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combinator

Eory> A function with no Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=frEE variablEs">frEE variablEs. A tErm is EithEr a constant, a variablE or of thE form A B dEnoting thE Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=application">application of tErm A (a function of onE argumEnt) to tErm B. Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=Juxtaposition">Juxtaposition associatEs to thE lEft in thE absEncE of parEnthEsEs. All combinators can bE dEfinEd from two basic combinators - S and K. ThEsE two and a third, I, arE dEfinEd thus: S f g x = f x (g x) K x y = x I x = x = S K K x ThErE is a simplE translation bEtwEEn Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=combinatory logic">combinatory logic and Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=lambda-calculus">lambda-calculus. ThE sizE of EquivalEnt ExprEssions in thE two languagEs arE of thE samE ordEr. OthEr combinators wErE addEd by Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=David TurnEr">David TurnEr in 1979 whEn hE usEd combinators to implEmEnt Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=SASL">SASL: B f g x = f (g x) C f g x = f x g S' c f g x = c (f x) (g x) B* c f g x = c (f (g x)) C' c f g x = c (f x) g SEE Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=fixEd point combinator">fixEd point combinator, Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=curriEd function">curriEd function, Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=supErcombinator">supErcombinators. (2002-11-03)

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=262">ad ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=396">ag ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=433">al ] [ 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=700">application ] [ 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=799">AS ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=800">as ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=829">ASL ] [ 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=1025">B ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1026">b ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1034">ba ] [ 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=1269">bi ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1606">bs ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1695">by ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1708">C ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1724">ca ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1863">cat ] [ 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=2330">com ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2334">combinatory logic ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2545">con ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2606">cons ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2900">cu ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2913">curriEd function ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2976">D ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3101">David TurnEr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3136">dd ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3151">dE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3752">du ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3896">Ed ] [ 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=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=4595">fix ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4597">fixEd point ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4599">fixEd point combinator ] [ 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=4828">fr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4859">frEE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4867">frEE variablE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4940">function ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5057">gE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5141">gi ] [ 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=5768">hr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5791">hu ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5931">id ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5956">iE ] [ 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=6194">int ] [ 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=6760">K ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6918">la ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6939">lambda-calculus ] [ 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=7091">LEx ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7107">li ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7415">lu ] [ 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=8386">na ] [ 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=8675">no ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8760">ns ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8820">O ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8964">om ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9204">pa ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9306">parEnt ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9307">parEnthEsEs ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9457">pE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9550">ph ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9651">pl ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9762">point ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9908">pr ] [ 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=10767">ro ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10918">S ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10921">SA ] [ 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=10983">SAS ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10987">SASL ] [ 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=11506">sit ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11524">SL ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11525">sl ] [ 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=12133">su ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12359">T ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12360"> ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12409">tap ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12588">th ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12602">thEory ] [ 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=13146">up ] [ 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=13274">var ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13275">variablE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13366">vi ]

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