diff --git a/Library/Homebrew/development_tools.rb b/Library/Homebrew/development_tools.rb
index 9d900f5a0f101..5a379a04f12de 100644
--- a/Library/Homebrew/development_tools.rb
+++ b/Library/Homebrew/development_tools.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "version"
@@ -16,7 +16,7 @@ def locate(tool)
       # Don't call tools (cc, make, strip, etc.) directly!
       # Give the name of the binary you look for as a string to this method
       # in order to get the full path back as a Pathname.
-      (@locate ||= {}).fetch(tool) do |key|
+      (@locate ||= T.let({}, T.nilable(T::Hash[T.any(String, Symbol), T.untyped]))).fetch(tool) do |key|
         @locate[key] = if File.executable?((path = "/usr/bin/#{tool}"))
           Pathname.new path
         # Homebrew GCCs most frequently; much faster to check this before xcrun
@@ -62,12 +62,14 @@ def default_compiler
     # @api public
     sig { returns(Version) }
     def clang_version
-      @clang_version ||= if (path = locate("clang")) &&
-                            (build_version = `#{path} --version`[/(?:clang|LLVM) version (\d+\.\d(?:\.\d)?)/, 1])
-        Version.new build_version
-      else
-        Version::NULL
-      end
+      @clang_version ||= T.let(
+        if (path = locate("clang")) &&
+           (build_version = `#{path} --version`[/(?:clang|LLVM) version (\d+\.\d(?:\.\d)?)/, 1])
+          Version.new(build_version)
+        else
+          Version::NULL
+        end, T.nilable(Version)
+      )
     end
 
     # Get the Clang build version.
@@ -75,13 +77,14 @@ def clang_version
     # @api public
     sig { returns(Version) }
     def clang_build_version
-      @clang_build_version ||= if (path = locate("clang")) &&
-                                  (build_version = `#{path} --version`[
-%r{clang(-| version [^ ]+ \(tags/RELEASE_)(\d{2,})}, 2])
-        Version.new build_version
-      else
-        Version::NULL
-      end
+      @clang_build_version ||= T.let(
+        if (path = locate("clang")) &&
+          (build_version = `#{path} --version`[%r{clang(-| version [^ ]+ \(tags/RELEASE_)(\d{2,})}, 2])
+          Version.new(build_version)
+        else
+          Version::NULL
+        end, T.nilable(Version)
+      )
     end
 
     # Get the LLVM Clang build version.
@@ -89,15 +92,14 @@ def clang_build_version
     # @api public
     sig { returns(Version) }
     def llvm_clang_build_version
-      @llvm_clang_build_version ||= begin
+      @llvm_clang_build_version ||= T.let(begin
         path = Formulary.factory("llvm").opt_prefix/"bin/clang"
-        if path.executable? &&
-           (build_version = `#{path} --version`[/clang version (\d+\.\d\.\d)/, 1])
-          Version.new build_version
+        if path.executable? && (build_version = `#{path} --version`[/clang version (\d+\.\d\.\d)/, 1])
+          Version.new(build_version)
         else
           Version::NULL
         end
-      end
+      end, T.nilable(Version))
     end
 
     # Get the GCC version.
@@ -105,12 +107,12 @@ def llvm_clang_build_version
     # @api internal
     sig { params(cc: String).returns(Version) }
     def gcc_version(cc)
-      (@gcc_version ||= {}).fetch(cc) do
+      (@gcc_version ||= T.let({}, T.nilable(T::Hash[String, Version]))).fetch(cc) do
         path = HOMEBREW_PREFIX/"opt/#{CompilerSelector.preferred_gcc}/bin"/cc
         path = locate(cc) unless path.exist?
         version = if path &&
                      (build_version = `#{path} --version`[/gcc(?:(?:-\d+(?:\.\d)?)? \(.+\))? (\d+\.\d\.\d)/, 1])
-          Version.new build_version
+          Version.new(build_version)
         else
           Version::NULL
         end
@@ -120,8 +122,8 @@ def gcc_version(cc)
 
     sig { void }
     def clear_version_cache
-      @clang_version = @clang_build_version = nil
-      @gcc_version = {}
+      @clang_version = @clang_build_version = T.let(nil, T.nilable(Version))
+      @gcc_version = T.let({}, T.nilable(T::Hash[String, Version]))
     end
 
     sig { returns(T::Boolean) }
diff --git a/Library/Homebrew/extend/os/mac/unpack_strategy/zip.rb b/Library/Homebrew/extend/os/mac/unpack_strategy/zip.rb
index da2ec316920e0..f220474ddd040 100644
--- a/Library/Homebrew/extend/os/mac/unpack_strategy/zip.rb
+++ b/Library/Homebrew/extend/os/mac/unpack_strategy/zip.rb
@@ -8,7 +8,7 @@ class Zip
     module MacOSZipExtension
       private
 
