diff --git a/Library/Homebrew/extend/os/linux/requirements/osxfuse_requirement.rb b/Library/Homebrew/extend/os/linux/requirements/osxfuse_requirement.rb
index 1a2ed81272..1f4d2ce132 100644
--- a/Library/Homebrew/extend/os/linux/requirements/osxfuse_requirement.rb
+++ b/Library/Homebrew/extend/os/linux/requirements/osxfuse_requirement.rb
@@ -21,7 +21,7 @@ class OsxfuseRequirement < Requirement
   end
 
   def message
-    msg = "libfuse is required to install this formula.\n"
+    msg = "libfuse is required for this software.\n"
     if libfuse_formula_exists?
       <<~EOS
         #{msg}Run `brew install libfuse` to install it.
diff --git a/Library/Homebrew/extend/os/mac/requirements/osxfuse_requirement.rb b/Library/Homebrew/extend/os/mac/requirements/osxfuse_requirement.rb
index bdf2d9e933..3ae4716a47 100644
--- a/Library/Homebrew/extend/os/mac/requirements/osxfuse_requirement.rb
+++ b/Library/Homebrew/extend/os/mac/requirements/osxfuse_requirement.rb
@@ -21,4 +21,8 @@ class OsxfuseRequirement < Requirement
       ENV.append_path "HOMEBREW_INCLUDE_PATHS", "/usr/local/include/osxfuse"
     end
   end
+
+  def message
+    "FUSE for macOS is required for this software. #{super}"
+  end
 end
diff --git a/Library/Homebrew/extend/os/mac/requirements/x11_requirement.rb b/Library/Homebrew/extend/os/mac/requirements/x11_requirement.rb
index 647c485b73..8b64a4ce00 100644
--- a/Library/Homebrew/extend/os/mac/requirements/x11_requirement.rb
+++ b/Library/Homebrew/extend/os/mac/requirements/x11_requirement.rb
@@ -17,6 +17,6 @@ class X11Requirement < Requirement
   end
 
   def message
-    "XQuartz #{min_version} (or newer) is required to install this formula. #{super}"
+    "XQuartz #{min_version} (or newer) is required for this software. #{super}"
   end
 end
diff --git a/Library/Homebrew/formula.rb b/Library/Homebrew/formula.rb
index 6812b905f4..4ef03f4a81 100644
--- a/Library/Homebrew/formula.rb
+++ b/Library/Homebrew/formula.rb
@@ -1772,7 +1772,7 @@ class Formula
         "name"     => req.name,
         "cask"     => req.cask,
         "download" => req.download,
-        "version"  => req.try(:version),
+        "version"  => req.try(:version) || req.try(:arch),
         "contexts" => req.tags,
       }
     end
diff --git a/Library/Homebrew/requirement.rb b/Library/Homebrew/requirement.rb
index a6d8545cb0..1f10e4aee7 100644
--- a/Library/Homebrew/requirement.rb
+++ b/Library/Homebrew/requirement.rb
@@ -48,7 +48,7 @@ class Requirement
     if download
       s += <<~EOS
         You can download from:
-          #{download}
+          #{Formatter.url(download)}
       EOS
     end
     s
@@ -122,11 +122,11 @@ class Requirement
   end
 
   def inspect
-    "#<#{self.class.name}: #{name.inspect} #{tags.inspect}>"
+    "#<#{self.class.name}: #{tags.inspect}>"
   end
 
   def display_s
-    name
+    name.capitalize
   end
 
   def mktemp(&block)
diff --git a/Library/Homebrew/requirements/arch_requirement.rb b/Library/Homebrew/requirements/arch_requirement.rb
index d4499ee065..e05e71645e 100644
--- a/Library/Homebrew/requirements/arch_requirement.rb
+++ b/Library/Homebrew/requirements/arch_requirement.rb
@@ -9,6 +9,8 @@ require "requirement"
 class ArchRequirement < Requirement
   fatal true
 
+  attr_reader :arch
+
   def initialize(tags)
     @arch = tags.shift
     super(tags)
@@ -16,13 +18,17 @@ class ArchRequirement < Requirement
 
   satisfy(build_env: false) do
     case @arch
-    when :x86_64 then Hardware::CPU.is_64_bit?
-    when :intel, :ppc then Hardware::CPU.type == @arch
+    when :x86_64 then Hardware::CPU.intel? && Hardware::CPU.is_64_bit?
+    when :arm, :intel, :ppc then Hardware::CPU.type == @arch
     end
   end
 
   def message
-    "This formula requires an #{@arch} architecture."
+    "The #{@arch} architecture is required for this software."
+  end
+
+  def inspect
+    "#<#{self.class.name}: arch=#{@arch.to_s.inspect} #{tags.inspect}>"
   end
 
