Path: utzoo!utgpu!news-server.csri.toronto.edu!torsqnt!geac!itcyyz!yrloc!hui
From: hui@yrloc.ipsa.reuter.COM (Roger Hui)
Newsgroups: comp.lang.apl
Subject: Re: Do While in J?
Message-ID: <1991Mar26.053718.4160@yrloc.ipsa.reuter.COM>
Date: 26 Mar 91 05:37:18 GMT
References: <MJAB.91Mar22144533@nanna.think.com>
Reply-To: hui@yrloc.ipsa.reuter.COM (Roger Hui)
Distribution: comp
Organization: Iverson Software Inc.
Lines: 27

A gerund is a verbal form that can be used as a noun, as "programming"
in "programming is an art".  Gerunds in J are arrays of atomic representations 
of verbs, and can be manipulated like other nouns.  When recognized by adverbs 
and conjunctions, gerunds give rise to many useful verbs, such as do-while, 
if-then-else, case, and recursion.  (See Bernecky and Hui paper in APL91.)

The notation for gerunds has evolved since J 2.9.  In particular,
u`v (previously u .v) yields the atomic representations of u and v.

If g=.v0`v1`v2 ... , then g/x inserts v0, v1, v2 between the items of x,
repeating v0, v1, ... cyclically.  It is therefore a generalization of
the ordinary insert f/x (which inserts the single verb f).  For example,
+`*/}.,x,"0 y  evaluates polynomial y at x using Horner's rule.

If g=.p`b`c`r and f=.g\ , then f y is b y if p y is 0, and f y is y c f r y
otherwise.  Thus factorial can be define as  fac=.*`1:`*`<: .  From their
use in g\, the verbs p, b, c, and r may be remembered as follows:
  proposition  (*   signum in factorial example)
  basis        (1:  constant function 1)
  combine      (*   multiply)
  reduce       (<:  decrement)

Other verbs can be derived similarly, usually as g`:k for the conjunction
`: (previously spelt : ), but also as  g adv  for certain cases (as with \).

Roger Hui, Iverson Software Inc., 33 Major Street, Toronto, Ontario  M5S 2K9
(416) 925 6096