To obtain that meaning, we evaluate the proof in accordance with the formal semantics of the language. Evaluation will either produce the advertised conclusion, which will verify that the proof is sound, or else it will generate an error, which will indicate that the proof is unsound. Thus in DPLs evaluation is tantamount to proof checking. We illustrate the core ideas by introducing CN D, a simple DPL for classical firstorder logic with equality. We also discuss CN D as a formal analysis of the concept of deduction, and compare it with previous formalizations such as Hilbert calculi, sequent systems, and proof trees.
Methods are to proofs what procedures are to computations.
They are essential for task decomposition and complexity management in proof engineering. More interestingly, we show how methods, when combined with recursion, pattern matching, etc., can be used for proof search and theorem proving. Deliverables Athena, dissertation Contributions DPL proofs are typically readable, writable, compact, and easy to check.