Cool Programs in Prolog

1
Cool Programs in Prolog

• CS 581
• 02/28/05
• Flora Tan

2
A Graph Example

• A connected graph.
• Vertices 1, 2, 3, 4, 5.
• Edges are the
• connecting lines.
• Find all paths between
• any two vertices.
• Easy to implement in
• Prolog.

3
Prolog

• List the edges as facts.
• edge(1,2).
• edge(1,3).
• edge(1,4).
• edge(2,3).
• edge(2,5).
• edge(3,4).
• edge(3,5).
• edge(4,5).

4
Prolog

• Add the rules. Options
• The edges are bi-directional. We could list out
  another eight edges as facts.
• Ex edge(2,1), edge(3,1), edge(3,2), edge(4,1),
  edge(4,3), edge(5,2), edge(5,3), edge(5,4)
• Use disjunction.
• connected(X,Y) - edge(X,Y) edge(Y,X).

5
Prolog

• Add the rules. Options (continue)
• Alternatively, we could write this as two rules.
• connected(X,Y) - edge(X,Y).
• connected(X,Y) - edge(Y,X).
• But we dont want to do this. An infinite loop.
• edge(X,Y) - edge(Y,X).

6
Prolog

• The rest of the code.
• path(A,B,Path) -
• travel(A,B,A,Q),
• reverse(Q,Path).
• travel(A,B,P,BP) -
• connected(A,B).
• travel(A,B,Visited,Path) -
• connected(A,C),
• C \ B,
• not(member(C,Visited)),
• travel(C,B,CVisited,Path).

• Note the following
• Conjunction
• Goal matching
• Recursive search
• List processing reverse, member
• Accumulator

7
Prolog

• Base case
• travel(A,B,P,BP) -
• connected(A,B).
• Inductive case
• travel(A,B,Visited,Path) -
• connected(A,C),
• C \ B,
• not(member(C,Visited)),
• travel(C,B,CVisited,Path).

• A path from A to B is obtained if A and B are
  connected.
• A path from A to B is obtained provided that A is
  connected to a vertex C different from B that is
  not on the previously visited part of the path,
  and one continues finding a path from C to B.

8
Running the program

• Load the program into SWI-Prolog
• ?- swi('demo/test').
• Run the program.
• ?- path(1,5,P).
• P 1, 2, 5
• P 1, 2, 3, 5
• P 1, 2, 3, 4, 5
• P 1, 4, 5
• P 1, 4, 3, 5

9
Continue

• The paths.
• P 1, 4, 3, 2, 5
• P 1, 3, 5
• P 1, 3, 4, 5
• P 1, 3, 2, 5

10
Why is this cool?

• Graph search algorithms uses DFS/BFS and
  Adjacency List/Adjacency Matrix.
• Prolog uses Depth First Search.
• Other graphs examples searching a maze,
  Dijkstras algorithm, graph coloring.
• Coding in C is about 300 lines because we have to
  implement our own DFS and Adjacency List/Matrix.

11
Adjacency List / Matrix

• Adjacency List
• an array of pointers to linked lists
• 1 -gt 2 -gt 3 -gt 4
• 2 -gt 1 -gt 3 -gt 5
• 3 -gt 1 -gt 4 -gt 5
• 4 -gt 1 -gt 3 -gt 5
• 5 -gt 2 -gt 3 -gt 4

• Adjacency Matrix
• a 2D array of integers
• 1 2 3 4 5
• 1 0 1 1 1 0
• 2 1 0 1 0 1
• 3 1 0 0 1 1
• 4 1 0 1 0 1
• 5 0 1 1 1 0

12
References

• Programming in Prolog by W. F. Clocksin and C. S.
  Mellish.
• Prolog tutorial
• http//www.csupomona.edu/jrfisher/www/prolog_tuto
  rial/2_15.html