დისკრეტული სტრუქტურების გაფართოვება: პროგრამული ენა ჰასკელი

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1 Tbilisis saxelmwifo universiteti zusti da sabunebismetyvelo mecnierebata fakulteti ინტერდისციპლინური (მათემატიკა, კომპიუტერული მეცნიერებები) ქვემიმართულება: მათემატიკური ლოგიკა და დისკრეტული სტრუქტურები bakalavriati დისკრეტული სტრუქტურების გაფართოვება: პროგრამული ენა ჰასკელი K. Doets, J. van Eijck. The Haskell Road to Logic, Maths and Programming. Texts in Computer Series, 2004; Website: haskell.org.; Graham Hutton.Programming in Haskell. 2005; Tutorials:Learn You a Haskell for Great Good! საფუძველზე ლექციათა კურსი revaz grigolia da tatianა kiseliova Tbilisi 2011

2 leqcia # 1 1 samusaos mizani enis interpretatoris Haskell-is musaobis unarebis atviseba. Haskell-is tipis enis safuzvlebze warmodgenis mireba. martivi funqciebis gansazrvris atviseba 2 Hugs-is interpretatortan musaobis safuzvlebi laboratoriuli samusaoebis Casatareblad gamoiyeneba Haskellis tipis enis interpretatori. arsebobs interpretatorebis ramodenime realizacia; warmodgenil kurssi gamoiyeneba interpretatori Hugs (es dasaxeleba aris sityvebis Haskell users Gofer system abreviatura, Gofer aris programirebis enis dasaxeleba, romelic iyo Haskell-is enis erterti winamorbedi). Hugs-is interpretatoris gasvebis Semdeg ekranze Cndeba dammusavebeli garemos dialoguri fanjara, avtomaturad itvirteba tipebis winaswar gansazrvris da standartuli funqciebis gansazrvris faili Haskell-is enaze (P relude.hs), da gamoiyvaneba standartuli SemoTavzeba samusaoze. am SemaTavazebas aqvs saxe P relude >; zogadad, > simbolos win gamoiyvaneba bolo CatvirTuli modulis saxeli. SemoTavazebis gamotanis Semdeg SeiZleba avkrifot enis gamosaxuleba an interpretatoris brzaneba. interpretatoris brzaneba gansxvavdeba Haskell-is gamosaxulebisgan imit, rom iwyeba simbolo oriwertilit (:). magalitad, interpretatoris brzanebaa : quit, romelis Sesrulebac iwvevs interpretatoris musaobis damtavrebas. interpretatoris brzanebebi SeiZleba Semokldes ert asomde. ase, rom, brzanebebi : quit da : q eqvivalenturia. brzaneba : set gamoiyeneba interpretatoris sxvadasxva ofciebis dasayeneblad. brzaneba :? -s gamohyavs interpretatoris yvela brzanebis sia. SemdgomSi Cven sxva brzanebebsac ganvixilavt. 1

3 3 tipebi Haskell enis programebi arian gamosaxulebebi, romelta gamotvlebs mivyavart mnisvnelobebamde. TiToeul mnisvnelobas aqvs tipi. intuiciurad, tipi SeiZleba gavigot rogorc gamosaxulebis dasasvebi mnisvnelobebis simravle. imisatvis, rom ganvsazrrot, ra tipi aqvs mocemul gamosaxulebas, sawiroa gamoviyenot interpretatoris brzaneba : type (an : t). amas garda, SesaZloa gamoviyenot brzaneba : set + t, rata interpretatorma avtomaturad dabewdos yoveli gamotvlili gamosaxulebis tipi. ena Haskell -is tipebs warmoadgens: tipebi Integer da Int - gamoiyeneba mteli ricxvebis warmosadgenad, amastan tipi Integer -is sigrze ar aris SezRuduli. tipebi F loat da Double gamoiyeneba namdvili ricxvebis warmosadgenad. tipi Bool Seicavs or mnisvnelobas: T rue da F alse da danisnulia logikuri gamosaxulebebis Sedegis warmosadgenad. tipi Char gamoiyeneba simboloebis warmosadgenad. tipebis saxelebi Haskell enasi yoveltvis iwyeba didi (mtavruli) asoebit. ena Haskell warmoadgens Zlier tipizirebul programirebis enas. miuxedavad amisa, xsir SemTxvevebSi programisti ar aris valdebuli ganacxados, Tu romel tips ekutvnis mis mier Semotanili cvladi. interpretators TviTon aqvs SesaZlebloba gamoiyvanos momxmareblis mier gamoyenebuli cvladis tipi. Tumca, Tu raime miznistvis sawiroa gamocxaddes, rom mnisvneloba ekutvnis romelirac tips, gamoiyeneba konstruqcia: cvladi :: tipi. Tu CarTulia interpretatoris ofcia +t, masin interpretatori amave formatsi dabewdavs mnisvnelobebs. qvemot moyvanilia interpretatortan musaobis sesia. igulisxmeba, rom teqsti mosawvevi P relude > -is Semdeg, Seyvanilia momxmareblis mier, xolo misi momdevno teqsti aris sistemis pasuxi. P relude >: set + t 2

4 P relude > 1 1 :: Integer P relude > :: Double P relude > a a :: Char P relude > T rue T rue :: Bool mocemuli oqmidan Cans, rom tipebi Integer, Double da Char -is mnisvenlobebi moicema igive wesebit, rogorc ena C -Si. tipebis sistemis ganvitarebisa da mkacri tipizaciis Sedegad Haskell enis programebi aris usafrtxo tipebis mixedvit. garantirebulia, rom Haskell enis swor programasi tipebi sworad gamoiyeneba. praqtikulad, es nisnavs, rom Haskell enaze programa Sesrulebisas ver gamoiwvevs Secdomas mexsierebis SeRwevadobaze (Access violation). aseve, garantirebulia, rom programasi cvladebis gamoyeneba sawyisi inicializebis garese ar moxdeba. amrigad, programasi mravali Secdomis arseboba mowmdeba kompilaciis etapze da ara Sesrulebis etapze. 4 aritmetika interpretatori Hugs SeiZleba gamoyenebuli iyos aritmetikuli gamosaxulebebis gamosatvlelad. amastan, SesaZloa gamoyenebuli iyos operatorebi: +,,, / (mimateba, gamokleba, gamravleba, gayofa) prioritetebis Cveulebrivi wesebit. amastan, Sei- Zleba gamoyenebuli iyos operatori (xarisxsi ayvana). amrigad, musaobis seans SeiZleba hqondes Semdegi saxe: P relude > :: Integer P relude > :: Integer P relude > :: Integer amastan, SeiZleba gamoviyenot standartuli matematikuri funqciebi sqrt (kvadratuli fesvi), sin, cos, exp da a.s. programirebis sxva enebisgan gansxvavebit, Haskell -Si funqciis gamoza- 3

5 xebisas ar aris aucilebeli argumentis frcxilebsi Casma. amrigad, SeiZleba martivad daiweros sqrt2, da ara sqrt(2). magaliti: P relude > sqrt :: Double P relude > 1 + sqrt :: Double P relude > sqrt :: Double P relude > sqrt (2 + 1) :: Double am magalitidan SeiZleba davaskvnat, rom funqciis gamozaxebas ufro marali prioriteti aqvs, vidre aritmetikul operaciebs, ase, rom gamosaxuleba sqrt interpretirdeba rogorc (sqrt 2) + 1, da ara rogorc sqrt (2 + 1). gamotvlebis zusti rigis misatiteblad sawiroa gamoyenebuli iyos fr- Cxilebi. funqciis gamozaxebas yoveltvis ufro marali prioriteti aqvs, vidre nebismier binarul operacias. sawiroa aseve arinisnos, rom programirebis bevri sxva enisgan gansxvavebit, mtelricxvebiani gamosaxuleba Haskell -ze gamoitvleba Tanrigebis SeuzRudavi ricxvit. (SeecadeT gamotvalot gamosaxuleba ) C enisgan gansxvavebit, sadac int tipis maqsimaluri mnisvneloba SezRudulia manqanis TanrigebriobiT (Tanamedrove manqanebze igi tolia = ), Haskell enasi tipma Integer -ma SeiZleba warmoadginos nebismieri sigrzis mteli ricxvi. 5 kortejebi zemot CamoTvlili martivi tipebis garda askell-si Sei- Zleba ganvsazrvrot Sedgenili tipis mnisvnelobebic. magalitad, sibrtyeze wertilebis mosacemad aucilebelia ori ricxvi, romlebic mat koordinatebs Seesabameba. ena Haskell -Si ricxvebis wyvili SeiZleba movcet ase: CamovTaloT komponentebi, gamovyot mzimeebit da avirot frcxilebsi: (5,3). ar aris aucilebeli, rom ricxvebis komponentebi iyos er- Tidaigive tipis. SeiZleba SevadginoT wyvili, romlis pirveli komponenti SeiZleba iyos striqoni, meore mteli ricxvi da a.s. 4

