }
   def cppflags
     self["CPPFLAGS"]
   end
 
+  sig { returns(T.nilable(String)) }
   def ldflags
     self["LDFLAGS"]
   end
 
+  sig { returns(T.nilable(String)) }
   def fc
     self["FC"]
   end
 
+  sig { returns(T.nilable(String)) }
   def fflags
     self["FFLAGS"]
   end
 
+  sig { returns(T.nilable(String)) }
   def fcflags
     self["FCFLAGS"]
   end
@@ -164,8 +197,7 @@ module SharedEnvExtension
   #   # modify CFLAGS CXXFLAGS OBJCFLAGS OBJCXXFLAGS in one go:
   #   ENV.append_to_cflags "-I ./missing/includes"
   # end</pre>
-  #
-  # @return [Symbol]
+  sig { returns(T.any(Symbol, String)) }
   def compiler
     @compiler ||= if (cc = @cc)
       warn_about_non_apple_gcc(cc) if cc.match?(GNU_GCC_REGEXP)
@@ -189,27 +221,31 @@ module SharedEnvExtension
     end
   end
 
-  # @private
+  sig { returns(T.any(String, Pathname)) }
   def determine_cc
     COMPILER_SYMBOL_MAP.invert.fetch(compiler, compiler)
   end
+  private :determine_cc
 
   COMPILERS.each do |compiler|
     define_method(compiler) do
       @compiler = compiler
-      self.cc  = determine_cc
-      self.cxx = determine_cxx
+
+      send(:cc=, send(:determine_cc))
+      send(:cxx=, send(:determine_cxx))
     end
   end
 
   # Snow Leopard defines an NCURSES value the opposite of most distros.
   # @see https://bugs.python.org/issue6848
   # Currently only used by aalib in core.
+  sig { void }
   def ncurses_define
     append "CPPFLAGS", "-DNCURSES_OPAQUE=0"
   end
 
   # @private
+  sig { void }
   def userpaths!
     path = PATH.new(self["PATH"]).select do |p|
       # put Superenv.bin and opt path at the first
@@ -228,6 +264,7 @@ module SharedEnvExtension
     self["PATH"] = path
   end
 
+  sig { void }
   def fortran
     # Ignore repeated calls to this function as it will misleadingly warn about
     # building with an alternative Fortran compiler without optimization flags,
@@ -260,6 +297,7 @@ module SharedEnvExtension
   end
 
   # @private
+  sig { returns(Symbol) }
   def effective_arch
     if @build_bottle && @bottle_arch
       @bottle_arch.to_sym
@@ -269,6 +307,7 @@ module SharedEnvExtension
   end
 
   # @private
+  sig { params(name: String).returns(Formula) }
   def gcc_version_formula(name)
     version = name[GNU_GCC_REGEXP, 1]
     gcc_version_name = "gcc@#{version}"
@@ -282,6 +321,7 @@ module SharedEnvExtension
   end
 
   # @private
+  sig { params(name: String).void }
   def warn_about_non_apple_gcc(name)
     begin
       gcc_formula = gcc_version_formula(name)
@@ -299,30 +339,40 @@ module SharedEnvExtension
     EOS
   end
 
+  sig { void }
   def permit_arch_flags; end
 
   # A no-op until we enable this by default again (which we may never do).
+  sig { void }
   def permit_weak_imports; end
 
   # @private
+  sig { params(cc: T.any(Symbol, String)).returns(T::Boolean) }
   def compiler_any_clang?(cc = compiler)
     %w[clang llvm_clang].include?(cc.to_s)
   end
 
   private
 
+  sig { params(_flags: T::Array[String], _map: T::Hash[Symbol, String]).void }
+  def set_cpu_flags(_flags, _map = {}); end
+
+  sig { params(val: T.any(String, Pathname)).returns(String) }
   def cc=(val)
     self["CC"] = self["OBJC"] = val.to_s
   end
 
+  sig { params(val: T.any(String, Pathname)).returns(String) }
   def cxx=(val)
     self["CXX"] = self["OBJCXX"] = val.to_s
   end
 
