I think rank 1 literals might be more related. Or, at least, are more immediately suitable for implementation here.
Thanks, -- Raul On Thu, Dec 21, 2017 at 9:57 AM, Erling Hellenäs <[email protected]> wrote: > Hi all ! > > This is SGML, HTML, XML, the Windows Registry and LDAP. It's old > hierarchical databases? At least related? > > Could the algebra proposed help us handle them? > > Cheers, > > Erling Hellenäs > > > > Den 2017-12-20 kl. 18:52, skrev 'Bo Jacoby' via Programming: >> >> I am impressed by the J programming language and by the array concept. >> However, boxed arrays and sparse arrays and empty arrays illustrate >> shortcomings in the array concept of J. >> I suggest using ordinal fractions for structuring, storing and handling >> data. Then there is no need for boxing, nor for differentiating between >> sparse arrays and other arrays. However I have not constructed a programming >> language like J to manipulate such data. >> The concept is introduced in the old article behind this link. (Sadly the >> e-mail software tend to disrupt my links. I hope this link survives). >> https://www.academia.edu/10031088/ORDINAL_FRACTIONS_-_the_algebra_of_data >> >> Here are some differences between arrays and Ordinal Fractions (OFs): >> - Arrays have different shapes. OFs have the same shape: (_$9) >> >> - J-arrays have zero-origin indexing. OFs have one-origin indexing. >> >> - Arrays may have elements. OFs have no elements. >> >> - Array elements contain data. OFs may contain data. >> - Arrays may contain subarrays. OFs always contain subordinate OFs. >> - An array may have a name. An OF may contain a name. >> - In J a scalar differs from a shape 1 array. Not so in OFs. >> >> Here are some differences between nonnegative integers and (OFs): >> - Any sequence of digits (0 1 . . . 9) represents a base-ten >> integer, or a base-nine OF. >> - Integers may be padded with zeroes to the left, OFs to the right. >> - Digit 0 in an integer indicate that a term is omitted. Digit 0 in an >> OF indicate that a condition is omitted. >> - The integer 0 means "nothing". The OF 0 means "everything". >> >> I think that ordinal fractions is a unified way of structuring data: >> scalars, arrays, trees, databases.alike. >> Thanks >> Bo. >> >> Den 13:32 onsdag den 20. december 2017 skrev Raul Miller >> <[email protected]>: >> >> Actually, J does support arrays of nothing. That's what i.0 is, after >> all. And, if you want a scalar containing an array of nothing, then a: >> matches that specification. >> >> And we have an algebra here - though if (as in your previous message) >> you do multiplication and call it addition, this becomes very >> difficult to talk about. >> >> That said, remember that we can add an arbitrary number of leading 1 >> dimensions to any array without changing the number of elements in >> that array. >> >> Thanks, >> > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
