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To explain the notion of a 'cache' and many other Logiweb data structures, we first need to introduce the notion of a Logiweb 'array'. A Logiweb array is an associative structure which can map integers to arbitrary values. Logiweb arrays are organized such that the access time is logarithmic in the number of entries of the array in the cases of interest to Logiweb.
The values of an array may themselves be arrays. We shall refer to an arbitrary value as a 0-dimensional array and to an array of n-dimensional arrays as an (n+1)-dimensional array.
For an array A and a cardinal n we shall use A[n] to denote the value that A associates to n. For an e.g. 3-dimensional array B, B[u][v][w] denotes ((B[u])[v])[w].
Arrays may be sparse: an array may map e.g. 10 and 20 to values without mapping the numbers in between to anything. In the cases of interest to Logiweb, the access time of an array A is logarithmic in the number of indexes i for which A[i] is defined.
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