diff --git a/Library/Homebrew/dev-cmd/audit.rb b/Library/Homebrew/dev-cmd/audit.rb
index 7451f2124f547..21682ae9ed7cc 100644
--- a/Library/Homebrew/dev-cmd/audit.rb
+++ b/Library/Homebrew/dev-cmd/audit.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
@@ -329,6 +329,7 @@ def run
 
       private
 
+      sig { params(results: T::Hash[[Symbol, Pathname], T::Array[T::Hash[Symbol, T.untyped]]]).void }
       def print_problems(results)
         results.each do |(name, path), problems|
           problem_lines = format_problem_lines(problems)
@@ -343,6 +344,7 @@ def print_problems(results)
         end
       end
 
+      sig { params(problems: T::Array[T::Hash[Symbol, T.untyped]]).returns(T::Array[String]) }
       def format_problem_lines(problems)
         problems.map do |problem|
           status = " #{Formatter.success("[corrected]")}" if problem.fetch(:corrected)
diff --git a/Library/Homebrew/dev-cmd/bottle.rb b/Library/Homebrew/dev-cmd/bottle.rb
index 32c04a66edfa5..6f96a13ee84d5 100644
--- a/Library/Homebrew/dev-cmd/bottle.rb
+++ b/Library/Homebrew/dev-cmd/bottle.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
@@ -20,7 +20,7 @@ module DevCmd
     class Bottle < AbstractCommand
       include FileUtils
 
-      BOTTLE_ERB = <<-EOS.freeze
+      BOTTLE_ERB = T.let(<<-EOS.freeze, String)
   bottle do
     <% if [HOMEBREW_BOTTLE_DEFAULT_DOMAIN.to_s,
            "#{HOMEBREW_BOTTLE_DEFAULT_DOMAIN}/bottles"].exclude?(root_url) %>
@@ -39,9 +39,9 @@ class Bottle < AbstractCommand
 
       MAXIMUM_STRING_MATCHES = 100
 
-      ALLOWABLE_HOMEBREW_REPOSITORY_LINKS = [
+      ALLOWABLE_HOMEBREW_REPOSITORY_LINKS = T.let([
         %r{#{Regexp.escape(HOMEBREW_LIBRARY)}/Homebrew/os/(mac|linux)/pkgconfig},
-      ].freeze
+      ].freeze, T::Array[Regexp])
 
       cmd_args do
         description <<~EOS
@@ -110,6 +110,10 @@ def run
         end
       end
 
+      sig {
+        params(tag: Symbol, digest: T.any(Checksum, String), cellar: T.nilable(T.any(String, Symbol)),
+               tag_column: Integer, digest_column: Integer).returns(String)
+      }
       def generate_sha256_line(tag, digest, cellar, tag_column, digest_column)
         line = "sha256 "
         tag_column += line.length
@@ -125,6 +129,7 @@ def generate_sha256_line(tag, digest, cellar, tag_column, digest_column)
         %Q(#{line}"#{digest}")
       end
 
+      sig { params(bottle: BottleSpecification, root_url_using: T.nilable(String)).returns(String) }
       def bottle_output(bottle, root_url_using)
         cellars = bottle.checksums.filter_map do |checksum|
           cellar = checksum["cellar"]
@@ -153,12 +158,14 @@ def bottle_output(bottle, root_url_using)
         erb.result(erb_binding).gsub(/^\s*$\n/, "")
       end
 
+      sig { params(filenames: T::Array[String]).returns(T::Array[T::Hash[String, T.untyped]]) }
       def parse_json_files(filenames)
         filenames.map do |filename|
           JSON.parse(File.read(filename))
         end
       end
 
+      sig { params(json_files: T::Array[T::Hash[String, T.untyped]]).returns(T::Hash[String, T.untyped]) }
       def merge_json_files(json_files)
         json_files.reduce({}) do |hash, json_file|
           json_file.each_value do |json_hash|
@@ -172,6 +179,10 @@ def merge_json_files(json_files)
         end
       end
 
+      sig {
+        params(old_keys: T::Array[String], old_bottle_spec: BottleSpecification,
+               new_bottle_hash: T::Hash[String, T.untyped]).returns(T::Array[T::Array[String]])
+      }
       def merge_bottle_spec(old_keys, old_bottle_spec, new_bottle_hash)
         mismatches = []
         checksums = []
@@ -214,16 +225,20 @@ def merge_bottle_spec(old_keys, old_bottle_spec, new_bottle_hash)
 
       private
 
+      sig {
+        params(string: String, keg: Keg, ignores: T::Array[String],
+               formula_and_runtime_deps_names: T.nilable(T::Array[String])).returns(T::Boolean)
+      }
       def keg_contain?(string, keg, ignores, formula_and_runtime_deps_names = nil)
         @put_string_exists_header, @put_filenames = nil
 
         print_filename = lambda do |str, filename|
           unless @put_string_exists_header
             opoo "String '#{str}' still exists in these files:"
-            @put_string_exists_header = true
+            @put_string_exists_header = T.let(true, T.nilable(T::Boolean))
           end
 
-          @put_filenames ||= []
+          @put_filenames ||= T.let([], T.nilable(T::Array[T.any(String, Pathname)]))
 
           return false if @put_filenames.include?(filename)
 
@@ -265,6 +280,7 @@ def keg_contain?(string, keg, ignores, formula_and_runtime_deps_names = nil)
         keg_contain_absolute_symlink_starting_with?(string, keg) || result
       end
 
+      sig { params(string: String, keg: Keg).returns(T::Boolean) }
       def keg_contain_absolute_symlink_starting_with?(string, keg)
         absolute_symlinks_start_with_string = []
         keg.find do |pn|
@@ -283,6 +299,7 @@ def keg_contain_absolute_symlink_starting_with?(string, keg)
         !absolute_symlinks_start_with_string.empty?
       end
 
