Hints for Hw5

Puzzle
------

You can think of the problem as that of finding a path in a graph:
Given an initial state (everything on one side of the river bank), the
Prolog program needs to find a path to the final state (everything on
the other side of the river). So the problem is that of 
	(i) representing the puzzle in terms of a graph by defining
	nodes and arcs/edges of the graph, and 
	(ii) defining a program that will find a path in the above 
	graph.

Let us first look at representing the puzzle as a graph. For our
problem, nodes are state of the puzzle, indicating the location of the
farmer, wolf, goat, and cabbage Thus, you will need to specify what is
a node in the graph: it includes all valid states and does not include
any an invalid state (and hence the Prolog program should not include
it in any searches).  You will need to define rules for specifying
valid and invalid states. An example:

		unsafe(state(A, B, B, C)) :- opposite(A, B).

For edges/arcs you need to define how two nodes are connected. In
other words, how can the Prolog program go from one valid state to
another valid state. An example rule could be:

	arc(take(wolf, A, B), state(A, A, C D), state(B, B, C, D))
			:- opposite(A, B).

	This specifies that (i) wolf is being moved from one side to
	another, and (ii) corresponding changes in states.

You will need to define all rules that specify such moves.

Finally you need to define a set of rules for traversing a graph with nodes and
edges/arcs. Look at your book for graph traversal and plug it with what
you have defined earlier. 

Given that go(A, B) prints out path from node A to node B, you can
solve the puzzle with:
	go(state(left, left, left, left), state(right, right, right, right)).