Name capture

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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