Figure 6: Various alternative reductions used in TOAST.
We have shown how the cooking problem can be solved by a series of reductions and conventions. Binding allows the reduction of the problem to a schematic world in which action is greatly restricted and so action selection is greatly simplified. This world can be further reduced, given algorithms for resetting tools, to a world in which tools are always reset. This world, in turn, is equivalent to a world in which there is only one object, the material being cooked, and only one action can be taken at any given time. Such actions can be found by table lookup.
Multiple materials can be cooked by interleaving the execution of processes for cooking the individual materials. Interleaving the processes is equivalent, however, to interleaving the bindings, so the schematic-world algorithm need not even be aware that it is pursuing multiple goals. If tool bindings are continuously changed as tools are dirtied then tools are effectively disposable, tools effectively have only a single state, and the separate reduction from general tools to single-state tools is unnecessary. Material bindings can be maintained by any number of conventions involving the states and/or positions of objects.
In short, we can describe a TOAST algorithm as a path through a network of possible simplifications of the problem (see Figure 6) in which every path from the actual world to the idealized single-object world defines a possible (and correct) version of the TOAST algorithm.