-      sig { params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+      sig { params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
       def extract_to_dir(unpack_dir, basename:, verbose:)
         with_env(TZ: "UTC") do
           if merge_xattrs && contains_extended_attributes?(path)
diff --git a/Library/Homebrew/formula_assertions.rb b/Library/Homebrew/formula_assertions.rb
index a7d6d0dd77e40..db3320b62a5f4 100644
--- a/Library/Homebrew/formula_assertions.rb
+++ b/Library/Homebrew/formula_assertions.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module Homebrew
@@ -10,15 +10,18 @@ module Assertions
     require "minitest/assertions"
     include ::Minitest::Assertions
 
+    sig { params(assertions: Integer).returns(Integer) }
     attr_writer :assertions
 
+    sig { returns(Integer) }
     def assertions
-      @assertions ||= 0
+      @assertions ||= T.let(0, T.nilable(Integer))
     end
 
     # Returns the output of running cmd and asserts the exit status.
     #
     # @api public
+    sig { params(cmd: String, result: Integer).returns(String) }
     def shell_output(cmd, result = 0)
       ohai cmd
       output = `#{cmd}`
@@ -33,6 +36,7 @@ def shell_output(cmd, result = 0)
     # optionally asserts the exit status.
     #
     # @api public
+    sig { params(cmd: String, input: T.nilable(String), result: T.nilable(Integer)).returns(String) }
     def pipe_output(cmd, input = nil, result = nil)
       ohai cmd
       output = IO.popen(cmd, "w+") do |pipe|
diff --git a/Library/Homebrew/unpack_strategy.rb b/Library/Homebrew/unpack_strategy.rb
index 74e49473cbcaa..b3581c8ad75f9 100644
--- a/Library/Homebrew/unpack_strategy.rb
+++ b/Library/Homebrew/unpack_strategy.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "system_command"
@@ -6,11 +6,30 @@
 # Module containing all available strategies for unpacking archives.
 module UnpackStrategy
   extend T::Helpers
-
   include SystemCommand::Mixin
+  abstract!
+
+  # FIXME: Enable cop again when https://github.com/sorbet/sorbet/issues/3532 is fixed.
+  # rubocop:disable Style/MutableConstant
+  UnpackStrategyType = T.type_alias { T.all(T::Class[UnpackStrategy], UnpackStrategy::ClassMethods) }
+  # rubocop:enable Style/MutableConstant
+
+  module ClassMethods
+    extend T::Helpers
+    abstract!
+
+    sig { abstract.returns(T::Array[String]) }
+    def extensions; end
 
+    sig { abstract.params(path: Pathname).returns(T::Boolean) }
+    def can_extract?(path); end
+  end
+
+  mixes_in_class_methods(ClassMethods)
+
+  sig { returns(T.nilable(T::Array[UnpackStrategyType])) }
   def self.strategies
-    @strategies ||= [
+    @strategies ||= T.let([
       Tar, # Needs to be before Bzip2/Gzip/Xz/Lzma/Zstd.
       Pax,
       Gzip,
@@ -43,10 +62,11 @@ def self.strategies
       Sit,
       Rar,
       Lha,
-    ].freeze
+    ].freeze, T.nilable(T::Array[UnpackStrategyType]))
   end
   private_class_method :strategies
 
+  sig { params(type: Symbol).returns(T.nilable(UnpackStrategyType)) }
   def self.from_type(type)
     type = {
       naked:     :uncompressed,
@@ -61,23 +81,31 @@ def self.from_type(type)
     end
   end
 
+  sig { params(extension: String).returns(T.nilable(UnpackStrategyType)) }
   def self.from_extension(extension)
-    strategies.sort_by { |s| s.extensions.map(&:length).max || 0 }
-              .reverse
-              .find { |s| s.extensions.any? { |ext| extension.end_with?(ext) } }
+    return unless strategies
+
+    strategies&.sort_by { |s| s.extensions.map(&:length).max || 0 }
+              &.reverse
+              &.find { |s| s.extensions.any? { |ext| extension.end_with?(ext) } }
   end
 
+  sig { params(path: Pathname).returns(T.nilable(UnpackStrategyType)) }
   def self.from_magic(path)
-    strategies.find { |s| s.can_extract?(path) }
+    strategies&.find { |s| s.can_extract?(path) }
   end
 
-  def self.detect(path, prioritize_extension: false, type: nil, ref_type: nil, ref: nil, merge_xattrs: nil)
+  sig {
+    params(path: Pathname, prioritize_extension: T::Boolean, type: T.nilable(Symbol), ref_type: T.nilable(Symbol),
+           ref: T.nilable(String), merge_xattrs: T::Boolean).returns(T.untyped)
+  }
+  def self.detect(path, prioritize_extension: false, type: nil, ref_type: nil, ref: nil, merge_xattrs: false)
     strategy = from_type(type) if type
 
     if prioritize_extension && path.extname.present?
       strategy ||= from_extension(path.extname)
-      strategy ||= strategies.select { |s| s < Directory || s == Fossil }
-                             .find { |s| s.can_extract?(path) }
+
+      strategy ||= strategies&.find { |s| (s < Directory || s == Fossil) && s.can_extract?(path) }
     else
       strategy ||= from_magic(path)
       strategy ||= from_extension(path.extname)
@@ -88,24 +116,31 @@ def self.detect(path, prioritize_extension: false, type: nil, ref_type: nil, ref
     strategy.new(path, ref_type:, ref:, merge_xattrs:)
   end
 
-  attr_reader :path, :merge_xattrs
+  sig { returns(Pathname) }
+  attr_reader :path
 
-  def initialize(path, ref_type: nil, ref: nil, merge_xattrs: nil)
-    @path = Pathname(path).expand_path
-    @ref_type = ref_type
-    @ref = ref
-    @merge_xattrs = merge_xattrs
+  sig { returns(T::Boolean) }
+  attr_reader :merge_xattrs
+
+  sig {
+    params(path: T.any(String, Pathname), ref_type: T.nilable(Symbol), ref: T.nilable(String),
+           merge_xattrs: T::Boolean).void
+  }
+  def initialize(path, ref_type: nil, ref: nil, merge_xattrs: false)
+    @path = T.let(Pathname(path).expand_path, Pathname)
+    @ref_type = T.let(ref_type, T.nilable(Symbol))
+    @ref = T.let(ref, T.nilable(String))
+    @merge_xattrs = T.let(merge_xattrs, T::Boolean)
   end
 
-  abstract!
-  sig { abstract.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+  sig { abstract.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
   def extract_to_dir(unpack_dir, basename:, verbose:); end
   private :extract_to_dir
 
   sig {
     params(
       to: T.nilable(Pathname), basename: T.nilable(T.any(String, Pathname)), verbose: T::Boolean,
-    ).returns(T.untyped)
+    ).void
   }
   def extract(to: nil, basename: nil, verbose: false)
     basename ||= path.basename
@@ -131,7 +166,10 @@ def extract_nestedly(to: nil, basename: nil, verbose: false, prioritize_extensio
       children = tmp_unpack_dir.children
 
       if children.size == 1 && !children.fetch(0).directory?
-        s = UnpackStrategy.detect(children.first, prioritize_extension:)
+        first_child = children.first
+        next if first_child.nil?
+
+        s = UnpackStrategy.detect(first_child, prioritize_extension:)
 
         s.extract_nestedly(to:, verbose:, prioritize_extension:)
 
@@ -149,6 +187,7 @@ def extract_nestedly(to: nil, basename: nil, verbose: false, prioritize_extensio
     end
   end
 
+  sig { returns(T::Array[String]) }
   def dependencies
     []
   end
diff --git a/Library/Homebrew/unpack_strategy/air.rb b/Library/Homebrew/unpack_strategy/air.rb
index c4a6ba601a8b5..6415995419295 100644
--- a/Library/Homebrew/unpack_strategy/air.rb
+++ b/Library/Homebrew/unpack_strategy/air.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,18 +6,20 @@ module UnpackStrategy
   class Air
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".air"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       mime_type = "application/vnd.adobe.air-application-installer-package+zip"
       path.magic_number.match?(/.{59}#{Regexp.escape(mime_type)}/)
     end
 
+    sig { returns(T.nilable(T::Array[Cask::Cask])) }
     def dependencies
-      @dependencies ||= [Cask::CaskLoader.load("adobe-air")]
+      @dependencies ||= T.let([Cask::CaskLoader.load("adobe-air")], T.nilable(T::Array[Cask::Cask]))
     end
 
     AIR_APPLICATION_INSTALLER =
@@ -27,7 +29,7 @@ def dependencies
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       system_command! AIR_APPLICATION_INSTALLER,
                       args:    ["-silent", "-location", unpack_dir, path],
diff --git a/Library/Homebrew/unpack_strategy/bazaar.rb b/Library/Homebrew/unpack_strategy/bazaar.rb
index f73902b3aaf7f..770cca92aad86 100644
--- a/Library/Homebrew/unpack_strategy/bazaar.rb
+++ b/Library/Homebrew/unpack_strategy/bazaar.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "directory"
@@ -6,13 +6,14 @@
 module UnpackStrategy
   # Strategy for unpacking Bazaar archives.
   class Bazaar < Directory
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
-      super && (path/".bzr").directory?
+      !!(super && (path/".bzr").directory?)
     end
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       super
 
diff --git a/Library/Homebrew/unpack_strategy/bzip2.rb b/Library/Homebrew/unpack_strategy/bzip2.rb
index af1248c466f53..12190c6a6995d 100644
--- a/Library/Homebrew/unpack_strategy/bzip2.rb
+++ b/Library/Homebrew/unpack_strategy/bzip2.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,18 +6,19 @@ module UnpackStrategy
   class Bzip2
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".bz2"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\ABZh/n)
     end
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       FileUtils.cp path, unpack_dir/basename, preserve: true
       quiet_flags = verbose ? [] : ["-q"]
diff --git a/Library/Homebrew/unpack_strategy/cab.rb b/Library/Homebrew/unpack_strategy/cab.rb
index af73d82fdd008..a4cc7993a6c06 100644
--- a/Library/Homebrew/unpack_strategy/cab.rb
+++ b/Library/Homebrew/unpack_strategy/cab.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,16 +6,17 @@ module UnpackStrategy
   class Cab
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".cab"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\AMSCF/n)
     end
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       system_command! "cabextract",
                       args:    ["-d", unpack_dir, "--", path],
@@ -23,8 +24,9 @@ def extract_to_dir(unpack_dir, basename:, verbose:)
                       verbose:
     end
 
