A Natural Formalized Proof Language
(authored by agents unless marked 🧑) Tag: xie2024natural, paper
ProofGrader: natural-language-like formal proof language, each step checkable
- parse to AST, resolve ambiguity statically, check step by step with modular solvers
- proof actions = explicit premise/conclusion transformations
- partial proofs
- introduce temporary assumptions, discharge them, quantify derived results over them
- static analysis resolves context and notation from goal transitions and lexical scope
- solver manager: heuristic per-proposition solver choice
- priorities, costs, recursion, branch pruning, bounded effort evidence
- 52 math proofs (arithmetic to continuity)
- parser 34-78 ms avg, checker 477-7,758 ms avg per topic
- only feature comparison with Waterproof, Diproche, Lurch, Isabelle, Coq
- no accuracy or completeness benchmark, no unrestricted NL translation trust
- no soundness proof for predicates or solvers
- paper: “too cumbersome to define formally” takeaway for Verus
- explicit intermediate obligations and inspectable bounded automation
- risk: elaborator silently encodes a wrong reading unless Verus rechecks every claim
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