+      sig { params(cellar: T.nilable(T.any(String, Symbol))).returns(T::Boolean) }
       def cellar_parameter_needed?(cellar)
         default_cellars = [
           Homebrew::DEFAULT_MACOS_CELLAR,
@@ -292,6 +309,7 @@ def cellar_parameter_needed?(cellar)
         cellar.present? && default_cellars.exclude?(cellar)
       end
 
+      sig { returns(T.nilable(T::Boolean)) }
       def sudo_purge
         return unless ENV["HOMEBREW_BOTTLE_SUDO_PURGE"]
 
@@ -354,6 +372,7 @@ def setup_tar_and_args!(mtime)
         [gnu_tar(gnu_tar_formula), reproducible_gnutar_args(mtime)].freeze
       end
 
+      sig { params(formula: T.untyped).returns(T::Array[T.untyped]) }
       def formula_ignores(formula)
         ignores = []
         cellar_regex = Regexp.escape(HOMEBREW_CELLAR)
@@ -384,6 +403,7 @@ def formula_ignores(formula)
         ignores.compact
       end
 
+      sig { params(formula: Formula).void }
       def bottle_formula(formula)
         local_bottle_json = args.json? && formula.local_bottle_path.present?
 
@@ -453,6 +473,8 @@ def bottle_formula(formula)
 
         if local_bottle_json
           bottle_path = formula.local_bottle_path
+          return if bottle_path.blank?
+
           local_filename = bottle_path.basename.to_s
 
           tab_path = Utils::Bottles.receipt_path(bottle_path)
@@ -471,6 +493,7 @@ def bottle_formula(formula)
         else
           tar_filename = filename.to_s.sub(/.gz$/, "")
           tar_path = Pathname.pwd/tar_filename
+          return if tar_path.blank?
 
           keg = Keg.new(formula.prefix)
         end
@@ -681,6 +704,7 @@ def bottle_formula(formula)
         json_path.write(JSON.pretty_generate(json))
       end
 
+      sig { returns(T::Hash[String, T.untyped]) }
       def merge
         bottles_hash = merge_json_files(parse_json_files(args.named))
 
@@ -750,7 +774,7 @@ def merge
             end
           end
 
-          all_bottle_hash = T.let(nil, T.nilable(Hash))
+          all_bottle_hash = T.let(nil, T.nilable(T::Hash[String, T.untyped]))
           bottle_hash["bottle"]["tags"].each do |tag, tag_hash|
             filename = ::Bottle::Filename.new(
               formula_name,
@@ -801,7 +825,7 @@ def merge
           checksums = old_checksums(formula, formula_ast, bottle_hash)
           update_or_add = checksums.nil? ? "add" : "update"
 
-          checksums&.each(&bottle.method(:sha256))
+          checksums&.each { |checksum| bottle.sha256(checksum) }
           output = bottle_output(bottle, args.root_url_using)
           puts output
 
@@ -835,8 +859,12 @@ def merge
         end
       end
 
+      sig {
+        params(formula: Formula, formula_ast: Utils::AST::FormulaAST,
+               bottle_hash: T::Hash[String, T.untyped]).returns(T.nilable(T::Array[String]))
+      }
       def old_checksums(formula, formula_ast, bottle_hash)
-        bottle_node = formula_ast.bottle_block
+        bottle_node = T.cast(formula_ast.bottle_block, T.nilable(RuboCop::AST::BlockNode))
         return if bottle_node.nil?
         return [] unless args.keep_old?
 
diff --git a/Library/Homebrew/dev-cmd/bump-formula-pr.rb b/Library/Homebrew/dev-cmd/bump-formula-pr.rb
index 1bbbc6b9d8c50..74dea4cf15aa5 100644
--- a/Library/Homebrew/dev-cmd/bump-formula-pr.rb
+++ b/Library/Homebrew/dev-cmd/bump-formula-pr.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
@@ -145,10 +145,10 @@ def run
 
         old_mirrors = formula_spec.mirrors
         new_mirrors ||= args.mirror
-        new_mirror ||= determine_mirror(new_url)
-        new_mirrors ||= [new_mirror] if new_mirror.present?
-
-        check_for_mirrors(formula, old_mirrors, new_mirrors) if new_url.present?
+        if new_url.present? && (new_mirror = determine_mirror(new_url))
+          new_mirrors ||= [new_mirror]
+          check_for_mirrors(formula, old_mirrors, new_mirrors)
+        end
 
         old_hash = formula_spec.checksum&.hexdigest
         new_hash = args.sha256
@@ -190,12 +190,14 @@ def run
         elsif new_url.blank? && new_version.blank?
           raise UsageError, "#{formula}: no `--url` or `--version` argument specified!"
         else
-          new_url ||= PyPI.update_pypi_url(old_url, T.must(new_version))
+          return unless new_version.present?
+
+          new_url ||= PyPI.update_pypi_url(old_url, new_version)
           if new_url.blank?
-            new_url = update_url(old_url, old_version, T.must(new_version))
+            new_url = update_url(old_url, old_version, new_version)
             if new_mirrors.blank? && old_mirrors.present?
               new_mirrors = old_mirrors.map do |old_mirror|
-                update_url(old_mirror, old_version, T.must(new_version))
+                update_url(old_mirror, old_version, new_version)
               end
             end
           end
@@ -271,9 +273,9 @@ def run
 
         old_contents = formula.path.read
 
-        if new_mirrors.present?
+        if new_mirrors.present? && new_url.present?
           replacement_pairs << [
-            /^( +)(url "#{Regexp.escape(T.must(new_url))}"[^\n]*?\n)/m,
+            /^( +)(url "#{Regexp.escape(new_url)}"[^\n]*?\n)/m,
             "\\1\\2\\1mirror \"#{new_mirrors.join("\"\n\\1mirror \"")}\"\n",
           ]
         end
@@ -395,6 +397,7 @@ def run
 
       private
 
+      sig { params(url: String).returns(T.nilable(String)) }
       def determine_mirror(url)
         case url
         when %r{.*ftp\.gnu\.org/gnu.*}
@@ -408,6 +411,7 @@ def determine_mirror(url)
         end
       end
 
+      sig { params(formula: String, old_mirrors: T::Array[String], new_mirrors: T::Array[String]).void }
       def check_for_mirrors(formula, old_mirrors, new_mirrors)
         return if new_mirrors.present? || old_mirrors.empty?
 
