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custom notation - How to re-parse (or re-map) character '.' to user-defined function


The default behavior of the character . between two non-numeric characters is to be interpreted as the infix of the Mathematica function Dot.


Is there a command that can be placed in a package to get the front-end to parse . as an infix for another function -- say user-defined one, myDot[]?


That is,




  1. a.b should be interpreted as myDot[a, b]





  2. myDot[a.b] should map to a.b




  3. Dot[a,b] should not get mapped to a.b, but the functionality of the built-in function Dot should not be lost.




  4. 3.14 should remain a single number, where here the dot indicates a decimal separator.






Answer



Updated


First, let's stop Dot from creating these box structures.


MakeBoxes[Dot[x__], form_] := 
 RowBox[{"Dot", "[", RowBox@Riffle[MakeBoxes /@ {x}, ","], "]"}]

Next, let's specify that these structures should instead be interpreted as myDot:


MakeExpression[RowBox@(row : {PatternSequence[_, "."] .., _}), form_] := 
 MakeExpression[
  RowBox@{"myDot", "[", RowBox@Riffle[row[[1 ;; -1 ;; 2]], ","], "]"}, form]


The slicing and riffling is ugly... there is probably a cleaner way to do it. ReplacePart seemed to be doing weird things when I tried it but I didn't spend any time on it.


The last step is to specify that myDot should also be rendered into the same structure:


MakeBoxes[myDot[x__], form_] := RowBox@Riffle[MakeBoxes /@ {x}, "."]

Now,


Dot[a, b, c]


Dot[a, b, c]




Dot[{a, b, c}, {x, y, z}]


a x + b y + c z



a.b.c


a.b.c




a.b.c // FullForm


myDot[a, b, c]



{a, b, c}.{x, y, z} // InputForm


myDot[{a, b, c}, {x, y, z}]




a.(b^2).c


a.b2.c



% // InputForm


myDot[a, b^2, c]




In all cases you will have to use MakeExpression to override the interpretation of user input, but you may also find TagBox and InterpretationBox interesting alternatives to the MakeBoxes implementations above.


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