+    sig { returns(T.nilable(T::Array[Formula])) }
     def dependencies
-      @dependencies ||= [Formula["cabextract"]]
+      @dependencies ||= T.let([Formula["cabextract"]], T.nilable(T::Array[Formula]))
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/compress.rb b/Library/Homebrew/unpack_strategy/compress.rb
index 00823122144e6..504f31390bb0c 100644
--- a/Library/Homebrew/unpack_strategy/compress.rb
+++ b/Library/Homebrew/unpack_strategy/compress.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "tar"
@@ -6,11 +6,12 @@
 module UnpackStrategy
   # Strategy for unpacking compress archives.
   class Compress < Tar
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".Z"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\A\037\235/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/cvs.rb b/Library/Homebrew/unpack_strategy/cvs.rb
index af6f0a3a7755b..7e3c5b018b178 100644
--- a/Library/Homebrew/unpack_strategy/cvs.rb
+++ b/Library/Homebrew/unpack_strategy/cvs.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "directory"
@@ -6,8 +6,9 @@
 module UnpackStrategy
   # Strategy for unpacking CVS repositories.
   class Cvs < Directory
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
-      super && (path/"CVS").directory?
+      !!(super && (path/"CVS").directory?)
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/directory.rb b/Library/Homebrew/unpack_strategy/directory.rb
index 90b5ade18e772..62c76284bd014 100644
--- a/Library/Homebrew/unpack_strategy/directory.rb
+++ b/Library/Homebrew/unpack_strategy/directory.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,18 +6,19 @@ module UnpackStrategy
   class Directory
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       []
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.directory?
     end
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       path.children.each do |child|
         system_command! "cp",
diff --git a/Library/Homebrew/unpack_strategy/dmg.rb b/Library/Homebrew/unpack_strategy/dmg.rb
index 92c7f8ca49fd5..b63bd439f507f 100644
--- a/Library/Homebrew/unpack_strategy/dmg.rb
+++ b/Library/Homebrew/unpack_strategy/dmg.rb
@@ -121,9 +121,15 @@ def eject(verbose: false)
         end
       end
 
+      sig { override.returns(T::Array[String]) }
+      def self.extensions = []
+
+      sig { override.params(_path: Pathname).returns(T::Boolean) }
+      def self.can_extract?(_path) = false
+
       private
 
-      sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+      sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
       def extract_to_dir(unpack_dir, basename:, verbose:)
         tries = 3
         bom = begin
@@ -165,7 +171,7 @@ def extract_to_dir(unpack_dir, basename:, verbose:)
     end
     private_constant :Mount
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".dmg"]
     end
@@ -177,7 +183,7 @@ def self.can_extract?(path)
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       mount(verbose:) do |mounts|
         raise "No mounts found in '#{path}'; perhaps this is a bad disk image?" if mounts.empty?
diff --git a/Library/Homebrew/unpack_strategy/executable.rb b/Library/Homebrew/unpack_strategy/executable.rb
index 4c5e712da815f..51cf812786e55 100644
--- a/Library/Homebrew/unpack_strategy/executable.rb
+++ b/Library/Homebrew/unpack_strategy/executable.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "uncompressed"
@@ -6,11 +6,12 @@
 module UnpackStrategy
   # Strategy for unpacking executables.
   class Executable < Uncompressed
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".sh", ".bash"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\A#!\s*\S+/n) ||
         path.magic_number.match?(/\AMZ/n)
diff --git a/Library/Homebrew/unpack_strategy/fossil.rb b/Library/Homebrew/unpack_strategy/fossil.rb
index 1e2dcc00a8871..8914c05aa8a7f 100644
--- a/Library/Homebrew/unpack_strategy/fossil.rb
+++ b/Library/Homebrew/unpack_strategy/fossil.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "system_command"
@@ -9,11 +9,12 @@ class Fossil
     include UnpackStrategy
     extend SystemCommand::Mixin
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       []
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       return false unless path.magic_number.match?(/\ASQLite format 3\000/n)
 
