epicours/Algo/CM/Lists.md

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 : element x list -> 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

cons add en element to the head of the list (eg. li <- cons(cloud, li)) headreturn the element in the head of the list (eg. pl <- head(li)) contentsreturn what is the element of the head firstreturn the first element of the list (is equivalent to contents) tailremove the first element of the list (eg. fl <- tail (li)) nextreturn the element after a box (eg. pspt <= next(head(li))))

Array implementation

Let's take a list l = E ; D ; C ; B ; A. An array implementation of the list l will be:

1	2	3	4	5
A	B	C	D	E
5

The first line of the table is the n^{th} place of the element, the second line is all the element of the list, and the third line is the place of the first element of the list (here E is at the 5^{th} position).