Cours no 1 : Introduction à la programmation fonctionnelle 1

A B A
B f x A f(x)
B x f(x)x f
f:R−→ R
x7−→ f(x) = √x2+1
x−1
.
A B Rx6= 1
f
A
length :A∗−→ N
u7−→ |u|.
AA∗ABN
add :Z×Z−→ Z
(n1, n2)7−→ n1+n2
.
AZ×ZBZ
add
double f(double x) {
return sqrt(x*x + 1)/(x - 1) ;
}
f(3) f
1.581139
x∈A
f:A→B y ∈B f(x)
y f(x)y
f(x)y

int i=0;
int g(int j) {
i+=j;
return i ;
}
g g(1)
g(1)
g(1)
i g g
f(i)
f(i) - f(i)
3+1

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#
;;
-
# 132 ;;
- : int = 132
# 2*(45+10) ;;
- : int = 110
# 7/4 ;;
-:int=1
# 7 mod 4 ;;
-:int=3
# 2. ;;
- : float = 2.
# 2. +. 3. ;;
- : float = 5.
# 7./.4. ;;
- : float = 1.75
# float_of_int 2 ;;
- : float = 2.
#true ;;
- : bool = true
#true &false ;;
- : bool = false
# 1 = 2-1 ;;
- : bool = true
# "Hello" ;;
- : string = "Hello"
# "Hello " ^ "le monde " ;;
- : string = "Hello le monde "
# ’A’ ;;
- : char = ’A’
# int_of_char ’B’ ;;
- : int = 66

int int
[[−230,230 −1]]
int
# min_int ;;
- : int = -1073741824
# max_int ;;
- : int = 1073741823
+
-
*
/
mod
float
2int 2. float
+.
-.
*.
/.
**
int float
#2+3.;;
Characters 4-6:
2 + 3. ;;
^^
This expression has type float but is here used with type int
# 2. +. 3 ;;
Characters 6-7:
2. +. 3 ;;
^
This expression has type int but is here used with type float
float_of_int int float
ceil
floor
sqrt
exp
log
log10
string 264 −6
^
string_of_int int string
int_of_string string int
string_of_float float string
float_of_string string float
String.length
char
char_of_int int char
int_of_char char int