Proofs are Programs: 19th Century Logic and 21st Century Computing
As the 19th century drew to a close, logicians formalized an ideal notion of proof. They were driven by nothing other than an abiding interest in truth, and their proofs were as ethereal as the mind of God. Yet within decades these mathematical abstractions were realized by the hand of man, in the digital stored-program computer. How it came to be recognized that proofs and programs are the same thing is a story that spans a century, a chase with as many twists and turns as a thriller. At the end of the story is a new principle for designing programming languages that will guide computers into the 21st century.
This paper by Philip Wadler was a Dr Dobbs article in 2000 and has a matching a Netcast interview.
This nifty paper starts with Frege's Begriffschrift in 1879 and goes to Gentzen's sequent calculus, Church's untyped and then typed lambda calculus, and then brings it all together to describe the Curry-Howard correspondence. For the grand finale, Wadler connects this to Theorem Provers and Proof Carrying Code and gives commercial examples where it all pays off.
This is an enjoyable story and a fun introduction to type theory and the Curry-Howard correspondence.
For more of Wadler's writings along these lines check out his History of Logic and Programming Languages paper collection.
edit: fixed the dr dobbs article link
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