vault backup: 2023-09-14 16:20:59

Algo/Séminaire/Chapter 4 - A bit of imperative.md

@@ -1,3 +1,5 @@
+
+![](https://gitea.louisgallet.fr/lgallet/epicours/raw/branch/main/Algo/S%C3%A9minaire/assets/unitaire-meme.png)
 ## 0.1. Print
 If we want to print something in CAML, we have to use this structure
 

Algo/Séminaire/Chapter 5 - Recursivity.md

@@ -1,4 +1,5 @@
-![Alt](https://gitea.louisgallet.fr/lgallet/epicours/raw/branch/main/Algo/S%C3%A9minaire/assets/recursivite-meme.png "recursivity problem")
+
+<center><img src="https://gitea.louisgallet.fr/lgallet/epicours/raw/branch/main/Algo/S%C3%A9minaire/assets/recursivite-meme.png " width=512 height=auto /> </center>
 
 ### 5.1. Simple functions
 To create a recursive function we have to use this structure
@@ -64,3 +65,29 @@ A[ctd 3] --> B[ctd 2] --> C[ctd 1] --> D[ctd 0] --> E[ctd -1] --> F[ ] --> E -->
 > ctd is countdown
 
 ## 5.3. Several recursive calls
+A function that have several recursive calls is defind like this
+$$
+Fn = {1 -> \text{if } n\eqslantless{1} \brace{Fn+1+Fn+2} }
+$$
+**Fibonacci functions**
+```Ocaml
+let rec fibonacci n =
+	if n = 0 then
+		0
+	else if n = 1 then
+		1
+	else
+		fibonacci(n-1) + fibonacci(n-2);;
+
+let add n = 
+	if n = 0 then
+		false
+	else
+		even (n-1);;
+
+let even n =
+	if n = 0 then
+		true
+	else
+		add (n-1);;
+```