Three-Tier Architecture

1. CS 290C: Formal Models for Web Software Lecture 9: Analyzing Data Models Using Alloy Analyzer and SMT-SolversInstructor: Tevfik Bultan

2. Three-Tier Architecture Browser Web Server Backend Database

3. Three-Tier Arch. + MVC Pattern Browser • MVC pattern has become the standard way to structure web applications: • Ruby on Rails • Zend for PHP • CakePHP • Struts for Java • Django for Python • … Controller Views Web Server Model Backend Database

4. Benefits of the MVC-Architecture • Benefits of the MVC architecture: • Separation of concerns • Modularity • Abstraction • These are the basic principles of software design • Can we exploit these principles for analysis?

5. A Data Model Verification Approach MVC Design Principles Automatic Extraction Add data model properties

6. Rails Data Models • Data model verification: Analyzing the associations/relations between data objects • Specified in Rails using association declarations inside the ActiveRecord files • The basic relation types • One-to-one • One-to-many • Many-to-many • Extensions to the basic relations using Options • :through, :conditions, :polymorphic, :dependent

7. The Three Basic Relations in Rails class User < ActiveRecord::Base has_one:account end. class Account < ActiveRecord::Base belongs_to :user end User 1 • One-to-One (One-to-ZeroOrOne) . • One-to-Many 0..1 Account class User < ActiveRecord::Base has_many :projects end. class Project < ActiveRecord::Base belongs_to :user end User 1 * Project

8. The Three Basic Relations in Rails class Author < ActiveRecord::Base has_and_belongs_to_many :books end class Book < ActiveRecord::Base has_and_belongs_to_many :authors end Author • Many-to-Many * * Book

9. Options to Extend the Basic Relations • :through Option • To express transitive relations, or • To express a many-to-many relation using a join model as opposed to a join table • :conditions Option • To relate a subset of objects to another class • :polymorphic Option • To express polymorphic relations • :dependent Option • On delete, this option expresses whether to delete the associated objects or not

10. The :through Option class Book < ActiveRecord::Base has_many :editions belongs_to:author end class Author < ActiveRecord::Base has_many:books has_many :editions, :through => :books end class Edition < ActiveRecord::Base belongs_to :book end Book * 1 * 1 Edition Author * 1

11. The :conditions Option class Account < ActiveRecord::Base has_one :address, :conditions => “address_type=‘Billing” end .class Address < ActiveRecord::Base belongs_to :account end Account Address 1 0..1 address_type=‘Billing’

12. The :polymorphic Option class Address < ActiveRecord::Base belongs_to :addressable, :polymorphic => true end class Account < ActiveRecord::Base has_one :address, :as => :addressable end class Contact < ActiveRecord::Base has_one :address, :as => :addressable end 1 Account 0..1 Address 0..1 Contact 1

13. The :dependent Option • :delete directly deletes the associated objects without looking at its dependencies • :destroy first checks whether the associated objects themselves have associations with the :dependent option set class User < ActiveRecord::Base has_many :contacts, :dependent => :destroy end class Contact < ActiveRecord::Base belongs_to :user has_one :address, :dependent => :destroy end User Contact Address 1 * 1 0..1

14. Formalizing Rails Semantics Formal data model: M = <S, C, D> • S: The sets and relations of the data model (data model schema) • e.g. {Account, Address, Project, User} and the relations between them • C: Constraints on the relations • Cardinality constraints, transitive relations, conditional relations, polymorphic relations • D: Dependency constraints express conditions on two consecutive instances of a relation such that deletion of an object from the fist instance leads to the other instance

15. Formalizing Rails Semantics • Data model instance: I = <O,R> where O = {o1, o2, . . . on} is a set of object classes and R = {r1, r2, . . . rm} is a set of object relations and for each riϵ R there exists oj, okϵO such that rioj × ok • I = <O,R> is an instance of the data model M = <S,C,D>, denoted by I |= M, if and only if • the sets in O and the relations in R follow the schema S, and • R |= C

16. Formalizing Rails Semantics • Given a pair of data model instances I = <O,R> and I’ = <O’,R’>, (I, I’) is a behavior of the data model M = <S,C,D>, denoted by (I, I’) |= M, if and only if • O and R and O’and R’follow the schema S • R |= C and R’|= C, and • (R,R’) |= D

