
mulyankan dwara saamaanyikaran

prograaming bhasha shabdarth mein, mulyankan dwara saamaanyikaran (nbe) λ-calculus mein shabdon key samanya roop koo praapt karane kii ack shally haye joe unake avyakhyatmak shabdarth koo aakarshit karati haye. ack shabd koo pahale λ-shabd sanrachana key ack niroopak model mein "vyakhya" kii jaati haye, aur phir ack vihit (β-samanya aur η-lamba) pratinidhi koo niroopan koo "punah paribhaashit" karke nikala jaataa haye. iss tarah kaa ack anivarya roop seey shabdarthik, kamee-mukt, drishtikon adhik paaramparik vakyavinyas, kamee-adharit, saamaanyikaran key vivaran seey alag haye, ack shabd punarlekhan pranali mein kamee key roop mein jahaan β-katauti kii anumati λ-shabdon key ander gaharaai seey dee jaati haye.
aine. bee. ee. koo pahali baar saral type kiye gaye lambda cullon key liye varnit kiya gayaa thaa. isake baad seey ise kamjor prakaar kii pranaliyon jaise kii ack domen saiddhaantik drishtikon kaa upayog karke untype kiye gaye lambda cullon aur martin-loff prakaar siddhant key kaee roopon jaisi samriddh prakaar kii pranaliyon donon taka vistaarit kiya gayaa haye.
ruprekha.
saralata seey type kiye gaye lambda cullon parr vichaar karein, jahaan prakaar τ buniyaadi prakaar (α), kaary prakaar (→), yaa utpaad (×) hoe sakate hain, joe nimnalikhit bacus-norr roop vyaakaran (hamesha kii tarah, daaeen or seey sambaddh) dwara diye gaye hainh
inhen metaa-bhasha mein ack detta type key roop mein lagu kiya jaa sakata haye; udaaharan key liye, maanak ml key liye, humm upayog curr sakate hainh
 detta type tye = string kaa mool
 . teer kaa teer
 . tii * tii kaa utpaad
shabdon koo dou staron parr paribhaashit kiya gayaa haye. nichala "vaakya rachana" star (jise kabhi-kabhi "gatishil" star kahaa jaataa haye) vaha pratinidhitva haye jise samanya karane kaa irada haye.
yahaan laam/aip (resp. jodee/fst, snd), parichay/nishkasana form hain joe kii '(resp') key liye hain. x), aur "x" charr hain. inn shabdon koo metaa-bhasha mein pratham-crum datatype key roop mein lagu karane kaa irada haih
 detta type tii. aim. = string kaa vaar
 . taar kaa laim * tii. aim. . tii. aim. * tii. aim. kaa aip
 . tii. aim. * tii. aim. kii jodee . tii. aim. kaa aff. aiss. tii. . tii. aim. kaa aiss. aine. dee.
metaa-bhasha mein (bund) shabdon key sangyaatmak shabdarth metaa-bhasha kii visheshtaon key sandarbh mein vakyavinyas key nirmaan kii vyakhya karate hain; iss prakaar, laam koo amurtata, aip koo anuprayog key roop mein, aadi key roop mein vyakhya kii jaati haye. nirmit shabdarth vastuein iss prakaar hainh
dhyaan dein kii shabdarth mein koee charr yaa unmoolan roop naheen hain; unhein kewal vaakya rachana key roop mein darshaaya jaataa haye. inn shabdarth vastuon koo nimnalikhit detta prakaar dwara darshaaya gayaa haih
 datatype same = laim off (same-> same)
 . same * same kii jodee
 . tii. aim. kaa sinn
prakaar-anukramit karyon kii ack jodee hoti haye joe vaakya rachana aur shabdarth parat key beach aage-peechhe chalati haye. pahala falan, jise aamtaur parr likhaa jaataa haye, vakyavinyas shabd koo shabdarth mein "darshaata haye", jabaki doosara shabdarth koo ack vakyavinyas shabd (Âτ key roop mein likhaa jaataa haye) key roop mein "punah paribhaashit" kartaa haye. unaki paribhaashaaen nimnanusar parasparik roop seey punaraavarti hainh
sootra _ 1
inn paribhashaon koo metaa-bhasha mein aasaani seey lagu kiya jaataa haih
 (* taaja _ vaarah ikai-> string *)
 vail charr _ ctr = ref ~ 1
 majedar taaza _ vaar () = 
 (charr _ ctr: = 1 +!charr (_ c); 
 "v" ^ int.tustering (!charr (_ ctr))
 (* pratibimbit karenh ti-> tm-> same *)
 majedar pratibimb (teer (aeye, bee)) tii =
 laam (fns => bee koo pratibimbit kartaa haye (aip (tii, (reefai ass))))
 . reflect (prode (aeye, bee)) tii =
