This document discusses basic data structures in Prolog, including lists and graphs. It provides an overview of lists, their properties, and common list operations like head, tail, member, append, delete, length, and concat. It also discusses graph representations using adjacency matrices and lists. Graph operations in Prolog include using terms to represent edges and checking if nodes are connected. Depth first search is demonstrated to return a path between nodes. Graphs can be represented as terms with nodes and their edge nodes.

1. Basic Data Structures in Prolog
Lists and Graphs

2. Overview
Lists
List Operations
Graphs
Graph Operations

3. Lists
What are the classic properties of lists?
 Easy to insert and delete at end (free pointer)
 Harder to change in the middle
 O(n) to search unless ordered
 Variable size

4. Prolog Lists
The major complex data structure
Can contain atoms, variables, etc.
Have 2 parts, a Head and a Tail
 Head is the first element in a list
 Tail is everything else
 [Head|Tail]
The empty list [] is a list
Every list has an empty list at the end

5. Getting a Feel for Lists
head( [H|T], H ).
tail( [H|T], T ).
Every nontrivial list operation involves
recursion

6. Member
member( H, [H|T] ).
member( H, [_|T] ):-
member( H, T ).

7. Append
append( H, [], [H] ).
append( X, [H|T], [H|T2] ):-
append( X, T, T2 ).

8. Delete
delete( H, [H|T], T ).
delete( X, [H|T], [H|T2] ):-
delete( X, T, T2 ).
Delete can test membership!

9. Length
length( [], 0 ).
length( [H|T], X+1 ):-
length( T, X ).

10. Concat
concat( H, [], H ).
concat( [H|T], [H2|T2], [H|T3] ):-
append( H2, T, H3 ),
concat( H3, T2, T3 ).
concat2( [], H, H ).
concat2( [H|T], L2, [H|T2] ):-
concat2( T, L2, T2 ).

11. Sort
sort1( [], [] ).
sort1( L1, L2 ):-
permute( L1, L2 ),
ordered( L2 ).

12. Permute
permute( [], [] ).
permute( L, [H|T] ):-
delete( H, L, L2 ),
permute( L2, T ).

13. Ordered
ordered( [] ).
ordered( [X|[]] ).
ordered( [H|[H2|T]] ):-
H < H2,
ordered( [H2|T] ).

14. Flatten - Double Recursion
flatten( [], [] ).
flatten( X, [X] ):-
atomic( X ),
X == [].
flatten( [H|T], L ):-
flatten( H, H2 ),
flatten( T, T2 ),
concat( H2, T2, L ).

15. Graphs
Representations
 Adjacency matrix
A
E
D
C
B
a b c d e
a 0 1 0 0 1
b 0 0 1 1 0
c 0 0 0 0 0
d 0 0 0 0 0
e 0 0 0 0 0

16. Graphs
Representations
 Adjacency list
 a : b,e
 b : c,d
 c :
 d :
 e :
A
E
D
C
B

17. Graphs in Prolog
Using terms
 arc( a, b ).
 arc( a, e ).
 arc( b, c ).
 arc( b, d ).
Technically, a graph is a set of nodes
and edges, but you may not care...
A
E
D
C
B

18. Graphs in Prolog
Are a and d connected?
 connected( X, Y ):-
 arc( X, Y ).
 connected( X, Z ):-
 arc( X, Y ),
 connected( Y, Z ).
A
E
D
C
B

19. Depth First Search
Return path to goal state
 dfs( N, [] ):-
 goal( N ).
 dfs( N, [H|T] ):-
 connected( N, H ),
 dfs( H, T ).
A
E
D
C
B

20. Graphs in Prolog
What if you want a graph/tree to be an
argument to a predicate?
graph([nodes],[edges])
 graph([a,b,c,d,e],[arc(a,b),arc(a,e),arc(b,c)
,arc(b,d)]
graph( t(node, [edgenodes]), ... )
 graph( t(a, [b,e]), t(b, [c,d]), t(c, []), t(d,
[]), t(e,[]) )