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# 15-815 Automated Theorem Proving

# Lecture 4: Intercalation

We introduce a first proof search procedure for natural deductions which
searches from the goal towards the hypotheses by introduction rules, and from
the hypotheses towards the goal by elimination rules. The result is
called an *intercalation calculus* which permits only normal
deductions. We show how this leads to more compact proof terms via
bi-directional proof-checking. Later, we relate the intercalation calculus
to a sequent calculus.
### Reading

### Key Concepts

- Intercalation
- Normal and extracting derivations
- Strategies as judgments
- Soundness and completeness
- Annotated derivations
- Intro and elim terms
- Bi-directional proof-checking

### Links

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Frank Pfenning
fp@cs