
<center><img src="https://gitea.louisgallet.fr/lgallet/epicours/raw/branch/main/Algo/S%C3%A9minaire/assets/basics-meme.png " width=auto height=400 /> </center>  

CAML is a categorical abstract machine language. It is strongly typed. It was created by INRIA in 1984.

## 1.1. General idea
It's a simple language to write. 
```Ocaml
# 1+2 ;;
```

- **#** is the prompt (we don't have to write it)
- **1 + 2** is the program
- **;;** is the end of the line

```Ocaml
_: int=3 (*That a Caml answer to the previous program*)
```

```Ocaml
# 1+2.2;; (*That an error*)

# 1. +. 2.2;; (*This is good*)
```
## 1.2. CAML interaction
```Ocaml
# 1;; (*He can be a simple expression*)
_: int=1

# "Hello World";; (*He can be a string*)
_:string = "Hello World"
```

The general form is :
```Ocaml
# expr ;;
-: type of the evaluation = result  of the evaluation
```

## 1.3. Definitions
### Global definitions
```Ocaml
# let x=1+2;;
val x:int = 3 (*our current env is x -> 3*)

# let y=x/2;;
val y:int = 1 (*our current env is x -> 3 ; y -> 1*)

# let x = 2
val x : int = 2

# x;;
_: int = 2

# let name = expr;;
val name: type of evaluation
```
### Local definitions
```Ocaml
# let r = 1. in let pi = 3.14 in 2*pi*r;;
- : float = 6.28

# let x = 10 in y = 2*x in x+y;;
- : float = 30

# x;;
- : int =2 (*see global definition section*)

# pi;;
error: unbound value pi
```

when there is the keyword ``len``and ``in`` that create a local definition. A local definition is something that only exist in our expression and then it disappear. You can define a local definition into a variable : `` let x = let r = 1. in let pi = 3.14 in 2*pi*r;;`` (for example)

### Multiple definitions
```Ocaml
# let r = 1. and pi = 3.14 in 2 *. pi *. r;; (*local version*)
- : float = 6.28 

# let x = 1.2 and y = "Hello";;
val x: float = 1.2 (*our current env is x -> 3 ; y -> 1 ; x -> 1.2 *)
val y: string = "Hello" (*our current env is x -> 3 ; y -> 1 ; x -> 1.2 ; y -> "Hello"*)
# let x = 2 and y = x + 1 in y + 2;;
Error (*because x is 1.2 in our current evaluation*)
```
> ⚠️ We have only one `let` and one `in` for the multiple definitions methods

## 1.4 Basic types
- Integer: ``int``
	- Compatible operator : + ; - ; * ; / ; mod
	- Same operator priority than in mathematics
	  ```Ocaml
	  # 2+3*2;;
	  _: int = 8
	  
	  # (2+3)*3;;
	  _: int = 10
	  
	  # max_int 1 073 741 823
	  _: int = 2^30-1
	  
	  # max_int -1 073 741 824
	  _: int = -2^30
	  ```
- Float: ``float``
	- Compatible operator : -. ;  +. ; * .  ; /.
- Booleans: ``bool``
	- Can be ``true``or ``false``
	```Ocaml
	# let x = 2 and y = 1 in x/y > 1;;
	_: bool = true
	
	# let x = 2 and y = 0 in x/y > 1;;
	Exception: Division by zero
	
	# let x = 2 and y = 0 in y<>0 && x/y> 1;;
	_: bool = false
	```


- Char: `char`
	- 8 bits -> extended ASCII table
```Ocaml
# 'a'= 'A';;
_: bool = false

# 'a'
- : char = 'a'
```

- String: `string`
```Ocaml
# "ab" < "abc" ;;
_: bool = true (*because O chars -> 2^24 - 6 chars*)

# "Hello" ^" World"
_: string = "Hello World"

# "abc".[1]
_: char = "b"
```
⚠️ Les minuscules passent avant les majuscules

### Comparaison

|Mathematics|$=$|$\not=$|$<$|$>$|$\eqslantgtr$|$\eqslantless$|
|:----:|:----:|:----:|:----:|:----:|:----:|
|CAML|`=`|`<>`|`<`|`>`|`<=`|`>=`|

|CAML|Maths|English|
|:-----|:-----|:-----|
|not|$\neg$|negation|
|&&|$\land$|and|
|// (vertical bar)|$\lor$|or (inclusive)|
