state_machine adds support for creating state machines for attributes on any Ruby class.
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Source
- git://github.com/pluginaweek/state_machine.git
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State machines make it dead-simple to manage the behavior of a class. Too often, the state of an object is kept by creating multiple boolean attributes and deciding how to behave based on the values. This can become cumbersome and difficult to maintain when the complexity of your class starts to increase.
state_machine simplifies this design by introducing the various parts of a real state machine, including states, events, transitions, and callbacks. However, the api is designed to be so simple you don't even need to know what a state machine is :)
Some brief, high-level features include:
- Defining state machines on any Ruby class
- Multiple state machines on a single class
- Namespaced state machines
- before/after/around/failure transition hooks with explicit transition requirements
- Integration with ActiveModel, ActiveRecord, DataMapper, Mongoid, MongoMapper, and Sequel
- State predicates
- State-driven instance / class behavior
- State values of any data type
- Dynamically-generated state values
- Event parallelization
- Attribute-based event transitions
- Path analysis
- Inheritance
- Internationalization
- GraphViz visualization creator
- YARD integration (Ruby 1.9+ only)
- Flexible machine syntax
Examples of the usage patterns for some of the above features are shown below. You can find much more detailed documentation in the actual API.
Below is an example of many of the features offered by this plugin, including:
- Initial states
- Namespaced states
- Transition callbacks
- Conditional transitions
- State-driven instance behavior
- Customized state values
- Parallel events
- Path analysis
Class definition:
class Vehicle
attr_accessor :seatbelt_on, :time_used, :auto_shop_busy
state_machine :state, :initial => :parked do
before_transition :parked => any - :parked, :do => :put_on_seatbelt
after_transition :on => :crash, :do => :tow
after_transition :on => :repair, :do => :fix
after_transition any => :parked do |vehicle, transition|
vehicle.seatbelt_on = false
end
after_failure :on => :ignite, :do => :log_start_failure
around_transition do |vehicle, transition, block|
start = Time.now
block.call
vehicle.time_used += Time.now - start
end
event :park do
transition [:idling, :first_gear] => :parked
end
event :ignite do
transition :stalled => same, :parked => :idling
end
event :idle do
transition :first_gear => :idling
end
event :shift_up do
transition :idling => :first_gear, :first_gear => :second_gear, :second_gear => :third_gear
end
event :shift_down do
transition :third_gear => :second_gear, :second_gear => :first_gear
end
event :crash do
transition all - [:parked, :stalled] => :stalled, :if => lambda {|vehicle| !vehicle.passed_inspection?}
end
event :repair do
# The first transition that matches the state and passes its conditions
# will be used
transition :stalled => :parked, :unless => :auto_shop_busy
transition :stalled => same
end
state :parked do
def speed
0
end
end
state :idling, :first_gear do
def speed
10
end
end
state all - [:parked, :stalled, :idling] do
def moving?
true
end
end
state :parked, :stalled, :idling do
def moving?
false
end
end
end
state_machine :alarm_state, :initial => :active, :namespace => 'alarm' do
event :enable do
transition all => :active
end
event :disable do
transition all => :off
end
state :active, :value => 1
state :off, :value => 0
end
def initialize
@seatbelt_on = false
@time_used = 0
@auto_shop_busy = true
super() # NOTE: This *must* be called, otherwise states won't get initialized
end
def put_on_seatbelt
@seatbelt_on = true
end
def passed_inspection?
false
end
def tow
# tow the vehicle
end
def fix
# get the vehicle fixed by a mechanic
end
def log_start_failure
# log a failed attempt to start the vehicle
end
end
Note the comment made on the initialize
method in the class. In order for
state machine attributes to be properly initialized, super()
must be called.
See StateMachine::MacroMethods
for more information about this.
