Weak Head Normal Form

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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