@@ -24,7 +25,7 @@ def self.can_extract?(path)
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       args = if @ref_type && @ref
         [@ref]
diff --git a/Library/Homebrew/unpack_strategy/generic_unar.rb b/Library/Homebrew/unpack_strategy/generic_unar.rb
index 0aee0ce3ac347..ecc6e2c256ec9 100644
--- a/Library/Homebrew/unpack_strategy/generic_unar.rb
+++ b/Library/Homebrew/unpack_strategy/generic_unar.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,22 +6,24 @@ module UnpackStrategy
   class GenericUnar
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       []
     end
 
+    sig { override.params(_path: Pathname).returns(T::Boolean) }
     def self.can_extract?(_path)
       false
     end
 
+    sig { returns(T.nilable(T::Array[Formula])) }
     def dependencies
-      @dependencies ||= [Formula["unar"]]
+      @dependencies ||= T.let([Formula["unar"]], T.nilable(T::Array[Formula]))
     end
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       system_command! "unar",
                       args:    [
diff --git a/Library/Homebrew/unpack_strategy/git.rb b/Library/Homebrew/unpack_strategy/git.rb
index ab39f3c4e0cc5..42b906f125d6b 100644
--- a/Library/Homebrew/unpack_strategy/git.rb
+++ b/Library/Homebrew/unpack_strategy/git.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "directory"
@@ -6,8 +6,9 @@
 module UnpackStrategy
   # Strategy for unpacking Git repositories.
   class Git < Directory
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
-      super && (path/".git").directory?
+      !!(super && (path/".git").directory?)
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/gzip.rb b/Library/Homebrew/unpack_strategy/gzip.rb
index 2ece0befdc456..b525cc6d0b1f0 100644
--- a/Library/Homebrew/unpack_strategy/gzip.rb
+++ b/Library/Homebrew/unpack_strategy/gzip.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,18 +6,19 @@ module UnpackStrategy
   class Gzip
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".gz"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\A\037\213/n)
     end
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       FileUtils.cp path, unpack_dir/basename, preserve: true
       quiet_flags = verbose ? [] : ["-q"]
diff --git a/Library/Homebrew/unpack_strategy/jar.rb b/Library/Homebrew/unpack_strategy/jar.rb
index 892357b48be76..0be166bbaaebe 100644
--- a/Library/Homebrew/unpack_strategy/jar.rb
+++ b/Library/Homebrew/unpack_strategy/jar.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "uncompressed"
@@ -6,11 +6,12 @@
 module UnpackStrategy
   # Strategy for unpacking Java archives.
   class Jar < Uncompressed
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".apk", ".jar"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       return false unless Zip.can_extract?(path)
 
diff --git a/Library/Homebrew/unpack_strategy/lha.rb b/Library/Homebrew/unpack_strategy/lha.rb
index 1da3021ad70d4..0fdb49ed55a5a 100644
--- a/Library/Homebrew/unpack_strategy/lha.rb
+++ b/Library/Homebrew/unpack_strategy/lha.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,22 +6,24 @@ module UnpackStrategy
   class Lha
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".lha", ".lzh"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\A..-(lh0|lh1|lz4|lz5|lzs|lh\\40|lhd|lh2|lh3|lh4|lh5)-/n)
     end
 
+    sig { returns(T.nilable(T::Array[Formula])) }
     def dependencies
-      @dependencies ||= [Formula["lha"]]
+      @dependencies ||= T.let([Formula["lha"]], T.nilable(T::Array[Formula]))
     end
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       system_command! "lha",
                       args:    ["xq2w=#{unpack_dir}", path],
diff --git a/Library/Homebrew/unpack_strategy/lua_rock.rb b/Library/Homebrew/unpack_strategy/lua_rock.rb
index a01fcd2f88d31..f806364a0f046 100644
--- a/Library/Homebrew/unpack_strategy/lua_rock.rb
+++ b/Library/Homebrew/unpack_strategy/lua_rock.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "uncompressed"
@@ -6,11 +6,12 @@
 module UnpackStrategy
   # Strategy for unpacking LuaRock archives.
   class LuaRock < Uncompressed
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".rock"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       return false unless Zip.can_extract?(path)
 
diff --git a/Library/Homebrew/unpack_strategy/lzip.rb b/Library/Homebrew/unpack_strategy/lzip.rb
index 668aa4fdcfc18..710f3684db1d5 100644
--- a/Library/Homebrew/unpack_strategy/lzip.rb
+++ b/Library/Homebrew/unpack_strategy/lzip.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,22 +6,24 @@ module UnpackStrategy
   class Lzip
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".lz"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\ALZIP/n)
     end
 
+    sig { returns(T.nilable(T::Array[Formula])) }
     def dependencies
-      @dependencies ||= [Formula["lzip"]]
+      @dependencies ||= T.let([Formula["lzip"]], T.nilable(T::Array[Formula]))
     end
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       FileUtils.cp path, unpack_dir/basename, preserve: true
       quiet_flags = verbose ? [] : ["-q"]
diff --git a/Library/Homebrew/unpack_strategy/lzma.rb b/Library/Homebrew/unpack_strategy/lzma.rb
index d529e2de4c4f3..d1b6710c42e54 100644
--- a/Library/Homebrew/unpack_strategy/lzma.rb
+++ b/Library/Homebrew/unpack_strategy/lzma.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,22 +6,24 @@ module UnpackStrategy
   class Lzma
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".lzma"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\A\]\000\000\200\000/n)
     end
 
