A Shapes World

A micro world is a (computer) model of a restricted type of "reality".
It is used (by artificial intelligence designers) to study the types
of relations (spatial, stimulus, response, etc.) between elements
of the world.

A shapes world consists of various shapes (2-D in this case)
and their relationships to one another.  For our purposes, a shape
is modeled in terms of three properties,
its kind (square, rectangle, circle, etc.), its size,
and its position.

"Natural language" input to the system consists of "queries" of the
following forms:

Form:     'place' IndefArticle Color 'square' 'at' Number Number 'with' 
             'side' Number '.'
Meaning:  Add a square to the knowledge base at give (x,y) coordinates.
          Article may be either 'a' or 'an'.  Color must be among the colors
          specified by the grammar (red, blue, green for now). The first
          Number is an X coordinate, the second is a Y coordinate.

Form:     'place' IndefArticle Color 'rectangle' 'at' Number Number 
          'of' 'height' Number 'and' 'width' Number '.'
Meaning:  Add a rectangle...

Form:     'place' IndefArticle Color 'circle' 'at' Number Number 
          'of' 'radius' Number '.'
Meaning:  Add a circle...

Form:     'what' ( 'squares' | 'rectangles' | 'circles' | 'shapes' )
             'are' 'there' '?'
Meaning:  enumerate the specified objects.

Form:     'what' 'color' Shapes 'are' 'present' '?'
Meaning:  respond with the colors.

Form:     'are' 'there' 'any' Color Shapes 'present' '?'
Meaning:  respond with yes/no

Form:     'how' 'big' 'is' DefArticle Shape 'at' Number Number '?'
Meaning:  respond with length for squares, height and width for
          rectangles, radius for circles

Form:     'what' 'is' 'the' 'area' 'of' DefArticle Shape 'at' Number Number '?'
Meaning:  respond with the area of the named shape

Form:     'where' 'is' Shape '?'
Meaning:  respond with the set of X and Y coordinates

Form:     'what' Shapes 'are' 'to' 'the' ( 'left' | 'right' ) 'of'
              DefArticle Shape 'at' Number Number '?'
Meaning:   respond with the appropriate list

Form:      'are' 'there' 'any' Shapes 'to' 'the' ( 'left' | 'right' )
              'of' IndefArticle Shape '?'
Meaning:   respond YES if there are any objects in class Shape such that
           right(left)most part of the first shape named
           is less(greater) than the left(right)most part of the
           second shape named,
           NO if not.

Form:      'which' 'shape' 'is' 'smallest' '?'
Meaning:   respond with the name of the shape which is smallest in area.

Form:      'which' Shape 'is' ( 'smallest' | 'largest' ) '?'
Meaning:   respond with the name of the shape which is smallest (largest)
           in area.

Form:      'stop' '.'
Meaning:   return to Prolog