Teaching Functional Programmers Logic and Metatheory

Abstract

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.

ProofBuddy: A Proof Assistant for Learning and Monitoring

“…The second and fifth author have previously conducted a study of student experiences using Isabelle, but our methods suffered from a lack of data on actual student behavior and interactions when using the proof assistant [18]. Knobelsdorf et al limited themselves to manually observing student behavior and categorizing the types of questions asked by students [21].…”

“…• Proof assistants are useful for teaching mathematics [2,4,10,11,17] • Proof assistants are useful for teaching functional programming [4,5,17,18,21,26] • Proof assistants are useful for teaching logic [2,4,5,8,15,17,18,21,26,34,36,41] • Proof assistants are useful for teaching abstract thinking [4,11,34,36] • Proof assistants make the rules of formal reasoning clear [2,4,11] • Proof assistants help students learn how to structure proofs [4,5,8,10,11,17,19,21,31] • Students are helped by instant feedback on their proofs [2, 4, 8, 10-12, 15, 21, 26] • Proof competence gained using a proof assistant transfers to pen-and-paper [2,12,26,34] • Proof assistants help students fix their proof errors as early as possible [4,11] • Proof assistants make it easier for stude...…”

“…• No suitable quantitative measures of proof competence exist [2] • It is difficult to collect evidence about how students interact with proof assistants [5,18] • It is unclear how to compare the efficacy of approaches based on proof assistants with approaches based on pen-and-paper approaches in a fair way [18,26]…”