1 Abstract Model Specification Tarang Garg Srikumar Nagaraj.

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Abstract Model Specification

Tarang Garg

Srikumar Nagaraj

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Abstract Model Specification

• Explicitly describes behavior in terms of a model using well-defined types (viz. set, sequences, relations, functions) & defines operations by showing effects on model

• Specification includes• type - syntax of object being specified

• model - underlying structure

• invariant - properties of modeled object

• pre/post conditions – semantics of operations

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Notation

• Is used to test the results

• Independent of program code

• Mathematical Data model

• Represent both static and dynamic aspects of a system

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Features( Z-notation)

• Decompose specification into small pieces (Schemas)

• Schemas are used to describe both static and dynamic aspects of a system

• Data Refinement

• Direct Refinement

• You can ignore details in order to focus on the aspects of the problem you are interested in

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Schema

Static Aspect The state can occupy. The invariant relationships that are

maintained as the system moves from state to state

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Schema(cont.)

Dynamic Aspect The operations that are possibleThe relationship between their inputs and

outputs.The change of state that happen.

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Notation - Example

Some variables are declared.

Relationship between the values of the variables

Name

Init Birthday Book

Known =

Birthday Book

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ExampleBirthday book

known: NAME

birthday: NAME DATE

Known : dom birthday

Add BirthdayBirthday Book

name?: NAME

date?: DATE

name? known

birthday’ = birthday { name? date}

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Example(cont.)

Find Birthday Birthday book

name?: NAME

date? : DATE

name? Known

date != birthday(name?)

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Race conditionWe have not handled the condition when user tries to add a

birthday, which is already known to the system, or tries to find the birthday of someone not known.

Handle this by adding an extra result! To each operation.

Result := of| already_known | not_known

Success

Result! : REPORT

Result! = ok

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Operators

(Conjunction of the two predicate parts) – any common variables of the two schemas are merged

V (the effect of the schema operator is to make a schema in which the predicate part is the result of joining the predicate parts of its two arguments with the logical connective V).

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Logical Conjunction Operator

The conjunction operator of the schema calculus allows us to combine this description with our previous description of AddBirthday

AddBirthday Success

This describes an operation which, for correct input, both acts as described by AddBirthday and produces the result ok.

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Logical Disjunction operator

This declaration specifies that if error occurs, the state of the system should not change.

Robust version of AddBirthday can be

RAddBirthday (AddBirthday Success) V Alreadyknown

AlreadyKnown BirthdayBook

name? : NAMEresult?: REPORT

Name? knownResult! = already_known

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Use of OperatorsRAdd Birthday

Birthday Book

name?: NAME

date?: DATE

result!: REPORT

(name? known

birthday’= birthday {name? Date?}

result!= ok) V

(name? known

birthday’ = birthday

result != already_known)

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Data Refinement

“ to describe the concrete data structures which the program will use to represent the abstract data in the specification, and to derive description of the operation in terms of the concrete data structures”

Direct Refinement: method to go directly from abstract specification to program in one step

From specification to design

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Data RefinementData Structures:

Two arrays : names [1…] of NAME

dates [1…] of DATES

names’ = names{i v} ; names[i] := vthe right side of this equation is a function which takes the same value as names everywhere except at the argument i, where it takes the value ‘v’.

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Example(Data and Direct Refinement)FindBirthday1

BirthdayBook1 name?:NAME date?:DATE

i : 1.. hwmname?=names(i) date! = dates(i)

Procedure FindBirthday(name: NAME; var date : DATE);var i: INTEGER;

begini:=1;while names[i] name do i := i+1;dates := dates[i]

end;

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Advantages The flexibility to model a specification

which can directly lead to the code. Easy to understand A large class of structural models can be

described in Z without higher – order features, and can thus be analyzed efficiently.

Independent Conditions can be added later

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Chemical Abstract Model

CHAM: for architectural description and analysis.

Software Systems chemicals (whose reactions are controlled by explicitly stated rules).

Where floating molecules can only interact according to a stated set of reaction rules.

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Features(CHAM)- Modular specification- Chemical reactions- Molecules (components)- Reactions (Connectors)- Solutions (States of CHAM)- This is used in areas where intended

architecture will tend to be large, complex, and assembled from existing components.

- Architectural elements: Processing elements, data elements, and connecting elements.

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Alloy: A Lightweight Object Modeling Notation

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Introduction

• Alloy– Is a modeling notation that describes structural

properties– Has a declaration syntax compatible with

graphical object models– Has a “set-based” formula syntax– Is based on “Z”

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Example

File System

DirEntry NameObject

contents

!

name!

Parent(~children)

entries!

DirFile

Root!

