cs-4400-sp26

Lecture 17: Propositions as Types

Outline

• Logical connectives:
  • Conjunction (and, &)
  • Implication (implies, ->)
• Example proofs:
  • A -> (B -> (A & B))
  • A & B -> B & A
  • (A -> B & C) -> (A -> B) & (A -> C)
• Logical connectives:
  • Disjunction (V)
  • Falsehood (F)
  • Truth (T)
• Example proofs:
  • (T -> A) -> A
  • A V B -> B V A
  • A V F -> A
• Proof terms
• Plait code

Resources

• Frank Pfenning on Natural Deduction
• Tutch (web version)

References

• Per Martin-Löf: Constructive Mathematics and Computer Programming (1980)
  • https://www.cs.tufts.edu/~nr/cs257/archive/per-martin-lof/constructive-math.pdf
• W. A. Howard. The formulae-as-types notion of construction. (1980)
  • https://www.cs.cmu.edu/~crary/819-f09/Howard80.pdf