Programare declarativa - Tipuri de date algebriceold.unibuc.ro/~ileustean/files/05-adt-il.pdf ·...

Programare declarativa1

Tipuri de date algebrice

Traian Florin S, erbanut,aIoana Leus, tean

Departamentul de Informatica, FMI, [email protected]

[email protected]

1bazat pe cursul Informatics 1: Functional Programming de la University of EdinburghTraian Florin S, erbanut,a Ioana Leus, tean (UB) PD—Tipuri date algebrice 1 / 22

Tipul de date Boolean


data Bool = False | True

not : : Bool −> Boolnot False = Truenot True = False

(&&) : : Bool −> Bool −> BoolFalse && q = FalseTrue && q = q

( | | ) : : Bool −> Bool −> BoolFalse | | q = qTrue | | q = True



Definirea egalitat, ii s, i a reprezentariiEq s, i Show

Eq

eqBool : : Bool −> Bool −> Bool

eqBool False False = TrueeqBool True True = TrueeqBool _ _ = False

Show

showBool : : Bool −> String

showBool False = " False "showBool True = " True "




Eq

eqBool : : Bool −> Bool −> BooleqBool False False = TrueeqBool True True = TrueeqBool _ _ = False

Show

showBool : : Bool −> StringshowBool False = " False "showBool True = " True "


Anotimpuri

Anotimpuri

data Season = Spring | Summer | Autumn | Winter

next : : Season −> Seasonnext Spring = Summernext Summer = Autumnnext Autumn = Winternext Winter = Spr ing


Anotimpuri


eqSeason : : Season −> Season −> BooleqSeason Spr ing Spr ing = TrueeqSeason Summer Summer = TrueeqSeason Autumn Autumn = TrueeqSeason Winter Winter = TrueeqSeason _ _ = False

showSeason : : Season −> StringshowSeason Spr ing = " Spr ing "showSeason Summer = "Summer"showSeason Autumn = " Autumn "showSeason Winter = " Winter "


Anotimpuri

Enumerari s, i indici

data Season = Winter | Spr ing | Summer | F a l lto In t : : Season −> I n tto In t Winter = 0to In t Spring = 1to In t Summer = 2to In t F a l l = 3

fromInt : : I n t −> SeasonfromInt 0 = WinterfromInt 1 = SpringfromInt 2 = SummerfromInt 3 = F a l l

next : : Season −> Season

next x = fromInt ( ( to In t x + 1) ‘mod‘ 4)

eqSeason : : Season −> Season −> Bool

eqSeason x y = ( to In t x == to In t y )


Anotimpuri

Enumerari s, i indici

data Season = Winter | Spr ing | Summer | F a l lto In t : : Season −> I n tto In t Winter = 0to In t Spring = 1to In t Summer = 2to In t F a l l = 3

fromInt : : I n t −> SeasonfromInt 0 = WinterfromInt 1 = SpringfromInt 2 = SummerfromInt 3 = F a l l

next : : Season −> Seasonnext x = fromInt ( ( to In t x + 1) ‘mod‘ 4)

eqSeason : : Season −> Season −> BooleqSeason x y = ( to In t x == to In t y )


Forme geometrice

Cercuri s, i dreptunghiuri

type Radius = Floattype Width = Floattype Height = Float

data Shape = C i r c l e Radius| Rectangle Width Height

area : : Shape −> Floatarea ( C i r c l e r ) = pi * r ^2area ( Rectangle w h ) = w * h


Forme geometrice


eqShape : : Shape −> Shape −> Bool

eqShape ( C i r c l e r ) ( C i r c l e r ’ ) = ( r == r ’ )eqShape ( Rectangle w h ) ( Rectangle w’ h ’ ) = (w == w ’ ) && (

h == h ’ )eqShape _ _ = False

showShape : : Shape −> String

showShape ( C i r c l e r ) = " C i r c l e " ++ showF rshowShape ( Rectangle w h ) = " Rectangle " ++ showF w

++ " " ++ showF h

showF : : Float −> StringshowF x | x >= 0 = show x

| otherwise = " ( " ++ show x ++ " ) "


Forme geometrice


eqShape : : Shape −> Shape −> BooleqShape ( C i r c l e r ) ( C i r c l e r ’ ) = ( r == r ’ )eqShape ( Rectangle w h ) ( Rectangle w’ h ’ ) = (w == w ’ ) && (

h == h ’ )eqShape _ _ = False

showShape : : Shape −> StringshowShape ( C i r c l e r ) = " C i r c l e " ++ showF rshowShape ( Rectangle w h ) = " Rectangle " ++ showF w

++ " " ++ showF h

showF : : Float −> StringshowF x | x >= 0 = show x

| otherwise = " ( " ++ show x ++ " ) "


Forme geometrice

Teste s, i operatori de proiect, ie

i s C i r c l e : : Shape −> Booli s C i r c l e ( C i r c l e r ) = Truei s C i r c l e _ = False

i sRectang le : : Shape −> Booli sRectang le ( Rectangle w h ) = Truei sRectang le _ = False

rad ius : : Shape −> Floatrad ius ( C i r c l e r ) = r

width : : Shape −> Floatwidth ( Rectangle w h ) = w

he igh t : : Shape −> Floathe igh t ( Rectangle w h ) = h


Forme geometrice

Pattern-matching

area : : Shape −> Floatarea ( C i r c l e r ) = pi * r ^2area ( Rectangle w h ) = w * h

area : : Shape −> Floatarea s =

i f i s C i r c l e s thenl e t

r = rad ius sin

pi * r ^2else i f i sRectang le s then

l e tw = width sh = he igh t s

inw * h

else error " imposs ib le "Traian Florin S, erbanut,a Ioana Leus, tean (UB) PD—Tipuri date algebrice 11 / 22

