diff --git a/Library/Homebrew/formula.rb b/Library/Homebrew/formula.rb
index 8f13a0ff48..0837449691 100644
--- a/Library/Homebrew/formula.rb
+++ b/Library/Homebrew/formula.rb
@@ -353,18 +353,21 @@ class Formula
 
   # Is the currently active {SoftwareSpec} a {#stable} build?
   # @private
+  sig { returns(T::Boolean) }
   def stable?
     active_spec == stable
   end
 
   # Is the currently active {SoftwareSpec} a {#head} build?
   # @private
+  sig { returns(T::Boolean) }
   def head?
     active_spec == head
   end
 
   # Is this formula HEAD-only?
   # @private
+  sig { returns(T.nilable(T::Boolean)) }
   def head_only?
     head && !stable
   end
@@ -573,12 +576,14 @@ class Formula
   # This is actually just a check for if the {#latest_installed_prefix} directory
   # exists and is not empty.
   # @private
+  sig { returns(T::Boolean) }
   def latest_version_installed?
     (dir = latest_installed_prefix).directory? && !dir.children.empty?
   end
 
   # If at least one version of {Formula} is installed.
   # @private
+  sig { returns(T::Boolean) }
   def any_version_installed?
     installed_prefixes.any? { |keg| (keg/Tab::FILENAME).file? }
   end
@@ -652,11 +657,13 @@ class Formula
   end
 
