15-399 Constructive Logic
Lecture 4: Linear and Normal Deductions

The two-dimensional display for inference rules and proofs is used almost universally in logic and computer science. However, it is not well suited for writing down actual proofs. We therefore introduce a concrete syntax for proofs which can be checked by the software available to use in this course.

We also formalize our strategy for proof search by introducing two new judgments: A has a normal proof, and A has a neutral proofs. Intuitively, a proof is normal if it can be found by our strategy to apply introduction rules bottom-up and elimination rules top-down.

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Frank Pfenning