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Twelf is a programming language and system used to define, implement, and prove properties of formal systems. It's based on the LF logical framework and uses the dependently typed λ-tree syntax for representing logic. Twelf lets users describe object-level syntax, typing rules, and meta-theoretic properties in higher-order logic. By interfacing with automated theorem provers like Isabelle or Coq., Twelf helps achieve machine-checked correctness proofs of programming languages and software systems. The language is mainly used in academic research for verifying compiler correctness and creating certified software components where ensuring mathematical rigor can be more important than practical deployment considerations.

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