   # Is the formula linked?
+  sig { returns(T::Boolean) }
   def linked?
     linked_keg.symlink?
   end
 
   # Is the formula linked to `opt`?
+  sig { returns(T::Boolean) }
   def optlinked?
     opt_prefix.symlink?
   end
@@ -708,6 +715,7 @@ class Formula
   #
   # No `make install` available?
   # <pre>bin.install "binary1"</pre>
+  sig { returns(Pathname) }
   def bin
     prefix/"bin"
   end
@@ -715,6 +723,7 @@ class Formula
   # The directory where the formula's documentation should be installed.
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
+  sig { returns(Pathname) }
   def doc
     share/"doc"/name
   end
@@ -725,6 +734,7 @@ class Formula
   #
   # No `make install` available?
   # <pre>include.install "example.h"</pre>
+  sig { returns(Pathname) }
   def include
     prefix/"include"
   end
@@ -732,6 +742,7 @@ class Formula
   # The directory where the formula's info files should be installed.
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
+  sig { returns(Pathname) }
   def info
     share/"info"
   end
@@ -742,6 +753,7 @@ class Formula
   #
   # No `make install` available?
   # <pre>lib.install "example.dylib"</pre>
+  sig { returns(Pathname) }
   def lib
     prefix/"lib"
   end
@@ -754,6 +766,7 @@ class Formula
   # <pre>libexec.install "foo.jar"
   # bin.write_jar_script libexec/"foo.jar", "foo"
   # </pre>
+  sig { returns(Pathname) }
   def libexec
     prefix/"libexec"
   end
@@ -763,6 +776,7 @@ class Formula
   # `brew link` for formulae that are not keg-only.
   # Often one of the more specific `man` functions should be used instead,
   # e.g. {#man1}.
+  sig { returns(Pathname) }
   def man
     share/"man"
   end
@@ -773,6 +787,7 @@ class Formula
   #
   # No `make install` available?
   # <pre>man1.install "example.1"</pre>
+  sig { returns(Pathname) }
   def man1
     man/"man1"
   end
@@ -780,6 +795,7 @@ class Formula
   # The directory where the formula's man2 pages should be installed.
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
+  sig { returns(Pathname) }
   def man2
     man/"man2"
   end
@@ -790,6 +806,7 @@ class Formula
   #
   # No `make install` available?
   # <pre>man3.install "man.3"</pre>
+  sig { returns(Pathname) }
   def man3
     man/"man3"
   end
@@ -797,6 +814,7 @@ class Formula
   # The directory where the formula's man4 pages should be installed.
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
+  sig { returns(Pathname) }
   def man4
     man/"man4"
   end
@@ -804,6 +822,7 @@ class Formula
   # The directory where the formula's man5 pages should be installed.
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
+  sig { returns(Pathname) }
   def man5
     man/"man5"
   end
@@ -811,6 +830,7 @@ class Formula
   # The directory where the formula's man6 pages should be installed.
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
+  sig { returns(Pathname) }
   def man6
     man/"man6"
   end
@@ -818,6 +838,7 @@ class Formula
   # The directory where the formula's man7 pages should be installed.
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
+  sig { returns(Pathname) }
   def man7
     man/"man7"
   end
@@ -825,6 +846,7 @@ class Formula
   # The directory where the formula's man8 pages should be installed.
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
+  sig { returns(Pathname) }
   def man8
     man/"man8"
   end
@@ -833,6 +855,7 @@ class Formula
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
   # Generally we try to migrate these to {#bin} instead.
+  sig { returns(Pathname) }
   def sbin
     prefix/"sbin"
   end
@@ -852,6 +875,7 @@ class Formula
   #
   # Install `./example_code/simple/ones` to `share/demos/examples`:
   # <pre>(share/"demos").install "example_code/simple/ones" => "examples"</pre>
+  sig { returns(Pathname) }
   def share
     prefix/"share"
   end
@@ -863,6 +887,7 @@ class Formula
   #
   # No `make install` available?
   # <pre>pkgshare.install "examples"</pre>
+  sig { returns(Pathname) }
   def pkgshare
     prefix/"share"/name
   end
@@ -872,6 +897,7 @@ class Formula
   #
   # To install an Emacs mode included with a software package:
   # <pre>elisp.install "contrib/emacs/example-mode.el"</pre>
+  sig { returns(Pathname) }
   def elisp
     prefix/"share/emacs/site-lisp"/name
   end
@@ -880,6 +906,7 @@ class Formula
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
   # This is not symlinked into `HOMEBREW_PREFIX`.
+  sig { returns(Pathname) }
   def frameworks
     prefix/"Frameworks"
   end
@@ -888,6 +915,7 @@ class Formula
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
   # This is not symlinked into `HOMEBREW_PREFIX`.
+  sig { returns(Pathname) }
   def kext_prefix
     prefix/"Library/Extensions"
   end
@@ -897,6 +925,7 @@ class Formula
   # but will write a new file named `*.default`.
   # This directory is not inside the `HOMEBREW_CELLAR` so it persists
   # across upgrades.
+  sig { returns(Pathname) }
   def etc
     (HOMEBREW_PREFIX/"etc").extend(InstallRenamed)
   end
@@ -905,6 +934,7 @@ class Formula
   # e.g. `$HOMEBREW_PREFIX/etc/openssl@1.1`
   # Anything using `pkgetc.install` will not overwrite other files on
   # e.g. upgrades but will write a new file named `*.default`.
+  sig { returns(Pathname) }
   def pkgetc
     (HOMEBREW_PREFIX/"etc"/name).extend(InstallRenamed)
   end
@@ -912,6 +942,7 @@ class Formula
   # The directory where the formula's variable files should be installed.
   # This directory is not inside the `HOMEBREW_CELLAR` so it persists
   # across upgrades.
+  sig { returns(Pathname) }
   def var
     HOMEBREW_PREFIX/"var"
   end
@@ -920,6 +951,7 @@ class Formula
   # installed.
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
+  sig { returns(Pathname) }
   def zsh_function
     share/"zsh/site-functions"
   end
@@ -928,6 +960,7 @@ class Formula
   # installed.
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
+  sig { returns(Pathname) }
   def fish_function
     share/"fish/vendor_functions.d"
   end
@@ -936,6 +969,7 @@ class Formula
   # installed.
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
+  sig { returns(Pathname) }
   def bash_completion
     prefix/"etc/bash_completion.d"
   end
@@ -944,6 +978,7 @@ class Formula
   # installed.
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
+  sig { returns(Pathname) }
   def zsh_completion
     share/"zsh/site-functions"
   end
@@ -952,6 +987,7 @@ class Formula
   # installed.
   # This is symlinked into `HOMEBREW_PREFIX` after installation or with
   # `brew link` for formulae that are not keg-only.
+  sig { returns(Pathname) }
   def fish_completion
     share/"fish/vendor_completions.d"
   end
@@ -960,12 +996,14 @@ class Formula
   # installation so, despite not being in `HOMEBREW_CELLAR`, they are installed
   # there after pouring a bottle.
   # @private
+  sig { returns(Pathname) }
   def bottle_prefix
     prefix/".bottle"
   end
 
