Question

I would like to define a new operator of the form x /==> y, where
the operator /==> is treated as e.g. the /@ operator of Map, and
is translated to MyFunction[x, y]. There is one important aspect: I
want the resulting operator to behave in the frontend like any two-bit
operator does, that is, the two characters (a Divide and a
DoubleLongRightArrow) should be connected together, no syntax
coloration should appear, and they are to be selected together when
clicked, so precedence must be set. Also, I’d rather avoid using the
Notation` package. As a result, I’d like to see something like this:

In[11]:= FullForm[x/\[DoubleLongRightArrow]y]

Out[11]//FullForm= MyFunction[x,y]

Does anyone have an idea how to achieve this?

Answer 1

Thanks to Mr.Wizard’s links, I’ve found the only example in the documentation on how to parse new operators (the gplus example in Low-Level Input). According to this example, here is my version for the new operator PerArrow. Please comment/critize on the code below:

In[1]:= PerArrow /: MakeBoxes[PerArrow[x_, y_], StandardForm] := 
  RowBox[{MakeBoxes[x, StandardForm], 
    RowBox[{AdjustmentBox["/", BoxMargins -> -.2], 
      AdjustmentBox["\[DoubleLongRightArrow]", BoxMargins -> -.1]}], 
    MakeBoxes[y, StandardForm]}];

MakeExpression[
   RowBox[{x_, "/", RowBox[{"\[DoubleLongRightArrow]", y_}]}], 
   StandardForm] := 
  MakeExpression[RowBox[{"PerArrow", "[", x, ",", y, "]"}], 
   StandardForm];

In[3]:= PerArrow[x, y]

Out[3]= x /\[DoubleLongRightArrow] y

In[4]:= x /\[DoubleLongRightArrow]y

Out[4]= x /\[DoubleLongRightArrow] y

In[5]:= FullForm[x /\[DoubleLongRightArrow]y]

Out[5]//FullForm= \!\(\*
TagBox[
StyleBox[
RowBox[{"PerArrow", "[", 
RowBox[{"x", ",", "y"}], "]"}],
ShowSpecialCharacters->False,
ShowStringCharacters->True,
NumberMarks->True],
FullForm]\)

For sake of clarity, here is a screenshot as well:

Since the operator is not fully integrated, further concerns are:

• the operator is selected weird when clicked (DoubleLongRightArrow with y instead of with /).
• accordingly, the parsing part requires the DoubleLongRightArrow to be RowBox-ed with y, otherwise it yields syntax error
• syntax coloration (at In[4] and In[5])
• it prints weird if inputted directly (notice the large gaps at In[4] and In[5])

Now, I can live with these, though it would be nice to have some means to iron out all the minor issues. I guess all these boil down to basically some even lower-level syntax handler, which does not now how to group the new operator. Any idea on how to tackle these? I understand that Cell has a multitude of options which might come handy (like CellEvaluationFunction, ShowAutoStyles and InputAutoReplacements) though I’m again clueless here.