User blog:Wythagoras/Formal definition of BEAF

In this blog post I'll try to make a formal ruleset for BEAF.

Linear Array Notation
1. \(\{a,1,\#\} = a\)

2. \(\{a,b,1,1 \ldots 1,1\} = a^b\)

3. \(\{a,b,1,1 \ldots 1,1,c,\#\} = \{a,a,a,a \ldots a,\{a,b-1,1,1 \ldots 1,1,c,\#\},c-1,\#\}\)

Array of
4. \(a \text{&} b = \{\underbrace{b,b,b,b,\ldots,b,b,b,b}_a\}

5. \(\#+X \text{&} a = \#+a \text{&} a \)

6. \(\#+b+1 \text{&} a = \{a,a(\#+b)a\}\)

7. \(\{a,a(\#+b)2\} = \#+b \text{&} a\)

8. \(\{a,a(\#+b)c\} = \{\#+b \text{&} a(\#+b)c-1\}\)