<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".
(\ 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.