Students' Proof Assistant (SPA)

Abstract

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.