Path: utzoo!attcan!uunet!lll-winken!lll-lcc!ames!mailrus!iuvax!pur-ee!a.cs.uiuc.edu!uxc.cso.uiuc.edu!uicsrd.csrd.uiuc.edu!jaxon
From: jaxon@uicsrd.csrd.uiuc.edu
Newsgroups: comp.lang.apl
Subject: Re: encode question
Message-ID: <49700003@uicsrd.csrd.uiuc.edu>
Date: 18 Jul 88 15:23:00 GMT
References: <6238@umn-cs.cs.umn.edu>
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Nf-ID: #R:umn-cs.cs.umn.edu:6238:uicsrd.csrd.uiuc.edu:49700003:000:794
Nf-From: uicsrd.csrd.uiuc.edu!jaxon    Jul 18 10:23:00 1988


As author of the "Represent" (aka "encode") definition as printed in
the ISO standard, I should perhaps explain.

Just as 10 is not a valid digit in base 10, so 1 is not a valid digit
in base 1.   I realize that "unary notation" (tallying) is often mistaken
for a "positional" (fixed radix) number system, but the two concepts are
centuries apart.

Many APL statements produce a "unary" form of an integer argument, one
close to what you'd expect from encode is:

        (reverse iota LIMIT) jot . leq N     

for origin 1, non-negative integers N.  This is the traditional low-budget
histogram program.  (Actually ' *'[#IO + (above expr)]  looks better).

If you're wondering where the 2 goes in  1 1 1 1 encode 2, try
0 1 1 1 1 encode 2.  Also try 0 1 encode 2.71828.

regards - greg jaxon