Farmer, Wolf, Goat Cabbage

Prolog's powerful problem-solving capabilities can be seen with an example, the classic farmer-goat-cabbage-problem.

The problem: A farmer and his goat, wolf and cabbage come to a river that they wish to cross. There is a boat, but it only has room for two, and the farmer is the only one that can row. If the goat and cabbage get in the boat at the same time, the cabbage gets eaten. Similarly, if the wolf and goat are together without the farmer, the goat is eaten.

Devise a series of crossings of the river so that all concerned make it across safely. The state of the system is indicated by stating where the farmer, the goat the wolf and the cabbage are located. state( Farmer, Wolf, Goat, Cabbage) The problem is that a state must only be visited once, and some states are illegal. This is checked by 'unsafe' and 'member'. The Predicate "go" can be called with a start state and a final state

A farmer with his goat, wolf and cabbage come to a river that they wish to cross. There is a boat, but it only has room for two, and the farmer is the only one that can row. If the goat and cabbage get in the boat at the same time, the cabbage gets eaten. Similarly, if the wolf and goat are together without the farmer, the goat is eaten. Devise a series of crossings of the river so that all concerned make it across safely.

The state of the system is indicated by a structure STATE stating where the farmer, the goat the wolf and the cabbage are located. The goal is then how to transform the start state to the endstate through a series of valid states.

The valid states are checked by the predicate 'unsafe'

The problem is that a state must only be visited once, this is handled by collecing the visited stetes in a list, and checking that a new state isnot already in the list.

The Predicate "go" can be called with a start state and a final state

go( state(east,east,east,east), state(west,west,west,west) ).

FWGC.PRJ

DOMAINS
  LOC = east ; west
  STATE = state(LOC farmer,LOC wolf,LOC goat,LOC cabbage)
  PATH = STATE*

PREDICATES
  go(STATE,STATE)	% Start of the algorithm
  path(STATE,STATE,PATH,PATH)	% Finds a path from one state to another
  nondeterm move(STATE,STATE)	% Transfer a system from one side to another
  opposite(LOC,LOC)	% Gives a location on the opposite side
  nondeterm unsafe(STATE)	% Gives the unsafe states
  nondeterm member(STATE,PATH)	% Checks if the state is already visited
  write_path(PATH)
  write_move(STATE,STATE)

GOAL
	go(state(east,east,east,east),state(west,west,west,west)),
	write("solved").

CLAUSES
go(StartState,GoalState):-
	path(StartState,GoalState,[StartState],Path),
	write("A solution is:\n"),
	write_path(Path).

path(StartState,GoalState,VisitedPath,Path):-
	move(StartState,NextState),	% Find a move
	not( unsafe(NextState) ),	% Check that it is not unsage
	not( member(NextState,VisitedPath) ),	% Check that we have not had this situation before
	path( NextState,GoalState,[NextState|VisitedPath],Path),!.
path(GoalState,GoalState,Path,Path).	% The final state is reached

move(state(X,X,G,C),state(Y,Y,G,C)):-opposite(X,Y). % Move FARMER + WOLF
move(state(X,W,X,C),state(Y,W,Y,C)):-opposite(X,Y). % Move FARMER + GOAT
move(state(X,W,G,X),state(Y,W,G,Y)):-opposite(X,Y). % Move FARMER + CABBAGE
move(state(X,W,G,C),state(Y,W,G,C)):-opposite(X,Y). % Move ONLY FARMER

opposite(east,west).
opposite(west,east).

unsafe( state(F,X,X,_) ):- opposite(F,X),!. % The wolf eats the goat
unsafe( state(F,U,,))-opAs/tA(T,C)V!.   OhT oStReWt h abg}

2mme(,X_3)-.	
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