diff --git a/Library/Homebrew/brew.rb b/Library/Homebrew/brew.rb
index 6898eff1f13e0..dbe7acc2105c8 100644
--- a/Library/Homebrew/brew.rb
+++ b/Library/Homebrew/brew.rb
@@ -144,7 +144,7 @@
   end
 rescue UsageError => e
   require "help"
-  Homebrew::Help.help cmd, remaining_args: args&.remaining, usage_error: e.message
+  Homebrew::Help.help cmd, remaining_args: args&.remaining || [], usage_error: e.message
 rescue SystemExit => e
   onoe "Kernel.exit" if args&.debug? && !e.success?
   if args&.debug? || ARGV.include?("--debug")
diff --git a/Library/Homebrew/cask/migrator.rb b/Library/Homebrew/cask/migrator.rb
index 9f15da316cf0a..1b9648869500b 100644
--- a/Library/Homebrew/cask/migrator.rb
+++ b/Library/Homebrew/cask/migrator.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "cask/cask_loader"
@@ -6,6 +6,7 @@
 
 module Cask
   class Migrator
+    sig { returns(Cask) }
     attr_reader :old_cask, :new_cask
 
     sig { params(old_cask: Cask, new_cask: Cask).void }
@@ -38,7 +39,10 @@ def migrate(dry_run: false)
       old_caskroom_path = old_cask.caskroom_path
       new_caskroom_path = new_cask.caskroom_path
 
-      old_installed_caskfile = old_cask.installed_caskfile.relative_path_from(old_caskroom_path)
+      old_caskfile = old_cask.installed_caskfile
+      return if old_caskfile.nil?
+
+      old_installed_caskfile = old_caskfile.relative_path_from(old_caskroom_path)
       new_installed_caskfile = old_installed_caskfile.dirname/old_installed_caskfile.basename.sub(
         old_token,
         new_token,
diff --git a/Library/Homebrew/dependencies.rb b/Library/Homebrew/dependencies.rb
index 3e8bd125e83d6..354b12745e2b8 100644
--- a/Library/Homebrew/dependencies.rb
+++ b/Library/Homebrew/dependencies.rb
@@ -39,6 +39,11 @@ def dup_without_system_deps
   def inspect
     "#<#{self.class.name}: #{__getobj__}>"
   end
+
+  sig { returns(T::Array[Dependency]) }
+  def to_a
+    __getobj__.to_a
+  end
 end
 
 # A collection of requirements.
diff --git a/Library/Homebrew/formula_cellar_checks.rb b/Library/Homebrew/formula_cellar_checks.rb
index 45973181e7631..26e4f2f0665b8 100644
--- a/Library/Homebrew/formula_cellar_checks.rb
+++ b/Library/Homebrew/formula_cellar_checks.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "utils/shell"
@@ -191,6 +191,7 @@ def check_elisp_root(share, name)
     EOS
   end
 
+  sig { params(lib: Pathname, deps: Dependencies).returns(T.nilable(String)) }
   def check_python_packages(lib, deps)
     return unless lib.directory?
 
@@ -208,7 +209,8 @@ def check_python_packages(lib, deps)
 
     return if pythons.blank?
 
-    python_deps = deps.map(&:name)
+    python_deps = deps.to_a
+                      .map(&:name)
                       .grep(/^python(@.*)?$/)
                       .filter_map { |d| Formula[d].version.to_s[/^\d+\.\d+/] }
 
@@ -250,6 +252,7 @@ def check_shim_references(prefix)
     EOS
   end
 
+  sig { params(prefix: Pathname, plist: Pathname).returns(T.nilable(String)) }
   def check_plist(prefix, plist)
     return unless prefix.directory?
 
@@ -412,7 +415,7 @@ def check_binary_arches(formula)
 
   sig { void }
   def audit_installed
-    @new_formula ||= false
+    @new_formula ||= T.let(false, T.nilable(T::Boolean))
 
     problem_if_output(check_manpages)
     problem_if_output(check_infopages)
@@ -442,8 +445,9 @@ def relative_glob(dir, pattern)
     File.directory?(dir) ? Dir.chdir(dir) { Dir[pattern] } : []
   end
 
-  def cpuid_instruction?(file, objdump = "objdump")
-    @instruction_column_index ||= {}
+  sig { params(file: T.any(Pathname, String), objdump: Pathname).returns(T::Boolean) }
+  def cpuid_instruction?(file, objdump)
+    @instruction_column_index ||= T.let({}, T.nilable(T::Hash[Pathname, Integer]))
     @instruction_column_index[objdump] ||= begin
       objdump_version = Utils.popen_read(objdump, "--version")
 
diff --git a/Library/Homebrew/help.rb b/Library/Homebrew/help.rb
index 88b6e297baeb2..ef6d975f50221 100644
--- a/Library/Homebrew/help.rb
+++ b/Library/Homebrew/help.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "cli/parser"
@@ -7,6 +7,14 @@
 module Homebrew
   # Helper module for printing help output.
   module Help
+    sig {
+      params(
+        cmd:            T.nilable(String),
+        empty_argv:     T::Boolean,
+        usage_error:    T.nilable(String),
+        remaining_args: T::Array[String],
+      ).void
+    }
     def self.help(cmd = nil, empty_argv: false, usage_error: nil, remaining_args: [])
       if cmd.nil?
         # Handle `brew` (no arguments).
@@ -39,6 +47,13 @@ def self.help(cmd = nil, empty_argv: false, usage_error: nil, remaining_args: []
       exit 0
     end
 
+    sig {
+      params(
+        cmd:            String,
+        path:           Pathname,
+        remaining_args: T::Array[String],
+      ).returns(String)
+    }
     def self.command_help(cmd, path, remaining_args:)
       # Only some types of commands can have a parser.
       output = if Commands.valid_internal_cmd?(cmd) ||
@@ -58,6 +73,12 @@ def self.command_help(cmd, path, remaining_args:)
     end
     private_class_method :command_help
 
+    sig {
+      params(
+        path:           Pathname,
+        remaining_args: T::Array[String],
+      ).returns(T.nilable(String))
+    }
     def self.parser_help(path, remaining_args:)
       # Let OptionParser generate help text for commands which have a parser.
       cmd_parser = CLI::Parser.from_cmd_path(path)
@@ -69,14 +90,16 @@ def self.parser_help(path, remaining_args:)
     end
     private_class_method :parser_help
 
+    sig { params(path: Pathname).returns(T::Array[String]) }
     def self.command_help_lines(path)
       path.read
           .lines
           .grep(/^#:/)
-          .map { |line| line.slice(2..-1).delete_prefix("  ") }
+          .filter_map { |line| line.slice(2..-1)&.delete_prefix("  ") }
     end
     private_class_method :command_help_lines
 
+    sig { params(path: Pathname).returns(T.nilable(String)) }
     def self.comment_help(path)
       # Otherwise read #: lines from the file.
       help_lines = command_help_lines(path)