Formal Specification - Techniques for the unambiguous specification of software Objectives: To explain why formal specification techniques help discover problems in system requirements To describe the use of algebraic techniques (for interface specification) and model-based techniques(for behavioural specification) To introduce Abstract State Machine Model

Formal methods Formal specification is part of a more general collection of techniques that are known as ‘formal methods’ These are all based on mathematical representation and analysis of software Formal methods include Formal specification Specification analysis and proof Transformational development Program verification

Notations For Formal Specification Any notation with precise semantics can be used Formalism typically applied to just part of a specification Notations use discrete mathematics, some with graphics Several notations are sometimes used in the same specification: Z or VDM for data manipulation Statecharts for system states and transitions Natural language for non-functional specifications

Formal Specification Goals of formal specification: Complete Consistent Concise Unambiguous Valid—state exactly what the user wants Specifications based on formal semantic model What is/are semantics? What is a formal semantic model?

Formal Semantics Semantics means “meaning” Formal semantics: Meaning expressed in mathematics Formal semantic model: Complete semantic definition of a language in mathematics What mathematics? Discrete mathematics! Formal semantics permit dependable communication between all parties

Types Of Languages Procedural: Declarative: Functional: Computation defined by desired sequence of actions computer is to perform Most high-level languages are procedural Declarative: Computation defined by desired state that computer should be in Many specification languages are declarative Functional: Computation defined as desired function computer is to evaluate Most functional languages derive from LISP

Types Of Languages High-level language programs are actually specifications! Compilers write the program for you So you have been specifying programs, not writing them The big difference in languages is: Declarative: Says nothing about HOW, just WHAT Procedural: Says nothing about WHAT, just HOW

Types Of Languages—Examples Procedural: read (x); y := x; while y**2 > x loop y := y – 1; end loop; print (y); Declarative: y**2 <= x AND (y+1)**2 > x

Formal Methods Activities Write a specification using a formal notation Validate the specification Inspect it with domain experts Perform automated analysis to prove theorems Refine the specification to an implementation Semantics-preserving transformations to code Verify that the implementation matches the spec Mathematical argument

Library Example: Informal Statement A book can either be in the stacks, on reserve, or loaned out If a book is in the stacks or on reserve, then it can be requested We want to formalize the concepts and the statements prove some theorems to gain confidence that the spec is correct

Library Example: Formalization (1/2) First let’s formalize some concepts S: the book is in the stacks R: the book is on reserve L: the book is on loan Q: the book is requested

Library Example: Formalization (2/2) If a book is requested, then it is on the shelf or on reserve

Library Example: Proof of a Theorem

Library Example: Proof By Contradiction

Use of formal methods Their principal benefits are in reducing the number of errors in systems so their main area of applicability is critical systems: Air traffic control information systems, Railway signalling systems Spacecraft systems Medical control systems In this area, the use of formal methods is most likely to be cost-effective Formal methods have limited practical applicability

Use of formal specification Formal specification involves investing more effort in the early phases of software development This reduces requirements errors as it forces a detailed analysis of the requirements Incompleteness and inconsistencies can be discovered and resolved !!! Hence, savings as made as the amount of rework due to requirements problems is reduced

Acceptance of formal methods Formal methods have not become mainstream software development techniques as was once predicted Other software engineering techniques have been successful at increasing system quality. Hence the need for formal methods has been reduced Market changes have made time-to-market rather than software with a low error count as the key factor. Formal methods do not reduce time to market The scope of formal methods is limited. They are not well-suited to specifying and analysing user interfaces and user interaction Formal methods are hard to scale up to large systems

Two specification techniques Algebraic approach The system is specified in terms of its operations and their relationships Model-based approach The system is specified in terms of a state model that is constructed using mathematical constructs such as sets and sequences. Operations are defined by modifications to the system’s state

Interface specification Large systems are decomposed into subsystems with well-defined interfaces between these subsystems Specification of subsystem interfaces allows independent development of the different subsystems Interfaces may be defined as abstract data types or object classes The algebraic approach to formal specification is particularly well-suited to interface specification

Sub-system interfaces

The structure of an algebraic specification TION NAME > (Gener ic P ar ameter) sort < name > imports < LIST OF SPECIFICA TION NAMES > Inf or mal descr iption of the sor t and its oper ations Oper ation signatures setting out the names and the types of the parameters to the operations defined over the sort Axioms defining the operations over the sort. Axioms relate the operations used to construct entities with operations used to inspect their values.

Specification components Introduction Defines the sort (the type name) and declares other specifications that are used Description Informally describes the operations on the type Signature Defines the syntax of the operations in the interface and their parameters Axioms Defines the operation semantics by defining axioms which characterise behaviour

Specification operations Constructor operations. Operations which create entities of the type being specified Inspection operations. Operations which evaluate entities of the type being specified To specify behaviour, define the inspector operations for each constructor operation

Interface specification in critical systems Consider an air traffic control system where aircraft fly through managed sectors of airspace Each sector may include a number of aircraft but, for safety reasons, these must be separated In this example, a simple vertical separation of 300m is proposed The system should warn the controller if aircraft are instructed to move so that the separation rule is breached

A sector object Critical operations on an object representing a controlled sector are Enter. Add an aircraft to the controlled airspace Leave. Remove an aircraft from the controlled airspace Move. Move an aircraft from one height to another Lookup. Given an aircraft identifier, return its current height

