Functions are proofs.
Um, I can see how that might work. Go on.
Types are propositions. Really? In what sense?
In fact, a function is the proof of the proposition its type represents.
Woah, you've lost me now.
The Curry-Howard Correspondence is an elegant bridge between the planet of logic and the planet of programming, and it's not actually that hard to understand.
In this talk I'll use the Idris dependently-typed functional programming language for examples, as its type system is sophisticated enough to construct interesting automated proofs simply by writing functions. This talk is not designed to convert you into a theoretical computer scientist, but to share with you a wonderful sight in your journey through the vast and peculiar universe of programming.
A familiarity with functional programming would be useful for appreciating this talk, but it will not require any significant prior study of theoretical computer science.