weak head normal form

1 definition found

weak head normal form - Free On-line Dictionary of Computing (26 May 2007) :

  Weak Head Normal Form
  
     <reduction, lambda calculus> (WHNF) A lambda expression is
     in weak head normal form (WHNF) if it is a head normal form
     (HNF) or any lambda abstraction.  I.e. the top level is not
     a redex.
  
     The term was coined by Simon Peyton Jones to make explicit
     the difference between head normal form (HNF) and what
     graph reduction systems produce in practice.  A lambda
     abstraction with a reducible body, e.g.
  
     	\ x . ((\ y . y+x) 2)
  
     is in WHNF but not HNF.  To reduce this expression to HNF
     would require reduction of the lambda body:
  
     	(\ y . y+x) 2  -->  2+x
  
     Reduction to WHNF avoids the name capture problem with its
     need for alpha conversion of an inner lambda abstraction and
     so is preferred in practical graph reduction systems.
  
     The same principle is often used in strict languages such as
     Scheme to provide call-by-name evaluation by wrapping an
     expression in a lambda abstraction with no arguments:
  
     	D = delay E = \ () . E
  
     The value of the expression is obtained by applying it to the
     empty argument list:
  
     	force D = apply D ()
     		= apply (\ () . E) ()
     		= E
  
     (1994-10-31)