The monkey-and-bananas problem is faced by a monkey in a laboratory with some bananas hanging out of reach from the ceiling. A box is available that will enable the monkey to reach the bananas if he climbs on it. Initially, the monkey is at A, the bananas at B, and the box at C. The monkey and box have height Low, but if the monkey climbs onto the box he will have height High, the same as the bananas. The actions available to the monkey include Go from one place to another, Push an object from one place to another, ClimbUp onto or ClimbDown from an object, and Grasp or Ungrasp an object. The result of a Grasp is that the monkey holds the object if the monkey and object are in the same place at the same height.

a. Write down the initial state description.
b. Write the six action schemas.
c. Suppose the monkey wants to fool the scientists, who are off to tea, by grabbing the bananas, but leaving the box in its original place. Write this as a general goal (i. e., not assuming that the box is necessarily at C) in the language of situation calculus. Can this goal be solved by a classical planning system?
d. Your schema for pushing is probably incorrect, because if the object is too heavy, its position will remain the same when the Push schema is applied. Fix your action schema to account for heavy objects.