Using the above class as an example, you can interact with the state machine like so:
vehicle = Vehicle.new # => #<Vehicle:0xb7cf4eac @state="parked", @seatbelt_on=false>
vehicle.state # => "parked"
vehicle.state_name # => :parked
vehicle.human_state_name # => "parked"
vehicle.parked? # => true
vehicle.can_ignite? # => true
vehicle.ignite_transition # => #<StateMachine::Transition attribute=:state event=:ignite from="parked" from_name=:parked to="idling" to_name=:idling>
vehicle.state_events # => [:ignite]
vehicle.state_transitions # => [#<StateMachine::Transition attribute=:state event=:ignite from="parked" from_name=:parked to="idling" to_name=:idling>]
vehicle.speed # => 0
vehicle.moving? # => false
vehicle.ignite # => true
vehicle.parked? # => false
vehicle.idling? # => true
vehicle.speed # => 10
vehicle # => #<Vehicle:0xb7cf4eac @state="idling", @seatbelt_on=true>
vehicle.shift_up # => true
vehicle.speed # => 10
vehicle.moving? # => true
vehicle # => #<Vehicle:0xb7cf4eac @state="first_gear", @seatbelt_on=true>
# A generic event helper is available to fire without going through the event's instance method
vehicle.fire_state_event(:shift_up) # => true
# Call state-driven behavior that's undefined for the state raises a NoMethodError
vehicle.speed # => NoMethodError: super: no superclass method `speed' for #<Vehicle:0xb7cf4eac>
vehicle # => #<Vehicle:0xb7cf4eac @state="second_gear", @seatbelt_on=true>
# The bang (!) operator can raise exceptions if the event fails
vehicle.park! # => StateMachine::InvalidTransition: Cannot transition state via :park from :second_gear
# Generic state predicates can raise exceptions if the value does not exist
vehicle.state?(:parked) # => false
vehicle.state?(:invalid) # => IndexError: :invalid is an invalid name
# Namespaced machines have uniquely-generated methods
vehicle.alarm_state # => 1
vehicle.alarm_state_name # => :active
vehicle.can_disable_alarm? # => true
vehicle.disable_alarm # => true
vehicle.alarm_state # => 0
vehicle.alarm_state_name # => :off
vehicle.can_enable_alarm? # => true
vehicle.alarm_off? # => true
vehicle.alarm_active? # => false
# Events can be fired in parallel
vehicle.fire_events(:shift_down, :enable_alarm) # => true
vehicle.state_name # => :first_gear
vehicle.alarm_state_name # => :active
vehicle.fire_events!(:ignite, :enable_alarm) # => StateMachine::InvalidTransition: Cannot run events in parallel: ignite, enable_alarm
# Human-friendly names can be accessed for states/events
Vehicle.human_state_name(:first_gear) # => "first gear"
Vehicle.human_alarm_state_name(:active) # => "active"
Vehicle.human_state_event_name(:shift_down) # => "shift down"
Vehicle.human_alarm_state_event_name(:enable) # => "enable"
# States / events can also be references by the string version of their name
Vehicle.human_state_name('first_gear') # => "first gear"
Vehicle.human_state_event_name('shift_down') # => "shift down"
# Available transition paths can be analyzed for an object
vehicle.state_paths # => [[#<StateMachine::Transition ...], [#<StateMachine::Transition ...], ...]
vehicle.state_paths.to_states # => [:parked, :idling, :first_gear, :stalled, :second_gear, :third_gear]
vehicle.state_paths.events # => [:park, :ignite, :shift_up, :idle, :crash, :repair, :shift_down]
# Find all paths that start and end on certain states
vehicle.state_paths(:from => :parked, :to => :first_gear) # => [[
# #<StateMachine::Transition attribute=:state event=:ignite from="parked" ...>,
# #<StateMachine::Transition attribute=:state event=:shift_up from="idling" ...>
# ]]
# Skipping state_machine and writing to attributes directly
vehicle.state = "parked"
vehicle.state # => "parked"
vehicle.state_name # => :parked
# *Note* that the following is not supported (see StateMachine::MacroMethods#state_machine):
# vehicle.state = :parked
In addition to being able to define state machines on all Ruby classes, a set of out-of-the-box integrations are available for some of the more popular Ruby libraries. These integrations add library-specific behavior, allowing for state machines to work more tightly with the conventions defined by those libraries.
The integrations currently available include:
- ActiveModel classes
- ActiveRecord models
- DataMapper resources
- Mongoid models
- MongoMapper models
- Sequel models
A brief overview of these integrations is described below.
