Natural Deduction and the Isabelle Proof Assistant

Schlichtkrull

2019

Self Cite

We present the Natural Deduction Assistant (NaDeA) and discuss its advantages and disadvantages as a tool for teaching logic. NaDeA is available online and is based on a formalization of natural deduction in the Isabelle proof assistant. We first provide concise formulations of the main formalization results. We then elaborate on the prerequisites for NaDeA, in particular we describe a formalization in Isabelle of "Hilbert's Axioms" that we use as a starting point in our bachelor course on mathematical logic. We discuss a recent evaluation of NaDeA and also give an overview of the exercises in NaDeA.

Section: Main Formalization Resultssupporting

confidence: 59%

Section: Introductionmentioning

confidence: 75%

See 1 more Smart Citation

Natural Deduction Assistant (NaDeA)

Villadsen

Schlichtkrull

2019

Self Cite

“…SPA is an advanced e-learning tool for teaching proof assistants for students in computer science as well as in mathematics and complements our other e-learning tool, NaDeA (A Natural Deduction Assistant with a Formalization in Isabelle), which is available online and has been used by computer science bachelor students in regular courses at DTU [8].…”

Section: Resultsmentioning

confidence: 99%

Students' Proof Assistant (SPA)

Schlichtkrull¹,

Villadsen²,

2019

Self Cite

The Students' Proof Assistant (SPA) aims to both teach how to use a proof assistant like Isabelle and also to teach how reliable proof assistants are built. Technically it is a miniature proof assistant inside the Isabelle proof assistant. In addition we conjecture that a good way to teach structured proving is with a concrete prover where the connection between semantics, proof system, and prover is clear. The proofs in Lamport's TLAPS proof assistant have a very similar structure to those in the declarative prover SPA. To illustrate this we compare a proof of Pelletier's problem 43 in TLAPS, Isabelle/Isar and SPA. We also consider Pelletier's problem 34, also known as Andrews's Challenge, where students are encouraged to develop their own justification function and thus obtain a lot of insight into the proof assistant. Although SPA is fully functional we have so far only used it in a few educational scenarios.

“…While ProofJudge is designed to facilitate the human grading of submissions, we also run an automatic tableau prover in the background as the user works on their proof. This prover checks every current subgoal and if it seems likely that the subgoal is unprovable, it unobtrusively gives a warning by making the corresponding line number orange [22]. We have verified the soundness of the prover's kernel in Isabelle [11,12] and used the code export facilities to generate SML code for the full prover.…”

Section: The Natural Deduction Assistant (Nadea)mentioning

confidence: 99%

Isabelle/HOL as a Meta-Language for Teaching Logic

Villadsen

Blackburn

2020

Self Cite

Proof assistants are important tools for teaching logic. We support this claim by discussing three formalizations in Isabelle/HOL used in a recent course on automated reasoning. The first is a formalization of System W (a system of classical propositional logic with only two primitive symbols), the second is the Natural Deduction Assistant (NaDeA), and the third is a one-sided sequent calculus that uses our Sequent Calculus Verifier (SeCaV). We describe each formalization in turn, concentrating on how we used them in our teaching, and commenting on features that are interesting or useful from a logic education perspective. In the conclusion, we reflect on the lessons learned and where they might lead us next.