> the rank of the verb determins the cells. This is not correct. For example, it make sense to talk about the 1-cells of a matrix (the rows of a matrix) without reference to any verb.
----- Original Message ----- From: Dan Bron <[EMAIL PROTECTED]> Date: Friday, September 22, 2006 10:10 am Subject: Re: Cell (was Re: [Jgeneral] I expect a table of ordered pairs for this) > Short answer: > > The rank of the noun determines the items, > the rank of the verb determins the cells. > > Every noun can be thought of as a "list of something". For > example, a vector (a 1 dimensional noun) is a list of scalars, a > table (2D) is a list of vectors, a cube (3D) is a list of tables, > and so on. The items of a noun are whatever it's a list of. The > items of a vector are scalars, the items of a table are vectors, > the items of a cube are tables, and so on. > > Any verb can be limited to a certain rank of noun. That is, it > can be impossible for a verb to see a noun of higher than a > specific rank. For example, + can only see scalars, because > list+list makes no sense: only scalars can be added. So, no > matter how hard you try, + will only ever see a scalar at a > time. The highest rank of noun a certain verb can see is a "cell" > for that verb. > > Of course, you can feed a verb a higher ranked argument, in which > case there will be more than one cell, but the verb will still > only see one cell at a time. That's why list+list does work: > it's operating piecewise, adding a scalar at a time. > > A verb can have infinite (unbound) rank, in which case ANY > argument will only have one cell. Think of the monad < (box), > for example. No matter what argument you give it, it treats that > argument as an indivisible whole, and returns it in a box. > > A verb can also define its cells in terms of the rank of the noun, > so, for example, "_1 means "operate on rank one less than the > argument", which means "treat the argument like a list of cells", > which means "operate on the items of the argument". So, in the > special case of a verb "_1 , the items and the cells are the same. > > Does that clarify? ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