   def display_s
diff --git a/Library/Homebrew/requirements/java_requirement.rb b/Library/Homebrew/requirements/java_requirement.rb
index a519a2cdbb..3edab63aa8 100644
--- a/Library/Homebrew/requirements/java_requirement.rb
+++ b/Library/Homebrew/requirements/java_requirement.rb
@@ -39,13 +39,13 @@ class JavaRequirement < Requirement
 
   def message
     version_string = " #{@version}" if @version
-    s = "Java#{version_string} is required to install this formula.\n"
+    s = "Java#{version_string} is required for this software.\n"
     s += suggestion
     s
   end
 
   def inspect
-    "#<#{self.class.name}: #{tags.inspect} version=#{@version.inspect}>"
+    "#<#{self.class.name}: version=#{@version.inspect} #{tags.inspect}>"
   end
 
   def display_s
@@ -55,9 +55,9 @@ class JavaRequirement < Requirement
       else
         ">="
       end
-      "#{name} #{op} #{version_without_plus}"
+      "#{name.capitalize} #{op} #{version_without_plus}"
     else
-      name
+      name.capitalize
     end
   end
 
diff --git a/Library/Homebrew/requirements/linux_requirement.rb b/Library/Homebrew/requirements/linux_requirement.rb
index a744caeab6..1a0e496282 100644
--- a/Library/Homebrew/requirements/linux_requirement.rb
+++ b/Library/Homebrew/requirements/linux_requirement.rb
@@ -10,6 +10,6 @@ class LinuxRequirement < Requirement
   satisfy(build_env: false) { OS.linux? }
 
   def message
-    "Linux is required."
+    "Linux is required for this software."
   end
 end
diff --git a/Library/Homebrew/requirements/macos_requirement.rb b/Library/Homebrew/requirements/macos_requirement.rb
index b9d4fbc556..c00750b9a2 100644
--- a/Library/Homebrew/requirements/macos_requirement.rb
+++ b/Library/Homebrew/requirements/macos_requirement.rb
@@ -41,11 +41,11 @@ class MacOSRequirement < Requirement
   end
 
   def message(type: :formula)
-    return "macOS is required." unless version_specified?
+    return "macOS is required for this software." unless version_specified?
 
     case @comparator
     when ">="
-      "macOS #{@version.pretty_name} or newer is required."
+      "macOS #{@version.pretty_name} or newer is required for this software."
     when "<="
       case type
       when :formula
@@ -59,19 +59,19 @@ class MacOSRequirement < Requirement
     else
       if @version.respond_to?(:to_ary)
         *versions, last = @version.map(&:pretty_name)
-        return "macOS #{versions.join(", ")} or #{last} is required."
+        return "macOS #{versions.join(", ")} or #{last} is required for this software."
       end
 
-      "macOS #{@version.pretty_name} is required."
+      "macOS #{@version.pretty_name} is required for this software."
     end
   end
 
   def inspect
-    "#<#{self.class.name}: #{tags.inspect} version#{@comparator}#{@version}>"
+    "#<#{self.class.name}: version#{@comparator}#{@version.to_s.inspect} #{tags.inspect}>"
   end
 
   def display_s
-    return "macOS is required" unless version_specified?
+    return "macOS" unless version_specified?
 
     "macOS #{@comparator} #{@version}"
   end
diff --git a/Library/Homebrew/requirements/osxfuse_requirement.rb b/Library/Homebrew/requirements/osxfuse_requirement.rb
index 9a4a0f527f..6dbc3917e1 100644
--- a/Library/Homebrew/requirements/osxfuse_requirement.rb
+++ b/Library/Homebrew/requirements/osxfuse_requirement.rb
@@ -7,8 +7,14 @@ require "requirement"
 #
 # @api private
 class OsxfuseRequirement < Requirement
+  extend T::Sig
   cask "osxfuse"
   fatal true
+
+  sig { returns(String) }
+  def display_s
+    "FUSE"
+  end
 end
 
 require "extend/os/requirements/osxfuse_requirement"
diff --git a/Library/Homebrew/requirements/x11_requirement.rb b/Library/Homebrew/requirements/x11_requirement.rb
index 4fe5c98538..4418f2f8ef 100644
--- a/Library/Homebrew/requirements/x11_requirement.rb
+++ b/Library/Homebrew/requirements/x11_requirement.rb
@@ -39,7 +39,7 @@ class X11Requirement < Requirement
   end
 
   def message
-    "X11 is required to install this formula, either Xorg #{min_version} or " \
+    "X11 is required for this software, either Xorg #{min_version} or " \
     "xdpyinfo #{min_xdpyinfo_version}, or newer. #{super}"
   end
 
