-- commentaire : directive pour le compilateur ghc 
:opt no-lint

"2" + 3

<interactive>:1:1: error:
    • No instance for (Num String) arising from a use of ‘+’
    • In the expression: "2" + 3
      In an equation for ‘it’: it = "2" + 3

:t 'a'

:t []

:t 1

:t "Ab"
:t ['A','b']

:t (True, 'a', "cat")

:t ["True", "'a'", "cat"]

-- avec une annotation de type
:t ["True", "'a'", "cat"] :: [String]

x = 304140932017133780436126081660 :: Int

x

-4849135255881964932

x = 304140932017133780436126081660 :: Integer

x

304140932017133780436126081660

:t 304140932017133780436126081660

:t Int

<interactive>:1:1: error: Data constructor not in scope: Int

:k Int

-- quel est le type de la fonction head (pour les listes) ?
:t head

:t fst

-- quel est le type de la fonction (==) ?
:t (==)

-- quel est le type de la fonction (+) ?
:t (+)

:t Num

<interactive>:1:1: error:
    • Data constructor not in scope: Eq
    • Perhaps you meant ‘EQ’ (imported from Prelude)

:k Num

-- type explicite vs. classe de type :
:k Int
:k Num

:i Num

-- quel est le type de la fonction (==) ?
:t (==)

:i Eq

-- quel est le type de la fonction (<) ?
:t (<)

:i Ord

:i Int

-- quel est le type de la fonction sqrt ?
:t sqrt

-- quel est le type de la fonction even ?
:t even

-- quel est le type de la fonction (^) ?
:t (^)

3 ^ 4

81

3.4 ^ 5

454.3542399999999

3 ^ 4.5

<interactive>:1:1: error:
    • Could not deduce (Integral b0) arising from a use of ‘^’
      from the context: Num a bound by the inferred type of it :: Num a => a at <interactive>:1:1-7
      The type variable ‘b0’ is ambiguous
      These potential instances exist:
        instance Integral Integer -- Defined in ‘GHC.Real’
        instance Integral Int -- Defined in ‘GHC.Real’
        instance Integral Word -- Defined in ‘GHC.Real’
        ...plus 58 instances involving out-of-scope types
        (use -fprint-potential-instances to see them all)
    • In the expression: 3 ^ 4.5
      In an equation for ‘it’: it = 3 ^ 4.5
<interactive>:1:5: error:
    • Could not deduce (Fractional b0) arising from the literal ‘4.5’
      from the context: Num a bound by the inferred type of it :: Num a => a at <interactive>:1:1-7
      The type variable ‘b0’ is ambiguous
      These potential instances exist:
        instance Fractional Double -- Defined in ‘GHC.Float’
        instance Fractional Float -- Defined in ‘GHC.Float’
        ...plus 14 instances involving out-of-scope types
        (use -fprint-potential-instances to see them all)
    • In the second argument of ‘(^)’, namely ‘4.5’
      In the expression: 3 ^ 4.5
      In an equation for ‘it’: it = 3 ^ 4.5

3 ^ (-4)

Negative exponent

fac :: Int -> Int
fac n = product [1..n]

fac 10

3628800

fac 30

-8764578968847253504

fac2 :: Integer -> Integer
fac2 n = product [1..n]

fac2 30

265252859812191058636308480000000

:t fac2

fac3 :: Int -> Integer
fac3 n = product [1..fromIntegral n]

fac3 30

265252859812191058636308480000000

fac4 n = product [1..n]

fac4 30

265252859812191058636308480000000

:t fac4

fac5 0 = 1
fac5 n = n * fac5 (n-1)

fac5 30

265252859812191058636308480000000

:t fac5

Cours03 : le système de types¶

Rappel : Haskell est fortement typé¶

Les types explicites (ou concrets)¶

Deux types d'entiers¶

Type vs. expression¶

Les variables de type¶

Les classes de type¶

Les principales contraintes de type, leurs dépendances et les types explicites qui les implémentent.¶

Exemple de variations sur le typage¶

Éléments de correction du TP¶