The ActiveModel integration is useful for both standalone usage and for providing the base implementation for ORMs which implement the ActiveModel API. This integration adds support for validation errors, dirty attribute tracking, and observers. For example,
class Vehicle
include ActiveModel::Dirty
include ActiveModel::Validations
include ActiveModel::Observing
attr_accessor :state
define_attribute_methods [:state]
state_machine :initial => :parked do
before_transition :parked => any - :parked, :do => :put_on_seatbelt
after_transition any => :parked do |vehicle, transition|
vehicle.seatbelt = 'off'
end
around_transition :benchmark
event :ignite do
transition :parked => :idling
end
state :first_gear, :second_gear do
validates_presence_of :seatbelt_on
end
end
def put_on_seatbelt
...
end
def benchmark
...
yield
...
end
end
class VehicleObserver < ActiveModel::Observer
# Callback for :ignite event *before* the transition is performed
def before_ignite(vehicle, transition)
# log message
end
# Generic transition callback *after* the transition is performed
def after_transition(vehicle, transition)
Audit.log(vehicle, transition)
end
# Generic callback after the transition fails to perform
def after_failure_to_transition(vehicle, transition)
Audit.error(vehicle, transition)
end
end
For more information about the various behaviors added for ActiveModel state
machines and how to build new integrations that use ActiveModel, see
StateMachine::Integrations::ActiveModel
.
The ActiveRecord integration adds support for database transactions, automatically saving the record, named scopes, validation errors, and observers. For example,
class Vehicle < ActiveRecord::Base
state_machine :initial => :parked do
before_transition :parked => any - :parked, :do => :put_on_seatbelt
after_transition any => :parked do |vehicle, transition|
vehicle.seatbelt = 'off'
end
around_transition :benchmark
event :ignite do
transition :parked => :idling
end
state :first_gear, :second_gear do
validates_presence_of :seatbelt_on
end
end
def put_on_seatbelt
...
end
def benchmark
...
yield
...
end
end
class VehicleObserver < ActiveRecord::Observer
# Callback for :ignite event *before* the transition is performed
def before_ignite(vehicle, transition)
# log message
end
# Generic transition callback *after* the transition is performed
def after_transition(vehicle, transition)
Audit.log(vehicle, transition)
end
end
For more information about the various behaviors added for ActiveRecord state
machines, see StateMachine::Integrations::ActiveRecord
.
Like the ActiveRecord integration, the DataMapper integration adds support for database transactions, automatically saving the record, named scopes, Extlib-like callbacks, validation errors, and observers. For example,
class Vehicle
include DataMapper::Resource
property :id, Serial
property :state, String
state_machine :initial => :parked do
before_transition :parked => any - :parked, :do => :put_on_seatbelt
after_transition any => :parked do |transition|
self.seatbelt = 'off' # self is the record
end
around_transition :benchmark
event :ignite do
transition :parked => :idling
end
state :first_gear, :second_gear do
validates_presence_of :seatbelt_on
end
end
def put_on_seatbelt
...
end
def benchmark
...
yield
...
end
end
class VehicleObserver
include DataMapper::Observer
observe Vehicle
# Callback for :ignite event *before* the transition is performed
before_transition :on => :ignite do |transition|
# log message (self is the record)
end
# Generic transition callback *after* the transition is performed
after_transition do |transition|
Audit.log(self, transition) # self is the record
end
around_transition do |transition, block|
# mark start time
block.call
# mark stop time
end
# Generic callback after the transition fails to perform
after_transition_failure do |transition|
Audit.log(self, transition) # self is the record
end
end
Note that the DataMapper::Observer integration is optional and only available when the dm-observer library is installed.
For more information about the various behaviors added for DataMapper state
machines, see StateMachine::Integrations::DataMapper
.
The Mongoid integration adds support for automatically saving the record, basic scopes, validation errors, and observers. For example,
class Vehicle
include Mongoid::Document
state_machine :initial => :parked do
before_transition :parked => any - :parked, :do => :put_on_seatbelt
after_transition any => :parked do |vehicle, transition|
vehicle.seatbelt = 'off' # self is the record
end
around_transition :benchmark
event :ignite do
transition :parked => :idling
end
state :first_gear, :second_gear do
validates_presence_of :seatbelt_on
end
end
def put_on_seatbelt
...
end
def benchmark
...
yield
...
end
end
class VehicleObserver < Mongoid::Observer
# Callback for :ignite event *before* the transition is performed
def before_ignite(vehicle, transition)
# log message
end
# Generic transition callback *after* the transition is performed
def after_transition(vehicle, transition)
Audit.log(vehicle, transition)
end
end
For more information about the various behaviors added for Mongoid state
machines, see StateMachine::Integrations::Mongoid
.