@@ -427,11 +431,17 @@ def update_url(old_url, old_version, new_version)
         return new_url if (old_version_parts = old_version.split(".")).length < 2
         return new_url if (new_version_parts = new_version.split(".")).length != old_version_parts.length
 
-        partial_old_version = T.must(old_version_parts[0..-2]).join(".")
-        partial_new_version = T.must(new_version_parts[0..-2]).join(".")
+        partial_old_version = old_version_parts[0..-2]&.join(".")
+        partial_new_version = new_version_parts[0..-2]&.join(".")
+        return new_url if partial_old_version.blank? || partial_new_version.blank?
+
         new_url.gsub(%r{/(v?)#{Regexp.escape(partial_old_version)}/}, "/\\1#{partial_new_version}/")
       end
 
+      sig {
+        params(formula: Formula, new_version: T.nilable(String), url: String,
+               specs: Float).returns(T::Array[T.untyped])
+      }
       def fetch_resource_and_forced_version(formula, new_version, url, **specs)
         resource = Resource.new
         resource.url(url, **specs)
@@ -442,6 +452,7 @@ def fetch_resource_and_forced_version(formula, new_version, url, **specs)
         [resource.fetch, forced_version]
       end
 
+      sig { params(formula: Formula, contents: T.nilable(String)).returns(String) }
       def formula_version(formula, contents = nil)
         spec = :stable
         name = formula.name
@@ -453,17 +464,29 @@ def formula_version(formula, contents = nil)
         end
       end
 
+      sig { params(formula: Formula, tap_remote_repo: String).returns(T.nilable(T::Array[String])) }
       def check_open_pull_requests(formula, tap_remote_repo)
-        GitHub.check_for_duplicate_pull_requests(formula.name, tap_remote_repo,
-                                                 state: "open",
-                                                 file:  formula.path.relative_path_from(formula.tap.path).to_s,
-                                                 quiet: args.quiet?)
+        tap = formula.tap
+        return if tap.nil?
+
+        GitHub.check_for_duplicate_pull_requests(
+          formula.name, tap_remote_repo,
+          state: "open",
+          file:  formula.path.relative_path_from(tap.path).to_s,
+          quiet: args.quiet?
+        )
       end
 
+      sig {
+        params(formula: Formula, tap_remote_repo: String, version: T.nilable(String), url: T.nilable(String),
+               tag: T.nilable(String)).void
+      }
       def check_new_version(formula, tap_remote_repo, version: nil, url: nil, tag: nil)
         if version.nil?
           specs = {}
           specs[:tag] = tag if tag.present?
+          return if url.blank?
+
           version = Version.detect(url, **specs).to_s
           return if version.blank?
         end
@@ -472,9 +495,13 @@ def check_new_version(formula, tap_remote_repo, version: nil, url: nil, tag: nil
         check_closed_pull_requests(formula, tap_remote_repo, version:)
       end
 
+      sig { params(formula: Formula, new_version: String).returns(NilClass) }
       def check_throttle(formula, new_version)
+        tap = formula.tap
+        return if tap.nil?
+
         throttled_rate = formula.livecheck.throttle
-        throttled_rate ||= if (rate = formula.tap.audit_exceptions.dig(:throttled_formulae, formula.name))
+        throttled_rate ||= if (rate = tap.audit_exceptions.dig(:throttled_formulae, formula.name))
           odisabled "throttled_formulae.json", "Livecheck#throttle"
           rate
         end
@@ -486,27 +513,41 @@ def check_throttle(formula, new_version)
         odie "#{formula} should only be updated every #{throttled_rate} releases on multiples of #{throttled_rate}"
       end
 
+      sig {
+        params(formula: Formula, tap_remote_repo: String,
+               version: T.nilable(String)).returns(T.nilable(T::Array[String]))
+      }
       def check_closed_pull_requests(formula, tap_remote_repo, version:)
+        tap = formula.tap
+        return if tap.nil?
+
         # if we haven't already found open requests, try for an exact match across closed requests
-        GitHub.check_for_duplicate_pull_requests(formula.name, tap_remote_repo,
-                                                 version:,
-                                                 state:   "closed",
-                                                 file:    formula.path.relative_path_from(formula.tap.path).to_s,
-                                                 quiet:   args.quiet?)
+        GitHub.check_for_duplicate_pull_requests(
+          formula.name, tap_remote_repo,
+          version:,
+          state:   "closed",
+          file:    formula.path.relative_path_from(tap.path).to_s,
+          quiet:   args.quiet?
+        )
       end
 
+      sig { params(formula: Formula, new_formula_version: String).returns(T.nilable(T::Array[String])) }
       def alias_update_pair(formula, new_formula_version)
         versioned_alias = formula.aliases.grep(/^.*@\d+(\.\d+)?$/).first
         return if versioned_alias.nil?
 
