Introducing Formal Methods via Program Derivation

Abstract

Existing attempts towards including formal methods in introductory programming courses focus on introducing program verification tools. When using the verification tools, there is no structured help available to the students in the actual task of implementing the program, except for the hints provided by the failed proof obligations. In contrast, in the correct-by-construction programming methodology, programs are incrementally derived from their specifications.By restricting our attention to program derivation, we have identifed a small core of the formal method concepts that can easily be taught in the first two years of a computing curricula. Based on our learning from multiple years of paper and pencil based teaching, we have developed a programming assistant tool that addresses several of the issues faced by the students in the manual program derivation. The tool ensures that the most common students' error of performing incorrect proofs does not happen.

Program Construction Method for Sequential Statistics Class Algorithm Based on Bidirectional Scanning Induction

“…Chaudhari et al [11] focused on the typical steps in the program derivation process, starting from the program specifications. Ref.…”

“…Ref. [11] divided the post-assertion into multiple specifications based on the weakest predicate method and then formed a loop invariant for derivation [12] . Refs.…”

“…Refs. [11,12] are based on the decomposition of post-assertions. However, in the face of more complex program specifications, finding sub-specifications becomes difficult, and the derivation process becomes more complex as the number of sub-specifications increases.…”

Verifying Time Complexity of Binary Search using Dafny

“…This lemma adds the missing requirements for enabling the use of the log function: the precondition requires the sequence is non empty, and the lo index to be strictly smaller than the hi index. The ensures expression is the proof obligation as in expression (6). This lemma calls itself recursively.…”

“…The use of formal methods in software development education is described, e.g., in [6] and [20]. Both approaches are dedicated to verifying functional correctness while we can illustrate the time complexity of algorithms to developers.…”