diff --git a/Library/Homebrew/bottle_specification.rb b/Library/Homebrew/bottle_specification.rb
index eab4311ac2..83d81f62cc 100644
--- a/Library/Homebrew/bottle_specification.rb
+++ b/Library/Homebrew/bottle_specification.rb
@@ -4,18 +4,27 @@
 class BottleSpecification
   RELOCATABLE_CELLARS = [:any, :any_skip_relocation].freeze
 
+  sig { returns(T.nilable(Tap)) }
   attr_accessor :tap
-  attr_reader :collector, :root_url_specs, :repository
+
+  attr_reader :collector
+
+  sig { returns(T::Hash[String, T.untyped]) }
+  attr_reader :root_url_specs
+
+  sig { returns(String) }
+  attr_reader :repository
 
   sig { void }
   def initialize
-    @rebuild = 0
-    @repository = Homebrew::DEFAULT_REPOSITORY
-    @collector = Utils::Bottles::Collector.new
-    @root_url_specs = {}
+    @rebuild = T.let(0, Integer)
+    @repository = T.let(Homebrew::DEFAULT_REPOSITORY, String)
+    @collector = T.let(Utils::Bottles::Collector.new, Utils::Bottles::Collector)
+    @root_url_specs = T.let({}, T::Hash[String, T.untyped])
+    @root_url = T.let(nil, T.nilable(String))
   end
 
-  sig { params(val: Integer).returns(T.nilable(Integer)) }
+  sig { params(val: Integer).returns(Integer) }
   def rebuild(val = T.unsafe(nil))
     val.nil? ? @rebuild : @rebuild = val
   end
diff --git a/Library/Homebrew/cleanup.rb b/Library/Homebrew/cleanup.rb
index 7f879e044e..37ed04e13a 100644
--- a/Library/Homebrew/cleanup.rb
+++ b/Library/Homebrew/cleanup.rb
@@ -171,7 +171,7 @@ module Homebrew
 
         stable = formula.stable
         if resource_name == "patch"
-          patch_hashes = stable&.patches&.filter_map { _1.resource.version if _1.external? }
+          patch_hashes = stable&.patches&.filter_map { T.cast(_1, ExternalPatch).resource.version if _1.external? }
           return true unless patch_hashes&.include?(Checksum.new(version.to_s))
         elsif resource_name && stable && (resource_version = stable.resources[resource_name]&.version)
           return true if resource_version != version
diff --git a/Library/Homebrew/dependable.rb b/Library/Homebrew/dependable.rb
index f0d089491c..353ced54d1 100644
--- a/Library/Homebrew/dependable.rb
+++ b/Library/Homebrew/dependable.rb
@@ -5,12 +5,19 @@ require "options"
 
 # Shared functions for classes which can be depended upon.
 module Dependable
+  extend T::Helpers
+
   # `:run` and `:linked` are no longer used but keep them here to avoid their
   # misuse in future.
   RESERVED_TAGS = [:build, :optional, :recommended, :run, :test, :linked, :implicit].freeze
 
   attr_reader :tags
 
+  abstract!
+
+  sig { abstract.returns(T::Array[String]) }
+  def option_names; end
+
   def build?
     tags.include? :build
   end
diff --git a/Library/Homebrew/dependency_collector.rb b/Library/Homebrew/dependency_collector.rb
index cddae5fcdc..6fb78130ec 100644
--- a/Library/Homebrew/dependency_collector.rb
+++ b/Library/Homebrew/dependency_collector.rb
@@ -80,10 +80,10 @@ class DependencyCollector
     parse_spec(spec, Array(tags))
   end
 
-  sig { params(related_formula_names: T::Array[String]).returns(T.nilable(Dependency)) }
+  sig { params(related_formula_names: T::Set[String]).returns(T.nilable(Dependency)) }
   def gcc_dep_if_needed(related_formula_names); end
 
-  sig { params(related_formula_names: T::Array[String]).returns(T.nilable(Dependency)) }
+  sig { params(related_formula_names: T::Set[String]).returns(T.nilable(Dependency)) }
   def glibc_dep_if_needed(related_formula_names); end
 
   def git_dep_if_needed(tags)
diff --git a/Library/Homebrew/downloadable.rb b/Library/Homebrew/downloadable.rb
index 9d732e237a..a2365da4b5 100644
--- a/Library/Homebrew/downloadable.rb
+++ b/Library/Homebrew/downloadable.rb
@@ -32,7 +32,7 @@ module Downloadable
     @download_name = T.let(nil, T.nilable(String))
   end
 
-  sig { params(other: Object).void }
+  sig { overridable.params(other: Downloadable).void }
   def initialize_dup(other)
     super
     @checksum = @checksum.dup
diff --git a/Library/Homebrew/extend/os/linux/formula.rb b/Library/Homebrew/extend/os/linux/formula.rb
index 46489c1c0d..106f49a9a1 100644
--- a/Library/Homebrew/extend/os/linux/formula.rb
+++ b/Library/Homebrew/extend/os/linux/formula.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:disable Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 module OS
@@ -30,6 +30,7 @@ module OS
       def add_global_deps_to_spec(spec)
         return unless ::DevelopmentTools.needs_build_formulae?
 
