Theorem and Algorithm Checking for Courses on Logic and Formal Methods

Abstract

The RISC Algorithm Language (RISCAL) is a language for the formal modeling of theories and algorithms. A RISCAL specification describes an infinite class of models each of which has finite size; this allows to fully automatically check in such a model the validity of all theorems and the correctness of all algorithms. RISCAL thus enables us to quickly verify/falsify the specific truth of propositions in sample instances of a model class before attempting to prove their general truth in the whole class: the first can be achieved in a fully automatic way while the second typically requires our assistance. RISCAL has been mainly developed for educational purposes. To this end this paper reports on some new enhancements of the tool: the automatic generation of checkable verification conditions from algorithms, the visualization of the execution of procedures and the evaluation of formulas illustrating the computation of their results, and the generation of Web-based student exercises and assignments from RISCAL specifications. Furthermore, we report on our first experience with RISCAL in the teaching of courses on logic and formal methods and on further plans to use this tool to enhance formal education.

Is Deductive Program Verification Mature Enough to be Taught to Software Engineers?

“…The PEST framework [7] is similar to RISCAL in the sense that is provides both a specification language and a tool (available as a plug-in for Eclipse) that facilitates automated reasoning. Classroom experiences (the framework was used in two undergraduate courses taught at the computer science department of the University of Buenos Aires) confirm the preliminary results of [26].…”

“…The main advantage of using a proof assistant in the teaching is that it allows students to experiment with their specifications, and to make proofs that are guided by the proof assistant which gives them immediate feedback. RISCAL [26] is a language for modelling algorithms and their properties. This language comes with a tool supporting model development and automatic verification.…”

A Mobile Application for Self-Guided Study of Formal Reasoning

“…While this is understandably a good approach within a traditional course setting, the variety of applications of logic seen today require a more flexible system, which gives the instructor the ability to freely expand and contract the formal language to a particular problem. A few existing systems taking a step in this direction are the risc program navigator [33], RISCAL [34], and Theorema [7]. The first two systems consider first-order logic (FOL) over finite models, while Theorema, defined in Mathematica, considers FOL over arbitrary models and using Mathematica's interface restricts the student's view of the current state of the software.…”