+    sig { returns(T.nilable(T::Array[Formula])) }
     def dependencies
-      @dependencies ||= [Formula["xz"]]
+      @dependencies ||= T.let([Formula["xz"]], T.nilable(T::Array[Formula]))
     end
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       FileUtils.cp path, unpack_dir/basename, preserve: true
       quiet_flags = verbose ? [] : ["-q"]
diff --git a/Library/Homebrew/unpack_strategy/mercurial.rb b/Library/Homebrew/unpack_strategy/mercurial.rb
index c4a77d4d0df0f..146f686c9c0a6 100644
--- a/Library/Homebrew/unpack_strategy/mercurial.rb
+++ b/Library/Homebrew/unpack_strategy/mercurial.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "directory"
@@ -6,12 +6,14 @@
 module UnpackStrategy
   # Strategy for unpacking Mercurial repositories.
   class Mercurial < Directory
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
-      super && (path/".hg").directory?
+      !!(super && (path/".hg").directory?)
     end
 
     private
 
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       system_command! "hg",
                       args:    ["--cwd", path, "archive", "--subrepos", "-y", "-t", "files", unpack_dir],
diff --git a/Library/Homebrew/unpack_strategy/microsoft_office_xml.rb b/Library/Homebrew/unpack_strategy/microsoft_office_xml.rb
index 2ad2a40644cd8..cb54b9b1f7235 100644
--- a/Library/Homebrew/unpack_strategy/microsoft_office_xml.rb
+++ b/Library/Homebrew/unpack_strategy/microsoft_office_xml.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "uncompressed"
@@ -6,7 +6,7 @@
 module UnpackStrategy
   # Strategy for unpacking Microsoft Office documents.
   class MicrosoftOfficeXml < Uncompressed
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [
         ".doc", ".docx",
@@ -15,6 +15,7 @@ def self.extensions
       ]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       return false unless Zip.can_extract?(path)
 
diff --git a/Library/Homebrew/unpack_strategy/otf.rb b/Library/Homebrew/unpack_strategy/otf.rb
index 7a75f78c4cdc7..da593812a5639 100644
--- a/Library/Homebrew/unpack_strategy/otf.rb
+++ b/Library/Homebrew/unpack_strategy/otf.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "uncompressed"
@@ -6,11 +6,12 @@
 module UnpackStrategy
   # Strategy for unpacking OpenType fonts.
   class Otf < Uncompressed
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".otf"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\AOTTO/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/p7zip.rb b/Library/Homebrew/unpack_strategy/p7zip.rb
index 19e0154491d59..44a8c4b986544 100644
--- a/Library/Homebrew/unpack_strategy/p7zip.rb
+++ b/Library/Homebrew/unpack_strategy/p7zip.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,22 +6,24 @@ module UnpackStrategy
   class P7Zip
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".7z"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\A7z\xBC\xAF\x27\x1C/n)
     end
 
+    sig { returns(T.nilable(T::Array[Formula])) }
     def dependencies
-      @dependencies ||= [Formula["p7zip"]]
+      @dependencies ||= T.let([Formula["p7zip"]], T.nilable(T::Array[Formula]))
     end
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       system_command! "7zr",
                       args:    ["x", "-y", "-bd", "-bso0", path, "-o#{unpack_dir}"],
diff --git a/Library/Homebrew/unpack_strategy/pax.rb b/Library/Homebrew/unpack_strategy/pax.rb
index 9a47b9d1d531b..9cbc799c23f64 100644
--- a/Library/Homebrew/unpack_strategy/pax.rb
+++ b/Library/Homebrew/unpack_strategy/pax.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,18 +6,19 @@ module UnpackStrategy
   class Pax
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".pax"]
     end
 
+    sig { override.params(_path: Pathname).returns(T::Boolean) }
     def self.can_extract?(_path)
       false
     end
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       system_command! "pax",
                       args:    ["-rf", path],
diff --git a/Library/Homebrew/unpack_strategy/pkg.rb b/Library/Homebrew/unpack_strategy/pkg.rb
index b48a55244b07a..585edfbea95fd 100644
--- a/Library/Homebrew/unpack_strategy/pkg.rb
+++ b/Library/Homebrew/unpack_strategy/pkg.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "uncompressed"
@@ -6,11 +6,12 @@
 module UnpackStrategy
   # Strategy for unpacking macOS package installers.
   class Pkg < Uncompressed
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".pkg", ".mkpg"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.extname.match?(/\A.m?pkg\Z/) &&
         (path.directory? || path.magic_number.match?(/\Axar!/n))
diff --git a/Library/Homebrew/unpack_strategy/rar.rb b/Library/Homebrew/unpack_strategy/rar.rb
index 289da9134c480..7d8109d654cae 100644
--- a/Library/Homebrew/unpack_strategy/rar.rb
+++ b/Library/Homebrew/unpack_strategy/rar.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,22 +6,24 @@ module UnpackStrategy
   class Rar
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".rar"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\ARar!/n)
     end
 