 jodee (aeye (fst tii) koo pratibimbit karati haye, bee (snd tii) koo pratibimbit karati haye)
 . paraavartit (mool _) tii =
 sinn tii
 (* punahnirdhaarit karein-ti-> sem-> tm *)
 aur phir seey teer (aeye, bee)) (laam aiss) =
 maan leejiye kii vail x = taaza _ vaar ()
 laam (x, b koo punah paribhaashit karein (s (a (ver x) koo pratibimbit kartaa haye)))
 anta
 . reefai (prode (aeye, bee)) (jodee (aiss, tii)) =
 jodee (as koo phir seey banaaen, bt koo phir seey banaaen)
 . reefai (basic _) (sinn tii) = tii
prakaron kii sanrachana parr preran dwara, yeh iss prakaar haye kii yadi shabdarth vastu "s" prakaar τ key ack achchi tarah seey type kiye gaye shabd "s" koo darshaata haye, tou vastu koo phir seey sanshodhit karein (i.ee., Âτs) "s" key β-samanya η-lambe roop kaa utpaadan kartaa haye. isaliye, ack vaakya rachana shabd "s" seey praarambhik shabdarth vyakhya "s" kaa nirmaan karna hii shesh haye. yeh operation, likhaa gayaa γs γ, jahan γ binding kaa ack sandarbh haye, kewal shabd sanrachana parr preran dwara aage badhata haih
sootra _ 2
karyanvayan mein -
 detta type ctx = khaali 
 . ctx * (string * same) jodein
 (* khojah ctx-> string-> same *)
 majedar khoj (jodein (remder, (vaaee, maan))) x = 
 yadi x = y haye tou maan anyatha khoj remder x
 (* arthah ctx-> tm-> same *)
 majedar kaa arth haye jee tii =
 cases tii
 vaar x => g x kii khoj karein
 . laam (x, s) => laam (fn s => jiska arth haye (jodd (g, (x, s)) s)
 . aip (aiss, tii) => (mamle kaa arth haye jee aiss kaa
 laam aiss => aiss (jiska arth haye jee tii))
 . jodee (s, t) => jodee (jiska arth haye g s, jiska arth haye g t)
 . fst s => (mamle kaa arth haye gs kaa
 jodee (aiss, tii) => aiss)
 . aiss. aine. dee. tii => (mamle kaa arth haye jee. tii.
 jodee (aiss, tii) => tii)
dhyaan dein kii kaee gair-sampoorn mamle hain; haalaanki, yadi ack "bund" achchi tarah seey type kiye gaye shabd parr lagu kiya jaataa haye, tou inmein seey kissy bhee laapata mamle kaa kabhi saamana naheen kiya jaataa haye. bund sharton parr aine. bee. ee. operation taba haih
 (* nbeh ti-> tm-> tm *)
 majedar nbe a t = a koo phir seey banaaen (jiska arth haye khaali t)
isake upayog key ack udaaharan key roop mein, neeche paribhaashit vakyavinyas shabd cocksey _ 1 parr vichaar karein.
 vail key = laam ("aiks", laam ("vaaee", vaar "aiks"))
 vail aiss = laam ("aiks", laam ("vaaee", laam ("jaid", aip (aip (vaar "aiks", vaar "jaid"), aip (vaar "vaaee", vaar "jaid"))))))
 wall aiss. key. key. = aip (aip (aiss, key), key)
yeh sanyojan tark mein pehchaan kaary kaa prasiddh encoding haye. ise ack pehchaan prakaar parr samanya banaane seey utpann hotaa haih
 - aine. bee. ee. (teer (mool "aeye", mool "aeye")) aiss. key. key.;
 vail itt = laam ("v0", vaar "v0"): tm
parinam vaastav mein η-lambe roop mein haye, jaisa kii ise ack alag pehchaan prakaar parr samanya karke aasaani seey dekhaa jaa sakata haih
 - aine. bee. ee. (teer (mool "aeye", mool "bee"), teer (mool "aeye", mool "bee")))) scack;
 vail itt = laam ("v1", laam ("v2", aip (vaar "v1", vaar "v2")): tm
roop.
avashisht vakyavinyas mein naamon key bajaay dee bruyson staron kaa upayog karna cocksey _ 2 koo vishuddh roop seey karyatmak banaata haye kyonki cocksey _ 3 kii koee aavashyakta naheen haye.
avashisht shabdon kaa detta prakaar "samanya roop mein" avashisht shabdon kaa detta prakaar bhee hoe sakata haye.
cocksey _ 2 (aur isaliye cocksey _ 5) kaa prakaar taba yeh spasht kartaa haye kii parinam samanya haye.
aur yadi samanya roopon kii detta type type kii jaati haye, tou cocksey _ 2 (aur isaliye cocksey _ 5) kaa prakaar yeh spasht kartaa haye kii saamaanyikaran prakaar sanrakshan haye.
mulyankan dwara saamaanyikaran bhee pariseemit niyantran prachaalak cocksey _ 9 aur cocksey _ 10 kaa upayog karke yog (cocksey _ 8) key saath saral type kiye gaye lambda cullon koo maapata haye.