Bevisformer

Bevisformer is a term used in formal logic and proof engineering to denote a structured representation of a proof that emphasizes the form of inference steps. It encodes the logical derivation as a data object that captures not only the final result but the sequence and justification of each inference.

Formal representation: A bevisformer can be modeled as a labeled directed acyclic graph where nodes correspond to propositions or lemmas and edges correspond to applied inference rules. Each node carries metadata such as the rule used, dependencies, provenance, and an indication of whether the proposition is an axiom, assumption, or derived statement. This representation supports modular proof composition and reuse of subproofs.

Construction: Starting from a set of axioms, shorter bevisformer steps are added by applying inference rules, reusing existing subproofs where possible. The structure allows checking of correctness by traversing the graph and verifying rule applications against the premises of each edge.

Relation to other concepts: Bevisformers are related to proof trees, proof nets, and sequent calculus, but they emphasize form and reusability of subproofs, rather than linear scripting. They can be used to generate human-readable explanations and machine-checked certificates of correctness.

Applications and challenges: In formal verification, theorem proving, and education, bevisformers facilitate verification and auditing of proofs. Large proofs can become complex, requiring strategies for abstraction, compression, and visualization to maintain comprehensibility.

See also: formal proof, proof tree, proof net, theorem prover, proof assistant.