We aim to define a \(\texttt{Robot}\) ADT moving in a two dimensional space with functions allowing to:

• Create a robot from a position \((x, y)\) and a direction (\(\texttt{North}\), \(\texttt{South}\), \(\texttt{East}\), \(\texttt{West}\)) that becomes its current direction;
• Determine the current position;
• Determine the current direction;
• Move a step forward from the current direction;
• Move a step backward from the current direction;
• Rotate 90 degrees clockwise.

Define the \(\texttt{Robot}\) ADT.

Type 	robot

Parameter

Use 	real, direction
Operations
	Create : real x real x direction	->	robot
	Current_pos : robot			->	real x real 
	Current_dir : robot			->	direction
	Step_fwd : robot			->	robot
	Step_bkwd : robot			->	robot
	Rotate : robot				->	robot

Constructors
	Create

Preconditions
	-

Axioms
Let d be a direction, x and y 2 reals :
Current_pos(Create(x,y,d)) = (x,y)
Current_dir(Create(x,y,d)) = d
Step_fwd(Create(x,y,d)) = If d = East then Create(x+1,y,d) else id d = West then Create(x-1,y,d) else if d =
				North then Create(x,y+1,d) else Create(x,y-1,d)
Step_bkwd(Create(x,y,d)) = If d = East then Create(x-1,y,d) else If d = West then Create(x+1,y,d) else If d =
				North then Create(x,y-1,d) else Create(x,y+1,d)
Rotate(Create(x,y,d)) = If d = East then Create(x,y,South) else If d = West then Create(x,y,North) else If d =
				North then Create(x,y,East) else Create(x,y,West)