Lecture 3 Abstraction by Specification CS 201 j

Lecture 3: Abstraction by Specification CS 201 j: Engineering Software? University of Virginia David Evans 4 September 2003 CS 201 J Fall 2003 Computer Science http: //www. cs. virginia. edu/evans

Menu • Validation • Abstraction by Specification 4 September 2003 CS 201 J Fall 2003 2

Testing Recap • Testing can find problems, but can’t prove your program works – Since exhaustive testing is impossible, select test cases with maximum probability of finding bugs – A successful test case is one that reveals a bug in your program! • If we can’t test all possible paths through a program, how can we increase our confidence that it works? 4 September 2003 CS 201 J Fall 2003 3

Analysis • Make claims about all possible paths by examining the program code directly, not executing it • Use formal semantics of programming language to know what things mean • Use formal specifications of procedures to know that they do 4 September 2003 CS 201 J Fall 2003 4

Hopelessness of Analysis • It is impossible to correctly determine if any interesting property is true for an arbitrary program! The Halting Problem: it is impossible to write a program that determines if an arbitrary program halts. 4 September 2003 CS 201 J Fall 2003 5

Compromises • Accept unsoundness and incompleteness • False positives: sometimes an analysis tool will report warnings for a program, when the program is actually okay (unsoundness) • False negatives: sometimes an analysis tool will report no warnings for a program, even when the program violates properties it checks (incompleteness) 4 September 2003 CS 201 J Fall 2003 6

Extended Static Checking (ESC/Java) • Analysis tool developed at DEC/Compaq/HP Research Lab • Is unsound and incomplete: – False negatives: Just because it finds no warnings, doesn’t mean your code is correct – False positives: Sometimes it will warn even when your code is correct • PS 2: use without adding annotations • Later: use annotations to document program assumptions 4 September 2003 CS 201 J Fall 2003 7

Abstraction by Specification 4 September 2003 CS 201 J Fall 2003 8

Managing Complexity • Divide problem into subproblems that – Can be solved independently – Can be combined to solve the original problem • How do we know they can be solved independently? • How do we know they can be combined to solved the original problem? 4 September 2003 CS 201 J Fall 2003 9

Abstraction A I 3 I 4 I 1 I 2 I 5 An abstraction is a many-to-one map. 4 September 2003 CS 201 J Fall 2003 10

Using Abstractions A I 3 Client I 4 I 1 I 2 I 5 When a client uses an abstraction, it should work as the client expects it to no matter with implementation is provided. How should client know what to expect? 4 September 2003 CS 201 J Fall 2003 11

Specification • Tells the client of an abstraction what she can expect it to do • Tells the implementer of an abstraction what the implementation must do to satisfy the client • Contract between client and implementer: – Client will only rely on behavior described by specification – Implementer will provide an implementation that satisfies the specification 4 September 2003 CS 201 J Fall 2003 12

Good Specifications • Clear, precise and unambiguous – Clients and implementers will agree on what they mean • Complete – Describe the behavior of the abstraction in all situations • Declarative – Describe what the abstraction should do, not how it should do it 4 September 2003 CS 201 J Fall 2003 13

Formality of Specifications • Informal: written in a natural language (e. g. , English) – People can disagree on what it means – Degrees of informality • Formal: written in a specification language – Meaning is defined by specification language (whose meaning is defined precisely, but eventually informally) – May be analyzed by machines 4 September 2003 CS 201 J Fall 2003 14

What do you call people who decide what informal specifications mean? 4 September 2003 CS 201 J Fall 2003 15

Example Informal Specification Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted. 8 th Amendment 4 September 2003 CS 201 J Fall 2003 16

Correct Implementation? public static boolean violates. Eigth. Amendment (Punishment p) { // EFFECTS: Returns true if p violates the 8 th // amendment: cruel and unusual // punishments. return (p. is. Cruel () && p. is. Unusual ()); } Or did they mean p. is. Cruel () || p. is. Unusual () ? 4 September 2003 CS 201 J Fall 2003 17

Example (Good? ) Informal Specification A player is in an offside position if: he is nearer to his opponents’ goal line than both the ball and the second last opponent A player is not in an offside position if: he is in his own half of the field of play or he is level with the second last opponent or he is level with the last two opponents Offence A player in an offside position is only penalised if, at the moment the ball touches or is played by one of his team, he is, in the opinion of the referee, involved in active play by: interfering with play or interfering with an opponent or gaining an advantage by being in that position No Offence There is no offside offence if a player receives the ball directly from: a goal kick or a throw-in or a corner kick. http: //www. fifa. com/fifa/handbook/laws/2002/LOTG 2002_E. pdf, Law 11 4 September 2003 CS 201 J Fall 2003 18

Procedural Specifications • Specification for a procedure describes: – What its inputs are – What the mapping between inputs and outputs are – What it can do the state of the world 4 September 2003 CS 201 J Fall 2003 19

Requires and Effects • Header: name of procedure, types of parameters and return value – Java declaration • Clauses (comments in Java) – REQUIRES - precondition the client must satisfy before calling – EFFECTS – postcondition the implementation satisfy at return 4 September 2003 CS 201 J Fall 2003 20

Contract • Client promises to satisfy the precondition in the requires clause • Implementer promises if client satisfies the precondition, the return value and state when the function returns will satisfy the postcondition. 4 September 2003 CS 201 J Fall 2003 21

