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Last updated 4 days ago

Is logical theory of computable functions.

Lambda calculus is a formal language capable of expressing arbitrary computable functions. In combination with types it forms a compact way to denote on the one hand functional programs and on the other hand mathematical proofs.

Lambda calculus is Turing complete, meaning you can express everything computable in a regular computer in lambda calculus.

You can formalize the entire lambda calculus inside of category theory via cartesian closed categories.