6 zogadad, Tu a da b Haskell enis nebismieri tipia, masin im wyvilis tipi, romelsic pirveli elementi ekutvnis tips a, xolo meore - tips b, arinisneba ase: (a, b). magalitad, wyvils (5, 3) aqvs tipi (Integer, Integer); wyvili (1, a) ekutvnis tips (Integer, Char). SeiZleba moviyvanot ufro rtuli magaliti: wyvili ((1, a), 1.2) ekutvnis tips ((Integer, Char), Double). SeamowmeT es interpretatoris sasualebit. yuradreba mivaqciot imas, rom Tumca Semdegi saxis konstruqciebi (1,2) da (Integer, Integer) msgavsad gamoiyureba, ena Haskell -Si isini arnisnaven sxvadasxva cnebebs. pirveli matgani warmoadgens mnisvnelobas, masin roca meore aris tipi. wyvilebtan samusaod ena Haskell -Si arsebobs svandartuli funqciebi f st da snd,romlebic, Sesabamisad, abruneben siis pirvel da meore elementebs. am funqciebis dasaxeleba warmosobilia inglisuri sityvebidan f irst (pirveli) da second (meore). amrigad, isini SeiZleba gamoviyenot Semdegnairad: P relude > fst(5, T rue) 5 :: Integer P relude > snd(5, T rue) T rue :: Bool analogiurad, garda wyvilebisa, SeiZleba ganvsazrvrot sameulebi, otxeulebi da a.s. mati tipebi Caiwereba Sesabamisi saxit: P relude > (1, 2, 3) (1, 2, 3) :: (Integer, Integer, Integer) P relude > (1, 2, 3, 4) (1, 2, 3, 4) :: (Integer, Integer, Integer, Integer) monacemebis aset struqturas uwodeben kortejs. korte- JSi SeiZleba Senaxuli iyos fiqsirebuli raodenobis sxvadasxva monacemi. funqciebi f st da snd gansazrvrulia mxolod wyvilebistvis da ar musaobs sxva kortejebtan. Tu mat gamoviyenebt, magalitad, sameultan, interpretatori Segvatyobinebs Secdomis Sesaxeb. kortejis elementi SeiZleba iyos nebismieri tipis, mat Soris sxva kortejic. im kortejis elementebtan wvdomistvis, romlebic wyvilebs warmoadgenen, SeiZleba gamoviyenot f st 5

7 da snd funqciebis kombinacia. Semdegi magaliti gvicvenebs a elemetis amorebas kortejidan (1, ( a, 23.12)) : P relude > fst(snd(1, ( a, 23.12))) a :: Char 6 siebi kortejisagan gansxvavebit, siam SeiZleba Seinaxos elementebis nebismieri raodenoba. ena Haskell -Si sia ganisazrvreba ase: kvadratul frcxilebsi CamoiTvleba elementebi da ertmanetisgan mzimit gamoiyofa. elementebi aucileblad unda ekutvnodes ertidaigive tips. siis tipi, romelic Sedgeba a tipis elementebisgan, arinisneba rogorc [a]. P relude > [1, 2] [1, 2] :: [Integer] P relude > [ 1, 2, 3 ] [ 1, 2, 3 ] :: [Char] siasi SeiZleba arcerti elementi ar Sediodes. carieli sia arinisneba rogorc []. operatori : (ori wertili) gamoiyeneba siis TavSi elementis dasamateblad. misi marcxena argumenti unda iyos elementi, marjvena - sia: P relude > 1 : [2, 3] [1, 2, 3] :: [Integer] P relude > 5 : [1, 2, 3, 4, 5] [5, 1, 2, 3, 4, 5] :: [Char] P relude > F alse : [] [F alse] :: [Bool] operatori (:) da carieli siisgan SeiZleba avagot nebismieri sia: P relude > 1 : (2 : (3 : [])) [1, 2, 3] :: Integer operatori (:) marjvnidan asociatiuria, amitom zemot moyvanil gamosaxulebasi SeiZleba gamovtovot frcxilebi: 6

8 P relude > 1 : 2 : 3 : [] [1, 2, 3] :: Integer siis elementebi SeiZleba iyos nebismieri mnisvnelobebi - ricxvebi, simboloebi, kortejebi, sxva siebi da a.s. P relude > [(1, a ), (2, b )] [(1, a ), (2, b )] :: [(Integer, Char)] P relude > [[1, 2], [3, 4, 5]] [[1, 2], [3, 4, 5]] :: [[Integer]] ena Haskell -Si siebtan samusaod arsebobs funqciata didi raodenoba. Cven mxolod zogiert matgans ganvixilavt. funqcia head abrunebs siis pirvel elements. funqcia tail abrunebs sias pirveli elementis garese. funqcia length abrunebs siis sigrzes. funqciebi head da tail gansaxrvrulia aracarieli siebistvis. im SemTxvevaSi, Tu isini gamoiyeneba cariel siebtan, interpretators gamoaqvs Setyobineba Secdomis Sesaxeb. am funqciebtan musaobis magalitebia: P relude > head[1, 2, 3] 1 :: Integer P relude > tail[1, 2, 3] [2, 3] :: [Integer] P relude > tail[1] [] :: Integer P relude > length[1, 2, 3] 3 :: Int SevniSnoT, rom funqcia length ekutvnis tips Int da ara Integer -s. siebis gaertianebistvis (konkatenaciistvis) Haskell -Si gansazrvrulia operatori ++. P relude > [1, 2] + +[3, 4] [1, 2, 3, 4] :: Integer 7

9 7 striqonebi striqonuli mnisvnelobebi ena Haskell -Si, iseve rogorcc P relude > hello hello :: String striqoni warmoadgens simboloebis sias. ase, rom gamosaxulebebi hello, [ h, e, l, l, o ] da h : e : l : l : o : [ ] arnisnavs erti da imaves, xolo tipi String warmoadgens [Char] -is sinonims. yvela funqcia, romelic musaobs siebtan, Sei- Zleba gamoviyeniot stroqonebtanac: P relude > head hello h :: Char P relude > tail hello hello :: [Char] P relude > length hello 5 :: Int P relude > hello + +, world hello, world :: [Char] ricxviti mnisvnelobebis gardaqmnistvis striqonebad da piriqit, arsebobs funqciebi read da show: P relude > show 1 1 :: [Char] P relude > F ormula + +show 1 F ormula1 :: [Char] P relude > 1 + read :: Integer im SemTxvevaSi, Tu funqcia show ver gardaqmnis striqons ricxvad, gamodis Secdoma. 8 funqciebi Cven aqamde viyenebdit ena Haskell -is standartul funqciebs. vnaxot, rogor SeiZleba ganisazrvros momxmareblis funq- 8

10 ciebi. ganvixilot interpretatoris ramdenime brzaneba (gavixsenot, rom SesaZlebelia am brzanebebis Semokleba ert asomde). brzaneba : load sasualebas izleva CaitvirTos Haskell programa mocemuli failidan. brzaneba : edit usvebs bolo CatvirTuli failis redaqtirebis process. brzaneba : reload Tavidan kitxulobs bolos CatvirTul fails. momxmareblis mier gansazrvruli funqcia unda iyos failsi, romelic CaitvirTeba Hugs interpretatorit brzaneba : load -is sasualebit. CatvirTuli failis redaqtirebistvis Sei- Zleba gamoviyenot brzaneba : edit. is gausvebs gare redaqtors (SeTanxmebis principit - es aris N otepad). redaqtirebis procesis damtavrebis Semdeg aucilebelia davxurot redatori. Tumca, faili SeiZleba SevcvaloT usualod W indows operaciuli sistemis garsidan. am SemTxvevaSi, imistvis rom interpretatorma Tavidan waikitxos faili, sawiroa cxadad gamovizaxot brzaneba : reload. ganvixilot magaliti. SevqmnaT romelirac katalogsi faili lab1.hs. davusvat, am failis sruli gzaa - :\labs\lab1.hs. Hugs interpretatorsi SevasruloT Semdegi brzaneba: Prelude>:load "c:\\labs\\lab1.hs" Tu CatvirTva warmatebit damtavrda, interpretatoris mosawvevi icvleba Main > -it. saqme imasia, rom Tu ar mivu- TiTebT modulis saxels, itvleba, rom is aris M ain. Main>:edit aq unda gaixsnas redaqtoris fanjara, romelsic unda SevitanoT programis teqsti. SevitanoT: x = [1,2,3] SevinaxeT faili da davxurot redaqtori. interpretatori Hugs CatvirTavs fails :\labs\lab1.hs da exla x cvladis mnisvneloba iqneba gansazrvruli: 9

