By Wirth N.
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Additional info for Algorithms and data structures, Oberon version
In the notations of the KMP algorithm, the alignment position of the pattern is now i-j (and not i, as was the case with the simple algorithm). The central pont of the algorithm is the comparison of s[i] and p[j], if they are equal then i and j are both increased by 1, otherwise the pattern must be shifted by assigning to j of some smaller value D. The boundary case j = 0 shows that one should provide for a shift of the pattern entirely beyond the current comparison point (so that p becomes aligned with s[i+1]).
Apart from the actual data transfer, they also involve a transformation of representation. For example, numbers, usually considered as atomic units and represented in binary form, need be transformed into readable, decimal notation. Structures need to be represented in a suitable layout, whose generation is called formatting. Whatever the transformation may be, the concept of the sequence is once again instrumental for a considerable simplification of the task. The key is the observation that, if the data set can be considered as a sequence of characters, the transformation of the sequence can be implemented as a sequence of (identical) transformations of elements.
However, the interaction of two loops via a logical variable destroys the original transparency, which may cause errors in the program evolution. Formulation of such loops is facilitated by the so-called Dijkstra loop, which is a multibranch version of the WHILE loop with each branch having its own guard (see Appendix C). In the present case the two branches correspond to the steps in i and j, respectively. Recall Fig. 9 and introduce the predicate P(i, j) that expresses the match of the first j characters of the pattern with the characters of the text starting from position i: P(i, j) = Ak: 0 ≤ k < j : si+k = pk Then R(i) = P(i, M).
Algorithms and data structures, Oberon version by Wirth N.