@@ -48,10 +48,6 @@ class X11Requirement < Requirement
 
     0
   end
-
-  def inspect
-    "#<#{self.class.name}: #{tags.inspect}>"
-  end
 end
 
 require "extend/os/requirements/x11_requirement"
diff --git a/Library/Homebrew/requirements/xcode_requirement.rb b/Library/Homebrew/requirements/xcode_requirement.rb
index c58b72259f..b3e6973cfd 100644
--- a/Library/Homebrew/requirements/xcode_requirement.rb
+++ b/Library/Homebrew/requirements/xcode_requirement.rb
@@ -46,7 +46,13 @@ class XcodeRequirement < Requirement
   end
 
   def inspect
-    "#<#{self.class.name}: #{tags.inspect} version=#{@version.inspect}>"
+    "#<#{self.class.name}: version>=#{@version.inspect} #{tags.inspect}>"
+  end
+
+  def display_s
+    return name.capitalize unless @version
+
+    "#{name.capitalize} >= #{@version}"
   end
 end
 
diff --git a/Library/Homebrew/test/java_requirement_spec.rb b/Library/Homebrew/test/java_requirement_spec.rb
deleted file mode 100644
index 42a065faf2..0000000000
--- a/Library/Homebrew/test/java_requirement_spec.rb
+++ /dev/null
@@ -1,131 +0,0 @@
-# typed: false
-# frozen_string_literal: true
-
-require "cli/args"
-require "requirements/java_requirement"
-
-describe JavaRequirement do
-  subject { described_class.new([]) }
-
-  before do
-    ENV["JAVA_HOME"] = nil
-  end
-
-  describe "#message" do
-    its(:message) { is_expected.to match(/Java is required to install this formula./) }
-  end
-
-  describe "#inspect" do
-    subject { described_class.new(%w[1.7+]) }
-
-    its(:inspect) { is_expected.to eq('#<JavaRequirement: [] version="1.7+">') }
-  end
-
-  describe "#display_s" do
-    context "without specific version" do
-      its(:display_s) { is_expected.to eq("java") }
-    end
-
-    context "with version 1.8" do
-      subject { described_class.new(%w[1.8]) }
-
-      its(:display_s) { is_expected.to eq("java = 1.8") }
-    end
-
-    context "with version 1.8+" do
-      subject { described_class.new(%w[1.8+]) }
-
-      its(:display_s) { is_expected.to eq("java >= 1.8") }
-    end
-  end
-
-  describe "#satisfied?" do
-    subject { described_class.new(%w[1.8]) }
-
-    it "returns false if no `java` executable can be found" do
-      allow(File).to receive(:executable?).and_return(false)
-      expect(subject).not_to be_satisfied
-    end
-
-    it "returns true if #preferred_java returns a path" do
-      allow(subject).to receive(:preferred_java).and_return(Pathname.new("/usr/bin/java"))
-      expect(subject).to be_satisfied
-    end
-
-    context "when #possible_javas contains paths" do
-      let(:path) { mktmpdir }
-      let(:java) { path/"java" }
-
-      def setup_java_with_version(version)
-        IO.write java, <<~SH
-          #!/bin/sh
-          echo 'java version "#{version}"' 1>&2
-        SH
-        FileUtils.chmod "+x", java
-      end
-
-      before do
-        allow(subject).to receive(:possible_javas).and_return([java])
-      end
-
-      context "and 1.7 is required" do
-        subject { described_class.new(%w[1.7]) }
-
-        it "returns false if all are lower" do
-          setup_java_with_version "1.6.0_5"
-          expect(subject).not_to be_satisfied
-        end
-
-        it "returns true if one is equal" do
-          setup_java_with_version "1.7.0_5"
-          expect(subject).to be_satisfied
-        end
-
-        it "returns false if all are higher" do
-          setup_java_with_version "1.8.0_5"
-          expect(subject).not_to be_satisfied
-        end
-      end
-
-      context "and 1.7+ is required" do
-        subject { described_class.new(%w[1.7+]) }
-
-        it "returns false if all are lower" do
-          setup_java_with_version "1.6.0_5"
-          expect(subject).not_to be_satisfied
-        end
-
-        it "returns true if one is equal" do
-          setup_java_with_version "1.7.0_5"
-          expect(subject).to be_satisfied
-        end
-
-        it "returns true if one is higher" do
-          setup_java_with_version "1.8.0_5"
-          expect(subject).to be_satisfied
-        end
-      end
-    end
-  end
-
-  describe "#suggestion" do
-    context "without specific version" do
-      its(:suggestion) { is_expected.to match(/brew cask install adoptopenjdk/) }
-      its(:cask) { is_expected.to eq("adoptopenjdk") }
-    end
-
-    context "with version 1.8" do
-      subject { described_class.new(%w[1.8]) }
-
-      its(:suggestion) { is_expected.to match(%r{brew cask install homebrew/cask-versions/adoptopenjdk8}) }
-      its(:cask) { is_expected.to eq("homebrew/cask-versions/adoptopenjdk8") }
-    end
-
-    context "with version 1.8+" do
-      subject { described_class.new(%w[1.8+]) }
-
-      its(:suggestion) { is_expected.to match(/brew cask install adoptopenjdk/) }
-      its(:cask) { is_expected.to eq("adoptopenjdk") }
-    end
-  end
-end
diff --git a/Library/Homebrew/test/requirements/java_requirement_spec.rb b/Library/Homebrew/test/requirements/java_requirement_spec.rb
index 59e4dcc645..1b231d1fdd 100644
--- a/Library/Homebrew/test/requirements/java_requirement_spec.rb
+++ b/Library/Homebrew/test/requirements/java_requirement_spec.rb
@@ -1,33 +1,158 @@
 # typed: false
 # frozen_string_literal: true
 