11 Main>x [1,2,3] :: [Integer] yuradreba mivaqciot, rom failis saxelis Cawerisas : load brzanebis argumentsi sombolo \ dublirdeba. iseve, rogorc ena C -Si, ena Haskell -Sic simbolo \ it iwyeba mosamsaxure simboloebi ( \n da a.s.). TviTon simbolo \ is gamoyenebistvis sawiroa kidev erti \ is mititeba, iseve, rogorc C enasia. gadavidet funqciis gansazrvraze. zemot arwerili procesis Sesabamisad SevqmenaT raime faili da CavweroT massi Semdegi teqsti: square :: Integer -> Integer square x = x * x pirveli striqoni square (square :: Integer > Integer) miu- TiTebs, rom Cven Semogvaqvs funqcia square s gansazrvreba, romlis parametria Integer tipis da abrunebs Integer tipis mnisvnelobas. meore striqoni (square x = x x) warmoadgens usualod funqciis arweras. funqcia square Rebulobs ert arguments da abrunebs mis kvadrats. funqciebi ena Haskell Si warmoadgenen pirveli klasis mnisvnelobebs. es nisnavs, rom isini arian Tanabaruflebiani iseti mnisvnelobebis, rogoricaa mteli da namdvili ricxvebi, simboloebi, striqonebi, siebi da a.s. funqciebi SeiZleba gadaeces sxva funqciebs argumentad, dabrundes rogorc mnisvnelobebi da a.s. iseve rogorc yvela mnisvnelobas Haskell Si, funqciasa aqvs tipi. funqciis tipi, romelic irebs a tipis mnisvnelobas da abrunebs b tipis mnisvnelobas, arinisneba ase: a > b. Seqmnili faili CavtvirToT interpretatorsi da SevasruloT Semdegi brzanebebi: Main>:type square square :: Integer -> Integer Main>square 2 4 :: Integer SevniSnoT, rom square funqciis tipis gamocxadeba ar iyo aucilebeli: interpretators TviTon SeuZlia aucilebeli informaciis gamoyvana funqciis tipis Sesaxeb misi arweridan. Tumca, jer erti, gamoyvanili tipi iqneboda ufro didi, 10

12 vidre Integer > Integer, meorec, Haskell enaze programirebisas funqciis tipis cxadad mititeba itvleba karg tonad, radganac tipis gamocxadeba emsaxureba rarac azrit funqciis dokumentacias da exmareba programirebis Secdomebis gamovlenas. momxmareblia mier gansazrvruli funqciebisa da cvladebis saxelebi unda iwyebodes patara (qveda registris) latinuri asoebit. saxelebsi sxva simboloebi SeiZleba iyos didi an patara latinuri asoebi, cifrebi an simbolo _ da (xazgasma da apostrofi). ase, rom qvemot CamoTvlilia cvladebis swori saxelebi: var var1 variablename variable_name var 9 pirobiti gamosaxulebebi ena Haskell Si funqciis gansazrvrebisas SesaZlebelia gamoyenebuli iyos pirobiti gamosaxulebebi. CavweroT funqcia signum, romelic Tvlis gadacemuli argumentis nisans: signum :: Integer -> Integer signum x = if x > 0 then 1 else if x < 0 then -1 else 0 pirobiti gamosaxuleba Caiwereba ase: if piroba then gamosaxuleba else gamosaxuleba. yuradreba gavamaxvilot imaze, rom Tumca garegnulad es gamosaxuleba hgavs C an P ascal enebis operators, ena Haskell Si aucileblad unda iyos rogorc then, aseve else nawilebi. gamosaxulebebi pirobiti operatoris then da else nawilebsi aucileblad ertidaigive tipis unda iyos. piroba pirobiti operatoris gansazrvrebasi warmoadgens nebismier Bool is tipis gamosaxulebas. aseti gamosaxulebebis magalitad gamodgeba Sedareba. Sedarebisas SeiZleba gamoviyenot Semdegi operatoebi: 11

13 <, >, <=, >= am operatorebs igive azri aqvt, rac ena C -Si (naklebia, metia, naklebia da tolia, metia da tolia). == tolobaze Sedarebis operatori. /= utolobaze Sedarebis operatori. Bool is tipis gamosaxulebebi SeiZleba gavaertianot logikuri funqciebit && da ( da da an ), da uaryofis funqciit not. dasasvebi pirobebis magalitebia: x >= 0 && x <= 10 x > 3 && x /= 10 (x > 10 x < -10) && not (x == y) ra Tqma unda, SesaZlebelia ganvsazrvrot funqciebi, romlebic abruneben Bool is tipis mnisvnelobebs da gamoviyenot isini pirobebad. magalitad, SesaZlebelia ganvsazrvrot funqcia isp ositive, romelic abrunebs T rue s, Tu misi argumenti aris arauaryofiti da F alse winaarmdeg SemTxvevaSi: ispositive :: Integer -> Bool ispositive x = if x > 0 then True else False exla funqia signum SeiZleba ganisazrvros Semdegnairad: signum :: Integer -> Integer signum x = if ispositive x then 1 else if x < 0 then -1 else 0 SevniSnoT, rom funqcia isp ositive SeiZleba ganisazrvros ufro martivad: ispositive x = x > 0 10 mravalcvladiani funqciebi da funqciebis gansazrvris rigi aqamde Cven ganvsazrvravdit ertargumentian funqciebs. ra Tqma unda, askell enasi SesaZlebelia ganvsazrvrot funq- 12

14 ciebi, romlebic ireben nebismieri ricxvis argumentebs. funqcia add is gansazrvras, romelic irebs or mtel ricxvs da abrunebs mat jams, aqvs saxe: add :: Integer -> Integer -> Integer add x y = x + y funqcia add is tipi gamoiyureba ucnaurad. Haskell enasi itvleba, rom operacia asociatiuria marjvnidan. ase, rom add funqciis tipi SeiZleba ase wavikitxot Integer (Integer Integer), anu karirebis wesebis mixedvit, add funqciis gamoyenebis Sedegi ert argumenttan iqneba funqcia, romelic miirebs Integer tipis ert parametrs. sazogadod, funqciis tipi, romelic Rebulobs n arguments, romlebic ekutvnis t1, t2,..., tn, tipebs da abrunebs a tipis Sedegs, Caiwereba saxit t1 t2... tn a. sawiroa gavaketot kidev erti SeniSvna funqciebis gansazrvris rigis Sesaxeb. wina paragrafsi Cven ganvsazrvret ori funqcia signum da isp ositive, amatgan erti matgani iyenebda Tavis gansazrvrebasi meores. ismis kitxva, romeli matgani unda ganisazrvros adre? TiTqosda isp ositive is gansazrvreba unda uswrebdes signum is gansazrvrebas, magram Haskell enasi funqciebis gansazrvris rigs ar aqvs mnisvneloba! ase, rom funqcia isp ositive SeiZleba ganisazrvros rogorc signum funqciis gansazrvramde, ise mis Semdeg. 11 laboratoriuli davalebebi moiyvanet aratrivialuri gamosaxulebebis magalitebi, romlebic ekutvnis tipebs: 1. ((Char, Integer), String, [Double]) 2. [(Double, Bool, (String, Integer))] 3. ([Integer], [Double], [(Bool, Char)]) 4. [[[(Integer, Bool)]]] 5. (((Char, Char), Char), [String]) 13

