Alpha conversion

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An alpha conversion (also written α conversion) essentially involves renaming variables.

For example, suppose we have an expression such as

\x y -> 2*x*x + y

and we change this to

\a b -> 2*a*a + b

This is clearly the same function, even though it uses different variable names. This process of renaming variables is alpha conversion.

(Note that alpha conversion is not as simple as it first seems. For example, if we rename x to y in \x -> x + y then we end up with \y -> y + y, which is radically different!)