This is TeX, WAITS Version 0.95 (format=plain 83.1.31)  31 JAN 1983 15:21
**\tracingall

*$\hat P↑2 {\hat P}↑2\showlists
{math shift character $}
{horizontal mode: math shift character $}

\hat ->\mathaccent '17 
{math mode: \mathaccent}
{superscript character ↑}
{blank space}
{begin-group character {}

\hat ->\mathaccent '17 
{\mathaccent}
{end-group character }}
{superscript character ↑}
{\showlists}

### math mode entered at line 0
\accent\fam0 ∂
.\fam1 P
(\fam0 2
\mathord
.\accent\fam0 ∂
..\fam1 P
(\fam0 2
### horizontal mode entered at line 0
\hbox(0.0+0.0)x20.0
spacefactor 1000
### vertical mode entered at line 0
prevdepth ignored

! OK.
<*> $\hat P↑2 {\hat P}↑2\showlists
                                  
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*$\showlists
{math shift character $}
{horizontal mode: \showlists}

### horizontal mode entered at line 0
\hbox(0.0+0.0)x20.0
\mathon
\vbox(9.47223+0.0)x7.63889
.\hbox(6.94444+0.0)x0.0, shifted 1.31944
..\tenrm ∂
.\kern-4.30554
.\hbox(6.83333+0.0)x7.63889
..\teni P
\hbox(4.51111+0.0)x4.72221, shifted -7.00002
.\sevenrm 2
\hbox(9.47223+0.0)x7.63889
.\vbox(9.47223+0.0)x7.63889
..\hbox(6.94444+0.0)x0.0, shifted 1.31944
...\tenrm ∂
..\kern-4.30554
..\hbox(6.83333+0.0)x7.63889
...\teni P
\hbox(4.51111+0.0)x4.72221, shifted -7.00002
.\sevenrm 2
\mathoff
spacefactor 1000
### vertical mode entered at line 0
prevdepth ignored

! OK.
<*> $\showlists
               
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*$\hat{\hat P}↑2$\showlists
{math shift character $}

\hat ->\mathaccent '17 
{math mode: \mathaccent}

\hat ->\mathaccent '17 
{\mathaccent}
{end-group character }}
{superscript character ↑}
{math shift character $}
{horizontal mode: \showlists}

### horizontal mode entered at line 0
\hbox(0.0+0.0)x20.0
\mathon
\vbox(9.47223+0.0)x7.63889
.\hbox(6.94444+0.0)x0.0, shifted 1.31944
..\tenrm ∂
.\kern-4.30554
.\hbox(6.83333+0.0)x7.63889
..\teni P
\hbox(4.51111+0.0)x4.72221, shifted -7.00002
.\sevenrm 2
\hbox(9.47223+0.0)x7.63889
.\vbox(9.47223+0.0)x7.63889
..\hbox(6.94444+0.0)x0.0, shifted 1.31944
...\tenrm ∂
..\kern-4.30554
..\hbox(6.83333+0.0)x7.63889
...\teni P
\hbox(4.51111+0.0)x4.72221, shifted -7.00002
.\sevenrm 2
\mathoff
\mathon
\vbox(12.11113+0.0)x7.63889
.\hbox(6.94444+0.0)x0.0, shifted 1.31944
..\tenrm ∂
.\kern-4.30554
.\vbox(9.47223+0.0)x7.63889
..\hbox(6.94444+0.0)x0.0, shifted 1.31944
...\tenrm ∂
..\kern-4.30554
..\hbox(6.83333+0.0)x7.63889
...\teni P
\hbox(4.51111+0.0)x4.72221, shifted -9.63892
.\sevenrm 2
\mathoff
spacefactor 1000
### vertical mode entered at line 0
prevdepth ignored

! OK.
<*> $\hat{\hat P}↑2$\showlists
                              
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*\ddt
! Undefined control sequence.
<*> \ddt
        
? x
Here is how much of TeX's memory you used:
 1627 strings out of 3000
 25644 string characters out of 36000
 270&3396 words of memory out of 25000&35001
 757 multiletter control sequences out of 2100
 19673 words of font info for 76 fonts, out of 25000 for 100
 13 hyphenation exceptions out of 307
 1i,2n,0p,32b,10s stack positions out of 80i,40n,30p,500b,300s
No output file.