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

2. Three-Tier Architecture Backend Database Browser Web Server

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

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. MVC Application Ruby on Rails Data Model ActiveRecords Formal Model Alloy Bounded Verification Alloy Analyzer 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 One-to-One (One-to-ZeroOrOne). One-to-Many class User < ActiveRecord::Base has_one :account end. class Account < ActiveRecord::Base belongs_to :user end class User < ActiveRecord::Base has_many :projects end. class Project < ActiveRecord::Base belongs_to :user end User Account 0..1 User Project * 1 1

8. The Three Basic Relations in Rails Many-to-Many class Author < ActiveRecord::Base has_and_belongs_to_many :books end class Book < ActiveRecord::Base has_and_belongs_to_many :authors end Author 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 Author Edition * * * 1 1 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 Address Account address_type= ‘Billing’ 0..1 1

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 Account Address Contact 0..1 1 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 AddressContactUser * 110..1

14. Formalizing Rails Semantics Formal data model: M = 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 = where O = {o 1, o 2,... o n } is a set of object classes and R = {r 1, r 2,... r m } is a set of object relations and for each r i R there exists o j, o k O such that r i  o j × o k I = is an instance of the data model M =, denoted by I |= M, if and only if 1. the sets in O and the relations in R follow the schema S, and 2. R |= C

16. Formalizing Rails Semantics Given a pair of data model instances I = and I’ =, (I, I’) is a behavior of the data model M =, denoted by (I, I’) |= M, if and only if 1. O and R and O’ and R’ follow the schema S 2. R |= C and R’ |= C, and 3. (R,R’) |= D

17. Data Model Properties Given a data model M =, we define four types of properties: 1.state assertions (A S ): properties that we expect to hold for each instance of the data model 2.behavior assertions (A B ): properties that we expect to hold for each pair of instances that form a behavior of the data model 3.state predicates (P S ): predicates we expect to hold in some instance of the data model 4.behavior predicates (P B ): 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 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 } ALLOY: RAILS:

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 Author Edition * * * 1 1 1

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 :dependent option 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 Data Model Properties Active Records Alloy Specification Verified Counter- example Data Model Instance Translator Alloy Analyzer

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 TRACKSFat Free CRM LOC6062 lines12069 lines Data model classes 13 classes20 classes Alloy spec LOC301 lines1082 lines

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 UserProject

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 ContextUserTodo * * 11 :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. Web Application Ruby on Rails Data Model ActiveRecords Formal Model Sets and Relations Unbounded Verification SMT Solver 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 * 0..1 1 User Profile * 1 Video * 1 Taggable * Tag 1 * 1 Photo * 1 format=.‘mp4’

35. Translation to SMT-LIB Given a data model M = 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 class Profile has_many :videos end class Video belongs_to :profile end (declare-sort Profile 0) (declare-sort Video 0) (declare-fun my_relation (Video) Profile). SMT-LIB: RAILS: One-to-Many Relation

37. Translation to SMT-LIB class User has_one :profile end class Profile belongs_to :user end (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: RAILS: One-to-One Relation

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

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 User Photo 0..1 * * 1 1 1

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 :dependent option (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 = and a property p,  (M, p) = M P where M P = S, C P, D P is the projected data model such that C P ⊆ C and D P ⊆ 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 Property, p: A User’s Photos are the same as the User’s Profile’s Photos. Role * 0..1 1 User Profile * 1 Video * 1 Taggabl e * Tag 1 * 1 Photo * 1 Data Model, M: 0..1 1 User Profile * 1 Photo * 1  (M, p) =

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

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 LovdB y Less TracksOSR Fat Free CRM Substru ct LOC3787606242951206915639 Data Model Classes 13 152017

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 UserProject

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 BookmarkUser * 1

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

51. Performance To compare with bounded verification, we repeated these experiments using the tool from our previous work and Alloy Analyzer –The amount of time it took for Alloy to run –The number of variables generated in the boolean formula generated for the SAT solver –Taken over an increasing bound, from at most 10 objects for each class to at most 35 objects for each class

52. Performance: Verification Time

53. Performance: Formula Size (Variables) Z3 Alloy

54. Unbounded vs Bounded Performance Why does unbounded verification out-perform bounded so drastically? Possible reasons: SMT solvers operate at a higher level of abstraction than SAT solvers Z3 uses many heuristics to eliminate quantifiers in formulas Implementation languages are different –Z3 implemented in C++ –Alloy (as well as the SAT Solver it uses) is implemented in Java

55. Summary Automatically extract a formal data model, translate it to the theory of uninterpreted functions, and verify using an SMT- solver –Use property-based data model projection for efficiency An automatic translator from Rails ActiveRecords to SMT- LIB –Handles three basic relationships and several options (:through, :conditions, :polymorphic, :dependent) Found multiple data model errors on five open source applications –Unbounded verification of data models is feasible and more efficient than bounded verification!

56. Possible Extensions Analyzing dynamic behavior –Model object creation in addition object deletion –Fuse the data model with the navigation model in order to analyze dynamic data model behavior –Check temporal properties Automatic Property Inference –Manual property writing is error prone –Use the inherent graph structure in the the data model to automatically infer properties about the data model Automatic Repair –When verifier concludes that a data model is violated, automatically generate a repair that establishes the violated property