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
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