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ECI 2007: Specification and Verification of Object-Oriented Programs

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### ECI 2007: Specification and Verification of Object-Oriented Programs

Lecture 0

Course information

- Instructor: Shaz Qadeer
- Office: Office 19 in this building
- Office hours: 5:30-6:30pm

What is this course about?

- Automated techniques for verification of partial specifications for software

This course is not about…

- Programming languages and type systems
- Software engineering methodology
- Dynamic analysis
- Software testing

Prerequisites

- Algorithms
- Formal language theory
- Elementary mathematical logic
- But, none of that matters if you really want to understand the material

Goals

- Learn about the fundamental ideas
- Understand the current research problems
- Enable novel research

The best advances come from a combination

of techniques from different research areas!

Why should we care?

- NIST (National Institute of Standards and Technology) report
- software bugs cost $60 billion annually
- High profile incidents of systems failure
- Therac-25 radiation overdoses, 1985-87
- Pentium FDIV bug, 1994
- Northeast blackout, 2003
- Air traffic control, LA airport, 2004

Intellectual challenge

- Civil engineering
- Bridges don’t fail

Intellectual challenge

- Civil engineering
- Bridges don’t fail
- Mechanical engineering
- Cars are reliable

Intellectual challenge

- Civil engineering
- Bridges don’t fail
- Mechanical engineering
- Cars are reliable
- Software engineering

Why is software hard?

- The human element
- Getting a consistent and complete set of requirements is difficult
- Requirements often change
- Human beings use software in ways never imagined by the designers

Why is software hard?

- The mathematical element
- Huge set of behaviors
- Nondeterminism
- External due to inputs
- Internal due to concurrency
- Even if the requirements are unchanging, complete and formally specified, it is infeasible to check all the behaviors

Bubble Sort

BubbleSort(int[] a, int n)

{

for (i=0; i<n-1; i++) {

for (j=0; j<n-1-i; j++) {

if (a[j+1] < a[j]) {

tmp = a[j];

a[j] = a[j+1];

a[j+1] = tmp;

}

}

}

}

- n #inputs
- 2^32
- 2^64
- ..
- ..

Even for a small program, enumeration of the set

of all possible behaviors is impossible!

Simple programming language

x Variable

P Program = assert x | x++ | x-- |

P1 ; P2 | if x then P1 else P2 | while x P

Assertion checking for this language is undecidable!

Holy grail of algorithmic verification

- Soundness
- If the algorithm reports no failure, then the program does not fail
- Completeness
- If the algorithm reports a failure, then the program does fail
- Termination
- The algorithm terminates

It is impossible to achieve the holy grail in general!

Axiomatic progam verification

- Program verification similar to validity checking in a mathematical logic
- Axioms
- Rules of inference
- Programmer attempts to find a proof using the axioms and the rules of inference
- Manual proof discovery
- Automated proof checking

Program Verification

- Mechanical verification of software would improve software productivity, reliability, efficiency

- Such systems are still in experimental stage
- After 40 years !
- Research has revealed formidable obstacles
- Many believed that program verification is dead

“Social processes and proofs of theorems and

programs”, Richard A. DeMillo, Richard J. Lipton,

and Alan J. Perlis, 1977

The research agenda for program

verification is destined to fail.

Criticisms

- Mathematicians do not use automated proof checkers; they use social processes to check proofs of theorems
- Program specifications are often as complicated as the programs themselves
- Many mathematical theories have exponential or super-exponential proofs; it is unreasonable to expect that such proofs can be discovered automatically

Program Verification: Attack and Defense

- Attack:
- Mathematicians do not use formal methods to develop proofs
- Why then should we try to verify programs formally?

- Defense:
- In programming, we often lack an effective formal framework for describing and checking results
- Consider the statements
- The area bounded by y=0, x=1 and y=x2 is 1/3
- By splicing two circular lists we obtain another circular list with the union of the elements

Program Verification: Attack and Defense

- Attack:
- Verification is done with respect to a specification
- Is the specification simpler than the program ?
- What if the specification is not right ?

- Defense:
- Developing specifications is hard
- Redundancy exposes many bugs as inconsistencies
- We are interested in partial specifications
- An index is within bounds, a lock is released

Program Verification: Attack and Defense

- Attack:
- Many logical theories are undecidable or decidable by super-exponential algorithms
- There are theorems with super-exponential proofs

- Defense:
- Such limits apply to human proof discovery as well
- If the smallest correctness argument of program P is huge then how did the programmer find it?
- Theorems arising in program verification are usually shallow but tedious

Program Verification:Attack and Defense

- Myth:
- Think of the peace of mind you will have when the verifier finally says “Verified”, and you can relax in the mathematical certainty that no more errors exist

- Reality:
- Use instead to find bugs (like more powerful type checkers)
- We should change “Verified” to “Sorry, I can’t find more bugs”

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