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Church's formal system used in computatability, programming languages and proof theory to represent effective functions, programs and their computation, and proofs.
6
votes
Functions that typed lambda calculus cannot compute
The simply-typed lambda calculus is actually surprisingly weak. For example, it can't recognize the regular language $\mathtt{a}^*$. I've never found a precise characterization of the set of languag …
19
votes
Accepted
Historic Relationship between Typed Lambda Calculus and Lisp?
First, your friend is wrong about the history of the $\lambda$-calculus. Church created the untyped calculus first, which he intended as a foundation for mathematics. Fairly quickly, it was discovered …