15 6. (([Double], [Bool]), [Integer]) 7. [Integer, (Integer, [Bool])] 8. (Bool, ([Bool], [Integer])) 9. [([Bool], [Double])] 10. [([Integer], [Char])] am magalitis motxovna gamosaxulebebis aratrivialurobis Sesaxeb nisnavs, rom gamosaxulebebsi monawile siebi unda Seicavdnen ert elementze mets. 2. gansazrvret Semdegi funqciebi: 1) funqcia max3, romelic sami mteli ricxvidan abrunebs mat Soris udidess. 2) funqcia min3, romelic sami mteli ricxvidan abrunebs mat Soris umciress. 3) funqcia sort2, romelic ori mteli ricxvidan abrunebs wyvils, romelsic pirvel adgilas dgas am ori ricxvidan umciresi, meoreze ki udidesi. 4) funqcia botht rue :: Bool > Bool > Bool, romelic abrunebs T rue s, masin da mxolod masin, roca orive argumenti aris T rue. funqciis gansazrvrisatvis ar gamoiyenot logikuri operaciebi (&&, da a.s.) 5) funqcia solve2 :: Double > Double > (Bool, Double), romelic ori ricxvis mixedvit, romlebic warmoadgenen ax + b = 0 wrfivi gantolebis koeficientebs, abrunebs wyvils, romlis pirveli elementi aris T rue, Tu arsebobs amonaxsni da F alse winaarmdeg SemTxvevaSi; wyvilis meore elementi ki aris an fesvis mnisvneloba, an ) funqcia isp arallel, romelic abrunebs T rue s, Tu ori monakveti, romlebic warmoadgenen funqciis argumentebs, aris paraleluri (an devs ert wrfeze). magalitad, mnisvneloba gamosaxulebisa isp arallel (1, 1)(2, 2)(2, 0)(4, 2) aris T rue, vinaidan monakvetebi (1, 1) (2, 2) da (2, 0) (4, 2) paraleluria. 7) funqcia isincluded, romlis argumentebia sibrtyeze ori wrewiris parametrebi (centris koordinatebi da radiusebi); funqcia abrunebs T rue s, Tu meore wrewiri mtlianad Tavsdeba pirvelis SigniT. 14

16 8) funqcia isrectangular, romelic parametrad Rebulobs sibrtyeze sami wertilis koordinatebs da abrunebs T rue s, Tu mat mier Sedgenili samkutxedi aris martkutxa samkutxedi. 12 sakontrolo SekiTxvebi 1. rit gansxvavdeba interpretatoris brzanebebi Haskell is gamosaxulebebisgan? 2. ena Haskell is ZiriTadi tipebi. 3. kortejebtan musaobis funqciebi. 4. siebtan musaobis funqciebi. 5. cvladebisa da funqciebis dasasvebi saxelebi. 6. interpretatoris brzanebebi programebis failebtan samusaod. 7. pirobiti gamosaxulebebi ena Haskell Si. 8. funciebis gansazvreba ena Haskell Si 15

17 leqcia # 2 1 samusaos mizani rekursiuli funqciebis gansazrvra. nimustan Sedarebis meqanizmis gacnoba. siebtan musaobis unar Cvevebis SeZena. 2 komentarebi cxadia, rom aucilebelia programasi komentarebis arseboba. Haskell enasi, iseve, rogorc C + + Si, arsebobs ori tipis komentari: striqonuli da blokis. striqonuli komentari iwyeba simboloebit da grzeldeba striqonis bolomde. analogiurad, C + + Si striqonuli komentari iwyeba // simboloebit. blokuri komentari iwyeba simboloebit { da grzeldeba simboloebamde }. analogiurad, C + + Si komentarebi SemosazRvrulia simboloebit / da /. igulisxmeba, rom komentari ignorirdeba askell interpretatoris mier. magalitad, fx = x es aris komentari gxy = {- esec komentaria, mxolod grzeli komentaria - } x + y 3 rekursia programirebis imperatiul enebsi ZiriTad konstruqcias warmoadgens cikli. ena askell Si ciklebis nacvlad gamoiyeneba rekursia. funqcias ewodeba rekursiuli, Tu is izaxebs Tavis Tavs (anu, ufro zustad, gansazrvrulia Tavisive terminebsi). 1

18 rekursiuli funqciebi arsebobs imperatiul enebsic, magram ase fartod ar gamoiyeneba. ert erti rekursiuli funqcias warmoadgens faqtoriali: factorial :: Integer -> Integer factorial n = if n == 0 then 1 else n * factorial (n - 1) (SevniSnoT, rom Cven vwert factorial (n 1) da ara factorial n1 operaciebis prioritetebis Sesabamisad.) rekursiis gamoyenebam SeiZleba gamoiwvios sirtuleebi. rekursiis koncefcia Segvaxsenebs induqciuri damtkicebis xerxs, romelic matematikasi gamoiyeneba. faqtorialis ganmartebasi gamovyavit induqciis baza (SemTxveva n == 0) da induqciis biji (gadasvla f actorial n-dan f actorial (n 1) -ze). am komponentebis gamoyofa mnisvnelovani nabijia rekursiuli funqciebis gansazrvrisas. 4 amorcevis operacia da gamartvis wesebi Cven ukve ganvixilet n == 0 pirobiti operatori. exla ganvixilot amorcevis operatori case, romelic aris ena C-is switch konstruqciis analogi. davusvat, sawiroa funqciis gansazrvra, romelic abrunebs 1-s, Tu mas gadavcemt arguments 0-s; 5-s, Tu argumenti tolia 1; 2-s, Tu argumenti tolia 2-is da 1-s, yvela sxva SemTxvevaSi. ra Tqma unda, am funqciis Cawera operatori if-is sasualebitac aris Sesa- Zlebeli, Tumca gansazrvreba iqneba grzeli da bundovani. aset SemTxvevebSi gamoiyeneba case: f x = case x of 0 -> 1 1 -> 5 2 -> 2 _ -> -1 moyvanili magalitidan cxadia case operatoris sintaqsi. SevniSnoT, rom simbolo aris ena C-is default konstruqciis analogi. Tumca, unda ganisazrvros wesebi, rogor arkvevs ena Haskell-is interpretatori, Tu sad iwyeba erti SemTxveva da sad - meore. 2

19 ena Haskell-Si arsebobs teqstis struqturirebis organzomilebiani sistema (analoguri sistema gamoiyeneba far- Tod gavrcelebul ena P ython-sic). es sistema izleva sasualebas ar gamoviyenot specialuri simboloebi operatorebis gaertianebistvis, magalitad, isetebi, rogoricaa {, } da : ena C-Si. sinamdvilesi, ena Haskell-Sic SeiZleba am simboloebis gamoyeneba igive azrit. zemot moyvanili gansazrvreba SeiZleba asec Caiweros: f x = case x of { 0 -> 1; 1 -> 5; 2 -> 2; _ -> -1 } aseti Cawera cxadad gansazrvravs operatorebis dajgufebas, Tumca SeiZleba mat garesec. zogadi wesebi asetia: gasarebi sityvebis where, let, do da of Semdeg interpretatori svams gaxsnil frcxils ({) da imaxsovrebs svets, romelsic Semdegi brzaneba aris Cawerili. SemdgomSi, yoveli axali striqonis win, romelic gasworebulia damaxsovrebuli sididit, Caismeba gamyofi simbolo ;. Tu Semdegi striqoni naklebad aris gasworebuli (anu misi pirveli simbolo aris damaxsovrebuli poziciis marcxniv), masin Caismeba daxuruli frcxili (}). Tu am wess gamoviyenebt zemot arweril f funqciastan, mivirebt, rom interpretatori ariqvams mas Semdegnairad: f x = case x of{ ;0 -> 1 ;1 -> 5 ;2 -> 2 ;_ -> -1 } nebismier SemTxvevaSi SeiZleba cxadad miutitot simboloebi {, } da ;, Tumca am dros teqsti naklebad wakitxvadia da mat gamoyenebas laboratoriul mecadinoebebze ar gircevt. kidev erti SeniSvna. vinaidan Haskell enis programistvis cariel ujredebs aqvt mnisvneloba, amitom sawiroa yuradreba tabulaciis simbolostanac. interpretatori Tvlis, rom tabulaciis simbolo tolia 8 carieli ujredisa (simbolosi). Tumca, zogierti teqsturi redaqtori izleva tabulaciis 3

