Newsgroups: comp.lang.apl
Path: utzoo!utgpu!news-server.csri.toronto.edu!torsqnt!geac!itcyyz!yrloc!hui
From: hui@yrloc.ipsa.reuter.COM (Roger Hui)
Subject: Re: Forks, Hooks and With in J
Message-ID: <1991Jun11.000420.3398@yrloc.ipsa.reuter.COM>
Reply-To: hui@yrloc.ipsa.reuter.COM (Roger Hui)
Organization: Iverson Software Inc.
References: <kjell.675944273@ygdrasil> <ROCKWELL.91Jun3084928@socrates.umd.edu> <b6k78e.jss@wang.com>
Date: Tue, 11 Jun 91 00:04:20 GMT

Comments on recent postings by Kjell Post, Raul Rockwell, and Bill Wicker.
 
Expressions in J are better represented as trees than as DAGs.
For example, try representing  (a+b)*(b+c)  as a DAG.
 
&  , like all other conjunctions, accepts noun or verb arguments,
thereby giving rise to four possible cases of derivations.  In principle,
the four cases need not be related, nor do the monadic and dyadic defns.
   m & n    undefined
   m & v    with,     m&v y  is  m v y  ;  x m&v y  has empty domain
   u & n    with,     u&n y  is  y u n  ;  x u&n y  has empty domain
   u & v    compose,  u&v y  is  u v y  ;  x u&v y  is  (v x) u (v y)
 
Many useful verbs can be defined as  m&v  or  u&n  :
  0&-  negation     ^&0.5 square root    0&<     positive
  _1&* negation     10&^. base-10 log    a.&i.   ASCII code
  +&1  increment    0&{   first          -.&' '  remove blanks
  -&1  decrement    _1&{  last           2&(-~\) first difference
 
All verbs are ambivalent, although some verbs have empty monadic
or dyadic domains.  Whether the monadic or the dyadic definition of
a verb is applied, is determined by context, as defined by the first
three parsing rules in Table 2 of the dictionary.  These parsing rules
apply to all verbs (whatever their derivation).
 
In the fork (f g h), f and g are ambivalent, and whether f or h
have empty monadic or dyadic domains would not be "discovered"
until the derived verb is applied.  For  u=.f@[ g h@]  ,
  x u y                    u y
  x (f@[ g h@]) y          (f@[ g h@]) y          defn of u
  (x f@[ y) g (x h@] y)    (f@[ y) g (h@] y)      defn of fork
  (f x[y) g (h x]y)        (f [ y) g (h ] y)      defn of @
  (f x) g (h y)            (f y) g (h y)          defn of [ and ]
 
As in the above example, and as specified in the dictionary, a fork
(hook) is an isolated sequence of 3 verbs (2 verbs).  Parentheses may
be required to effect that isolation.
 
The explicit verb  trim=.'(-.'' ''=y.)#y.' : ''  can be stated tacitly
as  -.&' '  .  ("Explicit" because the argument is explicitly mentioned;
"tacit" because not.)  Translations more faithful to the original:
   -.@(' '&=) # [
   #~ -.@(' '&=)
 
As noted in Bill Ricker's msg,  #~ (-. ' '&=)  is not an equivalent
computation.  (-. ' '&=)  is a hook not because  -.  is dyadic
(it is ambivalent), but because the parsing rules specify that an
isolated sequence of 2 verbs is a hook.  This derives a verb v, whence
#~ v  is an isolated sequence of 2 verbs, and is another hook.
 
J 3.1 has an explicit-to-tacit translator:
   'x.+y.' : 11
+-+-+-+
|[|+|]|
+-+-+-+
   '(x.+y.)*(x.-y.)' : 11
+-------+-+-------+
|+-+-+-+|*|+-+-+-+|
||[|+|]|| ||[|-|]||
|+-+-+-+| |+-+-+-+|
+-------+-+-------+
   '+/y.' : 11
+-----+-+-+
|+-+-+|@|]|
||+|/|| | |
|+-+-+| | |
+-----+-+-+
   '(-.'' ''=y.)#y.' : 11
+--------------------+-+-+
|+--+-+-------------+|#|]|
||-.|@|+-------+-+-+|| | |
||  | ||+-+-+-+|@|]||| | |
||  | ||| |&|=|| | ||| | |
||  | ||+-+-+-+| | ||| | |
||  | |+-------+-+-+|| | |
|+--+-+-------------+| | |
+--------------------+-+-+
 
The last result is the verb  -.@((' '&=)@]) # ]  (a fork).  Not all
explicit verbs can be so translated.

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