+  sig { returns(T.nilable(String)) }
   def homebrew_cc
     self["HOMEBREW_CC"]
   end
 
+  sig { params(value: String, source: String).returns(Symbol) }
   def fetch_compiler(value, source)
     COMPILER_SYMBOL_MAP.fetch(value) do |other|
       case other
@@ -334,10 +384,9 @@ module SharedEnvExtension
     end
   end
 
+  sig { void }
   def check_for_compiler_universal_support
-    return unless homebrew_cc.match?(GNU_GCC_REGEXP)
-
-    raise "Non-Apple GCC can't build universal binaries"
+    raise "Non-Apple GCC can't build universal binaries" if homebrew_cc&.match?(GNU_GCC_REGEXP)
   end
 end
 
diff --git a/Library/Homebrew/extend/ENV/shared.rbi b/Library/Homebrew/extend/ENV/shared.rbi
new file mode 100644
index 0000000000..b1eac4cd3e
--- /dev/null
+++ b/Library/Homebrew/extend/ENV/shared.rbi
@@ -0,0 +1,15 @@
+# typed: strict
+
+module SharedEnvExtension
+  include EnvMethods
+end
+
+class Sorbet
+  module Private
+    module Static
+      class ENVClass
+        include SharedEnvExtension
+      end
+    end
+  end
+end
diff --git a/Library/Homebrew/extend/ENV/std.rb b/Library/Homebrew/extend/ENV/std.rb
index bea1efc156..8a8a648d81 100644
--- a/Library/Homebrew/extend/ENV/std.rb
+++ b/Library/Homebrew/extend/ENV/std.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: strict
 # frozen_string_literal: true
 
 require "hardware"
@@ -14,8 +14,16 @@ module Stdenv
   SAFE_CFLAGS_FLAGS = "-w -pipe"
 
   # @private
-  def setup_build_environment(**options)
-    super(**options)
+  sig do
+    params(
+      formula:      T.nilable(Formula),
+      cc:           T.nilable(String),
+      build_bottle: T.nilable(T::Boolean),
+      bottle_arch:  T.nilable(T::Boolean),
+    ).void
+  end
+  def setup_build_environment(formula: nil, cc: nil, build_bottle: false, bottle_arch: nil)
+    super
 
     self["HOMEBREW_ENV"] = "std"
 
@@ -49,13 +57,14 @@ module Stdenv
 
     send(compiler)
 
-    return unless cc.match?(GNU_GCC_REGEXP)
+    return unless cc&.match?(GNU_GCC_REGEXP)
 
     gcc_formula = gcc_version_formula(cc)
     append_path "PATH", gcc_formula.opt_bin.to_s
   end
   alias generic_setup_build_environment setup_build_environment
 
+  sig { returns(T::Array[Pathname]) }
   def homebrew_extra_pkg_config_paths
     []
   end
@@ -73,10 +82,11 @@ module Stdenv
   # Removes the MAKEFLAGS environment variable, causing make to use a single job.
   # This is useful for makefiles with race conditions.
   # When passed a block, MAKEFLAGS is removed only for the duration of the block and is restored after its completion.
-  def deparallelize
+  sig { params(block: T.proc.returns(T.untyped)).returns(T.untyped) }
+  def deparallelize(&block)
     old = self["MAKEFLAGS"]
     remove "MAKEFLAGS", /-j\d+/
-    if block_given?
+    if block
       begin
         yield
       ensure
@@ -89,30 +99,33 @@ module Stdenv
 
   %w[O3 O2 O1 O0 Os].each do |opt|
     define_method opt do
-      remove_from_cflags(/-O./)
-      append_to_cflags "-#{opt}"
+      send(:remove_from_cflags, /-O./)
+      send(:append_to_cflags, "-#{opt}")
     end
   end
 
-  # @private
+  sig { returns(T.any(String, Pathname)) }
   def determine_cc
     s = super
-    DevelopmentTools.locate(s) || Pathname.new(s)
+    DevelopmentTools.locate(s) || Pathname(s)
   end
+  private :determine_cc
 