20 simbolos gansazrvris sasualebas da xdis mas sxva ricxvis tolad (magalitad, V isualstudio- redaqtorsi gacumebis principit tabulacia aris 4 carieli ujredi (simbolo)). aman SeiZleba gamoiwviot Secdomebi, amitomac sjobs ena Haskellze programirebisas ar gamoiyenot tabulaciis simboloebi. 5 uban-uban mocemuli funqciebi funqcia SeiZleba ganisazrvros uban-uban. es nisnavs, rom funqciis erti versia SeiZleba ganisazrvros gansazrvruli parametrebistvis, meore versia - sxva parametrebistvis. ase, rom wina paragrafsi moyvanili f funqcia SeiZleba ganisazrvros Semdegnairadac: f 0 = 1 f 1 = 5 f 2 = 2 f _ = -1 am SemTxvevaSi mnisvneloba aqvs funqciis gansazrvris rigs. Tu Cven Tavdapirvelad CavwerT gansazrvrebas f _ = -1, masin f funqcia daabrunebs mnisvnelobas 1-s nebismieri argumentistvis. Tu am striqons saertod ar mivutitebt, mivirebt Secdomas argumentistvis, romelic ar aris toli 0-is, 1- is an 2-is. funqciis gansazrvris aseti ssualeba xsirad gamoiyeneba askell-si. is nawilobriv izleva sasualebas ar gamoviyenot operatorebi if da case. ase, rom funqcia faqtoriali SeiZleba ganisazrvros aseti stilitac: factorial 0 = 1 factorial n = n * factorial (n - 1) 6 nimustan Sedareba iseve, rogorc SesaZlebelia rekursiuli funqciebi ganisazrvros mtel ricxvebze, aseve SesaZlebelia ganisazrvros siebzec. 4

21 am SemTxvevaSi, rekursiis baza iqneba carieli sia ([]). ganvsazrvrot siis sigrzis gamotvlis funqcia (vinaidan saxeli length ukve dakavebulia standartul bibliotekasi, funqcias davarqvat len): len [] = 0 len s = 1 + len (tail s) gavixsenot, rom sia, romlis pirveli elementi (siis Tavi) aris x, xolo danarcen elementebs (siis kudi) warmoadgens xs, Caiwereba rogorc x : xs. amgvari konstruqcia SesaZloa gamoyenebuli iyos funqciis arwerisas: len [] = 0 len (x:xs) = 1 + len xs moviyvanot kidev erti magaliti. funqcia, romelic Sesasvlelze Rebulobs ricxvebis wyvils da abrunebs mat jams, SeiZleba ase ganisazrvros: sum_pair p = fst p + snd p Tumca, rogor moviqcet, Tu sawiroa ganisazrvros funqcia, romelic Rebulobs ricxvebis sameuls da abrunebs mat jams? Cven ar gvaqvs f st da snd funqciebis msgavsi funqciebi sameulebidan elementebis amosarebad. armocnda, rom aseti funqciebi Sei- Zleba Caiweros Semdegnairad: sum_pair (x,y) = x + y sum_triple (x,y,z) = x + y + z aset xerxs uwodeben nimustan Sedarebas (pattern matching). igi warmoadgens enis Zalze Zlier konstruqcias. nimusebi Caiwereba funqciis argumentebad da Sedardeba funqciaze gadacemul faqtiur parametrebs. rodesac xdeba nimustan Sedareba, massi monawile cvladebi Rebuloben Sesabamis mnisvnelobebs. Tu es mnisvnelobebi funqciis gamotvlistvis ar aris sawiro (magalitad, funqcia my_tail Semdeg magalitsi), masin zedmeti saxelebis Semotanis nacvlad SeiZleba gamoyenebuli iyos simbolo _. igi arnisnavs nimuss, romelsac Seesabameba nebismieri mnisvneloba, TviTon es mnisvneloba ki arcert cvlads ar ukavsirdeba. Semdegi magalitebi ucveneben nimustan Sedarebis gamoyenebis sxvadasxva variantebs: 5

22 -- funqcia, romelic Sekrebs siis pirvel or \geoac wevrs f1 (x:y:xs) = x + y -- funqciis gansazrvreba, romelic head-is analogia my_head (x:xs) = x -- funqciis gansazrvreba, romelic tail-is analogiuria. -- Cven viyenebt simbolo _-s imitom, rom siis -- pirveli elementis mnisvneloba ar aris sawiro my_tail (_:xs) = xs -- funqcia, romelic irebs pirvel wevrs sameulidan fst3 (x,_,_) = x nimustan Sedareba SeiZleba gamoyenebuli iyos operatorsi case: -- siis sigrzis gansazrvris kidev erti funqcia my_length s = case s of [] -> 0 (_:xs) -> 1 + my_length xs SeiZleba sakmaod rtuli nimusebis gansazrvra. ganvsazrvrot funqcia, romelic irebs ricxvta wyvilebs da abrunebs mati sxvaobebis jams ( anu f[(x1, y1), (x2, y2),..., (xn, yn)] = (x1 y1) + (x2 y2) (xn yn)): f [] = 0 f ((x,y):xs) = (x - y) + f xs 7 siebis ageba im funqciebis gansazrvristvis, romlebic abruneben siebs, xsirad gamoiyeneba operatori :. magalitad, funqcia, romelic Rebulobs ricxvebis sias da abrunebs am ricxvebis kvadratebs, SeiZleba ase ganisazrvros: square [] = [] square (x:xs) = x*x : square xs 6

23 8 zogierti sasargeblo funqciebi laboratoriuli funqciebis Sesrulebisas SesaZloa dag- WirdeT Haskell enis Semdegi standartuli funqciebi: even --- abrunebs True-s luwi argumentistvis da False-s kentebistvis. odd --- winas analoguri, mxolod argumens amowmebs kentobaze. 9 davalebebi 1. gansazrvret funqcia, romelic Sesasvlelze Rebulobs mtel ricxvs n-s da abrunebs sias, romelic Sedgeba n elementisgan, dalagebuls zrdadobit. 1. naturaluri ricxvebis sia. 2. kenti naturaluri ricxvebis sia. 3. luwi naturaluri ricxvebis sia. 4. naturaluri ricxvis kvadratebis sia. 5. faqtorialebis sia is xarisxebis sia. 7. samkutxeduris ricxvebis sia. (ganmarteba: n-uri samkutxeduri ricxvi tn tolia ertnairi monetebis raodenobisa, romlebidanac SeiZleba Sedges tolgverda samkutxedi, romlis TiToeul gverdzec daideba n moneta. cxadia, rom t 1 = 1 da t n = n + tn 1). 8. piramidaluri ricxvebis sia. (ganmarteba: n-uri piramidaluri ricxvi pn tolia ertnairi burtebis raodenobisa, romlebidanac SeiZleba aigos swori piramida samkutxedis ZiriT, romlis TiToeul gverdzec daideba n burti. cxadia, rom p 1 = 1 da = tn + pn 1). 7

24 2. gansazrvret Semdegi funqciebi: 1. funqcia, romelic Sesasvlelze Rebulobs namdvil ricxvebs da itvlis mat sasualo aritmetikuls. SeecadeT, rom funqciam mxolod ertxel gadaxedos sias. 2. funqcia gamoyofs mocemuli siis n wevrs. 3. ori siis elementebis ajamvis funqcia. abrunebs sias, romelic Sedgeba parametri siebis elementebis jamisgan. gaitvaliswinet, rom gadacemuli siebi SeiZleba iyos sxvadasxva sigrzis. 4. funqcia, romelic aadgilebs mocemul siasi mezobel luw da kent elementebs. 5. funqcia twopow n, romelic itvlis 2 n Semdegi mosazrebebidan gamomdinare. davusvat sawiroa aviyvanot 2 xarisxsi. Tu n luwia, anu n = 2k, masin 2 n = 2 2k = (2 k ) 2. Tu n kentia, anu n = 2k + 1, masin 2 n = 2 2k+1 = 2(2 k ) 2. funqciam twopow ar unda gamoiyenos operatori ˆ an sxva funqcia standartuli bibliotekidan, romelic itvlis xarisxs. funqciis rekursiuli gamozaxebebi unda iyos logn-is proporciuli. 6. funqcia removeodd, romlic mocemuli mteli ricxvebis siidan amoslis yvela kent ricxvs. magalitad, removeodd [1, 4, 5, 6, 10] unda daabrunos [4, 10]. 7. funqcia removeempty, romelic amoagdebs cariel striqonebs striqonebis mocemuli siidan. magalitad, removeempty [, Hello,,, W orld! ] unda daabrunos [ Hello, W orld! ]. 8. funqcia countt rue :: [Bool] > Integer, romelic abrunebs siis im elementebis raodenobas, romlebic aris T rue-s toli. 9. funqcia makep ositive, romelic ucvlis nisans ricxvebis siis yvela uaryofit elements. magalitad, makep ositive [ 1, 0, 5, 10, 20] gvazlevs [1, 0, 5, 10, 20]. 10. funqcia delete :: Char > String > String, romelic irebs Sesasvlelze striqons da simbolos da abrunebs striqons, 8

