In Section 2.4.1 we use meta-interpretation to describe a control strategy for the dynamics of our model. In that example, we used a different meta-interpreter for the operator model than for the decision procedure model but the same principle applies to both. To emphasise the basic principle let us use a simplified interpreter, which is:
where: the first expression finds a solution for some input, X, to the operator model if there is an output via some operator, Op, which yields X; the second expression finds a solution for a conjunction from solutions for each side of the conjunction; and the third expression finds a solution for a decision goal, D, if there is a clause giving a condition, C for D and there is a solution for that condition. This gives us a strategy for testing whether certain results are derivable from the model but it doesn't give us information about how these were derived. For example, we might want to have a record of the operators which were used in deriving a given result. To do this we extend the meta-interpreter with a pair of arguments which accumulate this extra information, giving the new interpreter:
where the first of the two additional arguments to P is the sequence of operators applied so far and the second of the additional arguments is the final sequence of operators once the result is obtained.