From ec8c78cf4e5950bcbbb5edea27db2a4b7a797579 Mon Sep 17 00:00:00 2001
From: Louis <me@louisgallet.fr>
Date: Wed, 11 Oct 2023 11:23:46 +0200
Subject: [PATCH] vault backup: 2023-10-11 11:23:46

---
 .obsidian/workspace.json    | 10 +++++-----
 Algo/CM/CM du 11 octobre.md |  2 --
 Algo/CM/Lists.md            | 38 +++++++++++++++++++++++++++++++++++++
 3 files changed, 43 insertions(+), 7 deletions(-)
 delete mode 100644 Algo/CM/CM du 11 octobre.md
 create mode 100644 Algo/CM/Lists.md

diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index 9ee5b82..e991bcc 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -25,7 +25,7 @@
             "state": {
               "type": "markdown",
               "state": {
-                "file": "Algo/CM/CM du 11 octobre.md",
+                "file": "Algo/CM/Lists.md",
                 "mode": "source",
                 "source": false
               }
@@ -98,7 +98,7 @@
             "state": {
               "type": "backlink",
               "state": {
-                "file": "Algo/CM/CM du 11 octobre.md",
+                "file": "Algo/CM/Lists.md",
                 "collapseAll": false,
                 "extraContext": false,
                 "sortOrder": "alphabetical",
@@ -115,7 +115,7 @@
             "state": {
               "type": "outgoing-link",
               "state": {
-                "file": "Algo/CM/CM du 11 octobre.md",
+                "file": "Algo/CM/Lists.md",
                 "linksCollapsed": false,
                 "unlinkedCollapsed": true
               }
@@ -138,7 +138,7 @@
             "state": {
               "type": "outline",
               "state": {
-                "file": "Algo/CM/CM du 11 octobre.md"
+                "file": "Algo/CM/Lists.md"
               }
             }
           },
@@ -172,7 +172,7 @@
   "active": "26919eaeae9a8f38",
   "lastOpenFiles": [
     "Algo/CM/CM du 27 septembre.md",
-    "Algo/CM/CM du 11 octobre.md",
+    "Algo/CM/Lists.md",
     "Algo/CM/CM du 04 octobre.md",
     "Algo/Courses/Chapter 6 - Lists (Exercises).md",
     "Algo/Courses/Chapter 6 - Lists.md",
diff --git a/Algo/CM/CM du 11 octobre.md b/Algo/CM/CM du 11 octobre.md
deleted file mode 100644
index a4469e9..0000000
--- a/Algo/CM/CM du 11 octobre.md	
+++ /dev/null
@@ -1,2 +0,0 @@
-List is the most fundamental data type. Is a sequencial argument, is a final sequence of element. It is no possible to have more than one element per box. 
-There is two different way to declare a list, the recursive one and the iterative one. 
diff --git a/Algo/CM/Lists.md b/Algo/CM/Lists.md
new file mode 100644
index 0000000..37ce20f
--- /dev/null
+++ b/Algo/CM/Lists.md
@@ -0,0 +1,38 @@
+List is the most fundamental data type. Is a sequencial argument, is a final sequence of element. It is no possible to have more than one element per box. 
+There is two different way to declare a list, the recursive one and the iterative one. 
+
+## Recursive list
+- The first box is the **head of the list**
+- The rest of the list is **the tail of the list**
+- The signature of the recursive list is the following:
+```
+TYPES
+   list, box
+     
+USES
+   element  
+   
+OPERATIONS
+   emptylist : -> list (* Internal operations of list*)
+        cons : list x element -> list (* Internal operations of list *)
+        tail : list -> list (* Internal operations of list *)
+        head : list -> box (* Internal operations of box *)
+    contents : box -> element (* Observer of box *)
+       first : list ->  element (* Observer of list *)
+        next : box -> box (* Internal operation of box *)
+        
+PRECONDITIONS
+   tail(_l_) is-defined-iaoi _l_ ≠ emptylist
+   head(_l_) is-defined-iaoi _l_ ≠ emptylist
+   first(_l_) is-defined-iaoi _l_ ≠ emptylist  
+   
+AXIOMS 
+   first(_l_) = contents(head(_l_))
+   tail(cons(_e,l_)) = _l_
+   first(cons(_e,l_)) = _e_
+   next(head(_l_)) = head(tail(_l_)) 
+    
+WITH 
+   list _l_
+   element _e_
+```