25 romlidanac amoslilia mocemuli simbolo. magali- Tad, delete l Hello world! unda daabrunos Heo word!. 11. funqcia substitute :: Char > Char > String > String, romelic cvlis mocemul simbolos meore somboloti. magalitad, substitute e i eigenvalue abrunebs iiginvalui. 10 sakontrolo SekiTxvebi 1. gasworebis wesebi. 2. Sedareba nimustan. 3. amorcevis operacia. 4. funqciis fragmentuli mocema. 9

26 leqcia # 3 1 let-dakavsireba funqciis arwerisas xsirad aucilebelia gamoviyenot droebiti cvladebi Sualeduri mnisvnelobebis Sesanaxad. gavixsenot, Tu rogor vitvlit ax2 + bx + c = 0 kvadratuli gantolebis fesvebs x 1,2 = ( b ± b 2 4ac)/2a SeiZleba Caiweros funqcia kvadratuli gantolebis fesvebis gamosatvlelad: roots a b c = ((-b + sqrt (b*b - 4*a*c)) / (2*a), (-b - sqrt (b*b - 4*a*c)) / (2*a)) aseti stilit programis dawera ramdenime problemas Seicavs. jer erti, SeiZleba advilad davusvat Secdoma er- Tidaigive gamosaxulebis orjer dawerisas. meore, am programis dawerisas sawiroa SevadaroT ori gamosaxuleba, rom davrwmundet, rom ertidaigivea. mesame, programa ufro grzeli xdeba. da bolos, is naklebad efeqturia, vinaidan kompiuteri itvlis ertidaigive gamosaxulebas orjer. am problebis asacileblad enasi Semotanilia lokaluri cvladis cneba. funqcia SeiZleba Caiweroas ase: roots a b c = let det = sqrt (b*b - 4*a*c) in ((-b + det / (2*a), (-b - det / (2*a)) lokaluri cvladi det mirwevadia mxolod roots funqciis gansazrvrebasi. SeiZleba ramdenime lokaluri funqcia ganvsazrvrot: roots a b c = let det = sqrt (b*b - 4*a*c) 1

27 twice_a = 2*a in ((-b + det) / twice_a, (-b - det) / twice_a) SevniSnoT, rom konstruqciasi let...in... gamoiyeneba gasworebis wesebi: xarvezisgan gansxavebuli pirveli simbolo, romelic mosdevs sityva let-s, asaxelebs svets, romlis mixedvitac unda gaswordes Semdgomi gansazrvrebebi. Tu gamoviyenebt simboloebs, da ;, masin gasworebis wesebi arar iqneba aucilebeli da masin funqcia roots SeiZleba ase Caiweros: roots a b c = let { let = sqrt (b*b - 4*a*c); twice_a = 2*a } in ((-b + det) / twice_a, (-b - det) / twice_a) let...in... komstruqciis garda, zogjer mosaxerxebelia...where... konstruqciis gamoyeneba. am konstruqciisas lokaluri cvladebis gamoyeneba mosdevs ZiriTad funqcias: roots a b c = ((-b + det) / twice_a, (-b - det) / twice_a) where det = sqrt (b*b - 4*a*c) twice_a = 2*a SevniSnoT, rom nacvlad lokaluri cvladis Semotanisa, SeiZleba gagvesazrvra globaluri funqcia: det a b c= sqrt (b*b - 4*a*c) twice_a a = 2*a roots a b c = ((-b + det a b c) / twice_a a, (-b - det a b c) / twice_a a) Tumca, am midgomis nakli TvalsaCinoa: SemovitaneT globalur saxelta aresi ori damxmare funqcia (es ki imas nisnavs, rom Cven arar gveqneba ufleba gamoviyenot, magali- Tad, saxeli det sxva funqciistvis), aseve gamosaxulebebis b 2 4ac da 2a gamosatvlelad unda gadavcet funqcias Sesabamisi 2

28 parametrebi, masin, roca lokalur cvladebs Tavisuflad SeuZliaT im funqciis parametrebis gamoyeneba, romlistvisac isini arian gansazrvruli. konstruqciebsi let da where SeiZleba ganisazrvros ara mxolod cvladebi, aramed funqciebic. ganvixilot, magali- Tad, funqcia, romelic abrunebs mocemuli n ricxvis mixedvit naturaluri ricxvebis sias [1,2,...,n]. SemovitanoT damxmare funqcia numsrom, romelic mocemuli m ricxvis mixedvit abrunebs sias [m, m + 1, m + 2,..., n] da ganvsazrvrot igi, rogorc lokaluri funqcia: numsto n = let numsfrom m = if m == n then [m] else m:numsfrom (m + 1) in numsfrom 1 SevniSnoT, rom funqcia numsf rom Tavis gansazrrebasi iyenebs cvlads n, Tumca mas igi ar gadaecema parametrad. 2 signalizacia Secdomebis Sesaxeb Cvens mier gansazrvruli funqciebi SeiZleba ar iyos gamotvladi argumentebis zogierti mnisvnelobistvis. gavixsenot funqcia faqtorialis ganmarteba: factorial 0 = 1 factorial n = n * factorial (n - 1) es funqcia swored musaobs manam, sanam ar SevecdebiT gamovtvalot uaryofiti ricxvis faqtoriali. rtuli ar aris mivxvdet, rom am dros rekursia usasrulod grzeldeba, imitom rom bazuri SemTxveva arasdros miirweva. aseti Secdomebis Sesaxeb Setyobinebis martivi sasualebaa standartuli funqcia error-is gamoyeneba. es funqcia argumentad irebs striqons, misi gamotvla ki iwvevs programis damtavrebas da am striqonis gamotanas ekranze. amrigad, funqcia ase CavweroT: factorial 0 = 1 factorial n = if n > 0 then n * factorial (n - 1) else error "factorial: negative argument" 3

29 3 damcavi pirobebi nimustan Sedareba izleva funqciis gansazrvrebis did Sesa- Zloblebebs, Tumca misi sasualebit ara mxolod funqciistvis gadasacemi parametrebis struqturis gamoyofa da am elementebis Sedareba aris SesaZlebeli parametrebis konstantur mnisvnelobebtan. Tumca, zogjer es ar aris sakmarisi: aucilebelia Sesasvlel parametrebs daedot ufro rtuli pirobebi. magalitad, funqcia f actorial-is zemot moyvanil magalitsi Cven gamoviyenet nimustan Sedarebisa da pirobiti operatoris kombinacia. nimustan Sedareba gamoiyureba ufro natlad da ekonomiurad. SeiZleba Tu ara msgavsi sintaqsi gamoviyenot pirobistvisac? diax, Tu gamoviyenebt damcvel pirobebs. mati gamoyenebit faqtorialis gamotvlis funqcia ase Caiwereba: factorial 0 = 1 factorial n n < 0 = error "factorial: negative argument" n >= 0 = n * factorial (n - 1) moyvanili magalitidan Cans gamosaxulebis Caweris sintaqsi. SevniSnoT, rom bolo pirobis nacvlad SeiZleba gamoyenebuli iyos gasarebi sityva otherwise (inglisurad-winaarmdeg SemTxvevaSi). magalitad, funqcia, romelic gansazrvravs ricxvis nisans, ase gamoiyureba: signum x x < 0 = -1 x == 0 = 0 otherwise = 1 funqciia aseti stilit ganmarteba ufro TvalsaCinoa da Haskell-is programebsi xsirad gamoiyeneba (sesabamisad, pirobiti operatori gamoiyeneba isviatad). TvalsaCinoebisTvis, ganvsazrvrot funqcia signum pirobiti operatorebis gamoyenebit: signum x = if x < 0 then -1 else if x == 0 then 0 else -1 4

