Web Reference: At the time of Curry, and also at the time of Howard, the proofs-as-programs correspondence concerned only intuitionistic logic, i.e. a logic in which, in particular, Peirce's law was not deducible. According to the Curry-Howard correspondence, the notions of programs correspond to proofs, and a program proves its type according to the typing rules of the programming language. Thanks to the Curry-Howard correspondence, we’ve just translated our proof into a working program! Not only do we know this is possible, we can see exactly how the change is made for any given value.
YouTube Excerpt: Programs are proofs

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Celebrity Proofs as Programs | Curry-Howard Correspondence Wealth
Proofs as Programs | Curry-Howard Correspondence
The Architecture of Formal Proofs and Programming Wealth
The Architecture of Formal Proofs and Programming
Code Meets Proof - #lexfridman w/ Tim Sweeney Wealth
Code Meets Proof - #lexfridman w/ Tim Sweeney
Famous The Curry-Howard Isomorphism: Proofs as Programs Net Worth
The Curry-Howard Isomorphism: Proofs as Programs
Famous Proofs ARE Programs! Curry-Howard Explained (and Counter-Evidence!) #shorts Wealth
Proofs ARE Programs! Curry-Howard Explained (and Counter-Evidence!) #shorts
Famous Curry-Howard Correspondence: Correct Code [by just writing more code] Net Worth
Curry-Howard Correspondence: Correct Code [by just writing more code]
The Curry-Howard Correspondence | Breakthrough Junior Challenge Wealth
The Curry-Howard Correspondence | Breakthrough Junior Challenge
Famous Proofs as Programs: Unifying Logic and Code Wealth
Proofs as Programs: Unifying Logic and Code
Famous Talia Ringer — Proof Transformation: The Curry-Howard of Program Transformation Net Worth
Talia Ringer — Proof Transformation: The Curry-Howard of Program Transformation

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