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Algo/B1/Séminaire/Chapter 1 - CAML basics.md

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+<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)|