## 1.1 - Product

```
let rec product = function
	| [] -> 0
	| x::t -> x + product t;;
```
## 1.2 - Count
```
let rec count x n =
	if x = [] then
		0
	else
		let e::t = x in
		if e = x then
			1 + count t n
		else
			count t n;;
```

## 1.3 - Search
```
let rec search x n =
	if x = [] then
		0
	else
		let e::t = x in
		if e = x then
			true
		else
			search t n;;
```

## 1.4 - $n^{th}$
```
let rec length l = 
	if l = [] then
		0
	else
		let e::t = l in
			1 + length t;;
let rec nth x n =
	if (x = [] || n =< 0) then
		Invalid_arg "The number of element in the list is 0"
	else if length x < n then
		Failwith "The list is too short"
	else
		let e::t = x in
		if e = x then
			1 + count t n
		else
			count t n;;
```