Liste

Pattern-matching

Declarat,ie ca tip de date algebric

data Lis t a = N i l| Cons a ( List a )

append : : List a −> List a −> List aappend N i l ys = ysappend ( Cons x xs ) ys = Cons x ( append xs ys )


Liste

Constructori simboluri

Declarat,ie ca tip de date algebric cu simboluri

data Lis t a = N i l| a : : : List a

deriving (Show)i n f i x r 5 : : :

(+++) : : List a −> List a −> List ai n f i x r 5 +++N i l +++ ys = ys( x : : : xs ) +++ ys = x : : : ( xs +++ ys )

Comparat,i cu versiunea folosind notat,ia predefinita

(++) : : [ a ] −> [ a ] −> [ a ][ ] ++ ys = ys( x : xs ) ++ ys = x : ( xs ++ ys )


Liste


eqL i s t : : Eq a => Lis t a −> List a −> BooleqL i s t N i l N i l = TrueeqL i s t ( x : : : xs ) ( y : : : ys ) = x == y && eqL is t xs yseqL i s t _ _ = False

showList : : Show a => Lis t a −> StringshowList N i l = " N i l "showList ( x : : : xs ) = show x ++ " : : : " ++ showList xs


Numere naturale

Numerele Naturale (Peano)

Declarat,ie ca tip de date algebric

data Nat = Zero| Succ Nat

( ^ ^ ^ ) : : Float −> Nat −> Floatx ^^^ Zero = 1.0x ^^^ ( Succ n ) = x * x ^^^ n

Comparat,i cu versiunea folosind notat,ia predefinita

( ^ ^ ) : : Float −> I n t −> Floatx ^^ 0 = 1.0x ^^ n = x * ( x ^^ ( n−1) )


Numere naturale

Adunare s, i înmult, ire

Definit,ie pe tipul de date algebric(+++) : : Nat −> Nat −> Natm +++ Zero = mm +++ ( Succ n ) = Succ (m +++ n )

( * * * ) : : Nat −> Nat −> Natm * * * Zero = Zerom * * * ( Succ n ) = (m * * * n ) +++ m

Comparat,i cu versiunea folosind notat,ia predefinita(+ ) : : I n t −> I n t −> I n tm + 0 = mm + n = (m + ( n−1) ) + 1

( * ) : : I n t −> I n t −> I n tm * 0 = 0m * n = (m * ( n−1) ) + m


Numere naturale

Tipuri de date algebrice

data Typename = Cons1 t11 . . . t1k1

|Cons2 t21 . . . t2k2

| . . .

|Consn tn1 . . . tnkn

unde k1, . . . , kn ≥ 0

Se pot defini tipuri parametrizate.

Se pot folosi definit,ii recursive.


Numere naturale

Date personale

type FirstName = Stringtype LastName = Stringtype Age = I n ttype Height = Floattype PhoneNumber = Stringtype Flavor = String

data Person = Person FirstName LastName Age HeightPhoneNumber F lavor


Numere naturale

Proiect, ii

f i rs tName : : Person −> Stringf i rs tName ( Person f i r s tname _ _ _ _ _ ) = f i r s tname

lastName : : Person −> StringlastName ( Person _ lastname _ _ _ _ ) = lastname

age : : Person −> I n tage ( Person _ _ age _ _ _ ) = age

he igh t : : Person −> Floathe igh t ( Person _ _ _ he igh t _ _ ) = he igh t

phoneNumber : : Person −> StringphoneNumber ( Person _ _ _ _ number _ ) = number

f l a v o r : : Person −> Stringf l a v o r ( Person _ _ _ _ _ f l a v o r ) = f l a v o r


Numere naturale

Utilizare

Main*> l e t i o n e l = Person " Ion " " Ionescu " 20 175.2" 0712334567 " " Caramel "

Main*> f i rs tName i o n e l" Ion "Main*> he igh t i o n e l175.2Main*> f l a v o r i o n e l" Caramel "


Înregistrari

Date personale ca înregistrari

data Person = Person { f i rs tName : : String, lastName : : String, age : : I n t, he igh t : : Float, phoneNumber : : String, f l a v o r : : String}


Înregistrari

Utilizare

Putem folosi atât forma algebrica cât s, i cea de înregistrare

i o n e l = Person " Ion " " Ionescu " 20 175.2" 0712334567 " " Caramel "

g i g e l = Person { f i rs tName = " Gheorghe ", lastName=" Georgescu ", age = 30 , he igh t = 192.3, phoneNumber = " 0798765432 ", f l a v o r = " V a n i l i e " }

Putem folosi s, i pattern-matching

Proiect,iile sunt definite automat; sintaxa specializata pentru actualizari

nextYear : : Person −> PersonnextYear person = person { age = age person + 1 }


Programare declarativa - Tipuri de date algebriceold.unibuc.ro/~ileustean/files/05-adt-il.pdf ·...

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