(reduction, lambda calculus) | **Weak Head Normal Form** - (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 | |