+        @global_deps ||= T.let(nil, T.nilable(T::Array[Dependency]))
         @global_deps ||= begin
           dependency_collector = spec.dependency_collector
           related_formula_names = Set.new([
diff --git a/Library/Homebrew/resource.rb b/Library/Homebrew/resource.rb
index 813d1486f5..a6a4c0e9fd 100644
--- a/Library/Homebrew/resource.rb
+++ b/Library/Homebrew/resource.rb
@@ -37,7 +37,7 @@ class Resource
     instance_eval(&block) if block
   end
 
-  sig { params(other: Object).void }
+  sig { override.params(other: T.any(Resource, Downloadable)).void }
   def initialize_dup(other)
     super
     @name = @name.dup
diff --git a/Library/Homebrew/software_spec.rb b/Library/Homebrew/software_spec.rb
index cb88a3c84c..b69655d2b3 100644
--- a/Library/Homebrew/software_spec.rb
+++ b/Library/Homebrew/software_spec.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "resource"
@@ -20,13 +20,46 @@ class SoftwareSpec
   extend Forwardable
   include OnSystem::MacOSAndLinux
 
-  PREDEFINED_OPTIONS = {
+  PREDEFINED_OPTIONS = T.let({
     universal: Option.new("universal", "Build a universal binary"),
     cxx11:     Option.new("c++11",     "Build using C++11 mode"),
-  }.freeze
+  }.freeze, T::Hash[T.any(Symbol, String), Option])
 
-  attr_reader :name, :full_name, :owner, :build, :resources, :patches, :options, :deprecated_flags,
-              :deprecated_options, :dependency_collector, :bottle_specification, :compiler_failures
+  sig { returns(T.nilable(String)) }
+  attr_reader :name
+
+  sig { returns(T.nilable(String)) }
+  attr_reader :full_name
+
+  sig { returns(T.nilable(T.any(Formula, Cask::Cask))) }
+  attr_reader :owner
+
+  sig { returns(BuildOptions) }
+  attr_reader :build
+
+  sig { returns(T::Hash[String, Resource]) }
+  attr_reader :resources
+
+  sig { returns(T::Array[T.any(EmbeddedPatch, ExternalPatch)]) }
+  attr_reader :patches
+
+  sig { returns(Options) }
+  attr_reader :options
+
+  sig { returns(T::Array[DeprecatedOption]) }
+  attr_reader :deprecated_flags
+
+  sig { returns(T::Array[DeprecatedOption]) }
+  attr_reader :deprecated_options
+
+  sig { returns(DependencyCollector) }
+  attr_reader :dependency_collector
+
+  sig { returns(BottleSpecification) }
+  attr_reader :bottle_specification
+
+  sig { returns(T::Array[CompilerFailure]) }
+  attr_reader :compiler_failures
 
   def_delegators :@resource, :stage, :fetch, :verify_download_integrity, :source_modified_time,
                  :cached_download, :clear_cache, :checksum, :mirrors, :specs, :using, :version, :mirror,
@@ -34,23 +67,29 @@ class SoftwareSpec
 
   def_delegators :@resource, :sha256
 
+  sig { params(flags: T::Array[String]).void }
   def initialize(flags: [])
     super()
 
+    @name = T.let(nil, T.nilable(String))
+    @full_name = T.let(nil, T.nilable(String))
+    @owner = T.let(nil, T.nilable(T.any(Formula, Cask::Cask)))
+
     # Ensure this is synced with `initialize_dup` and `freeze` (excluding simple objects like integers and booleans)
     @resource = T.let(Resource::Formula.new, Resource::Formula)
-    @resources = {}
-    @dependency_collector = DependencyCollector.new
-    @bottle_specification = BottleSpecification.new
-    @patches = []
-    @options = Options.new
-    @flags = flags
-    @deprecated_flags = []
-    @deprecated_options = []
-    @build = BuildOptions.new(Options.create(@flags), options)
-    @compiler_failures = []
+    @resources = T.let({}, T::Hash[String, Resource])
+    @dependency_collector = T.let(DependencyCollector.new, DependencyCollector)
+    @bottle_specification = T.let(BottleSpecification.new, BottleSpecification)
+    @patches = T.let([], T::Array[T.any(EmbeddedPatch, ExternalPatch)])
+    @options = T.let(Options.new, Options)
+    @flags = T.let(flags, T::Array[String])
+    @deprecated_flags = T.let([], T::Array[DeprecatedOption])
+    @deprecated_options = T.let([], T::Array[DeprecatedOption])
+    @build = T.let(BuildOptions.new(Options.create(@flags), options), BuildOptions)
+    @compiler_failures = T.let([], T::Array[CompilerFailure])
   end
 
+  sig { override.params(other: T.any(SoftwareSpec, Downloadable)).void }
   def initialize_dup(other)
     super
     @resource = @resource.dup
@@ -66,6 +105,7 @@ class SoftwareSpec
     @compiler_failures = @compiler_failures.dup
   end
 