+require "cli/args"
 require "requirements/java_requirement"
 
 describe JavaRequirement do
-  describe "initialize" do
+  subject { described_class.new([]) }
+
+  before do
+    ENV["JAVA_HOME"] = nil
+  end
+
+  describe "#initialize" do
     it "parses '1.8' tag correctly" do
       req = described_class.new(["1.8"])
-      expect(req.display_s).to eq("java = 1.8")
+      expect(req.display_s).to eq("Java = 1.8")
     end
 
     it "parses '9' tag correctly" do
       req = described_class.new(["9"])
-      expect(req.display_s).to eq("java = 9")
+      expect(req.display_s).to eq("Java = 9")
     end
 
     it "parses '9+' tag correctly" do
       req = described_class.new(["9+"])
-      expect(req.display_s).to eq("java >= 9")
+      expect(req.display_s).to eq("Java >= 9")
     end
 
     it "parses '11' tag correctly" do
       req = described_class.new(["11"])
-      expect(req.display_s).to eq("java = 11")
+      expect(req.display_s).to eq("Java = 11")
     end
 
     it "parses bogus tag correctly" do
       req = described_class.new(["bogus1.8"])
-      expect(req.display_s).to eq("java")
+      expect(req.display_s).to eq("Java")
+    end
+  end
+
+  describe "#message" do
+    its(:message) { is_expected.to match(/Java is required for this software./) }
+  end
+
+  describe "#inspect" do
+    subject { described_class.new(%w[1.7+]) }
+
+    its(:inspect) { is_expected.to eq('#<JavaRequirement: version="1.7+" []>') }
+  end
+
+  describe "#display_s" do
+    context "without specific version" do
+      its(:display_s) { is_expected.to eq("Java") }
+    end
+
+    context "with version 1.8" do
+      subject { described_class.new(%w[1.8]) }
+
+      its(:display_s) { is_expected.to eq("Java = 1.8") }
+    end
+
+    context "with version 1.8+" do
+      subject { described_class.new(%w[1.8+]) }
+
+      its(:display_s) { is_expected.to eq("Java >= 1.8") }
+    end
+  end
+
+  describe "#satisfied?" do
+    subject(:requirement) { described_class.new(%w[1.8]) }
+
+    it "returns false if no `java` executable can be found" do
+      allow(File).to receive(:executable?).and_return(false)
+      expect(requirement).not_to be_satisfied
+    end
+
+    it "returns true if #preferred_java returns a path" do
+      allow(requirement).to receive(:preferred_java).and_return(Pathname.new("/usr/bin/java"))
+      expect(requirement).to be_satisfied
+    end
+
+    context "when #possible_javas contains paths" do
+      let(:path) { mktmpdir }
+      let(:java) { path/"java" }
+
+      def setup_java_with_version(version)
+        IO.write java, <<~SH
+          #!/bin/sh
+          echo 'java version "#{version}"' 1>&2
+        SH
+        FileUtils.chmod "+x", java
+      end
+
+      before do
+        allow(requirement).to receive(:possible_javas).and_return([java])
+      end
+
+      context "and 1.7 is required" do
+        subject(:requirement) { described_class.new(%w[1.7]) }
+
+        it "returns false if all are lower" do
+          setup_java_with_version "1.6.0_5"
+          expect(requirement).not_to be_satisfied
+        end
+
+        it "returns true if one is equal" do
+          setup_java_with_version "1.7.0_5"
+          expect(requirement).to be_satisfied
+        end
+
+        it "returns false if all are higher" do
+          setup_java_with_version "1.8.0_5"
+          expect(requirement).not_to be_satisfied
+        end
+      end
+
+      context "and 1.7+ is required" do
+        subject(:requirement) { described_class.new(%w[1.7+]) }
+
+        it "returns false if all are lower" do
+          setup_java_with_version "1.6.0_5"
+          expect(requirement).not_to be_satisfied
+        end
+
