Formal Specification

Formal specification is the precise statement of what a program, theorem, chip, or system is supposed to satisfy. In 137. 对洪乐潼的4小时访谈：AI for Math、把数学变成Lean、数学天书中的证明、直觉、被创造与被发现的, Hong Letong / 洪乐潼 treats specification as one of the hardest parts of applying Formal Verification beyond mathematics.

Key Claims

• A proof can only prove the property it is given; a wrong, incomplete, or vague specification can still produce a formally correct but practically useless result.
• In software verification, the program, specification, verification condition, and proof are separate objects with different failure modes.
• Auto-Formalization is a mathematical version of the specification problem because informal papers must be translated into exact formal statements before proof can proceed.
• AI can help write specifications, but the human or organization still owns the question of what should count as correct.

Connections

• Formal Verification, AI Coding Verification, and AI Verification — verification layers that depend on clear specifications.
• Lean Theorem Prover, Interactive Theorem Proving, and Auto-Formalization — formal systems where specifications become machine-checkable.
• Human Judgment Under AI and Problem Definition In Research — adjacent human judgment concepts.