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 Lamports TLAPS proof assistant have a very similar structure to those in the declarative prover SPA. To illustrate this we compare a proof of Pelletiers problem 43 in TLAPS, Isabelle/Isar and SPA. We also consider Pelletiers problem 34, also known as Andrewss 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.
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