         name, old_alias_version = versioned_alias.split("@")
+        return if old_alias_version.blank?
+
         new_alias_regex = (old_alias_version.split(".").length == 1) ? /^\d+/ : /^\d+\.\d+/
         new_alias_version, = *new_formula_version.to_s.match(new_alias_regex)
+        return if new_alias_version.blank?
         return if Version.new(new_alias_version) <= Version.new(old_alias_version)
 
         [versioned_alias, "#{name}@#{new_alias_version}"]
       end
 
+      sig { params(formula: Formula, alias_rename: T.nilable(T::Array[String]), old_contents: String).void }
       def run_audit(formula, alias_rename, old_contents)
         audit_args = ["--formula"]
         audit_args << "--strict" if args.strict?
@@ -521,7 +562,9 @@ def run_audit(formula, alias_rename, old_contents)
           end
           return
         end
-        FileUtils.mv alias_rename.first, alias_rename.last if alias_rename.present?
+        if alias_rename && (source = alias_rename.first) && (destination = alias_rename.last)
+          FileUtils.mv source, destination
+        end
         failed_audit = false
         if args.no_audit?
           ohai "Skipping `brew audit`"
@@ -535,7 +578,9 @@ def run_audit(formula, alias_rename, old_contents)
         return unless failed_audit
 
         formula.path.atomic_write(old_contents)
-        FileUtils.mv alias_rename.last, alias_rename.first if alias_rename.present?
+        if alias_rename && (source = alias_rename.first) && (destination = alias_rename.last)
+          FileUtils.mv source, destination
+        end
         odie "`brew audit` failed!"
       end
     end
diff --git a/Library/Homebrew/dev-cmd/contributions.rb b/Library/Homebrew/dev-cmd/contributions.rb
index 2e6452937b1dd..96159227fa281 100644
--- a/Library/Homebrew/dev-cmd/contributions.rb
+++ b/Library/Homebrew/dev-cmd/contributions.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
@@ -10,12 +10,12 @@
 module Homebrew
   module DevCmd
     class Contributions < AbstractCommand
-      PRIMARY_REPOS = %w[brew core cask].freeze
-      SUPPORTED_REPOS = [
+      PRIMARY_REPOS = T.let(%w[brew core cask].freeze, T::Array[String])
+      SUPPORTED_REPOS = T.let([
         PRIMARY_REPOS,
         OFFICIAL_CMD_TAPS.keys.map { |t| t.delete_prefix("homebrew/") },
         OFFICIAL_CASK_TAPS.reject { |t| t == "cask" },
-      ].flatten.freeze
+      ].flatten.freeze, T::Array[String])
       MAX_REPO_COMMITS = 1000
 
       cmd_args do
@@ -50,9 +50,9 @@ def run
         results = {}
         grand_totals = {}
 
-        repos = if args.repositories.blank? || T.must(args.repositories).include?("primary")
+        repos = if args.repositories.blank? || args.repositories&.include?("primary")
           PRIMARY_REPOS
-        elsif T.must(args.repositories).include?("all")
+        elsif args.repositories&.include?("all")
           SUPPORTED_REPOS
         else
           args.repositories
@@ -116,7 +116,7 @@ def time_period(from:, to:)
         end
       end
 
-      sig { params(totals: Hash).returns(String) }
+      sig { params(totals: T::Hash[String, T::Hash[Symbol, Integer]]).returns(String) }
       def generate_csv(totals)
         CSV.generate do |csv|
           csv << %w[user repo author committer coauthor review total]
@@ -127,7 +127,14 @@ def generate_csv(totals)
         end
       end
 
-      sig { params(user: String, grand_total: Hash).returns(Array) }
+      sig {
+        params(
+          user:        String,
+          grand_total: T::Hash[Symbol, Integer],
+        ).returns(
+          [String, String, T.nilable(Integer), T.nilable(Integer), T.nilable(Integer), T.nilable(Integer), Integer],
+        )
+      }
       def grand_total_row(user, grand_total)
         [
           user,
@@ -140,7 +147,10 @@ def grand_total_row(user, grand_total)
         ]
       end
 
+      sig { params(repos: T.nilable(T::Array[String]), person: String, from: String).void }
       def scan_repositories(repos, person, from:)
+        return if repos.blank?
+
         data = {}
 
         repos.each do |repo|
@@ -168,7 +178,7 @@ def scan_repositories(repos, person, from:)
           data[repo] = {
             author:    author_commits,
             committer: committer_commits,
-            coauthor:  git_log_trailers_cmd(T.must(repo_path), person, "Co-authored-by", from:, to: args.to),
+            coauthor:  git_log_trailers_cmd(repo_path, person, "Co-authored-by", from:, to: args.to),
             review:    count_reviews(repo_full_name, person, from:, to: args.to),
           }
         end
@@ -176,7 +186,7 @@ def scan_repositories(repos, person, from:)
         data
       end
 
-      sig { params(results: Hash).returns(Hash) }
+      sig { params(results: T::Hash[Symbol, T.untyped]).returns(T::Hash[Symbol, Integer]) }
       def total(results)
         totals = { author: 0, committer: 0, coauthor: 0, review: 0 }
 
diff --git a/Library/Homebrew/dev-cmd/extract.rb b/Library/Homebrew/dev-cmd/extract.rb
index af8e3b6375d8a..5ffaac41ab780 100644
--- a/Library/Homebrew/dev-cmd/extract.rb
+++ b/Library/Homebrew/dev-cmd/extract.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: true # This cannot be `# typed: strict` due to the use of `undef`.
 # frozen_string_literal: true
 
