diff --git a/Library/Homebrew/cmd/untap.rb b/Library/Homebrew/cmd/untap.rb
index d900495104..3847bf8e35 100644
--- a/Library/Homebrew/cmd/untap.rb
+++ b/Library/Homebrew/cmd/untap.rb
@@ -1,13 +1,11 @@
-# typed: strict
+# typed: true
 # frozen_string_literal: true
 
 require "cli/parser"
 
 module Homebrew
-  module_function
-
   sig { returns(CLI::Parser) }
-  def untap_args
+  def self.untap_args
     Homebrew::CLI::Parser.new do
       description <<~EOS
         Remove a tapped formula repository.
@@ -20,46 +18,15 @@ module Homebrew
   end
 
   sig { void }
-  def untap
+  def self.untap
     args = untap_args.parse
 
     args.named.to_installed_taps.each do |tap|
       odie "Untapping #{tap} is not allowed" if tap.core_tap? && Homebrew::EnvConfig.no_install_from_api?
 
       if Homebrew::EnvConfig.no_install_from_api? || (!tap.core_tap? && !tap.core_cask_tap?)
-        installed_formula_names = T.let(nil, T.nilable(T::Set[String]))
-        installed_tap_formulae = tap.formula_names.filter_map do |formula_name|
-          # initialise lazily in case there's no formulae in this tap
-          installed_formula_names ||= Set.new(Formula.installed_formula_names)
-          next unless installed_formula_names.include?(formula_name.split("/").last)
-
-          formula = begin
-            Formulary.factory(formula_name)
-          rescue
-            # Don't blow up because of a single unavailable formula.
-            next
-          end
-
-          # Can't use Formula#any_version_installed? because it doesn't consider
-          # taps correctly.
-          formula if formula.installed_kegs.any? { |keg| keg.tab.tap == tap }
-        end
-
-        installed_cask_tokens = T.let(nil, T.nilable(T::Set[String]))
-        installed_tap_casks = tap.cask_tokens.filter_map do |cask_token|
-          # initialise lazily in case there's no casks in this tap
-          installed_cask_tokens ||= Set.new(Cask::Caskroom.tokens)
-          next unless installed_cask_tokens.include?(cask_token.split("/").last)
-
-          cask = begin
-            Cask::CaskLoader.load(cask_token)
-          rescue
-            # Don't blow up because of a single unavailable cask.
-            next
-          end
-
-          cask if cask.installed?
-        end
+        installed_tap_formulae = installed_formulae_for(tap: tap)
+        installed_tap_casks = installed_casks_for(tap: tap)
 
         if installed_tap_formulae.present? || installed_tap_casks.present?
           installed_names = (installed_tap_formulae + installed_tap_casks.map(&:token)).join("\n")
@@ -80,4 +47,48 @@ module Homebrew
       tap.uninstall manual: true
     end
   end
+
+  sig { params(tap: Tap).returns(T::Array[Formula]) }
+  def self.installed_formulae_for(tap:)
+    tap.formula_names.filter_map do |formula_name|
+      next unless installed_formulae_names.include?(T.must(formula_name.split("/").last))
+
+      formula = begin
+        Formulary.factory(formula_name)
+      rescue
+        # Don't blow up because of a single unavailable formula.
+        next
+      end
+
+      # Can't use Formula#any_version_installed? because it doesn't consider
+      # taps correctly.
+      formula if formula.installed_kegs.any? { |keg| keg.tab.tap == tap }
+    end
+  end
+
+  sig { returns(T::Set[String]) }
+  def self.installed_formulae_names
+    @installed_formulae_names ||= Formula.installed_formula_names.to_set
+  end
+
+  sig { params(tap: Tap).returns(T::Array[Cask::Cask]) }
+  def self.installed_casks_for(tap:)
+    tap.cask_tokens.filter_map do |cask_token|
+      next unless installed_cask_tokens.include?(T.must(cask_token.split("/").last))
+
+      cask = begin
+        Cask::CaskLoader.load(cask_token)
+      rescue
+        # Don't blow up because of a single unavailable cask.
+        next
+      end
+
+      cask if cask.installed?
+    end
+  end
+
+  sig { returns(T::Set[String]) }
+  def self.installed_cask_tokens
+    @installed_cask_tokens ||= Cask::Caskroom.tokens.to_set
+  end
 end