How can I change the default grouping on an operator without a built-in meaning?

I've created my own infix operator by defining LeftArrow.

SetAttributes[LeftArrow, {NumericFunction, OneIdentity}]
ex1_ ← ex2_ := ex1 /. Rule[ex2[[1]], ex2[[2]]]

(I'm using the Esc<-Esc form of LeftArrow in the second line)

When I use it, I need to string together applications like so:

eqIld2 = (((((((eqIld ← eqVrx) ← eqVct) ← eqIcr) ← eqVct) ← eqIcl) ← eqVtx) ← eqIin)

I'd like to be able to avoid all the parentheses, and to get the same result for the same input with the parentheses removed.

I don't see the default grouping for LeftArrow documented anywhere. I've tried playing with various Attributes, but I can't find one that does what I want. It looks like there's an InfixNotation that accepts options, but they aren't documented.

What's the trick?


2 Answers 2



As it was correctly noted the Notation package is not necessary here and the key point is recursive definition which builds the desired ordering:

LeftArrow[x_,y_,z__] := LeftArrow[LeftArrow[x,y],z] ;

Notice that the z__ argument is followed by a double underscore, which allows the pattern to match an arbitrary number of arguments.

Original answer

Perhaps Notation package might help:

<< Notation` ;
f[x_,y_,z__] := f[f[x,y],z] ;
Notation[ParsedBoxWrapper[RowBox[{"x_", " ", "\[LeftArrow]", " ", "y_", " "}]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{" ", RowBox[{"f", "[", RowBox[{"x_", ",", "y_"}], "]"}]}]]] ;

then try:

a \[LeftArrow] b
a \[LeftArrow] b \[LeftArrow] c
a \[LeftArrow] b \[LeftArrow] c \[LeftArrow] d
a \[LeftArrow] b \[LeftArrow] c \[LeftArrow] d \[LeftArrow] e
  • 1
    $\begingroup$ Thanks! Turns out the Notation package isn't necessary. If I just add LeftArrow[ex1_, ex2_, ex3__] := LeftArrow[LeftArrow[ex1, ex2], ex3], it seems to do the trick. I'm new to Mathematica, and the recursive definition wasn't intuitive, but it's good to know that the more specific match is identified and made first. I think if you remove the reference to Notation, and add text to emphasize the double underscore on the z__ arg (which I overlooked for a while), then this is the answer I'm looking for. $\endgroup$
    – Omegaman
    Aug 6, 2015 at 19:40
  • $\begingroup$ Thanks for your feedback. You are right, Notation package is not needed here. I used it just because I had a similar problem and just copied my example with minor changes. $\endgroup$
    – I.M.
    Aug 7, 2015 at 2:51

If you don't mind mucking with the internal file UnicodeCharacters.tr (make a copy first!) you can change the line:

0x2190  ←   ($<-$ $&LeftArrow;$ $\leftarrow$ $\gets$)   Infix   380 None    5   5


0x2190  ←   ($<-$ $&LeftArrow;$ $\leftarrow$ $\gets$)   Infix   380 Left    5   5

and then close and relaunch Mathematica so that the changes take affect. Afterwards I get:

a ← b ← c //FullForm



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