Implement SKI combinator calculus

Wolfram Language, 63 bytes

#//.{{I,x_}->x,{{K,x_},y_}->x,{{{S,x_},y_},z_}->{{x,z},{y,z}}}&

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God, I love pattern matching in Wolfram Language. Represents (xy) as {x,y} (a list of two elements).

Alternatively, if we represent (xy) with x>y, we can do it in 55 bytes.

#//.{I>x_->x,(K>x_)>y_->x,((S>x_)>y_)>z_->(x>z)>(y>z)}&

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C (gcc), 666 616 518 483 476 bytes

Who doesn't love classy, Arthur Whitney-styled code? No regular expressions involved, only clever parsing and evaluation.

PS: Yes, obviously, a few bytes can be shaved off, but for the artistic style of the obfuscated code, I'll keep them. Also for the byte count :p. Also, this code utilizes undefined behaviour in hope that nothing will break (hopefully).

@ceilingcat insisted on golfing it down from 666 bytes, so here is the golfed version:

#define J putchar
#define H O->a
#define G H->a
#define K O->b
typedef struct x{struct x*a,*b;int q;}Y;Y*O;z=1;A(q){O=calloc(6,4);O->q=q;}h(Y*O){Y*u;O=H&&H->q==2?z=K:H&&G&&G->q==1?z=H->b:H&&G&&G->a&&!G->a->q?u=A(3),(u->a=A(3))->a=G->b,(u->b=A(3))->a=H->b,u->a->b=u->b->b=K,z=u:(O->q==3?H=h(H),K=h(K):0,O);}r(x){Y*O;x=getchar()-73;x=x+33?A(x?x!=10:2):!getchar(K=r(H=r(O=A(3))))+O;}q(Y*O){O&&J(O->q["SKI "],O->q-3||J(41,q(K),q(H),J(40)));}main(){Y*O=r();for(;z;O=h(O))z=0;q(O);}

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Seed, 5929 bytes

112 17512502422339329988136970659215748808228380483715601708275685672232516607584795051956416794359280804448726712568450098282473893858441323811726505467144525002213711190498758779113159873818584231902062412643056057951581097157680216352705811864658294332485365399979619954263236941681270874935427174128431725073230232846905480378068547711286833416918885689101802395062937835483527386579675784841766933974338268758617424204945400621685145313113413442846321450879300790533771768113307031547198546642710067219291680435107353610019915176267886554188355005282543886231809520086965587573165264463447255346988847826073614176785390698591712839717942634477748742873958930458032397747116405695388286893138018725196729518940893538161415283915246840884080717134920520827651165874408741365222050330295518838808758322699584153873945664415639556010113981908076336010816978069651111450939612587961819411278093394213403525472865707297636106633222834065495250967247084005275157219995202161853869034938519443192957025929517233295867530485382205003206781378211321294327252917145628777013819743109880847611029029657759903936887753727717255571167326356177386406607532478311155283526241134825092678080334702426161180969235691643908708179370578394372844489289555861772662839379931352634406449024816399454666546503312172629394312880839240922034100207930802540247036737646129778762566209009901734073820127432199596040275379996731010046250181781743940427590223605774419863152198276471351741351349268475968201222035840663945399558509795562251877878163541978892729055642445504310468265085068678954814946551029316936937981141090475534434959116960793324070394548794779962060440184286525439976117312008339186321927370761110437566937483436973192485435298012480957536544910217032872964217108051037213352940033531286916151953824230439560555822266931113702480962942272315812744392996583885143469967324124078074007232529946277219323538107023241793156054437093936858795879197092100991955975898034113644809589814045841130495964239038389263408874245712641319993350583419625955142090879604617626373459965455976627086364631540057430986089110572897277967757386957829115112014098627927335467795185911185219894145567629819416275695821270731562167285516828869480343290524485797263688781455383936136017489839217050041164425580094069781604889646135784493769361050555681434091107761735109092016275690131205757441400882751600545471427147069031401666524911971903727045872397248040771508501472588643534959012492613357461855964121131759422588295612295510673830226556874277129321897744637366509835646449045356065691520490209313357484333495768791495060810678636899705255152921579917004376066815923229021533365868602757468196075405252047350891225048894461097217098110692727099485488235891289280647744868379046941894931500725530201947539195310174891142390657269409361047515729436287689384001303969366751208052958285951479422982596688545366529027290386004088870463067806759442458758213459310491197496917743557313704069203940641334297745083528078150290716336980662541163034663150946725578603064982694875662027093788816708243115297897114796126457030287046016773956363237511096578824432791994490470345338415917483522841810905504266707700742999613673189326362471465550968635207982829712718505173495890732885277548080485552057506786459203858888601458750364142197804745103431313221741719250686304401295060620639477577516231072221024300751340117993416549277713042022784679011874379615889911745776300303409198166514788655199048867295738546269966431184804421661858253944229831783398593737627433580752863409684366311268904168195713873458711498013097320249735989274243424169049966892548012095455267590586309629700648473675006237492733609521500644795443593219524648967210953867670667771426638345780109836532144820521570399318752638302951770510844131214239771302004293647221173227046351016326789993247317997309696488779430517377024854112719406126344253690318069230423686438020026580586179266157877178166460852458821870889837613533835503755942923224526625607342233255785544814783435959554721136761105039633407706606596522581137658727414287805141617186292359391475736938683592177295953493488465950926249150955202959642448902970380784118057151161685279118107372074152873061221031402927967067155212891127806362275435203168149991173071470569316713054250966318985474792473651526986802153343677052501623970024871156066381357752797455120376728971918616066679783595848872831327957568371457709225792348660361968612476090156304581417207202234585744370399840121330398587642972504525085216554860352303978890750905490025863403615340666477848326736540756627816597889721867323054795993505527943817164206879302245994298910165772119605202750411392864742232709851021150700654730338790648749227135805290685696230506285147598275035191111443996302313731946811902106814419303999605741738684832336000742465430035909694350903833770944950164265176899776839134193505199331205383382192902239757902425022920081212586504467898861934326003723651705276264507220030903416519747106125041103518317025525717366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Made possible thanks to Abigail's perl answer. Inspired by HighlyRadioactive's comment.

Golfed with the standard algorithm, I'll run BXn and modify the answer later.