-  # @private
+  sig { returns(Pathname) }
   def determine_cxx
-    dir, base = determine_cc.split
+    dir, base = Pathname(determine_cc).split
     dir/base.to_s.sub("gcc", "g++").sub("clang", "clang++")
   end
+  private :determine_cxx
 
   GNU_GCC_VERSIONS.each do |n|
     define_method(:"gcc-#{n}") do
       super()
-      set_cpu_cflags
+      send(:set_cpu_cflags)
     end
   end
 
+  sig { void }
   def clang
     super()
     replace_in_cflags(/-Xarch_#{Hardware::CPU.arch_32_bit} (-march=\S*)/, '\1')
@@ -124,16 +137,19 @@ module Stdenv
     set_cpu_cflags(map)
   end
 
+  sig { void }
   def m64
     append_to_cflags "-m64"
     append "LDFLAGS", "-arch #{Hardware::CPU.arch_64_bit}"
   end
 
+  sig { void }
   def m32
     append_to_cflags "-m32"
     append "LDFLAGS", "-arch #{Hardware::CPU.arch_32_bit}"
   end
 
+  sig { void }
   def universal_binary
     check_for_compiler_universal_support
 
@@ -141,33 +157,38 @@ module Stdenv
     append "LDFLAGS", Hardware::CPU.universal_archs.as_arch_flags
 
     return if compiler_any_clang?
-    return unless Hardware.is_32_bit?
+    return unless Hardware::CPU.is_32_bit?
 
     # Can't mix "-march" for a 32-bit CPU with "-arch x86_64"
     replace_in_cflags(/-march=\S*/, "-Xarch_#{Hardware::CPU.arch_32_bit} \\0")
   end
 
+  sig { void }
   def cxx11
     append "CXX", "-std=c++11"
     libcxx
   end
 
+  sig { void }
   def libcxx
     append "CXX", "-stdlib=libc++" if compiler == :clang
   end
 
+  sig { void }
   def libstdcxx
     append "CXX", "-stdlib=libstdc++" if compiler == :clang
   end
 
   # @private
+  sig { params(before: Regexp, after: String).void }
   def replace_in_cflags(before, after)
     CC_FLAG_VARS.each do |key|
-      self[key] = self[key].sub(before, after) if key?(key)
+      self[key] = fetch(key).sub(before, after) if key?(key)
     end
   end
 
   # Convenience method to set all C compiler flags in one shot.
+  sig { params(val: String).void }
   def define_cflags(val)
     CC_FLAG_VARS.each { |key| self[key] = val }
   end
@@ -175,6 +196,7 @@ module Stdenv
   # Sets architecture-specific flags for every environment variable
   # given in the list `flags`.
   # @private
+  sig { params(flags: T::Array[String], map: T::Hash[Symbol, String]).void }
   def set_cpu_flags(flags, map = Hardware::CPU.optimization_flags)
     cflags =~ /(-Xarch_#{Hardware::CPU.arch_32_bit} )-march=/
     xarch = Regexp.last_match(1).to_s
@@ -186,19 +208,23 @@ module Stdenv
     append flags, map.fetch(effective_arch)
   end
 
+  sig { void }
   def x11; end
 
   # @private
+  sig { params(map: T::Hash[Symbol, String]).void }
   def set_cpu_cflags(map = Hardware::CPU.optimization_flags) # rubocop:disable Naming/AccessorMethodName
     set_cpu_flags(CC_FLAG_VARS, map)
   end
 
+  sig { returns(Integer) }
   def make_jobs
     Homebrew::EnvConfig.make_jobs.to_i
   end
 
   # This method does nothing in stdenv since there's no arg refurbishment
   # @private
+  sig { void }
   def refurbish_args; end
 end
 
diff --git a/Library/Homebrew/extend/ENV/super.rb b/Library/Homebrew/extend/ENV/super.rb
index 4b1ba40b84..5e2c1da21f 100644
--- a/Library/Homebrew/extend/ENV/super.rb
+++ b/Library/Homebrew/extend/ENV/super.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "extend/ENV/shared"
@@ -22,6 +22,7 @@ module Superenv
   # @private
   attr_accessor :keg_only_deps, :deps, :run_time_deps, :x11
 
