three-tier architecture

CS 290C: Formal Models for Web Software

Lecture 9: Analyzing Data Models Using Alloy Analyzer and SMT-Solvers

Instructor: Tevfik Bultan

Three-Tier Architecture

Backend Database

Browser

Web Server

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• …

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?

A Data Model Verification Approach

MVC Design Principles

Automatic Extraction

Add data model properties

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

The Three Basic Relations in Rails• One-to-One (One-to-ZeroOrOne)

.

• One-to-Many

class User < ActiveRecord::Base has_one :accountend.

class Account < ActiveRecord::Base belongs_to :userend

class User < ActiveRecord::Base has_many :projectsend.class Project < ActiveRecord::Base belongs_to :userend

User

Account0..1

User

Project*

1

1

The Three Basic Relations in Rails

• Many-to-Manyclass Author < ActiveRecord::Base has_and_belongs_to_many :booksend

class Book < ActiveRecord::Base has_and_belongs_to_many :authorsend

Author

Book

*

*

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

The :through Option

class Book < ActiveRecord::Basehas_many :editionsbelongs_to :author

end

class Author < ActiveRecord::Basehas_many :bookshas_many :editions, :through => :books

end

class Edition < ActiveRecord::Base belongs_to :bookend Book

Author Edition

*

*

* 1

11

The :conditions Option

class Account < ActiveRecord::Base has_one :address,

:conditions => “address_type=‘Billing”end.class Address < ActiveRecord::Base belongs_to :accountend

AddressAccount address_type=

‘Billing’

0..11

The :polymorphic Option

class Address < ActiveRecord::Base belongs_to :addressable, :polymorphic => trueend

class Account < ActiveRecord::Base has_one :address, :as => :addressableend

class Contact < ActiveRecord::Base has_one :address, :as => :addressableend

Account

Address

Contact

0..1

0..1

1

1

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 => :destroyend

class Contact < ActiveRecord::Base belongs_to :user has_one :address, :dependent => :destroyend

AddressContactUser *1 1 0..1

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


• 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 ri ϵ R there exists oj, ok ϵ O 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


• 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

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

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

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

Translation to Alloy

class ObjectA has_one :objectBend.

class ObjectA has_many :objectBsend.

class ObjectA belongs_to :objectBend.

class ObjectA has_and_belongs_to_many

:objectBsend

.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:

Translating the :through Option

class Book < ActiveRecord::Base has_many :editions belongs_to :authorend

class Author < ActiveRecord::Base has_many :books has_many :editions,

:through => :booksend

class Edition < ActiveRecord::Base belongs_to :bookend

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

*

**

11

1

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 :accountend

.

class Account < ActiveRecord::Base belongs_to :user,

:dependent => :destroyend

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}


– 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)}

Translating the :dependent Optionpred 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)) ...

Verification Overview


Active Records

Alloy Specification

Verified

Counter-example

Data Model

Instance

TranslatorAlloy

Analyzer

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

TRACKS Fat Free CRMLOC 6062 lines 12069 lines

Data model classes

13 classes 20 classes

Alloy spec LOC 301 lines 1082 lines

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

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

ContextUser Todo* *1 1

:dependent => :delete

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

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!

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?

An Approach for Unbounded Verification

MVC DesignPattern

Automatic Extraction

AutomaticTranslation +AutomaticProjection+Properties

Another Rails Data Model Example

class User < ActiveRecord::Basehas_and_belongs_to_many :roleshas_one :profile, :dependent => :destroyhas_many :photos, :through => :profileendclass Role < ActiveRecord::Basehas_and_belongs_to_many :usersendclass Profile < ActiveRecord::Base belongs_to :user has_many :photos, :dependent => :destroy has_many :videos, :dependent => :destroy, :conditions => "format='mp4'"endclass Tag < ActiveRecord::Basebelongs_to :taggable, :polymorphic => trueendclass Video < ActiveRecord::Base belongs_to :profile has_many :tags, :as => :taggableendclass Photo < ActiveRecord::Base ...

Role

*

0..1

1

User

Profile

*

1

Video

*

1

Taggable

*

Tag

1

* 1Photo

*

1

format=.‘mp4’

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


class Profile has_many :videosendclass Video belongs_to :profileend

(declare-sort Profile 0)(declare-sort Video 0)(declare-fun my_relation (Video) Profile).

SMT-LIB:

RAILS:

• One-to-Many Relation


class User has_one :profileendclass Profile belongs_to :userend

(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


class User has_and_belongs_to_many :rolesendclass Role has_and_belongs_to_many :usersend

(declare-sort Role 0)(declare-sort User 0)(declare-fun my_relation (Role User) Bool)

SMT-LIB:

RAILS:

Many-to-Many Relation

Translating the :through Option

class Profile < ActiveRecord::Base belongs_to :user has_many :photosendclass Photo < ActiveRecord::Base belongs_to :profileEndclass User < ActiveRecord::Base has_one :profile has_many :photos, :through => :profileend

(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

**

11

1


• 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 => :destroyend

.

class Profile < ActiveRecord::Base belongs_to :userend

(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)


– 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)))

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?

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, C⟨ P, DP is the projected data model such ⟩that CP C and D⊆ P D⊆

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

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

Taggable

*

Tag

1

* 1Photo*

1

Data Model, M:

0..1

1

User

Profile* 1Photo*

1(M, p) =

Verification Overview

Translator

SMT Solver (Z3)

Verified

Counter-example

Data Model Instance

Unknown

Formal Data Model


Projection

SMT-LIB Specification

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

LovdBy

LessTracks OSR

Fat FreeCRM

Substruct

LOC 3787 6062 4295 12069 15639

Data Model Classes

13 13 15 20 17

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

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

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

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

Performance: Verification Time

Performance: Formula Size (Variables)

Z3 Alloy

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

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!

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

three-tier architecture

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