Lambda calculus

Last updated 7 hours ago

Is logical theory of computable functions.

Notes

  • 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.

Links

  • Caramel - Set of bidirectional, Haskell-inspired syntax-sugars that are expanded to, and contracted from, λ-Calculus terms.

  • LICK - Correct-by-construction implementation of the simply-typed lamba calculus' expressions, beta-reduction, and evaluation.

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