Primitive operations It is sometimes necessary to introduce additional operations to simplify the specification The other operations can then be defined using these more primitive operations Primitive operations Create. Bring an instance of a sector into existence Put. Add an aircraft without safety checks In-space. Determine if a given aircraft is in the sector Occupied. Given a height, determine if there is an aircraft within 300m of that height

Behavioural specification Algebraic specification can be cumbersome when the object operations are not independent of the object state Model-based specification exposes the system state and defines the operations in terms of changes to that state

Abstract State Machine Language (AsmL) AsmL is an executable specification language for modelling the structure and behaviour of digital systems AsmL can be used to faithfully capture the abstract structure and step-wise behaviour of any discrete systems, including very complex ones such as: Integrated circuits, software components, and devices that combine both hardware and software

Abstract State An AsmL model is said to be abstract because it encodes only those aspects of the system’s structure that affect the behaviour being modelled The goal is to use the minimum amount of detail that accurately reproduces (or predicts) the behaviour of the system Abstraction helps us reduce complex problems into manageable units and prevents us from getting lost in a sea of details AsmL provides a variety of features that allow you to describe the relevant state of a system in a very economical, high-level way

Abstract State Machine and Turing Machine An abstract state machine is a particular kind of mathematical machine, like the Turing machine (TM) But unlike a TM, ASMs may be defined a very high level of abstraction An easy way to understand ASMs is to see them as defining a succession of states that may follow an initial state

State transitions The behaviour of a machine (its run) can always be depicted as a sequence of states linked by state transitions paint in green paint in red A B Moving from state A to state B is a state transition

Configurations Each state is a particular “configuration” of the machine The state may be simple or it may be very large, with complex structure But no matter how complex the state might be, each step of the machine’s operation can be seen as a well-defined transition from one particular state to another

Evolution of state variables We can view any machine’s state as a dictionary of (Name, Value) pairs, called state variables paint in green paint in red A B (Colour, Red) is a variable, where “Colour” is the name of variable, “Red” is the value

Evolution of state variables Names are given by the machine’s symbolic vocabulary Values are fixed elements, like numbers and strings of characters The run of a machine is a series of states and state transitions that results form applying operations to each state in succession

Each transition operation: Example Diagram shows the run of a machine that models how orders might be processed S1 Mode = “Initial” Orders = 0 Balance = £0 Initialise Process All Orders S3 Mode = “Final” Balance = £500 S2 Mode = “Active” Orders = 2 Balance = £200 Each transition operation: can be seen as the result of invoking the machine’s control logic on the current state calculates the subsequence state as output

Control Logic Typical form of the operational text is: The machine’s control logic behaves like a fix set of transition rules that say how state may evolve Typical form of the operational text is: “ if condition then update ” We can think of the control logic as a text that precisely specifies, for any given state, what the values of the machine’s variables will be in the following step

Control Logic as a Black Box The machine control logic is a black box that takes as input a state dictionary S1 and gives as output a new dictionary S2 input mode “Initial” orders balance £0 The Machine’s Control Logic … if mode = “Initial” then mode := “Active” output Mode “Active” orders 2 balance £200 The two dictionaries S1 and S2 have the same set of keys, but the values associated with each variable name may differ between S1 and S2

Run of the Machine The run of the machine can be seen as what happens when the control logic is applied to each state in turn The run starts form initial state S1  S2  S3  … S1 is given to the black box yielding S2, processing S2 results in S3, and so on … When no more changes to state are possible, the run is complete

For example: mode:=“Active” Update operations We use the symbol “: =” (reads as “gets”) to indicate the value that a name will have in the resulting state For example: mode:=“Active” Update can be seen only during the following step (this is in contrast to Java, C, Pascal, …) All changes happen simultaneously, when you moving from one step to another. Then, all updates happen at once.(atomic transaction)

Programs Example 1. Hello, world Main() step WriteLine(“hello, world!”) ASML uses indentations to denote block structure, and blocks can be places inside other blocks Statement block affect the scope of variables Whitespace includes blanks and new-line character, ASML does not recognize tab character for indentation !!!!!!! Main() is like main() in Java and C

Example 2. Reading a file var F as File? = undef var Fcontents as String = “” var Mode as String = “Initial” Main() step until fixpoint if Mode = “Initial” then F :=open(“mfile.txt”) Mode :=“Reading” if Mode = “Reading” and length(FContents) =0 then FContents :=fread (F,1) if Mode = “Reading” and length(FContents) =1 then FContents := FContents + fread (F,1) if Mode = “Reading” and length(FContents) >1 then WriteLine (FContents) Mode :=“Finished”

Example 2. Graph representation Step 1 Step 2 S1 F= undef Fcontents =“” Mode = Initial S2 F= <open file 1> Fcontents =“” Mode = Reading S3 F= <open file 1> Fcontents =“a” Mode = Reading Step 3 S4 F= <open file 1> Fcontents =“ab” Mode = Reading S5 F= <open file 1> Fcontents =“ab” Mode = Finished Step5 Step 4

Key points Formal system specification complements informal specification techniques Formal specifications are precise and unambiguous. They remove areas of doubt in a specification Formal specification forces an analysis of the system requirements at an early stage. Correcting errors at this stage is cheaper than modifying a delivered system

Key points Formal specification techniques are most applicable in the development of critical systems and standards. Algebraic techniques are suited to interface specification where the interface is defined as a set of object classes Model-based techniques model the system using sets and functions. This simplifies some types of behavioural specification