Name capture
<reduction> In beta reduction, when a term containing a free occurrence of a variable v is substituted into another term where v is bound the free v becomes spuriously bound or "captured".
E.g.
(\ x . \ y . x y) y
-->
\ y . y y (WRONG)
This problem arises because two distinct variables have the same name.
The most common solution is to rename the bound variable using alpha conversion:
(\ x . \ y' . x y') y --> \ y' . y y'
Another solution is to use de Bruijn notation.
Note that the argument expression, y, contained a free variable.
The whole expression above must therefore be notionally contained within the body of some lambda abstraction which binds y.
If we never reduce inside the body of a lambda abstraction (as in reduction to weak head normal form) then name capture cannot occur.
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