<*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.

Last updated: 1995-03-14

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**Nearby terms:**
naive « naive user « NAK « **name capture** » named » named pipe » name resolution

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Copyright Denis Howe 1985