The MongoMapper integration adds support for automatically saving the record, basic scopes, validation errors and callbacks. For example,
class Vehicle
include MongoMapper::Document
state_machine :initial => :parked do
before_transition :parked => any - :parked, :do => :put_on_seatbelt
after_transition any => :parked do |vehicle, transition|
vehicle.seatbelt = 'off' # self is the record
end
around_transition :benchmark
event :ignite do
transition :parked => :idling
end
state :first_gear, :second_gear do
validates_presence_of :seatbelt_on
end
end
def put_on_seatbelt
...
end
def benchmark
...
yield
...
end
end
For more information about the various behaviors added for MongoMapper state
machines, see StateMachine::Integrations::MongoMapper
.
Like the ActiveRecord integration, the Sequel integration adds support for database transactions, automatically saving the record, named scopes, validation errors and callbacks. For example,
class Vehicle < Sequel::Model
state_machine :initial => :parked do
before_transition :parked => any - :parked, :do => :put_on_seatbelt
after_transition any => :parked do |transition|
self.seatbelt = 'off' # self is the record
end
around_transition :benchmark
event :ignite do
transition :parked => :idling
end
state :first_gear, :second_gear do
validates_presence_of :seatbelt_on
end
end
def put_on_seatbelt
...
end
def benchmark
...
yield
...
end
end
For more information about the various behaviors added for Sequel state
machines, see StateMachine::Integrations::Sequel
.
In all of the examples used throughout the documentation, you'll notice that states and events are almost always referenced as symbols. This isn't a requirement, but rather a suggested best practice.
You can very well define your state machine with Strings like so:
class Vehicle
state_machine :initial => 'parked' do
event 'ignite' do
transition 'parked' => 'idling'
end
# ...
end
end
You could even use numbers as your state / event names. The important thing to keep in mind is that the type being used for referencing states / events in your machine definition must be consistent. If you're using Symbols, then all states / events must use Symbols. Otherwise you'll encounter the following error:
class Vehicle
state_machine do
event :ignite do
transition :parked => 'idling'
end
end
end
# => ArgumentError: "idling" state defined as String, :parked defined as Symbol; all states must be consistent
There is an exception to this rule. The consistency is only required within the definition itself. However, when the machine's helper methods are called with input from external sources, such as a web form, state_machine will map that input to a String / Symbol. For example:
class Vehicle
state_machine :initial => :parked do
event :ignite do
transition :parked => :idling
end
end
end
v = Vehicle.new # => #<Vehicle:0xb71da5f8 @state="parked">
v.state?('parked') # => true
v.state?(:parked) # => true
Although state_machine introduces a simplified syntax, it still remains backwards compatible with previous versions and other state-related libraries by providing some flexibility around how transitions are defined. See below for an overview of these syntaxes.
In general, it's recommended that state machines use the implicit syntax for
transitions. However, you can be a little more explicit and verbose about
transitions by using the :from
, :except_from
, :to
,
and :except_to
options.
For example, transitions and callbacks can be defined like so:
class Vehicle
state_machine :initial => :parked do
before_transition :from => :parked, :except_to => :parked, :do => :put_on_seatbelt
after_transition :to => :parked do |transition|
self.seatbelt = 'off' # self is the record
end
event :ignite do
transition :from => :parked, :to => :idling
end
end
end
Some flexibility is provided around the context in which transitions can be defined. In almost all examples throughout the documentation, transitions are defined within the context of an event. If you prefer to have state machines defined in the context of a state either out of preference or in order to easily migrate from a different library, you can do so as shown below:
class Vehicle
state_machine :initial => :parked do
...
state :parked do
transition :to => :idling, :on => [:ignite, :shift_up], :if => :seatbelt_on?
def speed
0
end
end
state :first_gear do
transition :to => :second_gear, :on => :shift_up
def speed
10
end
end
state :idling, :first_gear do
transition :to => :parked, :on => :park
end
end
end
In the above example, there's no need to specify the from
state for each
transition since it's inferred from the context.
