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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.

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Constructing terms of function types out of the empty type

In a plain type theory with just dependent functions and a universe, you can define: $$ \textbf 0 \equiv (A: \textrm{Type}) \rightarrow (B: \textrm{Type}) \rightarrow A \rightarrow B $$ Then you get a …
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