+  sig { params(base: Superenv).void }
   def self.extended(base)
     base.keg_only_deps = []
     base.deps = []
@@ -29,8 +30,10 @@ module Superenv
   end
 
   # @private
+  sig { returns(T.nilable(Pathname)) }
   def self.bin; end
 
+  sig { void }
   def reset
     super
     # Configure scripts generated by autoconf 2.61 or later export as_nl, which
@@ -39,8 +42,16 @@ module Superenv
   end
 
   # @private
-  def setup_build_environment(**options)
-    super(**options)
+  sig do
+    params(
+      formula:      T.nilable(Formula),
+      cc:           T.nilable(String),
+      build_bottle: T.nilable(T::Boolean),
+      bottle_arch:  T.nilable(T::Boolean),
+    ).void
+  end
+  def setup_build_environment(formula: nil, cc: nil, build_bottle: false, bottle_arch: nil)
+    super
     send(compiler)
 
     self["HOMEBREW_ENV"] = "super"
@@ -89,18 +100,22 @@ module Superenv
 
   private
 
+  sig { params(val: T.any(String, Pathname)).returns(String) }
   def cc=(val)
     self["HOMEBREW_CC"] = super
   end
 
+  sig { params(val: T.any(String, Pathname)).returns(String) }
   def cxx=(val)
     self["HOMEBREW_CXX"] = super
   end
 
+  sig { returns(String) }
   def determine_cxx
     determine_cc.to_s.gsub("gcc", "g++").gsub("clang", "clang++")
   end
 
+  sig { returns(T::Array[Pathname]) }
   def homebrew_extra_paths
     []
   end
@@ -115,7 +130,7 @@ module Superenv
     path.append("/usr/bin", "/bin", "/usr/sbin", "/sbin")
 
     begin
-      path.append(gcc_version_formula(homebrew_cc).opt_bin) if homebrew_cc.match?(GNU_GCC_REGEXP)
+      path.append(gcc_version_formula(T.must(homebrew_cc)).opt_bin) if homebrew_cc&.match?(GNU_GCC_REGEXP)
     rescue FormulaUnavailableError
       # Don't fail and don't add these formulae to the path if they don't exist.
       nil
@@ -124,6 +139,7 @@ module Superenv
     path.existing
   end
 
+  sig { returns(T::Array[Pathname]) }
   def homebrew_extra_pkg_config_paths
     []
   end
@@ -143,6 +159,7 @@ module Superenv
     ).existing
   end
 
+  sig { returns(T::Array[Pathname]) }
   def homebrew_extra_aclocal_paths
     []
   end
@@ -156,6 +173,7 @@ module Superenv
     ).existing
   end
 
+  sig { returns(T::Array[Pathname]) }
   def homebrew_extra_isystem_paths
     []
   end
@@ -173,6 +191,7 @@ module Superenv
     PATH.new(keg_only_deps.map(&:opt_include)).existing
   end
 
+  sig { returns(T::Array[Pathname]) }
   def homebrew_extra_library_paths
     []
   end
@@ -187,6 +206,7 @@ module Superenv
     PATH.new(paths).existing
   end
 
+  sig { returns(String) }
   def determine_dependencies
     deps.map(&:name).join(",")
   end
@@ -199,6 +219,7 @@ module Superenv
     ).existing
   end
 
+  sig { returns(T::Array[Pathname]) }
   def homebrew_extra_cmake_include_paths
     []
   end
@@ -208,6 +229,7 @@ module Superenv
     PATH.new(homebrew_extra_cmake_include_paths).existing
   end
 
+  sig { returns(T::Array[Pathname]) }
   def homebrew_extra_cmake_library_paths
     []
   end
@@ -217,6 +239,7 @@ module Superenv
     PATH.new(homebrew_extra_cmake_library_paths).existing
   end
 
