proofar

Proofar is a term used in theoretical discussions to denote a compact, machine-checkable representation of mathematical proofs intended to facilitate verification and understanding. It is not a widely adopted standard and has no formal governance. In this usage, proofar describes a formal structure that encodes a proof as a directed acyclic graph, with nodes representing inference steps, lemmas, or assertions and edges indicating dependence. Each node carries metadata such as the inference rule applied, premises, conclusions, and optional annotations.

Encoding and syntax: Proponents envision a lightweight, rule-based language for constructing proofars. Common ideas include a small set of primitive rules, explicit scoping, and the ability to annotate assumptions and discharged conditions. Proofars can be serialized in human-readable formats like JSON or in compact binary forms, enabling storage, transmission, and integration with proof assistants and automated verifiers.

Applications: In education, proofars can visualize the flow of a proof and highlight dependencies. In research and verification, they can serve as certificates that a machine-checked proof exists for a given theorem, and as an intermediate representation within automated theorem provers.

Advantages and criticisms: Benefits include modular proof reuse, transparent dependencies, and compatibility with automated checking. Critics note that standardizing syntax is difficult, proofs can become verbose, and the added layer may obscure intuitive understanding for beginners.

Relation to existing concepts: Proofars share concepts with proof trees, sequent calculus, and proof certificates used in proof assistants, but they are not a widely adopted alternative to established systems.

Status and outlook: As of now, proofar remains informal and exploratory, discussed in academic and educational contexts. Its trajectory depends on community consensus, tool support, and demonstrations of practical value.