   # The directory where the formula's installation or test logs will be written.
   # @private
+  sig { returns(Pathname) }
   def logs
     HOMEBREW_LOGS + name
   end
@@ -1220,6 +1258,7 @@ class Formula
   # Rarely, you don't want your library symlinked into the main prefix.
   # See `gettext.rb` for an example.
   # @see .keg_only
+  sig { returns(T::Boolean) }
   def keg_only?
     return false unless keg_only_reason
 
@@ -1405,6 +1444,7 @@ class Formula
     end
   end
 
+  sig { returns(T.nilable(T::Boolean)) }
   def migration_needed?
     !oldnames_to_migrate.empty? && !rack.exist?
   end
@@ -1446,6 +1486,7 @@ class Formula
     end
   end
 
+  sig { returns(T::Boolean) }
   def new_formula_available?
     installed_alias_target_changed? && !latest_formula.latest_version_installed?
   end
@@ -1456,6 +1497,7 @@ class Formula
 
   # Has the target of the alias used to install this formula changed?
   # Returns false if the formula wasn't installed with an alias.
+  sig { returns(T::Boolean) }
   def installed_alias_target_changed?
     target = current_installed_alias_target
     return false unless target
@@ -1464,12 +1506,14 @@ class Formula
   end
 
   # Is this formula the target of an alias used to install an old formula?
+  sig { returns(T::Boolean) }
   def supersedes_an_installed_formula?
     old_installed_formulae.any?
   end
 
   # Has the alias used to install the formula changed, or are different
   # formulae already installed with this alias?
+  sig { returns(T::Boolean) }
   def alias_changed?
     installed_alias_target_changed? || supersedes_an_installed_formula?
   end
@@ -1490,6 +1534,7 @@ class Formula
   end
 
   # @private
+  sig { params(fetch_head: T::Boolean).returns(T::Boolean) }
   def outdated?(fetch_head: false)
     !outdated_kegs(fetch_head: fetch_head).empty?
   rescue Migrator::MigrationNeededError
@@ -1969,12 +2014,14 @@ class Formula
 
   # True if this formula is provided by Homebrew itself
   # @private
+  sig { returns(T.nilable(T::Boolean)) }
   def core_formula?
     tap&.core_tap?
   end
 
   # True if this formula is provided by external Tap
   # @private
+  sig { returns(T::Boolean) }
   def tap?
     return false unless tap
 
@@ -1984,6 +2031,7 @@ class Formula
   # True if this formula can be installed on this platform
   # Redefined in extend/os.
   # @private
+  sig { returns(T::Boolean) }
   def valid_platform?
     requirements.none?(MacOSRequirement) && requirements.none?(LinuxRequirement)
   end
@@ -2936,6 +2984,7 @@ class Formula
     # Whether a livecheck specification is defined or not.
     # It returns true when a livecheck block is present in the {Formula} and
     # false otherwise, and is used by livecheck.
+    sig { returns(T::Boolean) }
     def livecheckable?
       @livecheckable == true
     end
@@ -2943,6 +2992,7 @@ class Formula
     # Whether a service specification is defined or not.
     # It returns true when a service block is present in the {Formula} and
     # false otherwise, and is used by service.
+    sig { returns(T::Boolean) }
     def service?
       @service_block.present?
     end
@@ -3502,8 +3552,8 @@ class Formula
 
     # Whether this {Formula} is deprecated (i.e. warns on installation).
     # Defaults to false.
-    # @return [Boolean]
     # @see .deprecate!
+    sig { returns(T::Boolean) }
     def deprecated?
       @deprecated == true
     end
@@ -3542,8 +3592,8 @@ class Formula
 