17. Data Model Properties Given a data model M = <S,C,D>, we define four types of properties: • state assertions (AS): properties that we expect to hold for each instance of the data model • behavior assertions (AB): properties that we expect to hold for each pair of instances that form a behavior of the data model • state predicates (PS): predicates we expect to hold in some instance of the data model • behavior predicates (PB): predicates we expect to hold in some pair of instances that form a behavior of the data model

18. Data Model Properties

19. Data Model Verification • The data model verification problem: Given a data model property, determine if the data model satisfies the property. • An enumerative (i.e., explicit state) search technique not likely to be efficient for bounded verification • We can use SAT-based bounded verification! • Main idea: translate the verification query to a Boolean SAT instance and then use a SAT solver to search the state space

20. Data Model Verification • SAT-based bounded verification: This is exactly what the Alloy Analyzer does! • Alloy language allows specification of objects and relations, and the specification of constraints on relations using first-order logic • In order to do bounded verification of Rails data models, automatically translate the Active Record specifications to Alloy specifications

21. Translation to Alloy RAILS: ALLOY: class ObjectA has_one :objectB end . class ObjectA has_many :objectBs end . class ObjectA belongs_to :objectB end . class ObjectA has_and_belongs_to_many :objectBs end .sig ObjectA { objectB: lone ObjectB } . sig ObjectA { objectBs: set ObjectB } . sig ObjectA { objectB: one ObjectB } . sig ObjectA { objectBs: set ObjectB } fact { ObjectA <: objectBs = ~(ObjectB <: objectA }

22. Translating the :through Option class Book < ActiveRecord::Base has_many :editions belongs_to:author end class Author < ActiveRecord::Base has_many:books has_many :editions, :through => :books end class Edition < ActiveRecord::Base belongs_to :book end sig Book { editions: set Edition, author: one Author } sig Author { books: set Book, editions: set Edition } { editions = books.editions} sig Edition { book: one Book } fact { Book <: editions = ~(Edition <: book) Book <: authors = ~(Author <: book) } Book * 1 1 * 1 * Edition Author

23. Translating the :dependent Option • The :dependent option specifies what behavior to take on deletion of an object with regards to its associated objects • To incorporate this dynamism, the model must allow analysis of how sets of objects and their relations change from one state to the next class User < ActiveRecord::Base has_one :account end . class Account < ActiveRecord::Base belongs_to :user, :dependent => :destroy end sig User {} sig Account {} one sig PreState { accounts: set Account, users: set User, relation1: Account lone -> one User } one sig PostState { accounts’: set Account, users’: set User, relation1’: Account set -> set User }

24. Translating the :dependent Option • We also update relations of its associated object(s) based on the use of the :dependentoption pred deleteAccount [s: PreState, s’: PostState, x: Account] { all x0: Account | x0 in s.accounts all x1: User | x1 in s.users s’.accounts’ = s.accounts - x s’.users’ = s.users s’.relation1’ = s’.relation1 – (x <: s.relation1) }

25. Translating the :dependent Option pred deleteContext [s: PreState, s': PostState, x:Context] { all x0: Context | x0 in s.contexts all x1: Note | x1 in s.notes all x2: Preference | x2 in s.preferences all x3: Project | x3 in s.projects all x4: RecurringTodo | x4 in s.recurringtodos all x5: Tag | x5 in s.tags all x7: Todo | x7 in s.todos all x8: User | x8 in s.users s'.contexts' = s.contexts - x s'.notes' = s.notes s'.preferences' = s.preferences s'.projects' = s.projects s'.recurringtodos' = s.recurringtodos s'.tags' = s.tags s'.todos' = s.todos - x.(s.context_todos) s'.users' = s.users s'.notes_user' = s.notes_user s'.completed_todos_user' = s.completed_todos_user s'.recurring_todos_user' = s.recurring_todos_user s'.todos_user' = s.todos_user - (x.(s.context_todos) <: s.todos_user) s'.active_contexts_user' = s.active_contexts_user s'.active_projects_user' = s.active_projects_user s'.projects_user' = s.projects_user s'.contexts_user' = s.contexts_user - (x <: s.contexts_user) s'.recurring_todo_todos' = s.recurring_todo_todos - (s.recurring_todo_todos :> x.(s.context_todos)) ...