You can also define transitions completely outside the context of a particular state / event. This may be useful in cases where you're building a state machine from a data store instead of part of the class definition. See the example below:
class Vehicle
state_machine :initial => :parked do
...
transition :parked => :idling, :on => [:ignite, :shift_up]
transition :first_gear => :second_gear, :second_gear => :third_gear, :on => :shift_up
transition [:idling, :first_gear] => :parked, :on => :park
transition [:idling, :first_gear] => :parked, :on => :park
transition all - [:parked, :stalled] => :stalled, :unless => :auto_shop_busy?
end
end
Notice that in these alternative syntaxes:
- You can continue to configure
:if
and:unless
conditions - You can continue to define
from
states (when in the machine context) using theall
,any
, andsame
helper methods
In most cases, the definition of a state machine is static. That is to say, the states, events and possible transitions are known ahead of time even though they may depend on data that's only known at runtime. For example, certain transitions may only be available depending on an attribute on that object it's being run on. All of the documentation in this library define static machines like so:
class Vehicle
state_machine :state, :initial => :parked do
event :park do
transition [:idling, :first_gear] => :parked
end
...
end
end
However, there may be cases where the definition of a state machine is dynamic. This means that you don't know the possible states or events for a machine until runtime. For example, you may allow users in your application to manage the state machine of a project or task in your system. This means that the list of transitions (and their associated states / events) could be stored externally, such as in a database. In a case like this, you can define dynamically-generated state machines like so:
class Vehicle
attr_accessor :state
# Replace this with an external source (like a db)
def transitions
[
{:parked => :idling, :on => :ignite},
{:idling => :first_gear, :first_gear => :second_gear, :on => :shift_up}
# ...
]
end
# Create a state machine for this vehicle instance dynamically based on the
# transitions defined from the source above
def machine
vehicle = self
@machine ||= Machine.new(vehicle, :initial => :parked) do
vehicle.transitions.each {|attrs| transition(attrs)}
# Persist the state on the vehicle itself
after_transition do
vehicle.state = vehicle.machine.state
vehicle.save
end
end
end
def save
# Save the state change...
end
end
# Generic class for building machines
class Machine
def self.new(object, *args, &block)
machine = Class.new do
def definition
self.class.state_machine
end
end
machine.state_machine(*args, &block)
machine.new
end
end
vehicle = Vehicle.new # => #<Vehicle:0xb7236b50>
vehicle.machine # => #<#<Class:0xb723541c>:0xb722fa30 @state="parked">
vehicle.machine.state # => "parked"
vehicle.machine.ignite # => true
vehicle.machine.state # => "idling
vehicle.state # => "idling"
vehicle.machine.state_transitions # => [#<StateMachine::Transition ...>]
vehicle.machine.definition.states.keys # => :first_gear, :second_gear, :parked, :idling
As you can see, state_machine provides enough flexibility for you to be able to create new machine definitions on the fly based on an external source of transitions.
By default, state_machine extends the Ruby core with a state_machine
method on
Class
. All other parts of the library are confined within the StateMachine
namespace. While this isn't wholly necessary, it also doesn't have any performance
impact and makes it truly feel like an extension to the language. This is very
similar to the way that you'll find yaml
, json
, or other libraries adding a
simple method to all objects just by loading the library.
However, if you'd like to avoid having state_machine add this extension to the Ruby core, you can do so like so:
require 'state_machine/core'
class Vehicle
extend StateMachine::MacroMethods
state_machine do
# ...
end
end
If you're using a gem loader like Bundler, you can explicitly indicate which file to load:
# In Gemfile
...
gem 'state_machine', :require => 'state_machine/core'
This library comes with built-in support for generating di-graphs based on the
events, states, and transitions defined for a state machine using GraphViz.
This requires that both the ruby-graphviz
gem and graphviz library be
installed on the system.
To generate a graph for a specific file / class:
rake state_machine:draw FILE=vehicle.rb CLASS=Vehicle
To save files to a specific path:
rake state_machine:draw FILE=vehicle.rb CLASS=Vehicle TARGET=files
To customize the image format / orientation:
rake state_machine:draw FILE=vehicle.rb CLASS=Vehicle FORMAT=jpg ORIENTATION=landscape
To generate multiple state machine graphs:
rake state_machine:draw FILE=vehicle.rb,car.rb CLASS=Vehicle,Car
To use human state / event names:
rake state_machine:draw FILE=vehicle.rb CLASS=Vehicle HUMAN_NAMES=true
Note that this will generate a different file for every state machine defined
in the class. The generated files will use an output filename of the format
#{class_name}_#{machine_name}.#{format}
.
