Re: syntax extension, precedence, Notation`

*To*: mathgroup at smc.vnet.net*Subject*: [mg106577] Re: syntax extension, precedence, Notation`*From*: magma <maderri2 at gmail.com>*Date*: Sun, 17 Jan 2010 07:10:07 -0500 (EST)*References*: <201001120949.EAA15726@smc.vnet.net> <hik8s7$6j4$1@smc.vnet.net>

On Jan 14, 11:46 am, Richard Fateman <fate... at cs.berkeley.edu> wrote: > Jaebum Jung wrote: > > You might want to try Notation package. > > > In[1]:= <<Notation` > > In[2]:= BetterRules[x_->y_]:=x->y^2 > > In[3]:= Notation[x__/! y_ \[DoubleLongLeftRightArrow] > > ReplaceAll[x__,BetterRules[y_]]] > > In[4]:= (x+y)/!(x->3) > > Out[4]= 9+y > > I tried Jaebum's suggestion , and while a useful hint, it doesn't work. > > 1. line 3 is not typed in but selected from a pop-up menu. > > 2. After doing that, the notation CAN be defined but... > > 3. Jaebum's example requires all 4 extra parentheses as in In[4], which > I explicitly did not want. For people who know about parsing, "/!" has > too high a binding power (precedence). > > 4. After further correspondence with Jaebum (thanks!), I found that > Jaebum could not figure out how to alter the precedence of the new > operator. It was clear to me that the Notations facility would > be pretty useless if you could not set the precedence somehow, so > I read some more. > > 5. I DID figure out how to alter the precedence; (I gather) it is > based on the precedence of the character that begins the new > operator. Thus the default precedence of the new operator "/!" is > like the operator "/". We want the precedence to be more like "/.". > Too bad. > > There may in fact be a way of altering precedence of an arbitrary new > symbol, but I don't have a week to figure out the documentation and > whether tags have something to do with it. > > Instead I picked another new operator, "=/." , since the precedence I > want is lower precedence, more like = in Mathematica. (The table of > operator precedence is in tutorial/OperatorInputForms) > > It works. > > Here's what happens: > > start by providing input that looks like > > Notation[x__ =/. y__ <==> ReplaceAll[x__,BetterRules[y__]]] > > but can't really be fully typed in .. you have to select from a palette that > pops up when you do <<Notations` > > (In InputForm it looks like this ....) > > Notation`Private`myHold[ > \(\*Notation`Private`makeHeldRowBoxOfBoxes[{x}, StandardForm, None] = > \(/.\*Notation`Private`makeHeldRowBoxOfBoxes[{y}, StandardForm, > None]\)\) > ] > > Anyway, one can, in this case, write > > a+s^2+1/s^2+z =/. s^2->t > and get a+t+1/t+z > > compare to > > a+s^2+1/s^2+z /. s^2->t > which produces a +1/s^2+t+z, > > (also compare to Jaebum's solution that requires > > (a+s^2+1/s^2+z) /! (s^2->t) > > Other problems with Notations` : so far as I can tell, typing in the > alleged InputForm does not do the same work as selection from the > palette. While notebooks may be nice, I like to have a simple text > script that can be (for example) put in email. Also, it seems that > Notation` must be explicitly loaded, but perhaps there's some trick to > making this happen automatically. > > RJF > > > > > On 1/12/10 3:49 AM, Richard Fateman wrote: > >> Is there a neat way to create a new symbol, > >> say /!. so that > > >> expression /. BetterRules[rules] > > >> could be written as > > >> expression /!. rules > > >> I do not find writing something like > > >> (expression) ~BR~ (rules) > > >> to be quite adequate, especially with the extra parentheses. > >> RJF I agree with everything, except that the example you chose does not really work as you say, for the simple reason that 1/s^2 has a FullForm of Power[s,-2] so it is not picked up in the replacement. One other thing I would like to point out: the string =/. is displayed in red (syntax coloring) meaning that Mathematica does not really like it (because it is a combination of standard operators). Perhaps one should use Symbolize first, in order to have Mathematica accept the string as a single symbol.

**References**:**syntax extension***From:*Richard Fateman <fateman@cs.berkeley.edu>