Twelf

Twelf is a software tool for specifying, implementing, and proving properties of deductive systems within the Edinburgh LF logical framework. It is used primarily in programming language theory to formalize languages, type systems, and operational semantics. Twelf supports higher-order abstract syntax and employs a totality checker to verify that certain relations and judgments are complete with respect to their definitions.

In Twelf, users encode the syntax of the object language and its judgments as LF types and terms, then express inference rules as constants and relations in the Twelf language. Theorems about these systems, such as type safety or progress, are encoded as totality statements. Twelf checks these statements by examining all cases and ensuring that every derivation is accounted for. Proofs are represented as constructive witnesses or as total proofs produced by the checker, rather than as interactive, human-guided proofs.

Twelf emphasizes meta-theoretic reasoning and binding representations via higher-order abstract syntax. It is not a general-purpose interactive proof assistant; instead, it provides a structured framework for encoding and mechanically verifying meta-theoretic proofs. The tool is commonly used in academic research and teaching to model language specifications and to illustrate proofs of properties like type preservation and normalization. Twelf source files are written in its dedicated language, closely tied to the LF framework, and are typically processed on Unix-like platforms.