30 4 polimorfuli tipebi ena Haskell-Si gamoiyeneba tipebis polomorfuli sistema. arsebitad, es nisnavs, rom enasi arsebobs tipebis cvladebi. ganvixilot, CvenTvis ukve nacnobi funqcia tail,romelic gvibrunebs siis pirvel elements. rogoria an funqciis tipi? is ertnairad gamoiyeneba rogorc mteli ricxvebis siistvis, aseve simboloebisa da striqonebis siebistvisac: Prelude>tail [1,2,3] [2,3] Prelude>tail [ a, b, c ] [ b, c ] Prelude>tail ["list", "of", "lists"] ["of", "lists"] funqcia tail-s aqvs polimorfuli tipi: [a] > [a]. es nisnavs, rom igi argumentad irebs nebismier sias da abrunebs igive tipis sias. aq a arnisnavs tipis cvlads, anu igulisxmeba, rom mis magivrad SeiZleba Caisvas nebismieri konkretuli tipi. amrigad, Canaweri [a] > [a] izleva tipebis mtel klass, romlis warmomadgenlebic aris, magalitad, [Integer] > [Integer], [Char] > [Char], [[Char]] > [[Char]] da a.s. analogiurad, funqcias tail, romelic abrunebs siis pirvel elements, aqvs tipi [a] > a. tipebis am ojaxis warmomadgenlebi arian [Integer] > Integer, [Char] > Char da a.s. siebtan, wyvilebtan da kortejebtan momusave mraval funqcias polimorfuli tipi. ase, funqcias f st-s aqvs tipi (a, b) > a (SevniSnoT, rom am tipis gansazrvrasi gamopyenebulia tipis ori cvladi). 5 momxmareblis tipebi programists aqvs SesaZlebloba standartuli tipebis gverdit gansazrvros monacemebis Tavisi sakutari, specifiuri tipebi. amistvis sawiroa gamoyenebuli iyos gasarebi sityva data. 5

31 5.1 wyvilebi magalitistvis ganvixilot wyvilebis ganmarteba, romelic zalze waagavs standartuls: d data Pair a b = Pair a b detalurad ganvixilot es kodi. gasarebi sityva data gvicvenebs, rom Cven vgegmavt monacemebis tipis gansazrvras. mas mosdevs am tipis dasaxeleba, Cven SemTxvevaSi P air (gavixsenot, rom tipebis dasaxeleba yoveltvis didi, mtavruli asoti iwyeba). a da b warmoadgenen tipebbis cvladebs, romlebic tipebis parametrebs arnisnaven. amrigad, Cven arvwerot monacemta struqtura, romelic parametrizebulia ori tipit a da b. (es Zalze waagavs ena C + +-is Sablonebs). tolobis nisnis Semdeg Cven mivutitebt am tipis monacemebis konstruqtors. am SemTxvevaSi Cven gvaqvs ertaderti konstruqtori P air. (ar aris aucilebeli monacemebis konstuqtoris saxeli emtxveodes tipis saxels, Tumca Cvens magalitsi es bunebrivia). konstruqtoris saxelis Semdeg Cven isev vwert a. es arnisnavs, rom wyvilis konstruirebistvis sawiroa ori mnisvneloba: pirveli, romelic ekutvnis a-s, meore - b-s. am ganmartebas Semoyavs funqcia P air :: a > b > P airab, romeliv gamoiyeneba P air tipis wyvilebis asagebad. CavtvirToT es kodi interpretatorsi, vnaxot, rogor iqmneba wyvilebi: Main>:t Pair Pair :: a -> b -> Pair a b Main>:t Pair a Pair a :: a -> Pair Char a Main>:t Pair a "Hello" Pair a "Hello" :: Pair Char [Char] monacemebis konstruqtorebis Sesabamis funqciebs axasitebt is Tviseba, rom SeiZleba mati gamoyeneba nimustan Sedarebisas. ase, rom funqciebi, romlebitac vrebulobt Cveni wyvilistvis pirvel da meore elements, SeiZleba ganimartos Semdegnairad: pairfst (Pair x y) = x pairsnd (Pair x y) = y 6

32 gamxiluli magaliti iwvevs aset SekiTxvas: ristvisaa sawiro sakutari P air tipis gansazrvra, roca aris wyvilebis gansazrvris standartuli sasualeba? jer erti, P air tipis gamoyenebit SeiZleba ganisazrvros funqciata nakrebi, romelic mxolod am tiptan musaobs da gamoiyos es funqciebi im funqciebisgan, romlebic zogadad musaoben wyvilebta. meorec, wyvilebis misarebas SeiZleba daedos SezRudvebi, romelic ver moxerxdeba standartuli tipistvis. magakitad, warmoidginet, rom sawiroa tipi, romelic Seqmnis wyvils ertidaigive tipis elementebisgan. es tipi SeiZleba ase ganisazrvros: data SamePair a = SamePair a a aq tips aqvs erti parametri, Tumca monacemebis konstruqtori irebs erti da imave tipis or parametrs. 5.2 mravlobiti konstruqtorebi wina magalitsi Cven ganvixilet monacemta tipi erti konstruqtorit. aseve, SesaZlebelia da xsirad Zalze sasargebloa ganisazrvros tipi ramdenime konstruqtorit. konstruqtorebi ertmanetisgan gamoiyofa simboloti. ganvixilot tipi Color, romelic warmoadgens fers SesaZlo mnisvnelobebit Red, Green da Blue. igi SeiZleba ase ganisazrvros: data Color = Red Green Blue aq Color aris tipis dasaxeleba, xolo Red, Green da Blue monacemebis konstruqtorebi. SevniSnoT, rom es tipi ar Rebulobs parametrebs. aset tipebs uwodeben CamoTvlad tipebs da igi Seesabameba ena C + +-is enum konstruqcias. aseti tipebi zalze sasargebloa. magalitad, standartuli tipi Bool ase ganisazrvreba: data Bool = True False mravlobitma konstruqtorebma, aseve, SeiZleba miiron parametrebi. SevniSnoT, rom tipi Color sasualebas gva- Zlevs ganvsazrvrot mxolod sami fiqsirebuli feri. gavafartovot igi ise, rom mas SeeZlos gansazrvros nebismieri feri, mocemuli sami mteli ricxvit, romlebic Seesabameba 7

33 witeli, mwvane da lurji ferebis doneebs (standartuli rgb warmodgena): data Color = Red Green Blue RGB Int Int Int aq tipi Color standartuli ferebis Red, Green da Blue garda (es sia, ra Tqma unda, SeiZleba gafartovdes), SeiZleba ganisazrvros RGB konstruqtoris sasualebit, romelic Rebulobs sam mtel ricxvs rgb komponentebis gansasazrvrad. masin, magalitad, funqcia, romelic gamoyofs feris Red komponents, SeiZleba ase Caiweros: redcomponent :: Color -> Int redcomponent Red = 255 redcomponent (RGB r ) = r redcomponent _ = 0 mravalkonstruqtoriani tipebi, aseve, SeiZleba iyos polimorfuli. ganvixilot Semdegi problema. davusvat, funqcia abrunebs raime mnisvnelobas, an izleva Setyobinebas Secdomis Sesaxeb. magalitad, wrfivi gantolebis fesvebis povnis funqcia abrunebs napovn fesvebs; funqcia, romelic ezebs siasi pirvel arauaryofit ricxvs, abrunebs am ricxvs da a.s. amastan, gantolebis amoxsna SeiZleba ar arsebobdes, siasi ar iyos arauaryofiti ricxvebi da a.s. rogor moxdes amis Setyobineba imistvis, vinc funqcia gamoizaxa? zogjer, SesaZloa SeTanxmeba, rom romelime specialuri mnisvneloba (magalitad, 1) nisnavdes, rom ar aris Sedegi (C enis standartuli bibliotekis bevri funqcia swored ase iqceva). Tumca, es yoveltvis ar aris SesaZlebeli: wrfivi gantolebis amoxsnis SemTxvevaSi aseti mnisvneloba ar arsebobs. problema ixsneba standartuli tipis M aybe-is sasualebit, romelic ase ganisazrvreba: data Maybe a = Nothing Just a tipi M aybe (inglisurad, SesaZlebelia ) parametrizirebulia tipuri cvladit a da warmodgeba ori konstruqtorit: N othing (inglisurad, araferi ) da Just (inglisurad, zustad ) azroblivi SedegisTvis. masin Cveni funqciebi Sei- Zleba ase Caiweros: 8

