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Question concerning MakeBoxes


Let's start a new Mathematica (5.1) session and note that

FormatValues[And]

is the empty list. I want to define a rule for formatting logical 
conjunctions and disjunctionsin in such a way that, for example, 
the conjunction

p&&q&&r

is formatted in TraditionalForm as

RowBox[{"\[And]",
    RowBox[{StyleBox["{",SpanMaxSize->\[Infinity]],
        GridBox[{{"p"},{"q"},{"r"}},ColumnAlignments->{Left}],
        StyleBox["}",ShowContents->False]}]," "}]//DisplayForm

(As far as I know, the idea for this interesting and convenient "grid notation" is due to
Bruno BuchBerger, but this is another history.)

For me, one obvious solution to this problem should be something like

Unprotect[And];
And/:MakeBoxes[And[c__],TraditionalForm]:=
  RowBox[{"\[And]",
RowBox[{StyleBox["{",SpanMaxSize->\[Infinity]],
          GridBox[{#}&/@(MakeBoxes[#,TraditionalForm]&/@{c}),
            ColumnAlignments->{Left}],
          StyleBox["}",ShowContents->False]}]," "}];
Protect[And];

In fact, 

p&&q&&r//TraditionalForm

is now displayed as intended. However, it works only once: evaluating again

p&&q&&r//TraditionalForm

gives the built-in traditional formatting. After inspecting

FormatValues[And]

we see what is going on: my formatting rule is the LAST on the list. So, in order to 
force Mathematica to apply my definition first, I evaluate

Unprotect[And];
FormatValues[And]=Reverse@FormatValues[And];
Protect[And];

This solves my problem, but in a somewhat inelegant way.

My questions are: 

(1) what is the explanation for this behavior?
(2) how can I get the intended result without reversing FormatValues[And]?

My anticipated thanks for any help.

Carlos César de Araújo
Gregos & Troianos Educacional
www.gregosetroianos.mat.br
Belo Horizonte, MG, Brazil
(31) 3283-1122


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