 require "abstract_command"
diff --git a/Library/Homebrew/dev-cmd/generate-cask-api.rb b/Library/Homebrew/dev-cmd/generate-cask-api.rb
index d72b20118e0bf..4e6d424f265d2 100644
--- a/Library/Homebrew/dev-cmd/generate-cask-api.rb
+++ b/Library/Homebrew/dev-cmd/generate-cask-api.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
@@ -71,6 +71,7 @@ def run
 
       private
 
+      sig { params(title: String).returns(String) }
       def html_template(title)
         <<~EOS
           ---
diff --git a/Library/Homebrew/dev-cmd/generate-formula-api.rb b/Library/Homebrew/dev-cmd/generate-formula-api.rb
index 563fceb2b6f92..a3fe69de0d31a 100644
--- a/Library/Homebrew/dev-cmd/generate-formula-api.rb
+++ b/Library/Homebrew/dev-cmd/generate-formula-api.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
@@ -69,6 +69,7 @@ def run
 
       private
 
+      sig { params(title: String).returns(String) }
       def html_template(title)
         <<~EOS
           ---
diff --git a/Library/Homebrew/dev-cmd/irb.rb b/Library/Homebrew/dev-cmd/irb.rb
index 9caafbed5a07f..40a3fd9fc9c27 100644
--- a/Library/Homebrew/dev-cmd/irb.rb
+++ b/Library/Homebrew/dev-cmd/irb.rb
@@ -1,18 +1,20 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
+require "formula"
 require "formulary"
 require "cask/cask_loader"
 
 class String
   # @!visibility private
+  sig { params(args: Integer).returns(Formula) }
   def f(*args)
-    require "formula"
     Formulary.factory(self, *args)
   end
 
   # @!visibility private
+  sig { params(config: T.nilable(T::Hash[Symbol, T.untyped])).returns(Cask::Cask) }
   def c(config: nil)
     Cask::CaskLoader.load(self, config:)
   end
@@ -20,11 +22,13 @@ def c(config: nil)
 
 class Symbol
   # @!visibility private
+  sig { params(args: Integer).returns(Formula) }
   def f(*args)
     to_s.f(*args)
   end
 
   # @!visibility private
+  sig { params(config: T.nilable(T::Hash[Symbol, T.untyped])).returns(Cask::Cask) }
   def c(config: nil)
     to_s.c(config:)
   end
@@ -72,7 +76,6 @@ def run
           require "irb"
         end
 
-        require "formula"
         require "keg"
         require "cask"
 
@@ -94,6 +97,7 @@ def run
 
       # Remove the `--debug`, `--verbose` and `--quiet` options which cause problems
       # for IRB and have already been parsed by the CLI::Parser.
+      sig { returns(T.nilable(T::Array[Symbol])) }
       def clean_argv
         global_options = Homebrew::CLI::Parser
                          .global_options
diff --git a/Library/Homebrew/dev-cmd/livecheck.rb b/Library/Homebrew/dev-cmd/livecheck.rb
index 017f1a9d295a1..b2ffcbdb16205 100644
--- a/Library/Homebrew/dev-cmd/livecheck.rb
+++ b/Library/Homebrew/dev-cmd/livecheck.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
@@ -113,8 +113,9 @@ def run
 
       private
 
+      sig { returns(String) }
       def watchlist_path
-        @watchlist_path ||= File.expand_path(Homebrew::EnvConfig.livecheck_watchlist)
+        @watchlist_path ||= T.let(File.expand_path(Homebrew::EnvConfig.livecheck_watchlist), T.nilable(String))
       end
     end
   end
diff --git a/Library/Homebrew/dev-cmd/pr-pull.rb b/Library/Homebrew/dev-cmd/pr-pull.rb
index c880c436308a2..d3f8225109210 100644
--- a/Library/Homebrew/dev-cmd/pr-pull.rb
+++ b/Library/Homebrew/dev-cmd/pr-pull.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
@@ -141,7 +141,7 @@ def run
                   user, repo, pr, workflow_id: workflow, artifact_pattern:
                 )
                 if args.ignore_missing_artifacts.present? &&
-                   T.must(args.ignore_missing_artifacts).include?(workflow) &&
+                   args.ignore_missing_artifacts&.include?(workflow) &&
                    workflow_run.first.blank?
                   # Ignore that workflow as it was not executed and we specified
                   # that we could skip it.
@@ -183,8 +183,10 @@ def run
       end
 
       # Separates a commit message into subject, body and trailers.
+      sig { params(message: String).returns([String, String, String]) }
       def separate_commit_message(message)
-        subject = message.lines.first.strip
+        first_line = message.lines.first
+        return ["", "", ""] unless first_line
 
         # Skip the subject and separate lines that look like trailers (e.g. "Co-authored-by")
         # from lines that look like regular body text.
@@ -193,11 +195,15 @@ def separate_commit_message(message)
         trailers = trailers.uniq.join.strip
         body = body.join.strip.gsub(/\n{3,}/, "\n\n")
 
-        [subject, body, trailers]
+        [first_line.strip, body, trailers]
       end
 
+      sig { params(git_repo: GitRepository, pull_request: T.nilable(String), dry_run: T::Boolean).void }
       def signoff!(git_repo, pull_request: nil, dry_run: false)
-        subject, body, trailers = separate_commit_message(git_repo.commit_message)
+        msg = git_repo.commit_message
+        return if msg.blank?
+
+        subject, body, trailers = separate_commit_message(msg)
 
         if pull_request
           # This is a tap pull request and approving reviewers should also sign-off.
@@ -210,7 +216,7 @@ def signoff!(git_repo, pull_request: nil, dry_run: false)
 
