1 premier/2

p r e m i e r (X, L ) : L=[X| ] .

2 member/2

member (X, [X| ] ) .

member (X, [ | L ] ) :−
member (X, L ) .

2.1 inclus/2

inclus ([] , ).
i n c l u s ( [ X| L1 ] , L2 ) :−
member (X, L2 ) ,
i n c l u s ( L1 , L2 ) .

2.2 intersection/3

intersection ([] , , []).

i n t e r s e c t i o n ( [ X| L1 ] , L2 , [X| L3 ] ) :−
member (X, L2 ) ,
i n t e r s e c t i o n ( L1 , L2 , L3 ) .
i n t e r s e c t i o n ( [ | L1 ] , L2 , L3 ) :−
i n t e r s e c t i o n ( L1 , L2 , L3 ) .

2.3 different/1

differents ( [ ] ) .
d i f f e r e n t s ( [ Head | T a i l ] ) :−
\+ member ( Head , T a i l ) ,
d i f f e r e n t s ( Tail ) .

3 ajoute debut/3

a j o u t e d e b u t (X, L , [X| L ] ) .

1
4 append/3

append ( [ ] , L , L ) .
append ( [ X | Xs ] , Ys , [X| Zs ] ) : −
append ( Xs , Ys , Zs ) .

4.1 dernier/ 2 avec append

d e r n i e r (L ,X) :−
append ( , [X] , L ) .

4.2 sauf dernier/2 avec append

s a u f d e r n i e r (L , L1 ) :−
append ( L1 , [ ] , L ) .

4.3 ajoute fin/3

a j o u t e f i n (X, L , L1 ) :−
append (L , [X] , L1 ) .

4.4 palindrome/1

palindrome ( [ ] ) .
palindrome ( [X ] ) .
p a l i n d r o m e ( [ X| L ] ) :−
append ( L1 , [X] , L ) ,
p a l i n d r o m e ( L1 ) .

5 dernier/2

d e r n i e r ( [ X] , X ) .
d e r n i e r ( [ | L ] ,X) :−
d e r n i e r (L ,X ) .

2
6 sauf dernier/2

s a u f d e r n i e r ( [ X] , [ ] ) .
s a u f d e r n i e r ( [ X| L ] , [X| L1 ] ) :−
s a u f d e r n i e r (L , L1 ) .

6.1 reverse/2

reverse ( [ ] , [ ] ) .
r e v e r s e ( [ X| XS ] , L2 ) :−
d e r n i e r ( L2 , X) ,
s a u f d e r n i e r ( L2 , L3 ) ,
r e v e r s e (XS , L3 ) .

7 ajoute fin/3

a j o u t e f i n (Y, [ ] , [Y ] ) .
a j o u t e f i n (Y, [X| L ] , [X| L1 ] ) :−
a j o u t e f i n (Y, L , L1 ) .

8 pair/1

pair ( [ ] ) .
p a i r ( [ , | L ] ) :−
p a i r (L ) .

9 enleve/3

enleve ( , [ ] , [ ] ) .
e n l e v e (X, [X| Xs ] , Xs ) .
e n l e v e (X, [Y| Ys ] , [Y| Zs ] ) :−
e n l e v e (X, Ys , Zs ) .

9.1 inclus/2

inclus ([] , L).

i n c l u s ( [ X| L1 ] , L2 ) :−
e n l e v e (X, L2 , L3 ) ,
i n c l u s ( L1 , L2 ) .

3
9.2 permute/2

permute ( [ ] , [ ] ) .
permute ( [ X| Xs ] , Y) :−
permute ( Xs , Ys ) ,
e n l e v e (X, Y, Ys ) .

9.3 oter daublons/2

oter doublons ( [ ] , [ ] ) .
o t e r d o u b l o n s ( [ X| L1 ] , [X| L2 ] ) :−
e n l e v e (X, L1 , L3 ) ,
o t e r d o u b l o n s ( L3 , L2 ) .

10 delete/3

delete ( , [ ] , [ ] ) .
d e l e t e ( Element , [ Element | L i s t e ] , L i s t e S a n s E l e m e n t ) :−
d e l e t e ( Element , L i s t e , ListeSansElement ) .
d e l e t e ( Element , [ T| L i s t e ] , [ T | L i s t e S a n s E l e m e n t ] ) :−
Element \= T,
d e l e t e ( Element , L i s t e , ListeSansElement ) .

