// Tower of Hanoi Puzzle

// Rules
hanoi(return, source, target, auxiliary) >< (int n)
| n==0 => return~[], Eraser~source, Eraser~target, Eraser~auxiliary
| _    => source ~ Dup(src1, Dup(src2, src3)),
         target ~ Dup(tgt1, Dup(tgt2, tgt3)),
         auxiliary ~ Dup(aux1, aux2),
         hanoi(ret1, src1, aux1, tgt1)~(n-1),
         hanoi(ret2, aux2, tgt2, src2)~(n-1),
         Append(return, (n,src3,tgt3):ret2)~ret1;
	 // This Append is a bulit-in agent.

// The Dup is defined as built-in:
// Dup(a,b)><A => a~A, b~A;
// Dup(a,b)><B => a~B, b~B;
// Dup(a,b)><C => a~C, b~C;

// The `Eraser' is defined as a built-in agent for any agents as follows:
//Eraser >< Alpha(a1, ..., a5) => Eraser~a1, ..., Eraser~a5;


// Net
hanoi(result, A, C, B) ~ 3;
result; // should be [(1,A,C),(2,A,B),(1,C,B),(3,A,C),(1,B,A),(2,B,C),(1,A,C)]


// These are also written using abbreviation as follows:
//   hanoi(return, source, target, auxiliary) >< (int n)
//   | n==0 => return~[],
//             << Eraser(source), << Eraser(target), << Eraser(auxiliary)
//   | _    => src1, Dup(src2, src3) << Dup(source),
//            tgt1, Dup(tgt2, tgt3) << Dup(target),
//            aux1, aux2 << Dup(auxiliary),
//            ret1 << hanoi(src1, aux1, tgt1, n-1),
//            ret2 << hanoi(aux2, tgt2, src2, n-1),
//            return << Append(ret1, (n,src3,tgt3):ret2);
//
//   result << hanoi(A, C, B, 3);
//   result;