diff --git a/Library/Homebrew/unpack_strategy/air.rb b/Library/Homebrew/unpack_strategy/air.rb
index 1aeaa830da..6415995419 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
@@ -11,13 +11,15 @@ module UnpackStrategy
       [".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 =
diff --git a/Library/Homebrew/unpack_strategy/bazaar.rb b/Library/Homebrew/unpack_strategy/bazaar.rb
index b952ba206d..770cca92aa 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"
@@ -6,8 +6,9 @@ require_relative "directory"
 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
diff --git a/Library/Homebrew/unpack_strategy/bzip2.rb b/Library/Homebrew/unpack_strategy/bzip2.rb
index 6225b93388..12190c6a69 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
@@ -11,6 +11,7 @@ module UnpackStrategy
       [".bz2"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\ABZh/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/cab.rb b/Library/Homebrew/unpack_strategy/cab.rb
index 388ceb425c..a4cc7993a6 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
@@ -11,6 +11,7 @@ module UnpackStrategy
       [".cab"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\AMSCF/n)
     end
@@ -23,8 +24,9 @@ module UnpackStrategy
                       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 e2d6ce37f8..504f31390b 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"
@@ -11,6 +11,7 @@ module UnpackStrategy
       [".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 af6f0a3a77..7e3c5b018b 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 @@ require_relative "directory"
 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 50127031da..62c76284bd 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
@@ -11,6 +11,7 @@ module UnpackStrategy
       []
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.directory?
     end
diff --git a/Library/Homebrew/unpack_strategy/executable.rb b/Library/Homebrew/unpack_strategy/executable.rb
index 86c381ef13..51cf812786 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"
@@ -11,6 +11,7 @@ module UnpackStrategy
       [".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 8517d064f2..8914c05aa8 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"
@@ -14,6 +14,7 @@ module UnpackStrategy
       []
     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)
 
diff --git a/Library/Homebrew/unpack_strategy/generic_unar.rb b/Library/Homebrew/unpack_strategy/generic_unar.rb
index 1e3075e947..ecc6e2c256 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
@@ -11,12 +11,14 @@ module UnpackStrategy
       []
     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
diff --git a/Library/Homebrew/unpack_strategy/git.rb b/Library/Homebrew/unpack_strategy/git.rb
index ab39f3c4e0..42b906f125 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 @@ require_relative "directory"
 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 70ff74c56e..b525cc6d0b 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
@@ -11,6 +11,7 @@ module UnpackStrategy
       [".gz"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\A\037\213/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/jar.rb b/Library/Homebrew/unpack_strategy/jar.rb
index 8082d8602c..0be166bbaa 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"
@@ -11,6 +11,7 @@ module UnpackStrategy
       [".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 ece0b4b8cc..0fdb49ed55 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
@@ -11,12 +11,14 @@ module UnpackStrategy
       [".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
diff --git a/Library/Homebrew/unpack_strategy/lua_rock.rb b/Library/Homebrew/unpack_strategy/lua_rock.rb
index b054b9f810..f806364a0f 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"
@@ -11,6 +11,7 @@ module UnpackStrategy
       [".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 90150a40c6..710f3684db 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
@@ -11,12 +11,14 @@ module UnpackStrategy
       [".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
diff --git a/Library/Homebrew/unpack_strategy/lzma.rb b/Library/Homebrew/unpack_strategy/lzma.rb
index 5b6ed1c4e8..d1b6710c42 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
@@ -11,12 +11,14 @@ module UnpackStrategy
       [".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
diff --git a/Library/Homebrew/unpack_strategy/mercurial.rb b/Library/Homebrew/unpack_strategy/mercurial.rb
index c4a77d4d0d..146f686c9c 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 @@ require_relative "directory"
 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 dfc4c084f4..cb54b9b1f7 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"
@@ -15,6 +15,7 @@ module UnpackStrategy
       ]
     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 b4839b2a61..da593812a5 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"
@@ -11,6 +11,7 @@ module UnpackStrategy
       [".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 69e2c9deab..44a8c4b986 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
@@ -11,12 +11,14 @@ module UnpackStrategy
       [".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
diff --git a/Library/Homebrew/unpack_strategy/pax.rb b/Library/Homebrew/unpack_strategy/pax.rb
index bc5f89c15a..9cbc799c23 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
@@ -11,6 +11,7 @@ module UnpackStrategy
       [".pax"]
     end
 
+    sig { override.params(_path: Pathname).returns(T::Boolean) }
     def self.can_extract?(_path)
       false
     end
diff --git a/Library/Homebrew/unpack_strategy/pkg.rb b/Library/Homebrew/unpack_strategy/pkg.rb
index e4b288b827..585edfbea9 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"
@@ -11,6 +11,7 @@ module UnpackStrategy
       [".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 06394dbdf4..7d8109d654 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
@@ -11,12 +11,14 @@ module UnpackStrategy
       [".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
diff --git a/Library/Homebrew/unpack_strategy/self_extracting_executable.rb b/Library/Homebrew/unpack_strategy/self_extracting_executable.rb
index 078ce77365..58bad3be74 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"
@@ -11,6 +11,7 @@ module UnpackStrategy
       []
     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 631c446297..82c48e6d19 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"
@@ -11,6 +11,7 @@ module UnpackStrategy
       [".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 7ba74fa5e0..81c037d73e 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 @@ require_relative "directory"
 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 adbf59def5..ae3ff08cd2 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"
@@ -22,6 +22,7 @@ module UnpackStrategy
       ]
     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)
 
diff --git a/Library/Homebrew/unpack_strategy/ttf.rb b/Library/Homebrew/unpack_strategy/ttf.rb
index 3c73a6801e..c240f93679 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"
@@ -11,6 +11,7 @@ module UnpackStrategy
       [".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/xar.rb b/Library/Homebrew/unpack_strategy/xar.rb
index 0d571fa5ac..d6562f8d22 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
@@ -11,6 +11,7 @@ module UnpackStrategy
       [".xar"]
     end
 
+    sig { override.params(path: Pathname).returns(T::Boolean) }
     def self.can_extract?(path)
       path.magic_number.match?(/\Axar!/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/xz.rb b/Library/Homebrew/unpack_strategy/xz.rb
index a9ffc96a65..2e155c687b 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
@@ -11,12 +11,14 @@ module UnpackStrategy
       [".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
diff --git a/Library/Homebrew/unpack_strategy/zip.rb b/Library/Homebrew/unpack_strategy/zip.rb
index 59da683f35..28e413e00a 100644
--- a/Library/Homebrew/unpack_strategy/zip.rb
+++ b/Library/Homebrew/unpack_strategy/zip.rb
@@ -23,6 +23,7 @@ module UnpackStrategy
               .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 3dfa808f34..475b0ca518 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
@@ -11,12 +11,14 @@ module UnpackStrategy
       [".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