epicours/Algo/Courses/Chapter 7 - High Order (exercises).md

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## Ex 1.2
```Ocaml
# let sum n =
if n < 0 then
invalid_arg "n<0"
else
let rec sumrc n =
if n=0 then
0
else
n + sum(n-1)
in sumrc n;;
val sum : int -> int = <fun>
(*Correction*)
let sigma f n =
if n<0 then
invalid_arg "n<0"
else
let rec sig = function
| 0 -> f0
| n -> fn + sig (n-1)
in sig n;;
val sigma: (int -> int) -> int -> int = <fun>
```
## Ex 2.1
```
# let rec map f = function
| [] -> []
|e::t -> f e::map f t ;;
val map : ('a -> 'b) -> 'a list -> 'b list = <fun>
```
## Ex 2.2
```
# let rec for_all p = function
| [] -> true
| e::t -> p e && for_all p t;;
val for_all: ('a -> bool) -> 'a list -> bool = <fun>
```
## Ex 2.3
```
# let rec exists p = function
| [] -> true
| e::t -> p e || for_all p t;;
val exists: ('a -> bool) -> 'a list -> bool = <fun>
```
## Ex 2.4
```
# let rec find p = function
| [] -> true
| e::t -> if p e then e else find p t;;
val exists: (bool -> bool) -> bool list -> bool = <fun>
```
## Ex 2.5