+  sig { override.returns(T.self_type) }
   def freeze
     @resource.freeze
     @resources.freeze
@@ -81,6 +121,7 @@ class SoftwareSpec
     super
   end
 
+  sig { params(owner: T.any(Formula, Cask::Cask)).void }
   def owner=(owner)
     @name = owner.name
     @full_name = owner.full_name
@@ -106,23 +147,35 @@ class SoftwareSpec
     @resource.url
   end
 
+  sig { returns(T::Boolean) }
   def bottle_defined?
     !bottle_specification.collector.tags.empty?
   end
 
+  sig { params(tag: T.nilable(Utils::Bottles::Tag)).returns(T::Boolean) }
   def bottle_tag?(tag = nil)
     bottle_specification.tag?(Utils::Bottles.tag(tag))
   end
 
+  sig { params(tag: T.nilable(Utils::Bottles::Tag)).returns(T::Boolean) }
   def bottled?(tag = nil)
-    bottle_tag?(tag) &&
-      (tag.present? || bottle_specification.compatible_locations? || owner.force_bottle)
+    return false unless bottle_tag?(tag)
+
+    return true if tag.present?
+    return true if bottle_specification.compatible_locations?
+
+    owner = self.owner
+    return false unless owner.is_a?(Formula)
+
+    owner.force_bottle
   end
 
+  sig { params(block: T.proc.bind(BottleSpecification).void).void }
   def bottle(&block)
     bottle_specification.instance_eval(&block)
   end
 
+  sig { params(name: String).returns(T::Boolean) }
   def resource_defined?(name)
     resources.key?(name)
   end
@@ -149,15 +202,14 @@ class SoftwareSpec
     end
   end
 
+  sig { params(name: String).returns(T::Boolean) }
   def option_defined?(name)
     options.include?(name)
   end
 
+  sig { params(name: T.any(Symbol, String), description: String).void }
   def option(name, description = "")
     opt = PREDEFINED_OPTIONS.fetch(name) do
-      unless name.is_a?(String)
-        raise ArgumentError, "option name must be string or symbol; got a #{name.class}: #{name}"
-      end
       raise ArgumentError, "option name is required" if name.empty?
       raise ArgumentError, "option name must be longer than one character: #{name}" if name.length <= 1
       raise ArgumentError, "option name must not start with dashes: #{name}" if name.start_with?("-")
@@ -167,6 +219,7 @@ class SoftwareSpec
     options << opt
   end
 
+  sig { params(hash: T::Hash[T.any(String, Symbol), T.any(String, Symbol)]).void }
   def deprecated_option(hash)
     raise ArgumentError, "deprecated_option hash must not be empty" if hash.empty?
 
@@ -189,6 +242,7 @@ class SoftwareSpec
     @build = BuildOptions.new(Options.create(@flags), options)
   end
 
+  sig { params(spec: T.any(String, Symbol, T::Hash[String, T.untyped], T::Class[Requirement], Dependable)).void }
   def depends_on(spec)
     dep = dependency_collector.add(spec)
     add_dep_option(dep) if dep
@@ -214,14 +268,17 @@ class SoftwareSpec
     depends_on UsesFromMacOSDependency.new(dep, tags, bounds:)
   end
 
+  sig { returns(Dependencies) }
   def deps
     dependency_collector.deps.dup_without_system_deps
   end
 
+  sig { returns(Dependencies) }
   def declared_deps
     dependency_collector.deps
   end
 
+  sig { returns(T::Array[Dependable]) }
   def recursive_dependencies
     deps_f = []
     recursive_dependencies = deps.filter_map do |dep|
@@ -239,15 +296,21 @@ class SoftwareSpec
     recursive_dependencies
   end
 
+  sig { returns(Requirements) }
   def requirements
     dependency_collector.requirements
   end
 
+  sig { returns(Requirements) }
   def recursive_requirements
     Requirement.expand(self)
   end
 
-  def patch(strip = :p1, src = nil, &block)
+  sig {
+    params(strip: T.any(Symbol, String), src: T.nilable(T.any(String, Symbol)),
+           block: T.nilable(T.proc.bind(Patch).void)).void
+  }
+  def patch(strip = :p1, src = T.unsafe(nil), &block)
     p = Patch.create(strip, src, &block)
     return if p.is_a?(ExternalPatch) && p.url.blank?
 
@@ -255,16 +318,19 @@ class SoftwareSpec
     patches << p
   end
 
+  sig { params(compiler: T.any(T::Hash[Symbol, String], Symbol), block: T.nilable(T.proc.bind(CompilerFailure).void)).void }
   def fails_with(compiler, &block)
     compiler_failures << CompilerFailure.create(compiler, &block)
   end
 
+  sig { params(standards: T::Array[String]).void }
   def needs(*standards)
     standards.each do |standard|
       compiler_failures.concat CompilerFailure.for_standard(standard)
     end
   end
 
+  sig { params(dep: Dependable).void }
   def add_dep_option(dep)
     dep.option_names.each do |name|
       if dep.optional? && !option_defined?("with-#{name}")