Automated Theorem Prover Assisted Program Calculations

Abstract

Abstract. Calculational Style of Programming, while very appealing, has several practical difficulties when done manually. Due to the large number of proofs involved, the derivations can be cumbersome and errorprone. To address these issues, we have developed automated theorem provers assisted program and formula transformation rules, which when coupled with the ability to extract context of a subformula, help in shortening and simplifying the derivations. We have implemented this approach in a Calculational Assistant for Programming from Specifications (CAPS). With the help of simple examples, we show how the calculational assistant helps in taking the drudgery out of the derivation process while ensuring correctness.

Introducing Formal Methods via Program Derivation

“…Application of the tactic brings the context of the subcomponent under consideration in focus and hides the rest of the program. (The details of the context extraction process are described in [4].) After transforming the subcomponent to a desired form, users can apply the StepOut tactic to bring the focus back to the whole program.…”

“…But the students need not concern themselves at all with how the theorem prover works. The implementation details of the tool have been published in [4] and here we concern ourselves only with the use of the tool in classroom teaching. …”

“…To address these difficulties, we have developed a tool called CAPS [4], for deriving sequential programs from their formal specifications. To the best of our knowledge, no comparable tool exists.…”

Building an IDE for the Calculational Derivation of Imperative Programs

“…Consider the following programming task (adapted from exercise 4.3.4 in [19]. The informal derivation of this problem also appears in [11]).…”

“…Towards this goal, in our earlier work, we described the use of theorem prover assisted tactics [11] to automate the mundane tasks during the derivations. In this paper, we discuss the overall architecture of CAPS, the main features of the IDE, the GUI design, and the design trade-offs involved.…”