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# 15-815 Automated Theorem Proving

# Lecture 3: Proof Terms

We introduce a compact notation for proofs in natural deduction.
Such proof terms can be seen as functional programs, where propositions
act as their types. This is known as the Curry-Howard isomorphism.
We also show an implementation of a proof checker for natural deductions
in Standard ML.

### Key Concepts

- Proof term
- Propositions as types
- Proofs as programs
- Product, function, unit, sum, and void type
- Type checking
- Inherited and synthesized type

### Reading

### Links

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Frank Pfenning
fp@cs