+    sig { returns(T.nilable(T::Array[Formula])) }
     def dependencies
-      @dependencies ||= [Formula["libarchive"]]
+      @dependencies ||= T.let([Formula["libarchive"]], T.nilable(T::Array[Formula]))
     end
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       system_command! "bsdtar",
                       args:    ["x", "-f", path, "-C", unpack_dir],
diff --git a/Library/Homebrew/unpack_strategy/self_extracting_executable.rb b/Library/Homebrew/unpack_strategy/self_extracting_executable.rb
index b32cfa825cff4..58bad3be74057 100644
--- a/Library/Homebrew/unpack_strategy/self_extracting_executable.rb
+++ b/Library/Homebrew/unpack_strategy/self_extracting_executable.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "generic_unar"
@@ -6,11 +6,12 @@
 module UnpackStrategy
   # Strategy for unpacking self-extracting executables.
   class SelfExtractingExecutable < GenericUnar
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       []
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\AMZ/n) &&
         path.file_type.include?("self-extracting archive")
diff --git a/Library/Homebrew/unpack_strategy/sit.rb b/Library/Homebrew/unpack_strategy/sit.rb
index 7d447eaf69faa..82c48e6d19ba2 100644
--- a/Library/Homebrew/unpack_strategy/sit.rb
+++ b/Library/Homebrew/unpack_strategy/sit.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "generic_unar"
@@ -6,11 +6,12 @@
 module UnpackStrategy
   # Strategy for unpacking Stuffit archives.
   class Sit < GenericUnar
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".sit"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\AStuffIt/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/subversion.rb b/Library/Homebrew/unpack_strategy/subversion.rb
index 7ba74fa5e0f0b..81c037d73e81d 100644
--- a/Library/Homebrew/unpack_strategy/subversion.rb
+++ b/Library/Homebrew/unpack_strategy/subversion.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "directory"
@@ -6,12 +6,14 @@
 module UnpackStrategy
   # Strategy for unpacking Subversion repositories.
   class Subversion < Directory
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
-      super && (path/".svn").directory?
+      !!(super && (path/".svn").directory?)
     end
 
     private
 
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       system_command! "svn",
                       args:    ["export", "--force", ".", unpack_dir],
diff --git a/Library/Homebrew/unpack_strategy/tar.rb b/Library/Homebrew/unpack_strategy/tar.rb
index c3300e7155d47..ae3ff08cd233b 100644
--- a/Library/Homebrew/unpack_strategy/tar.rb
+++ b/Library/Homebrew/unpack_strategy/tar.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "system_command"
@@ -9,7 +9,7 @@ class Tar
     include UnpackStrategy
     extend SystemCommand::Mixin
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [
         ".tar",
@@ -22,6 +22,7 @@ def self.extensions
       ]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       return true if path.magic_number.match?(/\A.{257}ustar/n)
 
@@ -34,7 +35,7 @@ def self.can_extract?(path)
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       Dir.mktmpdir("homebrew-tar", HOMEBREW_TEMP) do |tmpdir|
         tar_path = if DependencyCollector.tar_needs_xz_dependency? && Xz.can_extract?(path)
diff --git a/Library/Homebrew/unpack_strategy/ttf.rb b/Library/Homebrew/unpack_strategy/ttf.rb
index d741378d29583..c240f936792b6 100644
--- a/Library/Homebrew/unpack_strategy/ttf.rb
+++ b/Library/Homebrew/unpack_strategy/ttf.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require_relative "uncompressed"
@@ -6,11 +6,12 @@
 module UnpackStrategy
   # Strategy for unpacking TrueType fonts.
   class Ttf < Uncompressed
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".ttc", ".ttf"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       # TrueType Font
       path.magic_number.match?(/\A\000\001\000\000\000/n) ||
diff --git a/Library/Homebrew/unpack_strategy/uncompressed.rb b/Library/Homebrew/unpack_strategy/uncompressed.rb
index 5d2c3dd511318..58e70082e96be 100644
--- a/Library/Homebrew/unpack_strategy/uncompressed.rb
+++ b/Library/Homebrew/unpack_strategy/uncompressed.rb
@@ -6,6 +6,12 @@ module UnpackStrategy
   class Uncompressed
     include UnpackStrategy
 
