Another example: , til *: til -: 5 25 2.5 (*:5),(-:5) 25 2.5 (*: , -:) 5 25 2.5
So far it looks like til is at least competitive with fork. Suppose you want f,g,h? For fork, it's (*: , -: , %:) 5 25 2.5 2.23607 For til, , til (, til *: til -:) til %: 5 25 2.5 2.23607 That little displacement of the , from the middle to the left, in the expression , til f til g to effect f,g , manifests undesirable consequences when you have to do f,g,h or f0,f1,f2,f3 etc. ----- Original Message ----- From: Roger Hui <[email protected]> Date: Wednesday, March 11, 2009 22:00 Subject: Re: [Jprogramming] algebraic formalism excluding trains To: Programming forum <[email protected]> > 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