34 --funqcia abrunebs ax + b = 0 gantolebis fesvs solve :: Double -> Double -> Maybe Double solve 0 b = Nothing solve a b = Just (-b / a) --funqcia abrunebs siis pirvel arauaryofit elements findpositive :: [Integer] -> Maybe Integer findpositive [] = Nothing findpositive (x:xs) x > 0 = Just x otherwise = findpositive xs M aybe tipis gamoyenebas aqvs mteli rigi upiratesobebi. misi gamoyenebit cxadad mivutitebt, rom funqciam SeiZleba daabrunos aranairi Sedegi. amastan, funqciis dasabrunebeli mnisvnelobis damusavebisas sawiroa cxadad iyos Sedareba nimustan, da tu Cven dagvaviwydeba N othing SemTxvevis damusaveba, kompilerma SeiZleba mogvces gafrtxileba. 5.3 tipebis klasebi tipebis klasebi mnisvnelovnad amartivebs momxmareblis tipeb- Tan musaobas. SemdgomSi mat detalurad SeviswavliT. tipebis klasi warmoadgens tipebis gansazrvrul simravles, romlebsac mteli rigi saerto Tvisebebi aqvt. magalitad, tipebis klassi Eq Sedis yvela tipi, romlebis obieqtebistvisac gansazrvrulia tolobis mimarteba, anu, Tu x da y ekutvnis ertidaigive tips, romelic Sedis q klassi, masin SeiZleba gamovtvalot gamosaxuleba x == y da x/ = y. yvela martivi tipi, aseve siebi da kortejebi Sedis am klassi, Tumca, magalitad, funqciistvis mimarteba toloba ar aris gansazrvruli da amitom tipi funqcia ar Sedis Eq klassi. Semdegi mnisvnelovani klasia Show klasi. massi Sedis yvela tipi, romlis obieqtebi SeiZleba gardaqmnili iyos striqonsi imisatis, rom moxdes mati ekranze asaxva. martivi tipebi, kortejebi da siebi Sedis am klassi, amitom interpretators SeuZlia dabewdos, magalitad, striqoni. funqcia ar Sedis am klassi. SeTanxmebis principit momxmareblis tipebi ar Sedis arcert klassi, amitom mati mnisvnelobebis Sedareba ar SeiZleba da verc interpretatori dabew- 9

35 davs. es, ra Tqma unda, mouxerxebelia, amitom tipebis gansazrvrisas SesaZlebelia is mivakutvnot sasurvel klass. amistvis, tipis gansazrvris Semdeg sairoa daematos gasarebi sityva deriving da frcxilebsi CamovTvaloT klasebi, romlebsac unda ekutvnodes tipi. magalitad: -- tipi, romelic warmoadgens dris periodia data DayTime = Morning Afternoon Evening Night deriving (Eq, Show) davalebebsi tipebis arwerisas miakutvnet isini klasebs Eq da Show. amit gaiadvilebt samusaos. 6 davalebebi 1. Tanamedrove web maraziasi xsirad iyideba wignebi, videokasetebi da kompaqt diskebi. am maraziis monacemta baza TiToeuli saxeobis saqonlistvis unda SeicavdesSemdeg maxasiateblebs: wignebistvis: dasaxeleba da avtori videokasetebistvis: dasaxeleba kompaqt diskebistvis: dasaxeleba, Semsrulebeli da kompoziciebis raodenoba. 1) SeqmeniT monacemta tipi P roduct, romelic warmoadgens saqonlis am tipebs. 2) gansazrvret funqcia gett itle, romelic daabrunebs saqonlis dasaxelebas. 3) am funqciis safuzvelze gansazrvret funqcia gett itles, romelic saqonlis siis mixedvit daabrunebs mat dasaxelebebis sias. 4) gansazrvret funqcia bookauthors, romelic saqonlis siis mixedvit daabrunebs wignebis avtorebis sias. 5) gansazrvret funqcia lookuptitle :: String -> [Product] -> Maybe Product 10

36 romelic daabrunebs saqonels mocemuli dasaxelebit (yuradreba miaqciet funqciis Sedegis tips). 6) gansazrvret funqcia lookuptitles :: [String] -> [Product] -> [Product] is parametrad irebs dasaxelebebis sias da saqonlis sias da TiToeuli dasaxelebistvis irebs meore siidan Sesabamis saqonels. is dasaxeleba, romelsac saqoneli ar Seesabameba, ignorirdeba. funqciis gansazrvrisas savaldebuloa gamoiyenot funqcia lookupt itle. 2. gansazrvret monacemta tipi, romelic warmoadgens karts kartis TamaSisas. TiToeul karts aqvs erti masti otxi SesaZlodan. karti SeiZleba iyos dabali (oridan atis CaTvliT) an surati (valeti, dama, babua, tuzi). gansazrvret Semdegi funqciebi: 1) funqcia ism inor, romelic amowmebs, rom misi argumenti aris dabali karti. 2) funqcia samesuit, romelic amowmebs, rom mastvis gadacemuli kartebi erti mastisaa. 3) funqcia beats :: Card > Card > Bool, romelic amowmebs, rom karti, romelic pirvel argumentad gadaecema, Wris karts, romelic meore argu,mentad gadaecema. 4) funqcia beats2 analogiuria beats is, mxolod damatebit argumentad irebs koziris masts. 5) funcia beatslist,romelic argumentad irebs kartebis sias, karts da koziris masts da abrunebs im kartis sias pirveli argumentidan, romlebic Wris mocemul karts koziris gatvaliswinebit. 6) funqcia, romelic kartis mocemuli siis mixedvit abrunebs ricxvebis sias, romlebis warmoadgens mocemuli kartis Sesa- Zlo qulata jams, romelic itvleba TamaSis Tormeti ert- Si wesebis mixedvit: patara karti itvleba nominalis mixedvit, valeti, dama da babua itvleba 10 qulad, xolo tuzi an 1 an 11 qulad. funqciam unda daabrunos yvela SesaZlo variantebi. 3. gansazrvret tipi, romelic warmoadgens geometriul funqcias. figura SeiZleba iyos an wrewiri (xasiatdeba centris koordinatebit da radiusit), martkutxedi (xasiatdeba marcxena zeda da qveda marjvena kutxeebis koordi- 11

37 natebit), samkutxedi (wveroebis koordinatebi) da teqsturi veli (mistvis aucilebelia Senaxuli iqnas marcxena qveda kutxe, Srifti da striqoni, romelic warweras warmoadgens). Srifti moicema sam elementiani simravlidan: Courier, Lucida da F ixedsys. gansazrvret semdegi funqciebi: 1) funqcia area, romelic abrunebs figuris fartobs. testuri velis fartobi damokidebulia SriftSi asoebis simarlesa da siganeze. vinaidan Cvens mier arceuli Sriftebi aris monosiganis (anu yvela asos sigane ertidaigivea), CvenTvis aucilebeli iqneba ganisazrvros damxmare funqcia, romelic mocemuli SriftisTvis daabrunebs mis gabaritebs. 2) funcia getrectangles, romelic siidan mxolod martkutxedebs arcevs. 3) funqcia getbound, romelic mocemuli figuristvis abrunebs martkutxeds, romelic sazrvravs am figuras. 4) funqcia getbounds, romelic figurebis mocemuli siistvis abrunebs mati SemomsazRvreli martkutxedebis sias. 5) funqcia getf igure, mocemuli figurebis siistvis da wertilis koordinatebis mixedvit abrunebs pirvel figuras, romlistvisac wertili xvdeba mis SemomsazRvrel martkutxedsi. gamoiyenet tipi M aybe mnisvnelobis dasabruneblad. 6) funqcia move, romelic mocemuli figuristvis da Zvris veqtoristvis abrunebs axal figuras, romelic dazruli iqneba mocemuli veqtorit. 4. uzravi qonebis saagentosi iyideba binebi, otaxebi da kerzo saxlebi. bina xasiatdeba sartulit, fartobit da saxlis sartulebis raodenobit. otaxi xasiatdeba amis garda kidev fartobit (damatebit mteli binis fartobisa). kerzo saxli xasiatdeba mxolod fartobit. monacemta bazasi inaxeba mnisvnelobebis wyvilebi, romeltagan pirveli warmoadgens uzrav obieqts, meore mis fass. gansazrvret monacemta tipi, romelic warmoadgens uzravi qonebis obieqtebze informacias. gansazrvret Semdegi funqciebi: 1) gethouses, arcevs monacemta bazidan mxolod kerzo saxlebs. 2) getbyp rice, arcevs monacemta bazidan mxolod uzravi qonebis im obieqtebs, romelta fasi naklebia mititebulze. 3) getbylevel, ircevs monacemta bazidan binebs, romlebic mocemul sartulze mdebareobs. 4) getexceptbounds, ircevs monacemta bazidan binebs, romlebic ar mdebareobs pirvel da bolo sartulebze. 12