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Re: Just another Mathematica "Gotcha", and HoldForm bug

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  • Subject: [mg121095] Re: Just another Mathematica "Gotcha", and HoldForm bug
  • From: Richard Fateman <fateman at>
  • Date: Sat, 27 Aug 2011 08:16:46 -0400 (EDT)
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  • References: <j1r5d3$fi4$> <j1tnpf$pnu$> <j22qe4$gop$>

On 8/12/2011 2:06 AM, Oleksandr Rasputinov wrote:

>>>(RJF) Did you know that
>>> HoldForm[x //@ y]      returns  x//@y
>>>     but
>>> HoldForm[x //  y]      returns  y[x]
>>> ?
>>> (version 7.0).
.. snip..

> On further consideration it strikes me that I may have misunderstood what
> you meant here.

Yes. but you got it right, below.

  HoldForm is simply printing the expressions in InputForm,
> so for example we also have
> HoldForm[MapAll[x,y]]
> printing:
> x //@ y
> Conversion between two equivalent syntactic forms (postfix notation, and
> InputForm) is not considered to be a form of evaluation;
I agree.
  it is simply the
> way in which the expressions are parsed.

Not really parsed, but displayed.  a[b] ,   a@b,   and b//a   are parsed 
into the same thing.
I view  Postfix, Prefix, InputForm  as output specifiers; hints to the 
display program on what to do, not actual conversions.  I suppose 
Mathematica could be doing something else, but this is the way I'd do 
it.  That is, I'd store Postfix[a[b]], but write the display program to
show it as b//a.

I find the specifications defective, anyway.  For instance,
Postfix[f[a,b]]  comes out  as  Postfix[f[a,b]]  instead of
the form   Sequence[a,b]//f,   which is in fact a postfix version of f[a,b].

  If you want an expression that
> prints in a particular way you can use
> HoldForm@Postfix[x // y]

Not really useful. That expression is not x//y.  It is 


The point of my posting is that there is an inconsistency in Mathematica 
that says that

x//y  is normally displayed as y[x].
x/.y  is normally displayed as x/.y  not ReplaceAll[x,y]

doing FullForm[everything]  is probably the only way to consistently
reduce the clutter of mystery, and the display program is clearly able 
to make more or less informed choices on preferred formats for any 
construct.  I think that f[a,b] is much preferable to Sequence[a,b]//f.
I think that, especially for novices, ReplaceAll[x,y] has more mnemonic
content than x/.y.

Someone's note (DanL?) raised the Dot issue.

More gotchas, but not nearly as likely to occur, are these puzzles.
One might wonder how to parse
x . y
x .. y
x . .. y
x.. . y

All of which are syntactically valid. Of lines 3,4,5,  two of them have
the same meaning.  Can you tell which?

Also consider the confusing lines below
3. ..4
3.. .4
3... .4
3. ...4

which are NOT the same at all when 3, 4 are x, y.

Hint.  FullForm[x..]  is Repeated[x],  and FullForm[x...] is 


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