+        it "returns true if one is equal" do
+          setup_java_with_version "1.7.0_5"
+          expect(requirement).to be_satisfied
+        end
+
+        it "returns true if one is higher" do
+          setup_java_with_version "1.8.0_5"
+          expect(requirement).to be_satisfied
+        end
+      end
+    end
+  end
+
+  describe "#suggestion" do
+    context "without specific version" do
+      its(:suggestion) { is_expected.to match(/brew cask install adoptopenjdk/) }
+      its(:cask) { is_expected.to eq("adoptopenjdk") }
+    end
+
+    context "with version 1.8" do
+      subject { described_class.new(%w[1.8]) }
+
+      its(:suggestion) { is_expected.to match(%r{brew cask install homebrew/cask-versions/adoptopenjdk8}) }
+      its(:cask) { is_expected.to eq("homebrew/cask-versions/adoptopenjdk8") }
+    end
+
+    context "with version 1.8+" do
+      subject { described_class.new(%w[1.8+]) }
+
+      its(:suggestion) { is_expected.to match(/brew cask install adoptopenjdk/) }
+      its(:cask) { is_expected.to eq("adoptopenjdk") }
     end
   end
 end
diff --git a/Library/Homebrew/test/requirements/osxfuse_requirement_spec.rb b/Library/Homebrew/test/requirements/osxfuse_requirement_spec.rb
index 4b9632a389..faa1b6e7f4 100644
--- a/Library/Homebrew/test/requirements/osxfuse_requirement_spec.rb
+++ b/Library/Homebrew/test/requirements/osxfuse_requirement_spec.rb
@@ -44,7 +44,7 @@ describe OsxfuseRequirement do
 
   describe "#message" do
     it "prompts for installation of 'libfuse' on Linux", :needs_linux do
-      expect(requirement.message).to match("libfuse is required to install this formula")
+      expect(requirement.message).to match("libfuse is required for this software")
     end
 
     it "prompts for installation of 'osxFuse' on macOS", :needs_macos do
diff --git a/Library/Homebrew/test/x11_requirement_spec.rb b/Library/Homebrew/test/requirements/x11_requirement_spec.rb
similarity index 71%
rename from Library/Homebrew/test/x11_requirement_spec.rb
rename to Library/Homebrew/test/requirements/x11_requirement_spec.rb
index 4076f1a553..3191b90643 100644
--- a/Library/Homebrew/test/x11_requirement_spec.rb
+++ b/Library/Homebrew/test/requirements/x11_requirement_spec.rb
@@ -5,26 +5,28 @@ require "cli/args"
 require "requirements/x11_requirement"
 
 describe X11Requirement do
+  subject(:requirement) { described_class.new([]) }
+
   let(:default_name) { "x11" }
 
   describe "#name" do
     it "defaults to x11" do
-      expect(subject.name).to eq(default_name)
+      expect(requirement.name).to eq(default_name)
     end
   end
 
   describe "#eql?" do
     it "returns true if the requirements are equal" do
       other = described_class.new
-      expect(subject).to eql(other)
+      expect(requirement).to eql(other)
     end
   end
 
   describe "#modify_build_environment" do
     it "calls ENV#x11" do
-      allow(subject).to receive(:satisfied?).and_return(true)
+      allow(requirement).to receive(:satisfied?).and_return(true)
       expect(ENV).to receive(:x11)
-      subject.modify_build_environment
+      requirement.modify_build_environment
     end
   end
 
@@ -32,12 +34,12 @@ describe X11Requirement do
     it "returns true if X11 is installed" do
       expect(MacOS::XQuartz).to receive(:version).and_return("2.7.5")
       expect(MacOS::XQuartz).to receive(:installed?).and_return(true)
-      expect(subject).to be_satisfied
+      expect(requirement).to be_satisfied
     end
 
     it "returns false if X11 is not installed" do
       expect(MacOS::XQuartz).to receive(:installed?).and_return(false)
-      expect(subject).not_to be_satisfied
+      expect(requirement).not_to be_satisfied
     end
   end
 end