     # Whether this {Formula} is disabled (i.e. cannot be installed).
     # Defaults to false.
-    # @return [Boolean]
     # @see .disable!
+    sig { returns(T::Boolean) }
     def disabled?
       @disabled == true
     end
diff --git a/Library/Homebrew/test/utils/inreplace_spec.rb b/Library/Homebrew/test/utils/inreplace_spec.rb
index 79217d0840..20c91672d9 100644
--- a/Library/Homebrew/test/utils/inreplace_spec.rb
+++ b/Library/Homebrew/test/utils/inreplace_spec.rb
@@ -7,7 +7,7 @@ describe Utils::Inreplace do
   let(:file) { Tempfile.new("test") }
 
   before do
-    file.write <<~EOS
+    File.binwrite(file, <<~EOS)
       a
       b
       c
@@ -52,4 +52,18 @@ describe Utils::Inreplace do
       end.to raise_error(Utils::Inreplace::Error)
     end
   end
+
+  describe "#gsub!" do
+    it "substitutes pathname within file" do
+      # For a specific instance of this, see https://github.com/Homebrew/homebrew-core/blob/a8b0b10/Formula/loki.rb#L48
+      described_class.inreplace(file.path) do |s|
+        s.gsub!(Pathname("b"), Pathname("f"))
+      end
+      expect(File.binread(file)).to eq <<~EOS
+        a
+        f
+        c
+      EOS
+    end
+  end
 end
diff --git a/Library/Homebrew/utils/inreplace.rb b/Library/Homebrew/utils/inreplace.rb
index b7e625b6ea..6cb8c25729 100644
--- a/Library/Homebrew/utils/inreplace.rb
+++ b/Library/Homebrew/utils/inreplace.rb
@@ -47,6 +47,7 @@ module Utils
     }
     def inreplace(paths, before = nil, after = nil, audit_result = true) # rubocop:disable Style/OptionalBooleanParameter
       after &&= after.to_s
+      before = before.to_s if before.is_a?(Pathname)
 
       errors = {}
 
@@ -59,7 +60,7 @@ module Utils
         if before.nil? && after.nil?
           yield s
         else
-          s.gsub!(T.must(before), after, audit_result)
+          s.gsub!(T.must(before), T.must(after), audit_result)
         end
 
         errors[path] = s.errors unless s.errors.empty?
diff --git a/Library/Homebrew/utils/string_inreplace_extension.rb b/Library/Homebrew/utils/string_inreplace_extension.rb
index 6288089891..4c4d4917d4 100644
--- a/Library/Homebrew/utils/string_inreplace_extension.rb
+++ b/Library/Homebrew/utils/string_inreplace_extension.rb
@@ -1,16 +1,20 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 # Used by the `inreplace` function (in `utils.rb`).
 #
 # @api private
 class StringInreplaceExtension
-  attr_accessor :errors, :inreplace_string
+  sig { returns(T::Array[String]) }
+  attr_accessor :errors
+
+  sig { returns(String) }
+  attr_accessor :inreplace_string
 
   sig { params(string: String).void }
   def initialize(string)
     @inreplace_string = string
-    @errors = []
+    @errors = T.let([], T::Array[String])
   end
 
   # Same as `String#sub!`, but warns if nothing was replaced.
@@ -27,11 +31,12 @@ class StringInreplaceExtension
   #
   # @api public
   sig {
-    params(before: T.any(Pathname, Regexp, String), after: T.nilable(String), audit_result: T::Boolean)
+    params(before: T.any(Pathname, Regexp, String), after: T.any(Pathname, String), audit_result: T::Boolean)
       .returns(T.nilable(String))
   }
   def gsub!(before, after, audit_result = true) # rubocop:disable Style/OptionalBooleanParameter
-    result = inreplace_string.gsub!(before, after)
+    before = before.to_s if before.is_a?(Pathname)
+    result = inreplace_string.gsub!(before, after.to_s)
     errors << "expected replacement of #{before.inspect} with #{after.inspect}" if audit_result && result.nil?
     result
   end
@@ -65,6 +70,6 @@ class StringInreplaceExtension
   # @api public
   sig { params(flag: String).returns(String) }
   def get_make_var(flag)
-    inreplace_string[/^#{Regexp.escape(flag)}[ \t]*[\\?+:!]?=[ \t]*((?:.*\\\n)*.*)$/, 1]
+    T.must(inreplace_string[/^#{Regexp.escape(flag)}[ \t]*[\\?+:!]?=[ \t]*((?:.*\\\n)*.*)$/, 1])
   end
 end