26. Verification Overview Counter-example Data Model Instance Active Records Alloy Specification Alloy Analyzer Translator Verified Data Model Properties

27. Experiments • We used two open-source Rails applications in our experiments: • TRACKS: An application to manage things-to-do lists • Fat Free CRM: Customer Relations Management software • We wrote 10 properties for TRACKS and 20 properties for Fat Free CRM

28. Types of Properties Checked • Relationship Cardinality • Is an Opportunity always assigned to some Campaign? • Transitive Relations • Is a Note’s User the same as the Note’s Project’s User? • Deletion Does Not Cause Dangling References • Are there any dangling Todos after a User is deleted? • Deletion Propagates to Associated Objects • Does the User related to a Lead still exist after the Lead has been deleted? Note User Project

29. Experimental Results • Of the 30 properties we checked 7 of them failed • For example, in TRACKS Note’s User can be different than Note’s Project’s User • Currently being enforced by the controller • Since this could have been enforced using the :through option, we consider this a data-modeling error • Another example from TRACKS: User deletion creates dangling Todos • User deletion does not get propagated into the relations of the Context object, including the Todos 1 1 * User * Context Todo :dependent => :delete

30. Performance • To measure performance, we recorded • the amount of time it took for Alloy to run and check the properties • the number of variables generated in the boolean formula generated for the SAT-solver • The time and number of variables are averaged over the properties for each application • Taken over an increasing bound, from at most 10 objects for each class to at most 35 objects for each class

31. Summary • An approach to automatically discover data model errors in Ruby on Rails web applications • Automatically extract a formal data model, verify using the Alloy Analyzer • An automatic translator from Rails ActiveRecords to Alloy • Handles three basic relationships and several options (:through, :conditions, :polymorphic, :dependent) • Found several data model errors on two open source applications • Bounded verification of data models is feasible!

32. What About Unbounded Verification? • Bounded verification does not guarantee correctness for arbitrarily large data model instances • Is it possible to do unbounded verification of data models?

33. An Approach for Unbounded Verification MVC Design Pattern Automatic Extraction Automatic Translation + Automatic Projection + Properties

34. Another Rails Data Model Example class User < ActiveRecord::Base has_and_belongs_to_many:roles has_one:profile, :dependent => :destroy has_many:photos, :through => :profile end class Role < ActiveRecord::Base has_and_belongs_to_many:users end class Profile < ActiveRecord::Base belongs_to:user has_many:photos, :dependent => :destroy has_many:videos, :dependent => :destroy, :conditions => "format='mp4'" end class Tag < ActiveRecord::Base belongs_to :taggable, :polymorphic => true end class Video < ActiveRecord::Base belongs_to:profile has_many:tags, :as => :taggable end class Photo < ActiveRecord::Base ... Role * * User 1 1 * 0..1 1 * Profile Photo 1 1 format=.‘mp4’ * 1 Video Taggable * Tag

35. Translation to SMT-LIB • Given a data model M = <S, C, D> we translate the constraints C and D to formulas in the theory of uninterpreted functions • We use the SMT-LIB format • We need quantification for some constraints

36. Translation to SMT-LIB • One-to-Many Relation class Profile has_many :videos end class Video belongs_to :profile end RAILS: (declare-sort Profile 0) (declare-sort Video 0) (declare-fun my_relation (Video) Profile). SMT-LIB:

37. Translation to SMT-LIB • One-to-One Relation class User has_one :profile end class Profile belongs_to :user end RAILS: (declare-sort User 0) (declare-sort Profile 0) (declare-fun my_relation (Profile) User). (assert (forall ((x1 Profile)(x2 Profile)) (=> (not (= x1 x2)) (not (= (my_relation x1) (my_relation x2) )) ) )) SMT-LIB:

38. Translation to SMT-LIB Many-to-Many Relation class User has_and_belongs_to_many :roles end class Role has_and_belongs_to_many :users end RAILS: (declare-sort Role 0) (declare-sort User 0) (declare-fun my_relation (Role User) Bool) SMT-LIB:

39. Translating the :through Option class Profile < ActiveRecord::Base belongs_to :user has_many :photos end class Photo < ActiveRecord::Base belongs_to :profile End class User < ActiveRecord::Base has_one :profile has_many :photos, :through => :profile end (declare-sort Profile 0) (declare-sort Photo 0) (declare-sort User 0) (declare-fun profile_photo (Photo) Profile) (declare-fun user_profile (Profile) User) (declare-fun user_photo (Photo) User) (assert (forall ((u User)(ph Photo)) (iff (= u (user_photo ph)) (exists ((p Profile)) (and (= u (user_profile p)) (= p (profile_photo ph)) )) )) ) Profile 0..1 1 1 * 1 * Photo User

40. Translating the :dependent Option • The :dependent option specifies what behavior to take on deletion of an object with regards to its associated objects • To incorporate this dynamism, the model must allow analysis of how sets of objects and their relations change from one state to the next class User < ActiveRecord::Base has_one :account, :dependent => :destroy end . class Profile < ActiveRecord::Base belongs_to :user end (declare-sort Profile 0) (declare-sort User 0) (declare-fun Post_User (User) Bool) (declare-fun Post_Profile (Profile) Bool) (declare-fun user_profile (Profile) User) (declare-fun Post_user_profile (Profile User) Bool)

41. Translating the :dependent Option • Update sets relations of its associated object(s) based on the use of the :dependentoption (assert (not (forall ((x User)) (=> (and (forall ((a User)) (ite (= a x) (not (Post_User a)) (Post_User a))) (forall ((b Profile)) (ite (= x (user_profile b)) (not (Post_Profile b)) (Post_Profile b) )) (forall ((a Profile) (b User)) (ite (and (= b (user_profile a)) (Post_Profile a)) (Post_user_profile a b) (not (Post_user_profile a b)) )) ) ;Remaining property-specific constraints go here )))

42. Verification • Once the data model is translated to SMT-LIB format we can state properties about the data model again in SMT-LIB and then use an SMT-Solver to check if the property holds in the data model • However, when we do that, for some large models, SMT-Solver times out! • Can we improve the efficiency of the verification process?

43. Property-Based Data Model Projection • Basic idea: Given a property to verify, reduce the size of the generated SMT-LIB specification by removing declarations and constraints that do not depend on the property • Formally, given a data model M = <S, C, D> and a property p,(M, p) = MP where MP = ⟨S, CP, DP⟩ is the projected data model such that CP ⊆ C and DP ⊆ D

44. Property-Based Data Model Projection • Key Property: For any property p, M |= p ⇔ (M, p) |= p • Projection Input: Active Record files, property p • Projection Output: The projected SMT-LIB specification • Removes constraints on those classes and relations that are not explicitly mentioned in the property nor related to them based on transitive relations, dependency constraints or polymorphic relations

45. Data Model Projection: Example Role Property, p: A User’s Photos are the same as the User’s Profile’s Photos. Data Model, M: * * User 1 User 1 1 1 * 0..1 * 0..1 1 * Profile 1 Photo * Profile Photo (M, p) = 1 1 * 1 Taggable Video * Tag

46. Verification Overview Data Model Properties Formal Data Model Projection Translator Active Records SMT-LIB Specification Counter-example Data Model Instance SMT Solver (Z3) Unknown Verified

47. Experiments • We used five open-source Rails apps in our experiments: • LovdByLess: Social networking site • Tracks: An application to manage things-to-do lists • OpenSourceRails(OSR): Social project gallery application • Fat FreeCRM: Customer relations management software • Substruct: An e-commerce application • We wrote 10 properties for each application

48. Types of Properties Checked • Relationship Cardinality • Is an Opportunity always assigned to some Campaign? • Transitive Relations • Is a Note’s User the same as the Note’s Project’s User? • Deletion Does Not Cause Dangling References • Are there any dangling Todos after a User is deleted? • Deletion Propagates to Associated Objects • Does the User related to a Lead still exist after the Lead has been deleted? Note User Project

49. Experimental Results • 50 properties checked, 16 failed, 11 were data model errors • For example in Tracks, a Note’s User can be different than Note’s Project’s User • Currently being enforced by the controller • Since this could have been enforced using the :through option, we consider this a data-modeling error • From OpenSourceRails: User deletion fails to propagate to associated Bookmarks • Leaves orphaned bookmarks in database • Could have been enforced in the data model by setting the :dependent option on the relation between User and Bookmark 1 * User Bookmark

50. Performance • To measure performance, we recorded • The amount of time it took for Z3 to run and check the properties • The number of variables produced in the SMT specification • The time and number of variables are averaged over the properties for each application