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

• Handout 2 on Proof Terms (also available in PDF format).
• Slides used in class.
• Code directory with implementations of proof checkers (also available as gzipped tar file)

Links

• Previous lecture: Natural Deduction
• Next lecture: Intercalation