Lists in Prolog - Thinking as Computation - page 149

Figure 7.4. Using the list version of the blocks world program

?- left(b1,b7).
Call: (7) left(b1, b7)
Call: (8) scene(_L205) % Get the scene.
Exit: (8) scene([[b1, b2], [b3, b4, b5, b6], [b7]])
% Generate a first pair of stacks.
Call: (8) before(_L206, _L207, ...)
Exit: (8) before([b1, b2], [b3, b4, b5, b6],...)
Call: (8) member(b1, [b1, b2]) % Test if X is in the first.
Exit: (8) member(b1, [b1, b2]) % YES
Call: (8) member(b7, [b3, b4, b5, b6]) % Test if Y is in the second.
Fail: (8) member(b7, [b3, b4, b5, b6]) % NO

Redo: (8) member(b1, [b1, b2])
Fail: (8) member(b1, [b1, b2])
% Generate another pair of stacks.
Redo: (8) before(_L206, _L207, ...)
Exit: (8) before([b1, b2], [b7], ...)
Call: (8) member(b1, [b1, b2]) % Test if X is in the first.

Exit: (8) member(b1, [b1, b2]) % YES

Call: (8) member(b7, [b7]) % Test if Y is in the second.

Exit: (8) member(b7, [b7]) % YES

Exit: (7) left(b1, b7) % The second pair works.

Yes

7.3.1 The blocks world revisited

The predicates member and append can be used to define a much more succinct version
of the blocks-world program (see section 4.2).
Here is the idea. An entire blocks-world scene can be represented by a left-to-right
list of stacks, where a stack is represented by a top-to-bottom list of blocks. So the
scene depicted in figure 4.1 is represented by the following list:

[[b1,b2],[b3,b4,b5,b6],[b7]]

The predicates above and left can then be defined using the before predicate:
A block X is above a block Y in the scene if there is a stack in the scene where X
appears before Y in the stack.

A block X is somewhere to the left of a block Y if there is a stack in the scene that
contains X that is before a stack in the scene that contains Y .

The full blocks-world program is shown in figure 7.3. A trace of the left predicate is
shown in figure 7.4.