Programming Theory. Mohamed Faouzi Atig. Uppsala University. M. F. Atig (Uppsala University) Programming Theory September 03, / 25

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1 Programming Theory Mohamed Faouzi Atig Uppsala University M. F. Atig (Uppsala University) Programming Theory September 03, / 25

2 People to help you! Lecturer: Mohamed Faouzi Atig, office 1452, mohamed Teacher Assistants: Othmane Rezine, office 1456, Aleksandar Zeljic, Webpage: (including related topics, schedule, old exams, etc.) M. F. Atig (Uppsala University) Programming Theory September 03, / 25

3 Prerequisites Background in Programming and Programming Languages. Basic understanding in Mathematical Logic. Course in Program Semantics is useful. M. F. Atig (Uppsala University) Programming Theory September 03, / 25

4 Registration The admitted students, including those who are admitted with a condition, must web-register themselves for the course in the Student Portal. Students who are unable to web-register, should contact IT-kansliet/the Student Office. Web-(un)registration is possible until September 17 M. F. Atig (Uppsala University) Programming Theory September 03, / 25

5 Admission/ Registration Non-admitted students wanting to be registered. Please apply for the course at via Late application ( Sen anmälan ). Master students should contact their programme coordinator/programme counsellor. Exchange students should contact Ulrika Jaresund, who is the exchange student coordinator at the IT Dept. Students with an older registration, who want to re-register, should contact IT-kansliet. Students who are reserves on the reserve list, will be contacted by IT-kansliet/the Student Office if they are admitted. M. F. Atig (Uppsala University) Programming Theory September 03, / 25

6 The course in a nutshell Course form: Lectures, tutorials, and labs. Mandatory Assignment: There are lab assignments that all participants have to complete before hard deadlines. Oral exam. Optional Assignment: There are three (optional) assignments. Each can earn you up to 4 points (out of 100) in the final exam. Quizzes: You can earn up to 4 points in the final exam by answering correctly to the quizzes at the beginning of lectures. Examination: Final written exam. No books are allowed only a sheet that will be distributed at the exam. Grade: To get the 10 credits of this course you must: Pass the mandatory assignment, and Get 50 out from 100 in the final exam: 50 3, 70 4, and M. F. Atig (Uppsala University) Programming Theory September 03, / 25

7 Literature Online materials in the course webpage. D. Gries, The Science of Programming. Springer Verlag. Parosh A. A., Logic in Programming, compendium. (can be purchased in the student shop at UTHgård (building 73).) M. F. Atig (Uppsala University) Programming Theory September 03, / 25

8 Introduction M. F. Atig (Uppsala University) Programming Theory September 03, / 25

9 Programs Solving a problem using computers 1 Design an algorithm. 2 Implement the algorithm as a program. Examples Order a list of integers. Find the shortest path between two nodes in a graph. Compute the first 100 prime numbers. M. F. Atig (Uppsala University) Programming Theory September 03, / 25

10 Properties of Programs Properties of programs Efficiency Reliability (Correctness ) This course: Software Reliability As society becomes dependent on software, the consequence of software failures are non-trivial: Money lost. Lives lost. Clients lost. Jobs lost. M. F. Atig (Uppsala University) Programming Theory September 03, / 25

11 Software Bug: Space Disaster Ariane 5 Space mission $ 7, 000, 000, Years in the making 40 seconds after take off the rocket exploded M. F. Atig (Uppsala University) Programming Theory September 03, / 25

12 Software Bug: Space Disaster Attempt to cram a 64-floating point number to a 16-bit integer failed M. F. Atig (Uppsala University) Programming Theory September 03, / 25

13 Software Bugs: Cause of Deaths Several deaths of cancer patients were due to overdoses of radiation resulting from a race condition between concurrent tasks in the Therac-25 software M. F. Atig (Uppsala University) Programming Theory September 03, / 25

14 Cost of Failure Software failures were estimated to cost the US economy about $60 billion annually [NIST 2002] Improvements in software verification infrastructure may save one-third of this cost Testing accounts for an estimated 50%-80% of the cost of software development [Beizer 1990] M. F. Atig (Uppsala University) Programming Theory September 03, / 25

15 What is a Bug? Specification An abstract description of the behavior of the programs (e.g., the computations performed by the program). Sorting Input: list x = (x 1,x 2,...,x n ) of natural numbers. Output: list y = (y 1,y 2,...,y n ) such that: y is a permutation of x. y1 y 2 y n. M. F. Atig (Uppsala University) Programming Theory September 03, / 25

16 Correctness (Reliability) Correctness (Reliability) Is the implementation correct with respect to the specification? Does the implementation satisfy the specification? Examples Does the program that accepts an array of integers produce a sorted array? Does the program never access unallocated memory? M. F. Atig (Uppsala University) Programming Theory September 03, / 25

17 Checking Correctness Testing Simulate the program for some input data. Check whether the output data is consistent with the specification. Disadvantages Exhaustive testing infeasible in practice. Testing can detect errors, but not prove their absence. M. F. Atig (Uppsala University) Programming Theory September 03, / 25

18 Verification Implementation Verification Yes / No Specification Verification Given an implementation and a specification, the verification system answers yes/no: Yes: the program satisfies the specification No: the program is faulty M. F. Atig (Uppsala University) Programming Theory September 03, / 25

19 Synthesis Specification Synthesis Implementation Synthesis Given a specification, derive a correct implementation. M. F. Atig (Uppsala University) Programming Theory September 03, / 25

20 Describing specifications and implementations Formal Methods Based on rigorous mathematical principles Concepts from discrete mathematics and mathematical logic Utility Eliminate inconsistencies and ambiguities Perform systematic analysis M. F. Atig (Uppsala University) Programming Theory September 03, / 25

21 Examples of formal methods (1/2) Hardware circuits Specification: Hardware description language (VHDL) Implementation: Hardware circuit Logical Programming Specification: First-order Predicate Logic Implementation: PROLOG M. F. Atig (Uppsala University) Programming Theory September 03, / 25

22 Examples of formal methods (2/2) Imperative programs Specification: First-order Predicate Logic Implementation: C Distributed systems Specification: Temporal logic Implementation: Transition systems M. F. Atig (Uppsala University) Programming Theory September 03, / 25

23 Goal of this course In this course we study how to: Write rigorous descriptions of implementations and specifications of programs. Verify programs, i.e., prove that the implementation of a program meets its specification using formal methods. Write a correct program from a given specification. M. F. Atig (Uppsala University) Programming Theory September 03, / 25

24 Relevance Connection between Mathematical Logic and Programming. Interesting research area. Industrial relevance: Volvo, Ericsson, Bell Labs, Prover Technology, NASA, Microsoft, Airbus,... M. F. Atig (Uppsala University) Programming Theory September 03, / 25

25 Schedule in a nutshell (lectures) Propositional Logic Predicate Logic Weakest Preconditions Operational Semantics Invariants Partial Correctness and Termination Synthesis M. F. Atig (Uppsala University) Programming Theory September 03, / 25