Newsgroups: comp.lang.apl
Path: watmath!watserv2.uwaterloo.ca!torn!cs.utexas.edu!wupost!uwm.edu!news.mr.med.ge.com!newsparc6!gurr
From: gurr@newsparc6 (David Gurr 4-6989 MR Sys)
Subject: rank vs. depth (was: box vs. nest)
Message-ID: <1992Oct9.130835.9740@mr.med.ge.com>
Sender: news@mr.med.ge.com
Nntp-Posting-Host: newsparc6
Organization: GE Medical Systems, Magnetic Resonance
X-Newsreader: Tin 1.1 PL3
References: <1992Oct6.153157.20602@yrloc.ipsa.reuter.COM>
Date: Fri, 9 Oct 92 13:08:35 GMT
Lines: 37

Associated with the boxing vs. nesting debate is the rank vs.
 depth debate.  Benkard gave a paper called rank vs. depth and 
gave the IBM side.  Is there a paper, or would someone like to 
give the Sharp side of rank vs. depth?

My own understanding of nested arrays and boxed arrays is as 
follows. The non-empty axies of a rank 3 array are 0,1,2.  The 
axies after the third axis are empty and do not contribute to 
the dimensionality of the array.  The axies of a rank 3 array 
with a rank 5 arrays nested in it are 0,1,2,...,\omega ,\omega +1,
\omega +2,\omega +3,\omega +4.  The axies between 2 and \omega 
are empty and the axies after \omega +4 are empty.  The axies 
of a rank 3 array of boxed arrays of rank 5 are 0,1,2,...,
\omega \squared ,\omega \squared +1,\omega  \squared +2,
\omega \squared + 3,\omega \squared +4.  The axies between 2 
and \omega \squared are empty and the axies after 
\omega \squared +4 are empty.

If this is true, then one can define pervasion in terms of rank, 
and APL2's pervasive functions are rank varients of Dictionary 
APL's functions.

I would be interested in knowing what people think of this.  
I'll not be offened if you think that this attempt to comprehend 
both Dictionary APL and APL2 is a perversion, but please detail 
how and where I went wrong.

This interpretation is based on a APL construction kit I am 
slowly putting together that will allow one to quickly prototype 
proposed extensions of APL and share them with others so that we 
can all have better first hand experence with various extensions 
and how they interact.  It is how I get the generality needed for 
various extended APLs.

David Gurr
gurr@mr.med.ge.com

