LAFF – On Programming for Correctness

Is my program correct? Will it give the right output for all possible permitted inputs? Computers are now essential in everyday life. Incorrect programs lead to frustration in the best case and disaster in the worst. Thus, knowing how to construct correct programs is a skill that all who program computers must strive to master. In this computer science course, we will present "goal oriented programming" the way Edsger Dijkstra, one of the most influential computer scientists, intended. You will learn how to derive programs hand-in-hand with their proofs of correctness. The course presents a methodology that illustrates goal-oriented programming, starting with the formalization of what is to be computed, and then growing the program hand-in-hand with its proof of correctness. The methodology demonstrates that, for a broad class of matrix operations, the development, implementation, and establishment of correctness of a program can be made systematic. Since this technique focuses on program specifications, it often leads to clearer, correct programs in less time. The approach rapidly yields a family of algorithms from which you can then pick the algorithm that has desirable properties, such as attaining better performance on a given architecture. The audience of this MOOC extends beyond students and scholars interested in the domains of linear algebra algorithms and scientific computing. This course shows how to make the formal derivation of algorithms practical and will leave you pondering how our results might extend to other domains. As a result of support from MathWorks, learners will be granted access to MATLAB for the duration of the course.

• Develop assertions describing states in a program.
• Prove programs correct using logic.
• Build algorithms using goal-oriented programming techniques.
• “Slice and dice” to discover families of loop-based algorithms for matrix computations.