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Example (File System)model FileSystem {domain {Object, DirEntry, fixed Name}state {

partition File, Dir: static ObjectRoot: fixed Dir!entries: Dir! -> DirEntryname: DirEntry -> static Name!contents: DirEntry -> static Object!parent (~children) : Object -> Dir }

def parent {all o | o.parent = o.~contents.~entries}inv UniqueNames {all d | all e1, e2: d.entries | e1.name = e2.name -> e1 = e2}inv Parents {

no Root.parentall d: Dir – Root | one d.parent}

inv Acyclic {no d | d in d.+parent}inv Reachable {Object in Root.*children}cond TwoDeep {some Root.children.children}assert FileHasEntry {all o | sole o.parent}assert AtMostOneParent {all o | sole o.parent}op NewDirEntries (d: Dir, es: DirEntry’) {

no es & DirEntryd.entries’ = d.entries + esall x: Dir – d | x.entries’ = x.entries }

op Create (d: Dir!, o: Object’!, n: Name) {n! in d.entries.namesome e: DirEntry’ | NewDirEntries (d, e) && e.contents’ = o && e.name’ = n}

assert EntriesCreated {all d: Dir, e: DirEntry’ | NewDirEntries (d, e) -> DirEntry’ = DirEntry + e}assert CreateWorks {all d, o, n | Create (d, o, n) -> o n d.children’}}

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Example (File System)

• Structure of the model– Domain paragraph

– State paragraph

– Definition paragraph

– Invariants

– Condition

– Assertions

– Operations

– Assertions

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Analysis

• Alloy supports two kinds of analysis– Simulation: Consistency of an invariant or

operation is demonstrated by generating a state or transition.

– Checking: A consequence of a specification is tested by attempting to generate a counterexample.

• Together they enable an incremental process of specification.

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Based On Z

• Alloy is based on Z because:

– Simple and intuitive semantics (based on sets).– Well suited for object oriented modeling.– Data structures are built from concrete

mathematical structures.

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Features

• Automatic analysis– Theorem proving is deep & automatic.

• Easier to read and write. Plain ASCII notation.

• Relational operators are powerful.

• Incorporates mutability notions from informal notations.

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Design Faults

• Omission of the let construct & relational operators

• No integers

• No distinction between attributes and relations

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Formalizing Style to Understand Descriptions of Software

Architecture

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Introduction

• Software architecture describes a software system

• Architectural descriptions are informal & diagrammatic

• Represented by boxes & lines– For one system they may mean filters & pipes– For another system boxes abstract data types

or objects & lines procedure calls

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Introduction

• Different graphical conventions used to describe more than one kind of component or connection type in a single system

• Generalized meanings to architectural descriptions

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How is it done?

• Formalize abstract syntax for architectures

• For a given style:– Define the semantic model– Discuss concrete syntax for easing syntactic

descriptions in a given style– Define the mapping from abstract syntax into

semantic model– Make explicit the constraints on the syntax

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How is it done?

• Demonstrate analysis within & between formally defined architectural styles

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Abstract Syntax of Software Architectures

• Component:– Relationship between component & it’s

environment is defined as a collection of interaction points or ports:

• [PORT, COMPDESC]

Componentports : P PORT

description : COMPDESC

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Abstract Syntax of Software Architectures

• Connectors:– Connector has an interface that consists of a set

of roles:• [ROLE, CONNDESC]

Connectorroles : P ROLE

description : CONNDESC

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Abstract Syntax of Software Architectures

• Instances of components & connectors are identified by naming elements from the syntactic class

[COMPNAME, CONNNAME]

PortInst == COMPNAME x PORT

RoleInst == CONNNAME x ROLE

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Step 1 (Define Semantic Model)Filter

Alphabet : DATAPORT P DATAPORT

States : P STATE

Start : STATE

Transitions : (STATE x (DATAPORT seq DATA))

(STATE x (DATAPORT seq DATA))

Inputs n outputs = oDom alphabet = inputs u outputs

Start states

Inputs, outputs : P DATAPORT

s1, s2 : STATE ; ps1, ps2 : DATAPORT seq DATA• ((s1, ps1), (s2, ps2)) transitions

s1 states s2 states dom ps1 = inputs dom ps2 = outputs ( i : inputs • ran (ps1(i)) alphabet(i))( o : outputs • ran (ps2(o)) alphabet(o))

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Step 1 (Define Semantic Model)

Pipe

source, sink : DATAPORTalphabet : P DATA

source = sink

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Step 2

Define Concrete SyntaxFilterDescriptions : P COMPDESCPipeDescription : P CONNDESC

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Step 3

• Mapping from Abstract Syntax to Semantic Model

PFComp : Connector P Pipe

c : Connector ; p1, p2 : Pipe | p1 PFComp (c )

• p2 PFComp (c ) p1.alphabet = p2.alphabet

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Step 4

• Highlight the constraints in the syntax

LegalPFComponentComponent

Description FilterDescriptions

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Advantages

• Provides a templates for formalizing new architectural styles in a uniform way

• Provides uniform criteria for demonstrating that the notational constraints on a style are sufficient to provide meanings for all described systems

• Makes possible a unified semantic base through which different stylistic interpretations can be compared