From http://keiapl.org/rhui/remember.htm#fork0
... For years, Ken had struggled to find a way to
write f+g as in calculus, from the “scalar operators”
in Operators and Functions [5, section 4], through
the “til” operator in Practical Uses of a Model of APL [6]
and Rationalized APL [7, p. 18], and finally forks.
Forks are defined as follows:
(f g h) y ↔ (f y) g (h y)
x (f g h) y ↔ (x f y) g (x h y)
Moreover, (f g p q r) ↔ (f g (p q r)) . Thus to write f+g
as in calculus, one writes f+g in J. ...
There are ways to create "fork-like" structures in J
using a conjunction. That is, it is possible to have
a "simpler" language by removing row 5 of the parse table
http://www.jsoftware.com/help/dictionary/dicte.htm
but fork is so overwhelmingly important and useful
and it is worth the extra parse rule.
A conjunction that resembles (f &&& g) is the "til"
operator in Rationalized APL. See pages 36 and 37 in
http://www.jsoftware.com/jwiki/Doc/Rationalized_APL
Til can be modeled in J as follows:
til=: 2 : 0
(v y) u y
:
(v y) u x
)
For example:
f=: ('(f '&,)@(,&')')@":
g=: ('(g '&,)@(,&')')@":
comma=: , (','&,)
comma til f til g 5
(f 5),(g 5)
But fork is much better.
----- Original Message -----
From: Tracy Harms <[email protected]>
Date: Wednesday, March 11, 2009 12:05
Subject: [Jprogramming] algebraic formalism excluding trains
To: Programming forum <[email protected]>
> I've been asked whether a particular combinator can be written readily
> in J without relying on verb trains. I've replied in the
> negative, but
> I'd like to put this before the J community so that my answer
> may be
> corrected if wrong, or perhaps supplemented.
>
> Here is the entire conversation between me and Conal Elliott, to date:
>
> TH: Rereading John Backus 1977; section 12.9 stands out.
> Is that
> aspect of this much-lauded paper applied in Haskell? ...
> Does Haskell
> follow Backus' advice (esp. 12.9)?
>
> CE: I love that backus paper. which advice in 12.9
> in particular?
>
> TH: I hear Backus advise an algebraic form, more
> restrictive than
> systems of Church or Curry, so that equivalence (e.g.) is more plain.
>
> CE: I hear the same. Haskell does not follow that advice.
>
> TH: Backus' example is [f , g]o h = [f o h , g o h] which
> I can write
> in J as (f;g)@h -: (f...@h;g...@h) How would I code it in Haskell?
>
> CE: it's called (&&&) in haskell and works for all arrows. on
> functions, it's (f &&& g) x = (f x , g x). See
> http://bit.ly/11G2IH .
> and yes, (f &&& g) . h == (f . h &&& g . h)
>
> TH: Thanks for identifying (&&&). I think there is no
> equiv. symbol
> in J. Instead, that meaning is implied syntactically; called "fork".
>
> CE: if "fork" weren't already in J, could you define it
> and use it
> conveniently?
>
> TH: No. J's verb trains (e.g. fork) allow separation-and-
> rejoining to
> be put in terms of functions, not structures of resulting values.
>
>
> My question to the J forum is: Have I erred or overlooked anything?
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
