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MathGroup Archive 1996

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Re:Programming: Replace Heads

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5219] Re:[mg5161] Programming: Replace Heads
  • From: fransm at win.tue.nl (Frans Martens)
  • Date: Fri, 15 Nov 1996 03:22:38 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

Xah Lee posed a programming problem and gave a solution. 


  Problem:
   Given an abritrary expression, how to replace all heads to List?

  Solution:
   Map[ {(Sequence@@#)}&, (*(* the arbitrary expression *)*), {0,-2}] 

    

I ran in some difficulties. Here is an example:

In[70]:=
  Hold[a[b[c[u+2]+3]+4]] /. Thread[{a,b,c,Plus}->List] // ReleaseHold
Out[70]=
  {{{{{{u, 2}}, 3}}, 4}}
In[71]:=
  Map[ {(Sequence@@#)}&, a[b[c[u+2]+3]+4], {0,-2}] 

Out[71]=
  {{{{9, 7 + u}}}}

The following function computes first the expression and replaces all  
heads by List.

In[74]:=
  Clear[changehead];
  changehead[expr_]:=ReleaseHold[Apply[List,Hold[expr],
    {1,Infinity}]]; 


In[78]:=
  changehead[a[b[c[u+2]+3]+4]]
Out[78]=
  {{4, {{3, {{2, u}}}}}}

Mind the difference with %70 !

In[80]:=
  Clear[a,b,c,d,e,f,g]
  f := ({a,b,c,d,e,g}[[Random[Integer, {1,6}] ]])
  Array[ Hold at f, {3,2,3},1, Hold at f]//ReleaseHold
  Map[ {(Sequence@@#)}&, %, {0,-2}]
  changehead[%%]
Out[82]=
  c[g[g[d[1, 1, 1], e[1, 1, 2], e[1, 1, 3]], 

 

     a[d[1, 2, 1], d[1, 2, 2], g[1, 2, 3]]], 

 

    e[b[c[2, 1, 1], a[2, 1, 2], e[2, 1, 3]], 

 

     e[a[2, 2, 1], c[2, 2, 2], b[2, 2, 3]]], 

 

    b[e[c[3, 1, 1], d[3, 1, 2], d[3, 1, 3]], 

 

     a[b[3, 2, 1], c[3, 2, 2], d[3, 2, 3]]]]
Out[83]=
  {{{{1, 1, 1}, {1, 1, 2}, {1, 1, 3}}, 

 

     {{1, 2, 1}, {1, 2, 2}, {1, 2, 3}}}, 

 

    {{{2, 1, 1}, {2, 1, 2}, {2, 1, 3}}, 

 

     {{2, 2, 1}, {2, 2, 2}, {2, 2, 3}}}, 

 

    {{{3, 1, 1}, {3, 1, 2}, {3, 1, 3}}, 

 

     {{3, 2, 1}, {3, 2, 2}, {3, 2, 3}}}}
Out[84]=
  {{{{1, 1, 1}, {1, 1, 2}, {1, 1, 3}}, 

 

     {{1, 2, 1}, {1, 2, 2}, {1, 2, 3}}}, 

 

    {{{2, 1, 1}, {2, 1, 2}, {2, 1, 3}}, 

 

     {{2, 2, 1}, {2, 2, 2}, {2, 2, 3}}}, 

 

    {{{3, 1, 1}, {3, 1, 2}, {3, 1, 3}}, 

 

     {{3, 2, 1}, {3, 2, 2}, {3, 2, 3}}}}

For the freaks I compared the timings!

In[112]:=
  Clear[a,b,c,d,e,f,g]
  f := ({a,b,c,d,e,g}[[Random[Integer, {1,6}] ]])
  Array[ Hold at f, {4,6,10},1, Hold at f]//ReleaseHold;
  Timing[aa = Map[ {(Sequence@@#)}&, %, {0,-2}];]
  Timing[bb = changehead[%%];]
  aa === bb
Out[115]=
  {0.15 Second, Null}
Out[116]=
  {0.0333333 Second, Null}
Out[117]=
  True

In[118]:=
  Clear[a,b,c,d,e,f,g]
  f := ({a,b,c,d,e,g}[[Random[Integer, {1,6}] ]])
  Array[ Hold at f, {8,8,10},1, Hold at f]//ReleaseHold;
  Timing[aa = Map[ {(Sequence@@#)}&, %, {0,-2}];]
  Timing[bb = changehead[%%];]
  aa === bb
Out[121]=
  {0.366667 Second, Null}
Out[122]=
  {0.05 Second, Null}
Out[123]=
  True

Frans Martens
Eindhoven
The Netherlands


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