10.1 delete list/3

d e l e t e l i s t ( [ X| XS ] , L1 , L2 ) :−
d e l e t e (X, L1 , L3 ) ,
d e l e t e l i s t (XS , L3 , L2 ) .
d e l e t e l i s t ( [ ] , L, L).

11 sublist/2

prefix ([] , ).
p r e f i x ( [ X| Xs ] , [X| Ys ] ) :−
p r e f i x ( Xs , Ys ) .

s u f f i x ( Sub , L i s t ) :−
append ( , Sub , L i s t ) .

4
append ( [ ] , L , L ) .
append ( [ X| Xs ] , Ys , [X| Zs ] ) :−
append ( Xs , Ys , Zs ) .

s u b l i s t ( Sub , L i s t ) :−
append ( , Sub , L i s t ) .

s u b l i s t ( Sub , L i s t ) :−
s u f f i x ( Suffix , List ) ,
p r e f i x ( Sub , S u f f i x ) .

s u b l i s t ( Sub , L i s t ) :−
append ( P r e f i x , , List ) ,
p r e f i x ( Sub , P r e f i x ) .

s u b l i s t ( Sub , L i s t ) :−
append ( , S u f f i x , L i s t ) ,
s u f f i x ( Sub , S u f f i x ) .

s u b l i s t ( Sub , L i s t ) :−
append ( P r e f i x , , List ) ,
append ( , Sub , P r e f i x ) .

12 tri insertion/2

tri insertion ([] , []).

t r i i n s e r t i o n ( [ Head | T a i l ] , S o r t e d ) :−
t r i i n s e r t i o n ( Tail , SortedTail ) ,
i n s e r t ( Head , S o r t e d T a i l , S o r t e d ) .

i n s e r t (X, [ ] , [X ] ) .
i n s e r t (X, [Y| T a i l ] , [ X,Y| T a i l ] ) :−
X =< Y.
i n s e r t (X, [Y| T a i l ] , [Y| R e s u l t ] ) :−
X > Y,
i n s e r t (X, T a i l , R e s u l t ) .

13 tri rapide/2

tri rapide ([] , [ ] ) .

t r i r a p i d e ( [ P i v o t | Rest ] , S o r t e d ) :−
p a r t i t i o n ( Rest , Pivot , S m a l l e r , G r e a t e r ) ,

5
 t r i r a p i d e ( Smaller , SmallerSorted ) ,
t r i r a p i d e ( Greater , G r e a t e r S o r t e d ) ,
append ( S m a l l e r S o r t e d , [ P i v o t | G r e a t e r S o r t e d ] , S o r t e d ) .

partition ([] , , [] , []).

p a r t i t i o n ( [ X| Rest ] , Pivot , [X| S m a l l e r ] , G r e a t e r ) :−
X =< Pivot ,
p a r t i t i o n ( Rest , Pivot , Smaller , Greater ) .
p a r t i t i o n ( [ X| Rest ] , Pivot , S m a l l e r , [X| G r e a t e r ] ) :−
X > Pivot ,
p a r t i t i o n ( Rest , Pivot , Smaller , Greater ) .

14 fusion/3

fusion ( [ ] , L, L).
f u s i o n (L , [ ] , L ) .
f u s i o n ( [ X| Xs ] , [Y| Ys ] , [X| Zs ] ) :−
X =< Y,
f u s i o n ( Xs , [Y| Ys ] , Zs ) .
f u s i o n ( [ X| Xs ] , [Y| Ys ] , [Y| Zs ] ) :−
X > Y,
f u s i o n ( [ X| Xs ] , Ys , Zs ) .

14.1 tri fusion/2

tri fusion ([] , [ ]) .

t r i f u s i o n ( [ X] , [X ] ) .
t r i f u s i o n ( L i s t , S o r t e d ) :−
length ( L i s t , Len ) ,
Len > 1 ,
LenDiv2 i s Len // 2 ,
length ( L e f t , LenDiv2 ) ,
append ( L e f t , Right , L i s t ) ,
t r i f u s i o n ( Left , LeftSorted ) ,
t r i f u s i o n ( Right , R i g h t S o r t e d ) ,
f u s i o n ( LeftSorted , RightSorted , Sorted ) .