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Algo/B1/Séminaire/Chapter 2 - Functions.md

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+<center><img src="https://gitea.louisgallet.fr/lgallet/epicours/raw/branch/main/Algo/S%C3%A9minaire/assets/functions-meme.jpg " width=auto height=400 /> </center>  
+
+
+## 2.1. One parameter function
+```Ocaml
+# let successor x=x+1;;
+val successor: int -> int =<fun>
+
+# successor;; 
+_ : int -> int =<fun>
+
+# successor 3;;
+_: int = 4
+
+# successor (-1)::
+_: int = 0
+```
+
+>`x` is call a formal parameter and `x+1` is call the body of the function. `3` is an effective parameter (= argument). For the last line, the paratheses are needed, without it, CAML will return an error
+
+
+#### ⚠️ ``f x = f(x)`` and ``fx+gy = (fx)+(gy)
+
+```Ocaml
+# let f x = x+1 and g x = x*2
+val f: int -> int = <fun>
+val g: int -> int = <fun>
+
+# fg 3;;
+Error: was expecting an integer and get a function
+# f(g 3);; (*This way there is no error*)
+_: int = 7
+```
+
+```Ocaml
+# let successor_of_double x=f(gx);;
+val successor_of_double: int -> int = <fun>
+
+# successor_of_double (-12);;
+_: int = -23
+```
+
+#### Existing functions
+```Ocaml
+# sqrt;;
+_: float -> float =<fun>
+
+# int_of_float;;
+_: float -> int =<fun>
+
+# length "toto" ;;
+Error : Unboud
+# String.lenght "toto";; (*String is a library*)
+_: int = 4
+```
+
+
+## 2.2. Functions and local definitions
+```Ocaml
+# let pred x = x - 1 in pred 3 + pred 4;;
+_: int = 6
+
+# pred;;
+Error
+
+# let square_of_pred x = let pred_x = x - 1 in pred_x * pred_x;;
+val square_of_pred: int -> int = <fun>
+
+# square_of_pred 3;;
+_: int = 4
+
+# let square_of_pred x = let pred x = x - 1 in pred x * pred x
+val square_of_pred: int -> int = <fun>
+val pred: int -> int = <fun>
+
+# square_of_pred 3;;
+_: int = 4 (*same things but with another method*)
+```
+
+## 2.3. Function with several parameters (2 or more)
+
+```Ocaml
+(*The logic way (for us)*)
+# let average(a,b) = (a+b)/2 ;;
+val average: int*int -> int = <fun>
+
+(*This method is not for several parameter, is just a one parameter wich is a couple*) (*f(x,y) ≠ f x y*)
+
+(*The OCaml way (the way that it work) *)
+# let average a b = (a+b)/2;;
+val average: int -> int -> int = <fun>
+# average (-2) (2);;
+-: int = 0
+```
+