           # Append the close message as well, unless the commit body already includes it.
           close_message = "Closes ##{pull_request}."
-          body += "\n\n#{close_message}" unless body.include? close_message
+          body.concat("\n\n#{close_message}") unless body.include?(close_message)
         end
 
         git_args = Utils::Git.git, "-C", git_repo.pathname, "commit", "--amend", "--signoff", "--allow-empty",
@@ -223,6 +229,7 @@ def signoff!(git_repo, pull_request: nil, dry_run: false)
         end
       end
 
+      sig { params(tap: Tap, subject_name: String, subject_path: Pathname, content: String).returns(T.untyped) }
       def get_package(tap, subject_name, subject_path, content)
         if subject_path.to_s.start_with?("#{tap.cask_dir}/")
           cask = begin
@@ -240,6 +247,10 @@ def get_package(tap, subject_name, subject_path, content)
         end
       end
 
+      sig {
+        params(old_contents: String, new_contents: String, subject_path: T.any(String, Pathname),
+               reason: T.nilable(String)).returns(String)
+      }
       def determine_bump_subject(old_contents, new_contents, subject_path, reason: nil)
         subject_path = Pathname(subject_path)
         tap          = Tap.from_path(subject_path)
@@ -268,6 +279,10 @@ def determine_bump_subject(old_contents, new_contents, subject_path, reason: nil
 
       # Cherry picks a single commit that modifies a single file.
       # Potentially rewords this commit using {determine_bump_subject}.
+      sig {
+        params(commit: String, file: String, git_repo: GitRepository, reason: T.nilable(String), verbose: T::Boolean,
+               resolve: T::Boolean).void
+      }
       def reword_package_commit(commit, file, git_repo:, reason: "", verbose: false, resolve: false)
         package_file = git_repo.pathname / file
         package_name = package_file.basename.to_s.chomp(".rb")
@@ -279,7 +294,10 @@ def reword_package_commit(commit, file, git_repo:, reason: "", verbose: false, r
         new_package = Utils::Git.file_at_commit(git_repo.to_s, file, "HEAD")
 
         bump_subject = determine_bump_subject(old_package, new_package, package_file, reason:).strip
-        subject, body, trailers = separate_commit_message(git_repo.commit_message)
+        msg = git_repo.commit_message
+        return if msg.blank?
+
+        subject, body, trailers = separate_commit_message(msg)
 
         if subject != bump_subject && !subject.start_with?("#{package_name}:")
           safe_system("git", "-C", git_repo.pathname, "commit", "--amend", "-q",
@@ -293,6 +311,10 @@ def reword_package_commit(commit, file, git_repo:, reason: "", verbose: false, r
       # Cherry picks multiple commits that each modify a single file.
       # Words the commit according to {determine_bump_subject} with the body
       # corresponding to all the original commit messages combined.
+      sig {
+        params(commits: T::Array[String], file: String, git_repo: GitRepository, reason: T.nilable(String),
+               verbose: T::Boolean, resolve: T::Boolean).void
+      }
       def squash_package_commits(commits, file, git_repo:, reason: "", verbose: false, resolve: false)
         odebug "Squashing #{file}: #{commits.join " "}"
 
@@ -304,7 +326,10 @@ def squash_package_commits(commits, file, git_repo:, reason: "", verbose: false,
         messages = []
         trailers = []
         commits.each do |commit|
-          subject, body, trailer = separate_commit_message(git_repo.commit_message(commit))
+          msg = git_repo.commit_message(commit)
+          next if msg.blank?
+
+          subject, body, trailer = separate_commit_message(msg)
           body = body.lines.map { |line| "  #{line.strip}" }.join("\n")
           messages << "* #{subject}\n#{body}".strip
           trailers << trailer
@@ -340,9 +365,12 @@ def squash_package_commits(commits, file, git_repo:, reason: "", verbose: false,
       end
 
       # TODO: fix test in `test/dev-cmd/pr-pull_spec.rb` and assume `cherry_picked: false`.
+      sig {
+        params(original_commit: String, tap: Tap, reason: T.nilable(String), verbose: T::Boolean, resolve: T::Boolean,
+               cherry_picked: T::Boolean).void
+      }
       def autosquash!(original_commit, tap:, reason: "", verbose: false, resolve: false, cherry_picked: true)
         git_repo = tap.git_repository
-        original_head = git_repo.head_ref
 
         commits = Utils.safe_popen_read("git", "-C", tap.path, "rev-list",
                                         "--reverse", "#{original_commit}..HEAD").lines.map(&:strip)
@@ -402,14 +430,18 @@ def autosquash!(original_commit, tap:, reason: "", verbose: false, resolve: fals
           end
         end
       rescue
+        original_head = git_repo&.head_ref
+        return if original_head.nil?
+
         opoo "Autosquash encountered an error; resetting to original state at #{original_head}"
-        system "git", "-C", tap.path, "reset", "--hard", original_head
-        system "git", "-C", tap.path, "cherry-pick", "--abort" if cherry_picked
+        system "git", "-C", tap.path.to_s, "reset", "--hard", original_head
+        system "git", "-C", tap.path.to_s, "cherry-pick", "--abort" if cherry_picked
         raise
       end
 
       private
 
+      sig { params(user: String, repo: String, pull_request: String, path: T.any(String, Pathname)).void }
       def cherry_pick_pr!(user, repo, pull_request, path: ".")
         if args.dry_run?
           puts <<~EOS
@@ -427,6 +459,7 @@ def cherry_pick_pr!(user, repo, pull_request, path: ".")
                                                                          resolve: args.resolve?)
       end
 
+      sig { params(tap: Tap, original_commit: String, labels: T::Array[String]).returns(T::Boolean) }
       def formulae_need_bottles?(tap, original_commit, labels)
         return false if args.dry_run?
 
