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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 …
Sam Tobin-Hochstadt's user avatar
19 votes
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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 …
Sam Tobin-Hochstadt's user avatar