slovodefinícia
name capture
(foldoc)
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.

(1995-03-14)
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