For linear and multidimensional arrays, BAN is the same as BEAF. * Rule 1. With one or two entries, we have \(\{a\} = a\), \(\{a,b\} = a^b\) (by the way, \(\lbrace a brace = a\) follows from \(\{a,b\} = a^b\), since \(\{a\} = \{a,1\} = a^1 = a\) (inverse of rule 2). * Rule 2. If the last entry is 1, it can be removed: \(\{\# 1\} = \{\#\}\). (The octothorpe indicates the unchanged remainder of the array.) * Rule 3. If the second entry is 1, the value is just the first entry: \(\{a,1 \#\} = a\). * Rule 4. If the third entry is 1: \(\{a,b,1,1,\cdots,1,1,c \#\} = \{a,a,a,a,\cdots,a,\{a,b-1,1,1,\cdots,1,1,c \#\},c-1 \#\}\) * Rule 5. Otherwise: \(\{a,b,c \#\} = \{a,\{a,b-1,c \#\},c-1 \#\}\)