@@ -437,6 +470,7 @@ def formulae_need_bottles?(tap, original_commit, labels)
         end
       end
 
+      sig { params(tap: Tap, original_commit: String).returns(T::Array[String]) }
       def changed_packages(tap, original_commit)
         formulae = Utils.popen_read("git", "-C", tap.path, "diff-tree",
                                     "-r", "--name-only", "--diff-filter=AM",
@@ -473,6 +507,7 @@ def changed_packages(tap, original_commit)
         formulae + casks
       end
 
+      sig { params(repo: String, pull_request: String).void }
       def pr_check_conflicts(repo, pull_request)
         long_build_pr_files = GitHub.issues(
           repo:, state: "open", labels: "no long build conflict",
diff --git a/Library/Homebrew/dev-cmd/pr-upload.rb b/Library/Homebrew/dev-cmd/pr-upload.rb
index 672086f3efacd..4217f27e08e2f 100644
--- a/Library/Homebrew/dev-cmd/pr-upload.rb
+++ b/Library/Homebrew/dev-cmd/pr-upload.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
@@ -120,6 +120,7 @@ def run
 
       private
 
+      sig { params(bottles_hash: T::Hash[String, T.untyped]).void }
       def check_bottled_formulae!(bottles_hash)
         bottles_hash.each do |name, bottle_hash|
           formula_path = HOMEBREW_REPOSITORY/bottle_hash["formula"]["path"]
@@ -131,22 +132,25 @@ def check_bottled_formulae!(bottles_hash)
         end
       end
 
+      sig { params(bottles_hash: T::Hash[String, T.untyped]).returns(T::Boolean) }
       def github_releases?(bottles_hash)
-        @github_releases ||= bottles_hash.values.all? do |bottle_hash|
+        @github_releases ||= T.let(bottles_hash.values.all? do |bottle_hash|
           root_url = bottle_hash["bottle"]["root_url"]
           url_match = root_url.match GitHubReleases::URL_REGEX
           _, _, _, tag = *url_match
 
           tag
-        end
+        end, T.nilable(T::Boolean))
       end
 
+      sig { params(bottles_hash: T::Hash[String, T.untyped]).returns(T::Boolean) }
       def github_packages?(bottles_hash)
-        @github_packages ||= bottles_hash.values.all? do |bottle_hash|
+        @github_packages ||= T.let(bottles_hash.values.all? do |bottle_hash|
           bottle_hash["bottle"]["root_url"].match? GitHubPackages::URL_REGEX
-        end
+        end, T.nilable(T::Boolean))
       end
 
+      sig { params(json_files: T::Array[String], args: T.untyped).returns(T::Hash[String, T.untyped]) }
       def bottles_hash_from_json_files(json_files, args)
         puts "Reading JSON files: #{json_files.join(", ")}" if args.verbose?
 
diff --git a/Library/Homebrew/dev-cmd/tap-new.rb b/Library/Homebrew/dev-cmd/tap-new.rb
index 1471b16f58f40..aeda5d721cd31 100644
--- a/Library/Homebrew/dev-cmd/tap-new.rb
+++ b/Library/Homebrew/dev-cmd/tap-new.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
@@ -197,6 +197,7 @@ def run
 
       private
 
+      sig { params(tap: Tap, filename: T.any(String, Pathname), content: String).void }
       def write_path(tap, filename, content)
         path = tap.path/filename
         tap.path.mkpath
diff --git a/Library/Homebrew/dev-cmd/test.rb b/Library/Homebrew/dev-cmd/test.rb
index 38e07963002e7..b2a9c47194598 100644
--- a/Library/Homebrew/dev-cmd/test.rb
+++ b/Library/Homebrew/dev-cmd/test.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
@@ -110,8 +110,9 @@ def run
 
       private
 
+      sig { params(formula: Formula).returns(T::Boolean) }
       def retry_test?(formula)
-        @test_failed ||= Set.new
+        @test_failed ||= T.let(Set.new, T.nilable(T::Set[T.untyped]))
         if args.retry? && @test_failed.add?(formula)
           oh1 "Testing #{formula.full_name} (again)"
           formula.clear_cache
diff --git a/Library/Homebrew/dev-cmd/tests.rb b/Library/Homebrew/dev-cmd/tests.rb
index 60845d6cc2e65..1ac6edfe2c372 100644
--- a/Library/Homebrew/dev-cmd/tests.rb
+++ b/Library/Homebrew/dev-cmd/tests.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
@@ -168,15 +168,17 @@ def run
 
       private
 
+      sig { returns(T.nilable(T::Boolean)) }
       def use_buildpulse?
         return @use_buildpulse if defined?(@use_buildpulse)
 
-        @use_buildpulse = ENV["HOMEBREW_BUILDPULSE_ACCESS_KEY_ID"].present? &&
+        @use_buildpulse = T.let(ENV["HOMEBREW_BUILDPULSE_ACCESS_KEY_ID"].present? &&
                           ENV["HOMEBREW_BUILDPULSE_SECRET_ACCESS_KEY"].present? &&
                           ENV["HOMEBREW_BUILDPULSE_ACCOUNT_ID"].present? &&
-                          ENV["HOMEBREW_BUILDPULSE_REPOSITORY_ID"].present?
+                          ENV["HOMEBREW_BUILDPULSE_REPOSITORY_ID"].present?, T.nilable(T::Boolean))
       end
 
+      sig { void }
       def run_buildpulse
         require "formula"
 
@@ -198,6 +200,7 @@ def run_buildpulse
                        ]
       end
 
+      sig { returns(T::Array[String]) }
       def changed_test_files
         changed_files = Utils.popen_read("git", "diff", "--name-only", "master")
 
@@ -215,6 +218,7 @@ def changed_test_files
         end.select(&:exist?)
       end
 
+      sig { returns(T::Array[String]) }
       def setup_environment!
         # Cleanup any unwanted user configuration.
         allowed_test_env = %w[
diff --git a/Library/Homebrew/dev-cmd/unbottled.rb b/Library/Homebrew/dev-cmd/unbottled.rb
index 359724dfbbe09..7a73caf4a1b81 100644
--- a/Library/Homebrew/dev-cmd/unbottled.rb
+++ b/Library/Homebrew/dev-cmd/unbottled.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
@@ -34,11 +34,15 @@ class Unbottled < AbstractCommand
       def run
         Formulary.enable_factory_cache!
 
-        @bottle_tag = if (tag = args.tag)
-          Utils::Bottles::Tag.from_symbol(tag.to_sym)
-        else
-          Utils::Bottles.tag
-        end
+        @bottle_tag = T.let(
+          if (tag = args.tag)
+            Utils::Bottles::Tag.from_symbol(tag.to_sym)
+          else
+            Utils::Bottles.tag
+          end,
+          T.nilable(Utils::Bottles::Tag),
+        )
+        return unless @bottle_tag
 
         if args.lost?
           if args.named.present?
@@ -98,12 +102,17 @@ def run
             ["installs", formula_installs]
           end
 
+          return if hash.nil?
+
           output_unbottled(formulae, deps_hash, noun, hash, args.named.present?)
         end
       end
 
       private
 
+      sig {
+        params(all: T::Boolean).returns([T::Array[Formula], T::Array[Formula], T.nilable(T::Hash[Symbol, Integer])])
+      }
       def formulae_all_installs_from_args(all)
         if args.named.present?
           formulae = all_formulae = args.named.to_formulae
@@ -115,7 +124,7 @@ def formulae_all_installs_from_args(all)
 
           formulae = all_formulae = Formula.all(eval_all: args.eval_all?)
 
-          @sort = " (sorted by number of dependents)"
+          @sort = T.let(" (sorted by number of dependents)", T.nilable(String))
         elsif all
           formulae = all_formulae = Formula.all(eval_all: args.eval_all?)
         else
@@ -142,7 +151,7 @@ def formulae_all_installs_from_args(all)
               nil
             end
           end
-          @sort = " (sorted by installs in the last 90 days; top 10,000 only)"
+          @sort = T.let(" (sorted by installs in the last 90 days; top 10,000 only)", T.nilable(String))
 
           all_formulae = Formula.all(eval_all: args.eval_all?)
         end
@@ -151,9 +160,11 @@ def formulae_all_installs_from_args(all)
         formulae = Array(formulae).reject(&:deprecated?) if formulae.present?
         all_formulae = Array(all_formulae).reject(&:deprecated?) if all_formulae.present?
 
-        [formulae, all_formulae, formula_installs]
+        [T.let(formulae, T::Array[Formula]), T.let(all_formulae, T::Array[Formula]),
+         T.let(formula_installs, T.nilable(T::Hash[Symbol, Integer]))]
       end
 
+      sig { params(all_formulae: T.untyped).returns([T::Hash[String, T.untyped], T::Hash[String, T.untyped]]) }
       def deps_uses_from_formulae(all_formulae)
         ohai "Populating dependency tree..."
 
@@ -175,7 +186,10 @@ def deps_uses_from_formulae(all_formulae)
         [deps_hash, uses_hash]
       end
 
+      sig { params(formulae: T::Array[Formula]).returns(NilClass) }
       def output_total(formulae)
+        return unless @bottle_tag
+
         ohai "Unbottled :#{@bottle_tag} formulae"
         unbottled_formulae = 0
 
@@ -188,7 +202,14 @@ def output_total(formulae)
         puts "#{unbottled_formulae}/#{formulae.length} remaining."
       end
 
+      sig {
+        params(formulae: T::Array[Formula], deps_hash: T::Hash[T.any(Symbol, String), T.untyped],
+               noun: T.nilable(String), hash: T::Hash[T.any(Symbol, String), T.untyped],
+               any_named_args: T::Boolean).returns(NilClass)
+      }
       def output_unbottled(formulae, deps_hash, noun, hash, any_named_args)
+        return unless @bottle_tag
+
         ohai ":#{@bottle_tag} bottle status#{@sort}"
         any_found = T.let(false, T::Boolean)
 
@@ -258,6 +279,7 @@ def output_unbottled(formulae, deps_hash, noun, hash, any_named_args)
         puts "No unbottled dependencies found!"
       end
 
+      sig { returns(NilClass) }
       def output_lost_bottles
         ohai ":#{@bottle_tag} lost bottles"
 
diff --git a/Library/Homebrew/dev-cmd/update-sponsors.rb b/Library/Homebrew/dev-cmd/update-sponsors.rb
index 248a290413d2b..26a2202418ec8 100644
--- a/Library/Homebrew/dev-cmd/update-sponsors.rb
+++ b/Library/Homebrew/dev-cmd/update-sponsors.rb
@@ -1,4 +1,4 @@
-# typed: true
+# typed: strict
 # frozen_string_literal: true
 
 require "abstract_command"
@@ -62,14 +62,17 @@ def run
 
       private
 
+      sig { params(sponsor: T::Hash[Symbol, T.untyped]).returns(T.nilable(String)) }
       def sponsor_name(sponsor)
         sponsor[:name] || sponsor[:login]
       end
 
+      sig { params(sponsor: T::Hash[Symbol, T.untyped]).returns(String) }
       def sponsor_logo(sponsor)
         "https://github.com/#{sponsor[:login]}.png?size=64"
       end
 
+      sig { params(sponsor: T::Hash[Symbol, T.untyped]).returns(String) }
       def sponsor_url(sponsor)
         "https://github.com/#{sponsor[:login]}"
       end