Specification Contract f () REQUIRES: precondition EFFECTS: postcondition precondition { f (); } postcondition 4 September 2003 If the precondition is true, after we call f (), the postcondition is true. CS 201 J Fall 2003 22

Specification Example public String best. Stock () // REQUIRES: false // EFFECTS: Returns the name of the // best stock to buy on the NASDAQ // tomorrow. Can we implement a procedure that satisfies this specification? Yes, any implementation will satisfy this specification! If the precondition in the requires clause is not satisfied, the procedure can do anything and still satisfy its specification! 4 September 2003 CS 201 J Fall 2003 23

Specification Example public String best. Stock () // REQUIRES: true // EFFECTS: Returns the name of the // best stock to buy on the NASDAQ // tomorrow. Can we implement a procedure that satisfies this specification? 4 September 2003 CS 201 J Fall 2003 24

Requires Clauses • The weaker (more easy to make true) the requires clause: – The more useful a procedure is for clients – The more difficult it is to implement correctly – The more difficult it is to test • Avoid requires clauses unless there is a good reason to have one – Default requires clause is: REQUIRES true – Client doesn’t need to satisfy anything before calling 4 September 2003 CS 201 J Fall 2003 25

Specification Example public static int biggest (int [ ] a) // REQUIRES: true // EFFECTS: Returns the value of the // biggest element of a. Is this a reasonable specification? No, what should client expect to happen if a is empty. 4 September 2003 CS 201 J Fall 2003 26

Specification Example public static int biggest (int [ ] a) // REQUIRES: a has at least one element. // EFFECTS: Returns the value of the // biggest element of a. Is this a good specification? Maybe, depends on the client. Its risky… 4 September 2003 CS 201 J Fall 2003 27

Specification Example public static int biggest (int [ ] a) // REQUIRES: true // EFFECTS: If a has at least one // element, returns the value biggest // element of a. Otherwise, returns // Integer. MIN_VALUE (smallest int // value). Better, but client has to deal with special case now. Best would probably be to use an exception… 4 September 2003 CS 201 J Fall 2003 28

Bad Use of Requires Clause • Bug discovered in Microsoft Outlook that treats messages that start with “begin ” as empty attachments (can be exploited by viruses) To workaround this problem: • Do not start messages with the word "begin" followed by two spaces. • Use only one space between the word "begin" and the following data. • Capitalize the word "begin" so that it is reads "Begin. " • Use a different word such as "start" or "commence". from http: //support. microsoft. com/default. aspx? scid=KB; EN-US; Q 265230& 4 September 2003 CS 201 J Fall 2003 29

Modifies • How does a client know a is the same after biggest returns? public static int biggest (int [ ] a) // REQUIRES: true // EFFECTS: If a has at least one element, // returns the value biggest element of a. // Otherwise, returns Integer. MIN_VALUE // (smallest int value). Reading the effects clause is enough – if biggest modifies anything, it should describe it. But, that’s a lot of work. 4 September 2003 CS 201 J Fall 2003 30

Modifies • Modifies clause: any state not listed in the modifies clause may not be changed by the procedure. public static int biggest (int [ ] a) // REQUIRES: true // MODIFIES: nothing // EFFECTS: If a has at least one element, // returns the value biggest element of a. // Otherwise, returns Integer. MIN_VALUE // (smallest int value). 4 September 2003 CS 201 J Fall 2003 31

Modifies Example public static int replace. Biggest (int [ ] a, int [] b) // REQUIRES: a and b both have at least one // element // MODIFIES: a // EFFECTS: Replaces the value of the biggest // element in a with the value of the biggest // element in b. 4 September 2003 CS 201 J Fall 2003 32

Defaults • What should it mean when there is no requires clause? REQUIRES: true • What should it mean when there is no modifies clause? MODIFIES: nothing • What should it mean when there is no effects clause? Meaningless. (Lose points for not writing a specification) 4 September 2003 CS 201 J Fall 2003 33

Specifications in CS 201 J • PS 2 – Informal, but precise – Use Requires/Modifies/Effects clauses • Need a very good reason to have a precondition stronger than true (especially after we cover Exceptions). • PS 3 and later – Informal and some formal – Formal specifications as ESC/Java annotations • Don’t describe all behavior (so still need the informal specs) 4 September 2003 CS 201 J Fall 2003 34

PS 1 Informal Specification • If a cell is currently dead cell and has three live neighbors, then it becomes a live cell. • If a cell is currently alive and has two or three live cells it remains alive. • Otherwise, the cell dies. Any ambiguities in this? 4 September 2003 CS 201 J Fall 2003 35

PS 1 Comments • Java has real Boolean type is. Alive () means is. Alive () == true Note this is not true in C++! • Read the coding guidelines – Choose names wisely – Comment usefully, but not gratuitiously • Don’t put your SSN on assignments – You should keep it as secret as possible – University shouldn’t use it as an identifier • Ask for a student ID number that is not your SSN 4 September 2003 CS 201 J Fall 2003 36

Charge • CS 201 J Bug Bounty – If you find a bug in the code we provide, you get 10 bonus points. – If you find a bug in the Java compiler or API code, you get 50 bonus points. – If you find a bug in ESC/Java or the ESC/Java Specs, you get 5 bonus points. • PS 2 Due Tuesday – Much longer than PS 1 4 September 2003 CS 201 J Fall 2003 37