For examples of actual images generated using this task, see those under the examples folder.
Jean Bovet's Visual Automata Simulator is a great tool for "simulating, visualizing and transforming finite state automata and Turing Machines". It can help in the creation of states and events for your models. It is cross-platform, written in Java.
If you use YARD to generate documentation for your projects, state_machine can be enabled to generate API docs for auto-generated methods from each state machine definition as well as providing embedded visualizations.
See the generated API documentation under the examples folder to see what the output looks like.
To enable the YARD integration, you'll need to add state_machine to the list of YARD's plugins by editing the global YARD config:
~/.yard/config:
load_plugins: true
autoload_plugins:
- state_machine
Once enabled, simply generate your documentation like you normally do.
Note that this only works for Ruby 1.9+.
Integrating state_machine into your Ruby on Rails application is straightforward and provides a few additional features specific to the framework. To get started, following the steps below.
If using Rails 2.x:
# In config/environment.rb
...
Rails::Initializer.run do |config|
...
config.gem 'state_machine', :version => '~> 1.0'
...
end
If using Rails 3.x or up:
# In Gemfile
...
gem 'state_machine'
gem 'ruby-graphviz', :require => 'graphviz' # Optional: only required for graphing
As usual, run bundle install
to load the gems.
Create a model with a field to store the state, along with other any other fields your application requires:
$ rails generate model Vehicle state:string
$ rake db:migrate
Add the state machine to your model. Following the examples above, app/models/vehicle.rb might become:
class Vehicle < ActiveRecord::Base
state_machine :initial => :parked do
before_transition :parked => any - :parked, :do => :put_on_seatbelt
...
end
end
There is a special integration Rake task for generating state machines for classes used in a Ruby on Rails application. This task will load the application environment, meaning that it's unnecessary to specify the actual file to load.
For example,
rake state_machine:draw CLASS=Vehicle
If you are using this library as a gem in Rails 2.x, the following must be added to the end of your application's Rakefile in order for the above task to work:
require 'tasks/state_machine'
Like Ruby on Rails, there is a special integration Rake task for generating state machines for classes used in a Merb application. This task will load the application environment, meaning that it's unnecessary to specify the actual files to load.
For example,
rake state_machine:draw CLASS=Vehicle
To run the core test suite (does not test any of the integrations):
bundle install
bundle exec rake test
To run integration tests:
bundle install
rake appraisal:install
rake appraisal:test
You can also test a specific version:
rake appraisal:active_model-3.0.0 test
rake appraisal:active_record-2.0.0 test
rake appraisal:data_mapper-0.9.4 test
rake appraisal:mongoid-2.0.0 test
rake appraisal:mongo_mapper-0.5.5 test
rake appraisal:sequel-2.8.0 test
The following caveats should be noted when using state_machine:
- Overridden event methods won't get invoked when using attribute-based event transitions
- DataMapper: Attribute-based event transitions are disabled when using dm-validations 0.9.4 - 0.9.6
- JRuby: around_transition callbacks in ORM integrations won't work on JRuby since it doesn't support continuations
- Factory Girl: Dynamic initial states don't work because of the way factory_girl
builds objects. You can work around this in a few ways:
- Use a default state that is common across all objects and rely on events to determine the actual initial state for your object.
- Assuming you're not using state-driven behavior on initialization, you can re-initialize states after the fact:
# Re-initialize in FactoryGirl
FactoryGirl.define do
factory :vehicle do
after_build {|user| user.send(:initialize_state_machines, :dynamic => :force)}
end
end
# Alternatively re-initialize in your model
class Vehicle < ActiveRecord::Base
...
before_validation :on => :create {|user| user.send(:initialize_state_machines, :dynamic => :force)}
end
- Ruby 1.8.6 or later
If using specific integrations:
- ActiveModel integration: 3.0.0 or later
- ActiveRecord integration: 2.0.0 or later
- DataMapper integration: 0.9.4 or later
- Mongoid integration: 2.0.0 or later
- MongoMapper integration: 0.5.5 or later
- Sequel integration: 2.8.0 or later
If graphing state machine:
- ruby-graphviz: 0.9.0 or later