>(x&f)^:n y is the same as x f^:n y, by definition. Right. Regarding the expressions ( x f^:3 y ) and ( (f&y)^:3 x ), they can be clearly different (even for an associative f) ; using symbolic verbs,
(X u ^:3 Y) (X u (X u (X u Y))) (u&Y)^:3 X (((X u Y) u Y) u Y) Ambrus already answered the original question, again, (X u ^:3 Y) (X u (X u (X u Y))) or indeed equivalently, (X&u)^:3 Y (X u (X u (X u Y))) -----Original Message----- From: Roger Hui <[email protected]> Sent: Saturday, March 20, 2010 1:52 PM To: Programming forum <[email protected]> Subject: Re: [Jprogramming] recursive composition (x&f)^:n y is the same as x f^:n y, by definition. ----- Original Message ----- From: Bo Jacoby <[email protected]> Date: Saturday, March 20, 2010 8:46 Subject: Re: [Jprogramming] recursive composition To: Programming forum <[email protected]> > Hi John > but > (x&f)^:3 y > _2 > - Bo > > --- Den lør 20/3/10 skrev John Randall > <[email protected]>: > Fra: John Randall <[email protected]> > Emne: Re: [Jprogramming] recursive composition > Til: "Programming forum" <[email protected]> > Dato: lørdag 20. marts 2010 16.17 > > Raul Miller wrote: > > On Fri, Mar 19, 2010 at 1:43 PM, David Ward Lambert > > <[email protected]> wrote: > >> NB. j programmers MUST understand data flow. > >> NB. x f^:3 y differs from (f&y)^:3 x > > > > To illustrate this we should find an operation which > > is not associative and which produces a plausible result > > for one of those two cases. > > It is easy to show by example that these are different, for example > > x=:2 > y=:4 > f=:- > x f^:3 y > _2 > (f&y)^:3 x > _10 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