+  sig { returns(T::Array[Pathname]) }
   def homebrew_extra_cmake_frameworks_paths
     []
   end
@@ -229,14 +252,17 @@ module Superenv
     ).existing
   end
 
+  sig { returns(String) }
   def determine_make_jobs
     Homebrew::EnvConfig.make_jobs
   end
 
+  sig { returns(String) }
   def determine_optflags
     Hardware::CPU.optimization_flags.fetch(effective_arch)
   end
 
+  sig { returns(String) }
   def determine_cccfg
     ""
   end
@@ -246,9 +272,10 @@ module Superenv
   # Removes the MAKEFLAGS environment variable, causing make to use a single job.
   # This is useful for makefiles with race conditions.
   # When passed a block, MAKEFLAGS is removed only for the duration of the block and is restored after its completion.
-  def deparallelize
+  sig { params(block: T.proc.returns(T.untyped)).returns(T.untyped) }
+  def deparallelize(&block)
     old = delete("MAKEFLAGS")
-    if block_given?
+    if block
       begin
         yield
       ensure
@@ -259,56 +286,64 @@ module Superenv
     old
   end
 
+  sig { returns(Integer) }
   def make_jobs
     self["MAKEFLAGS"] =~ /-\w*j(\d+)/
     [Regexp.last_match(1).to_i, 1].max
   end
 
+  sig { void }
   def universal_binary
     check_for_compiler_universal_support
 
     self["HOMEBREW_ARCHFLAGS"] = Hardware::CPU.universal_archs.as_arch_flags
   end
 
+  sig { void }
   def permit_arch_flags
     append_to_cccfg "K"
   end
 
+  sig { void }
   def m32
     append "HOMEBREW_ARCHFLAGS", "-m32"
   end
 
+  sig { void }
   def m64
     append "HOMEBREW_ARCHFLAGS", "-m64"
   end
 
+  sig { void }
   def cxx11
     append_to_cccfg "x"
     append_to_cccfg "g" if homebrew_cc == "clang"
   end
 
+  sig { void }
   def libcxx
     append_to_cccfg "g" if compiler == :clang
   end
 
+  sig { void }
   def libstdcxx
     append_to_cccfg "h" if compiler == :clang
   end
 
   # @private
+  sig { void }
   def refurbish_args
     append_to_cccfg "O"
   end
 
   %w[O3 O2 O1 O0 Os].each do |opt|
     define_method opt do
-      self["HOMEBREW_OPTIMIZATION_LEVEL"] = opt
+      send(:[]=, "HOMEBREW_OPTIMIZATION_LEVEL", opt)
     end
   end
 
+  sig { void }
   def set_x11_env_if_installed; end
-
-  def set_cpu_flags(_arg0, _arg1 = "", _arg2 = {}); end
 end
 
 require "extend/os/extend/ENV/super"
diff --git a/Library/Homebrew/extend/os/mac/extend/ENV/super.rb b/Library/Homebrew/extend/os/mac/extend/ENV/super.rb
index 4e541a2be9..d797ff7484 100644
--- a/Library/Homebrew/extend/os/mac/extend/ENV/super.rb
+++ b/Library/Homebrew/extend/os/mac/extend/ENV/super.rb
@@ -27,7 +27,7 @@ module Superenv
 
   def homebrew_extra_paths
     paths = []
-    paths << MacOS::XQuartz.bin.to_s if x11?
+    paths << MacOS::XQuartz.bin if x11?
     paths
   end
 
diff --git a/Library/Homebrew/utils/inreplace.rb b/Library/Homebrew/utils/inreplace.rb
index b414647aea..951b55148c 100644
--- a/Library/Homebrew/utils/inreplace.rb
+++ b/Library/Homebrew/utils/inreplace.rb
@@ -34,7 +34,7 @@ module Utils
     # @api public
     sig do
       params(
-        paths:        T.any(T::Array[T.untyped], String),
+        paths:        T.any(T::Array[T.untyped], String, Pathname),
         before:       T.nilable(T.any(Regexp, String)),
         after:        T.nilable(T.any(String, Symbol)),
         audit_result: T::Boolean,