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In lambda calculus there are three types of reduction,

  • $\alpha$-renaming

  • $\beta$-reduction

  • $\eta$-conversion

The use of $\eta$ in $\eta$-conversion seems rather strange to me. Since they already used $\alpha$ and $\beta$ I would expect the pattern to be continued with $\gamma$ the third Greek letter, but $\eta$ is used instead.

Why is $\eta$ used in $\eta$-conversion?

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