User blog:Primussupremus/My idea for a new notation.

A few days ago I was experimenting with a new type of notation that is similar to BEAF but at the same time is vastly different,

Define:

{a} = a.

{a,b} = a^b

{a,b,c} = a{b up arrows}c.

{a,b,c,d} = {a,b,c} recursed d-1 times.

To give an example of each of the 4 base levels we have:

{3} = 3.

{3,3} = 3^3 = 27.

{3,3,3} = 3{ 3 up arrows} 3 =

{3,3,3,3} = 3{(3{(3{3 up arrows}3) up arrows}3)up arrows}3.

To make this a bit clearer here is a brief explanation using letters and numbers.

Now that we have that defined we can move on to 5+ entry arrays.

{a,b,c,d,e} = {a,b,c,d} recursed ({a,b,c,d}-1) times for n>0.

Generally for an array of length k ( a k tuple) > 4 you recurse it ({k-1 tuple}-1) times.

Now lets move on to using the array of operator in my array notation:

{K&L} = array an of length K made up of a symbol called P:

For example {4&3} = {4,4,4}

Now lets move on to an even more powerful arrays of the form {(K&L)&P}

{(K&L)&P} = {K&L} recursed ({K&L}-1) times for P repeats.

Next we have {((K&L)&P)&Q} = {(K&L)&P} recursed ({(K&L)&P}-1) times for Q repeats.

We can generalise this second level part of the notation as :

An array closed under the & sign as shown above of length K>2 = the (k-1)th array of this format (where k is the length of the array you are using) recursed (k-1)th array ,  number of times for X repeats (where X is symbol outside of the brackets and connected to whats inside the brackets,  for example {(K&L)P} includes such a symbol called P).

To save space I have also defined an operator for compacting arrays of this kind to fit in a much smaller space.

{K(X) K} = An array of length X ( the array is of the form shown above) made up of a symbol called K.

For example {3(3)3) = {(3&3)&3}.

We could even have an array like this {K({K(X)K})K}:

This means that you recurse ({K(X)K}-1) times.

To generalise this for expansion arrays of length k>2 you recurse it the (k-1)th exapnsion array nuumber of tim