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Lexikon


Weak Head Normal Form


eduction, lambda calculus> (WHNF) A ef="module.php?name=Lexikon&file=search&eid=1&query=lambda expression">lambda expression is in weak head normal form (WHNF) if it is a ef="module.php?name=Lexikon&file=search&eid=1&query=head normal form">head normal form (HNF) or any ef="module.php?name=Lexikon&file=search&eid=1&query=lambda abstraction">lambda abstraction. I.e. the top level is not a ef="module.php?name=Lexikon&file=search&eid=1&query=redex">redex. The term was coined by ef="module.php?name=Lexikon&file=search&eid=1&query=Simon Peyton Jones">Simon Peyton Jones to make explicit the difference between ef="module.php?name=Lexikon&file=search&eid=1&query=head normal form">head normal form (HNF) and what ef="module.php?name=Lexikon&file=search&eid=1&query=graph reduction">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 ef="module.php?name=Lexikon&file=search&eid=1&query=name capture">name capture problem with its need for ef="module.php?name=Lexikon&file=search&eid=1&query=alpha conversion">alpha conversion of an inner lambda abstraction and so is preferred in practical ef="module.php?name=Lexikon&file=search&eid=1&query=graph reduction">graph reduction systems. The same principle is often used in ef="module.php?name=Lexikon&file=search&eid=1&query=strict">strict languages such as ef="module.php?name=Lexikon&file=search&eid=1&query=Scheme">Scheme to provide ef="module.php?name=Lexikon&file=search&eid=1&query=call-by-name">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)

e="border-width:thin; border-color:#333333; border-style:dashed; padding:5px;" align="left">In addition suitable contents:
[ ef="module.php?name=Lexikon&op=content&tid=31">2 ] [ ef="module.php?name=Lexikon&op=content&tid=134">= ] [ ef="module.php?name=Lexikon&op=content&tid=178">abstraction ] [ ef="module.php?name=Lexikon&op=content&tid=262">ad ] [ ef="module.php?name=Lexikon&op=content&tid=396">ag ] [ ef="module.php?name=Lexikon&op=content&tid=411">ai ] [ ef="module.php?name=Lexikon&op=content&tid=433">al ] [ ef="module.php?name=Lexikon&op=content&tid=523">alpha conversion ] [ ef="module.php?name=Lexikon&op=content&tid=544">am ] [ ef="module.php?name=Lexikon&op=content&tid=592">an ] [ ef="module.php?name=Lexikon&op=content&tid=683">app ] [ ef="module.php?name=Lexikon&op=content&tid=740">ar ] [ ef="module.php?name=Lexikon&op=content&tid=743">arc ] [ ef="module.php?name=Lexikon&op=content&tid=759">arg ] [ ef="module.php?name=Lexikon&op=content&tid=760">argument ] [ ef="module.php?name=Lexikon&op=content&tid=800">as ] [ ef="module.php?name=Lexikon&op=content&tid=894">at ] [ ef="module.php?name=Lexikon&op=content&tid=996">av ] [ ef="module.php?name=Lexikon&op=content&tid=1026">b ] [ ef="module.php?name=Lexikon&op=content&tid=1177">bd ] [ ef="module.php?name=Lexikon&op=content&tid=1181">be ] [ ef="module.php?name=Lexikon&op=content&tid=1444">bo ] [ ef="module.php?name=Lexikon&op=content&tid=1606">bs ] [ ef="module.php?name=Lexikon&op=content&tid=1624">bt ] [ ef="module.php?name=Lexikon&op=content&tid=1695">by ] [ ef="module.php?name=Lexikon&op=content&tid=1724">ca ] [ ef="module.php?name=Lexikon&op=content&tid=1765">call-by-name ] [ ef="module.php?name=Lexikon&op=content&tid=2001">ch ] [ ef="module.php?name=Lexikon&op=content&tid=2099">ci ] [ ef="module.php?name=Lexikon&op=content&tid=2247">co ] [ ef="module.php?name=Lexikon&op=content&tid=2545">con ] [ ef="module.php?name=Lexikon&op=content&tid=2900">cu ] [ ef="module.php?name=Lexikon&op=content&tid=2976">D ] [ ef="module.php?name=Lexikon&op=content&tid=3151">de ] [ ef="module.php?name=Lexikon&op=content&tid=3371">diff ] [ ef="module.php?name=Lexikon&op=content&tid=3752">du ] [ ef="module.php?name=Lexikon&op=content&tid=3834">e ] [ ef="module.php?name=Lexikon&op=content&tid=3896">ed ] [ ef="module.php?name=Lexikon&op=content&tid=3923">edu ] [ ef="module.php?name=Lexikon&op=content&tid=3929">ee ] [ ef="module.php?name=Lexikon&op=content&tid=4148">er ] [ ef="module.php?name=Lexikon&op=content&tid=4171">es ] [ ef="module.php?name=Lexikon&op=content&tid=4199">et ] [ ef="module.php?name=Lexikon&op=content&tid=4246">evaluation ] [ ef="module.php?name=Lexikon&op=content&tid=4317">expression ] [ ef="module.php?name=Lexikon&op=content&tid=4497">fi ] [ ef="module.php?name=Lexikon&op=content&tid=4520">file ] [ ef="module.php?name=Lexikon&op=content&tid=4700">fo ] [ ef="module.php?name=Lexikon&op=content&tid=4727">for ] [ ef="module.php?name=Lexikon&op=content&tid=5057">ge ] [ ef="module.php?name=Lexikon&op=content&tid=5291">gr ] [ ef="module.php?name=Lexikon&op=content&tid=5307">graph ] [ ef="module.php?name=Lexikon&op=content&tid=5326">graph reduction ] [ ef="module.php?name=Lexikon&op=content&tid=5403">gu ] [ ef="module.php?name=Lexikon&op=content&tid=5434">h ] [ ef="module.php?name=Lexikon&op=content&tid=5540">hat ] [ ef="module.php?name=Lexikon&op=content&tid=5768">hr ] [ ef="module.php?name=Lexikon&op=content&tid=5931">id ] [ ef="module.php?name=Lexikon&op=content&tid=5986">iff ] [ ef="module.php?name=Lexikon&op=content&tid=6013">il ] [ ef="module.php?name=Lexikon&op=content&tid=6064">in ] [ ef="module.php?name=Lexikon&op=content&tid=6068">inc ] [ ef="module.php?name=Lexikon&op=content&tid=6413">io ] [ ef="module.php?name=Lexikon&op=content&tid=6449">ir ] [ ef="module.php?name=Lexikon&op=content&tid=6482">is ] [ ef="module.php?name=Lexikon&op=content&tid=6558">it ] [ ef="module.php?name=Lexikon&op=content&tid=6589">J ] [ ef="module.php?name=Lexikon&op=content&tid=6789">ke ] [ ef="module.php?name=Lexikon&op=content&tid=6918">la ] [ ef="module.php?name=Lexikon&op=content&tid=6938">lambda abstraction ] [ ef="module.php?name=Lexikon&op=content&tid=6940">lambda expression ] [ ef="module.php?name=Lexikon&op=content&tid=6950">language ] [ ef="module.php?name=Lexikon&op=content&tid=7014">lc ] [ ef="module.php?name=Lexikon&op=content&tid=7023">ld ] [ ef="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ ef="module.php?name=Lexikon&op=content&tid=7107">li ] [ ef="module.php?name=Lexikon&op=content&tid=7220">list ] [ ef="module.php?name=Lexikon&op=content&tid=7415">lu ] [ ef="module.php?name=Lexikon&op=content&tid=7441">ly ] [ ef="module.php?name=Lexikon&op=content&tid=7463">ma ] [ ef="module.php?name=Lexikon&op=content&tid=8032">mo ] [ ef="module.php?name=Lexikon&op=content&tid=8040">mod ] [ ef="module.php?name=Lexikon&op=content&tid=8079">module ] [ ef="module.php?name=Lexikon&op=content&tid=8167">mp ] [ ef="module.php?name=Lexikon&op=content&tid=8228">ms ] [ ef="module.php?name=Lexikon&op=content&tid=8384">N ] [ ef="module.php?name=Lexikon&op=content&tid=8386">na ] [ ef="module.php?name=Lexikon&op=content&tid=8396">name capture ] [ ef="module.php?name=Lexikon&op=content&tid=8460">nc ] [ ef="module.php?name=Lexikon&op=content&tid=8472">ne ] [ ef="module.php?name=Lexikon&op=content&tid=8627">ng ] [ ef="module.php?name=Lexikon&op=content&tid=8672">nn ] [ ef="module.php?name=Lexikon&op=content&tid=8675">no ] [ ef="module.php?name=Lexikon&op=content&tid=8718">norm ] [ ef="module.php?name=Lexikon&op=content&tid=8720">normal form ] [ ef="module.php?name=Lexikon&op=content&tid=9014">op ] [ ef="module.php?name=Lexikon&op=content&tid=9550">ph ] [ ef="module.php?name=Lexikon&op=content&tid=9616">ping ] [ ef="module.php?name=Lexikon&op=content&tid=9651">pl ] [ ef="module.php?name=Lexikon&op=content&tid=9738">ply ] [ ef="module.php?name=Lexikon&op=content&tid=9908">pr ] [ ef="module.php?name=Lexikon&op=content&tid=10144">pt ] [ ef="module.php?name=Lexikon&op=content&tid=10253">query ] [ ef="module.php?name=Lexikon&op=content&tid=10364">rc ] [ ef="module.php?name=Lexikon&op=content&tid=10385">re ] [ ef="module.php?name=Lexikon&op=content&tid=10440">Red ] [ ef="module.php?name=Lexikon&op=content&tid=10444">redex ] [ ef="module.php?name=Lexikon&op=content&tid=10453">reduction ] [ ef="module.php?name=Lexikon&op=content&tid=10767">ro ] [ ef="module.php?name=Lexikon&op=content&tid=10918">S ] [ ef="module.php?name=Lexikon&op=content&tid=10922">sa ] [ ef="module.php?name=Lexikon&op=content&tid=10959">sam ] [ ef="module.php?name=Lexikon&op=content&tid=11047">Scheme ] [ ef="module.php?name=Lexikon&op=content&tid=11150">se ] [ ef="module.php?name=Lexikon&op=content&tid=11376">si ] [ ef="module.php?name=Lexikon&op=content&tid=11651">so ] [ ef="module.php?name=Lexikon&op=content&tid=11934">st ] [ ef="module.php?name=Lexikon&op=content&tid=12090">strict ] [ ef="module.php?name=Lexikon&op=content&tid=12133">su ] [ ef="module.php?name=Lexikon&op=content&tid=12246">sy ] [ ef="module.php?name=Lexikon&op=content&tid=12312">system ] [ ef="module.php?name=Lexikon&op=content&tid=12359">T ] [ ef="module.php?name=Lexikon&op=content&tid=12588">th ] [ ef="module.php?name=Lexikon&op=content&tid=12721">to ] [ ef="module.php?name=Lexikon&op=content&tid=12787">tr ] [ ef="module.php?name=Lexikon&op=content&tid=12939">tw ] [ ef="module.php?name=Lexikon&op=content&tid=12986">ua ] [ ef="module.php?name=Lexikon&op=content&tid=13030">um ] [ ef="module.php?name=Lexikon&op=content&tid=13175">us ] [ ef="module.php?name=Lexikon&op=content&tid=13252">va ] [ ef="module.php?name=Lexikon&op=content&tid=13260">value ] [ ef="module.php?name=Lexikon&op=content&tid=13310">ve ] [ ef="module.php?name=Lexikon&op=content&tid=13335">version ] [ ef="module.php?name=Lexikon&op=content&tid=13366">vi ] [ ef="module.php?name=Lexikon&op=content&tid=13703">WHNF ] [ ef="module.php?name=Lexikon&op=content&tid=14075">yt ]






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