Lambda the Ultimate

Propositions as Types, Philip Wadler. Draft, March 2014.

The principle of Propositions as Types links logic to computation. At first sight it appears to be a simple coincidence---almost a pun---but it turns out to be remarkably robust, inspiring the design of theorem provers and programming languages, and continuing to influence the forefronts of computing. Propositions as Types has many names and many origins, and is a notion with depth, breadth, and mystery.

Philip Wadler has written a very enjoyable (Like busses: you wait two thousand years for a definition of “effectively calculable”, and then three come along at once) paper about propositions as types that is accessible to PLTlettantes.