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
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