No abstract

No abstract

We present our experiences teaching two courses on formal methods and detail the contents of the courses and their positioning in the curriculum. The first course is a bachelor course on logical systems and logic programming, with a focus on classical first-order logic and automatic theorem proving. The second course is a master course on automated reasoning, with a focus on classical higher-order logic and interactive theorem proving. The proof assistant Isabelle is used in both courses, using Isabelle/Pure as well as Isabelle/HOL. We describe our online tools to be used with Isabelle/HOL, in particular the Sequent Calculus Verifier (SeCaV) and the Natural Deduction Assistant (NaDeA). We also describe our innovative Students' Proof Assistant which is formally verified in Isabelle/HOL and integrated in Isabelle/jEdit using Isabelle/ML.

We present a novel approach for teaching logic and the metatheory of logic to students who have some experience with functional programming. We define concepts in logic as a series of functional programs in the language of the proof assistant Isabelle/HOL. This allows us to make notions which are often unclear in textbooks precise, to experiment with definitions by executing them, and to prove metatheoretical theorems in full detail. We have surveyed student perceptions of our teaching approach to determine its usefulness and found that students felt that our formalizations helped them understand concepts in logic, and that they experimented with them as a learning tool. However, the approach was not enough to make students feel confident in their abilities to design and implement their own formal systems. Further studies are needed to confirm and generalize the results of our survey, but our initial results seem promising.

We present an approach for testing student learning outcomes in a course on automated reasoning using the Isabelle proof assistant. The approach allows us to test both general understanding of formal proofs in various logical proof systems and understanding of proofs in the higher-order logic of Isabelle/HOL in particular. The use of Isabelle enables almost automatic grading of large parts of the exam. We explain our approach through a number of example problems, and explain why we believe that each of the kinds of problems we have selected are adequate measures of our intended learning outcomes. Finally, we discuss our experiences using the approach for the exam of a course on automated reasoning and suggest potential future work.