<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.
(1995-03-14)
Nearby terms:
naive « naive user « NAK « name capture » named » named pipe » name resolution
