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
naive user ♦ NAK ♦ name capture ♦ named ♦ named pipe ♦ name resolution
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