+    sig { override.returns(T::Array[String]) }
+    def self.extensions = []
+
+    sig { override.params(_path: Pathname).returns(T::Boolean) }
+    def self.can_extract?(_path) = false
+
     sig {
       params(
         to:                   T.nilable(Pathname),
@@ -20,7 +26,7 @@ def extract_nestedly(to: nil, basename: nil, verbose: false, prioritize_extensio
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose: false)
       FileUtils.cp path, unpack_dir/basename.sub(/^[\da-f]{64}--/, ""), preserve: true, verbose:
     end
diff --git a/Library/Homebrew/unpack_strategy/xar.rb b/Library/Homebrew/unpack_strategy/xar.rb
index f473d35c79099..d6562f8d22f5f 100644
--- a/Library/Homebrew/unpack_strategy/xar.rb
+++ b/Library/Homebrew/unpack_strategy/xar.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,18 +6,19 @@ module UnpackStrategy
   class Xar
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".xar"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\Axar!/n)
     end
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       system_command! "xar",
                       args:    ["-x", "-f", path, "-C", unpack_dir],
diff --git a/Library/Homebrew/unpack_strategy/xz.rb b/Library/Homebrew/unpack_strategy/xz.rb
index 7ac0ceb4e6c38..2e155c687b114 100644
--- a/Library/Homebrew/unpack_strategy/xz.rb
+++ b/Library/Homebrew/unpack_strategy/xz.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,22 +6,24 @@ module UnpackStrategy
   class Xz
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".xz"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\A\xFD7zXZ\x00/n)
     end
 
+    sig { returns(T.nilable(T::Array[Formula])) }
     def dependencies
-      @dependencies ||= [Formula["xz"]]
+      @dependencies ||= T.let([Formula["xz"]], T.nilable(T::Array[Formula]))
     end
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       FileUtils.cp path, unpack_dir/basename, preserve: true
       quiet_flags = verbose ? [] : ["-q"]
diff --git a/Library/Homebrew/unpack_strategy/zip.rb b/Library/Homebrew/unpack_strategy/zip.rb
index dc4d6d350b5b9..28e413e00adad 100644
--- a/Library/Homebrew/unpack_strategy/zip.rb
+++ b/Library/Homebrew/unpack_strategy/zip.rb
@@ -6,12 +6,12 @@ module UnpackStrategy
   class Zip
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".zip"]
     end
 
-    sig { params(path: Pathname).returns(T::Boolean) }
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\APK(\003\004|\005\006)/n)
     end
@@ -23,6 +23,7 @@ def self.can_extract?(path)
               .returns(SystemCommand::Result)
     }
     def extract_to_dir(unpack_dir, basename:, verbose:)
+      odebug "in unpack_strategy, zip, extract_to_dir, verbose: #{verbose.inspect}"
       unzip = if which("unzip").blank?
         begin
           Formula["unzip"]
diff --git a/Library/Homebrew/unpack_strategy/zstd.rb b/Library/Homebrew/unpack_strategy/zstd.rb
index f8cdacb0abec3..475b0ca518e49 100644
--- a/Library/Homebrew/unpack_strategy/zstd.rb
+++ b/Library/Homebrew/unpack_strategy/zstd.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module UnpackStrategy
@@ -6,22 +6,24 @@ module UnpackStrategy
   class Zstd
     include UnpackStrategy
 
-    sig { returns(T::Array[String]) }
+    sig { override.returns(T::Array[String]) }
     def self.extensions
       [".zst"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\x28\xB5\x2F\xFD/n)
     end
 
+    sig { returns(T.nilable(T::Array[Formula])) }
     def dependencies
-      @dependencies ||= [Formula["zstd"]]
+      @dependencies ||= T.let([Formula["zstd"]], T.nilable(T::Array[Formula]))
     end
 
     private
 
-    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).returns(T.untyped) }
+    sig { override.params(unpack_dir: Pathname, basename: Pathname, verbose: T::Boolean).void }
     def extract_to_dir(unpack_dir, basename:, verbose:)
       FileUtils.cp path, unpack_dir/basename, preserve: true
       quiet_flags = verbose ? [] : ["-q"]
diff --git a/Library/Homebrew/utils/shebang.rb b/Library/Homebrew/utils/shebang.rb
index 3a5d784b1fa81..93df6425b1e66 100644
--- a/Library/Homebrew/utils/shebang.rb
+++ b/Library/Homebrew/utils/shebang.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 module Utils
@@ -8,13 +8,20 @@ module Shebang
 
     # Specification on how to rewrite a given shebang.
     class RewriteInfo
-      attr_reader :regex, :max_length, :replacement
+      sig { returns(Regexp) }
+      attr_reader :regex
+
+      sig { returns(Integer) }
+      attr_reader :max_length
+
+      sig { returns(T.any(String, Pathname)) }
+      attr_reader :replacement
 
       sig { params(regex: Regexp, max_length: Integer, replacement: T.any(String, Pathname)).void }
       def initialize(regex, max_length, replacement)
-        @regex = regex
-        @max_length = max_length
-        @replacement = replacement
+        @regex = T.let(regex, Regexp)
+        @max_length = T.let(max_length, Integer)
+        @replacement = T.let(replacement, T.any(String, Pathname))
       end
     end