Meta-interpreter

Note that I did restrict a grammar to consist only of a set of definite clauses defining the predicate sign/1. However, I will also use definite clauses of $\cal {R}$($\cal {L}$) to define meta-interpreters for such grammars. For these meta-interpreters I will assume the operational semantics sketched above. In such cases I treat the definite clauses defining sign as data; a clause:

$$\mbox{\it sign}(\mbox{\rm X}_{0}) \mbox{\tt :-} \mbox{\it si... ...box{\rm X}_{1}) \dots \mbox{\it sign}(\mbox{\rm X}_{n}), \phi.$$
is represented as the clause

$$\mbox{\it rule}(\mbox{\rm X}_{0},\langle \mbox{\rm X}_{1}, \dots \mbox{\rm X}_{n}\rangle) \mbox{\tt :-} \phi.$$
i.e. the body of the clause is represented as a list. A meta-interpreter for $\cal {R}$($\cal {L}$) thus may be defined as in program 6, which follows the procedural semantics of $\cal {R}$($\cal {L}$), i.e. it is a top-down proof procedure with a left-most computation rule and a depth-first search rule.

For example, a rightmost computation rule can be implemented by defining the predicate refutations as follows: