Editing Lambda calculus (section)

==== Alpha equivalence ====
A basic form of equivalence, definable on lambda terms, is ''alpha equivalence''. It captures the intuition that the particular choice of a bound variable, in an abstraction, does not (usually) matter.
For instance, <math>\lambda x.x</math> and <math>\lambda y.y</math> are alpha-equivalent lambda terms, and they both represent the same function (the identity function).
The terms <math>x</math> and <math>y</math> are not alpha-equivalent, because they are not bound in an abstraction.
In many presentations, it is usual to identify alpha-equivalent lambda terms.

The following definitions are necessary in order to be able to define β-reduction: