Cleanest way to take a[b[c]] to a[b][c]












18












$begingroup$


As indicated in the title I'm looking for the fastest way to transform a[b[c]] into a[b][c], and the natural generalization to an arbitrary chaining of arguments. I'm sure there's got to be a convenient way that I've overlooked.



In my cases a, b, and c can be any expression with any complicated internal structure they like.



As an example, we could have some terrible deeply nested thing like:



bleh =

  Nest[f, 10, 10]@

   Nest[b, 100, 100]@Nest[c, RandomReal[{}, {1000, 1000}], 1000];


And then we can to convert this into:



blehm =

  Nest[f, 10, 10][

   Nest[b, 100, 100]][Nest[c, RandomReal[{}, {1000, 1000}], 1000]]





function-construction expression-manipulation functional-style







share|improve this question











$endgroup$








  • 1




    $begingroup$
    The solution likely would use Operate.
    $endgroup$
    – QuantumDot
    Jan 23 at 6:20










  • $begingroup$
    f = Curry[Replace][a_[b_[c_]] :> a[b][c]] also works, so that a[b[c]] // f gives the desired result.
    $endgroup$
    – Shredderroy
    Jan 23 at 6:29










  • $begingroup$
    How about generalizing the question to taking a[b[c[d[...]]]] to a[b][c][d]...?
    $endgroup$
    – David G. Stork
    Jan 23 at 6:40








  • 1




    $begingroup$
    @b3m2a1: Oh.... well I recommend you alter the question... and seem my new solution.
    $endgroup$
    – David G. Stork
    Jan 23 at 6:49






  • 1




    $begingroup$
    If you want a b c to be any expression you better show some examples, what is a[b[c], d[e, f]] supposed to be converted to?
    $endgroup$
    – Kuba♦
    Jan 23 at 9:14


















18












$begingroup$


As indicated in the title I'm looking for the fastest way to transform a[b[c]] into a[b][c], and the natural generalization to an arbitrary chaining of arguments. I'm sure there's got to be a convenient way that I've overlooked.



In my cases a, b, and c can be any expression with any complicated internal structure they like.



As an example, we could have some terrible deeply nested thing like:



bleh =

  Nest[f, 10, 10]@

   Nest[b, 100, 100]@Nest[c, RandomReal[{}, {1000, 1000}], 1000];


And then we can to convert this into:



blehm =

  Nest[f, 10, 10][

   Nest[b, 100, 100]][Nest[c, RandomReal[{}, {1000, 1000}], 1000]]





function-construction expression-manipulation functional-style







share|improve this question











$endgroup$








  • 1




    $begingroup$
    The solution likely would use Operate.
    $endgroup$
    – QuantumDot
    Jan 23 at 6:20










  • $begingroup$
    f = Curry[Replace][a_[b_[c_]] :> a[b][c]] also works, so that a[b[c]] // f gives the desired result.
    $endgroup$
    – Shredderroy
    Jan 23 at 6:29










  • $begingroup$
    How about generalizing the question to taking a[b[c[d[...]]]] to a[b][c][d]...?
    $endgroup$
    – David G. Stork
    Jan 23 at 6:40








  • 1




    $begingroup$
    @b3m2a1: Oh.... well I recommend you alter the question... and seem my new solution.
    $endgroup$
    – David G. Stork
    Jan 23 at 6:49






  • 1




    $begingroup$
    If you want a b c to be any expression you better show some examples, what is a[b[c], d[e, f]] supposed to be converted to?
    $endgroup$
    – Kuba♦
    Jan 23 at 9:14
















18












18








18


4



$begingroup$


As indicated in the title I'm looking for the fastest way to transform a[b[c]] into a[b][c], and the natural generalization to an arbitrary chaining of arguments. I'm sure there's got to be a convenient way that I've overlooked.



In my cases a, b, and c can be any expression with any complicated internal structure they like.



As an example, we could have some terrible deeply nested thing like:



bleh =

  Nest[f, 10, 10]@

   Nest[b, 100, 100]@Nest[c, RandomReal[{}, {1000, 1000}], 1000];


And then we can to convert this into:



blehm =

  Nest[f, 10, 10][

   Nest[b, 100, 100]][Nest[c, RandomReal[{}, {1000, 1000}], 1000]]





function-construction expression-manipulation functional-style







share|improve this question











$endgroup$




As indicated in the title I'm looking for the fastest way to transform a[b[c]] into a[b][c], and the natural generalization to an arbitrary chaining of arguments. I'm sure there's got to be a convenient way that I've overlooked.



In my cases a, b, and c can be any expression with any complicated internal structure they like.



As an example, we could have some terrible deeply nested thing like:



bleh =

  Nest[f, 10, 10]@

   Nest[b, 100, 100]@Nest[c, RandomReal[{}, {1000, 1000}], 1000];


And then we can to convert this into:



blehm =

  Nest[f, 10, 10][

   Nest[b, 100, 100]][Nest[c, RandomReal[{}, {1000, 1000}], 1000]]





function-construction expression-manipulation functional-style




function-construction expression-manipulation functional-style






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited Jan 23 at 12:52









Kuba♦

106k12204526




106k12204526










asked Jan 23 at 5:58









b3m2a1b3m2a1

28k357161




28k357161








  • 1




    $begingroup$
    The solution likely would use Operate.
    $endgroup$
    – QuantumDot
    Jan 23 at 6:20










  • $begingroup$
    f = Curry[Replace][a_[b_[c_]] :> a[b][c]] also works, so that a[b[c]] // f gives the desired result.
    $endgroup$
    – Shredderroy
    Jan 23 at 6:29










  • $begingroup$
    How about generalizing the question to taking a[b[c[d[...]]]] to a[b][c][d]...?
    $endgroup$
    – David G. Stork
    Jan 23 at 6:40








  • 1




    $begingroup$
    @b3m2a1: Oh.... well I recommend you alter the question... and seem my new solution.
    $endgroup$
    – David G. Stork
    Jan 23 at 6:49






  • 1




    $begingroup$
    If you want a b c to be any expression you better show some examples, what is a[b[c], d[e, f]] supposed to be converted to?
    $endgroup$
    – Kuba♦
    Jan 23 at 9:14
















  • 1




    $begingroup$
    The solution likely would use Operate.
    $endgroup$
    – QuantumDot
    Jan 23 at 6:20










  • $begingroup$
    f = Curry[Replace][a_[b_[c_]] :> a[b][c]] also works, so that a[b[c]] // f gives the desired result.
    $endgroup$
    – Shredderroy
    Jan 23 at 6:29










  • $begingroup$
    How about generalizing the question to taking a[b[c[d[...]]]] to a[b][c][d]...?
    $endgroup$
    – David G. Stork
    Jan 23 at 6:40








  • 1




    $begingroup$
    @b3m2a1: Oh.... well I recommend you alter the question... and seem my new solution.
    $endgroup$
    – David G. Stork
    Jan 23 at 6:49






  • 1




    $begingroup$
    If you want a b c to be any expression you better show some examples, what is a[b[c], d[e, f]] supposed to be converted to?
    $endgroup$
    – Kuba♦
    Jan 23 at 9:14










1




1




$begingroup$
The solution likely would use Operate.
$endgroup$
– QuantumDot
Jan 23 at 6:20




$begingroup$
The solution likely would use Operate.
$endgroup$
– QuantumDot
Jan 23 at 6:20












$begingroup$
f = Curry[Replace][a_[b_[c_]] :> a[b][c]] also works, so that a[b[c]] // f gives the desired result.
$endgroup$
– Shredderroy
Jan 23 at 6:29




$begingroup$
f = Curry[Replace][a_[b_[c_]] :> a[b][c]] also works, so that a[b[c]] // f gives the desired result.
$endgroup$
– Shredderroy
Jan 23 at 6:29












$begingroup$
How about generalizing the question to taking a[b[c[d[...]]]] to a[b][c][d]...?
$endgroup$
– David G. Stork
Jan 23 at 6:40






$begingroup$
How about generalizing the question to taking a[b[c[d[...]]]] to a[b][c][d]...?
$endgroup$
– David G. Stork
Jan 23 at 6:40






1




1




$begingroup$
@b3m2a1: Oh.... well I recommend you alter the question... and seem my new solution.
$endgroup$
– David G. Stork
Jan 23 at 6:49




$begingroup$
@b3m2a1: Oh.... well I recommend you alter the question... and seem my new solution.
$endgroup$
– David G. Stork
Jan 23 at 6:49




1




1




$begingroup$
If you want a b c to be any expression you better show some examples, what is a[b[c], d[e, f]] supposed to be converted to?
$endgroup$
– Kuba♦
Jan 23 at 9:14






$begingroup$
If you want a b c to be any expression you better show some examples, what is a[b[c], d[e, f]] supposed to be converted to?
$endgroup$
– Kuba♦
Jan 23 at 9:14












4 Answers
4






active

oldest

votes


















10












$begingroup$

Operate[#[[0]], First@#] &[a[b[c]]]



a[b][c]




ClearAll[deCompose]

deCompose = Nest[Operate[#[[0]], First@#] &, #, Depth[#] - 2] &;



deCompose@a[b[c]]



a[b][c]




exp = Compose[a, b, c, d, e, f, g]



a[b[c[d[e[f[g]]]]]]




deCompose @ exp



a[b][c][d][e][f][g]







share|improve this answer











$endgroup$





















    23












    $begingroup$

    test = a[b[c[d]]];
    

    
Fold[
    
  Construct,   (* or Compose, see [1] *)
    
  Level[test, {-1}, Heads -> True]
    
]
    




    a[b][c][d]



    [1] - Is there a name for #1@#2&?



    Alternatively, thanks to OP and Mr.Wizard:



    HeadCompose @@ Level[test, {-1}, Heads -> True]





    share|improve this answer











    $endgroup$









    • 1




      $begingroup$
      No Operate, No # and no _, a clear winner here :P
      $endgroup$
      – Kuba♦
      Jan 23 at 9:20












    • $begingroup$
      Oh A+ that's slick
      $endgroup$
      – b3m2a1
      Jan 23 at 9:20






    • 3




      $begingroup$
      One issue is that this will die on nested stuff like my example case, but I still like how clean this is. You could even get away with HeadCompose @@ Level[test, {-1}, Heads -> True]
      $endgroup$
      – b3m2a1
      Jan 23 at 9:22






    • 1




      $begingroup$
      @evanb Compose will do as well.
      $endgroup$
      – Kuba♦
      Jan 23 at 9:37






    • 3




      $begingroup$
      +1, ++clever. yet another variant: Level[test, {-1}, HeadCompose, Heads -> True]
      $endgroup$
      – WReach
      Jan 23 at 22:49



















    10












    $begingroup$

    This works on any level:



    a[b[c]] //. x_[s : _[_]] :> Operate[x, s]
    
(* a[b][c] *)
    

    
a[b[c[d[e[f[g[h]]]]]]] //. x_[s : _[_]] :> Operate[x, s]
    
(* a[b][c][d][e][f][g][h] *)


    simpler syntax but same thing:



    a[b[c[d[e[f[g[h]]]]]]] //. x_[y_[z_]] -> x[y][z]
    
(* a[b][c][d][e][f][g][h] *)


    Of course, if the components a, b, c etc. have such complicated internal structure that they match the pattern x_[s:_[_]] (equivalent to x_[y_[z_]]), then this proposed solution will fail by over-matching. This could be remedied by constraining the pattern and fixing which elements must be atomic with _?AtomQ. It all depends on the use case.



    This way of pattern matching can also be expanded to specific other situations like a[b[c],d[e]] etc., depending on what result is desired.






    share|improve this answer











    $endgroup$













    • $begingroup$
      For your terribly nested example, what characterizes the composition is that none of the components are atomic. With NotAtomQ[x_] := !AtomQ[x] we have blehm == bleh //. x_?NotAtomQ[s : _?NotAtomQ[_?NotAtomQ]] :> Operate[x, s]. This breaks the a[b[c]] example though. I find that pattern matching gives more fine-grained control than Level in this situation.
      $endgroup$
      – Roman
      Jan 23 at 10:19










    • $begingroup$
      Or perhaps a[b[c[d[e[f]]]]] //. a_[b_[c_]] :> a[b][c].
      $endgroup$
      – march
      Jan 23 at 16:51










    • $begingroup$
      @march that's exactly the same as I wrote, just using a slightly different syntax. Yes maybe your version is clearer, sorry for being so cryptic.
      $endgroup$
      – Roman
      Jan 23 at 17:47



















    5












    $begingroup$

    Not particularly "clean," but it works:



    Operate[Head[#], Level[#, 2][[2]]] & @ a[b[c]]


    For the full generalization:



    Nest[Operate[Head[#], Level[#, 2][[2]]] & , #, Depth[#] -2] & @
    
 a[b[c[d[e]]]]





    share|improve this answer











    $endgroup$













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      4 Answers
      4






      active

      oldest

      votes








      4 Answers
      4






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      10












      $begingroup$

      Operate[#[[0]], First@#] &[a[b[c]]]



      a[b][c]




      ClearAll[deCompose]
      
deCompose = Nest[Operate[#[[0]], First@#] &, #, Depth[#] - 2] &;
      

      
deCompose@a[b[c]]



      a[b][c]




      exp = Compose[a, b, c, d, e, f, g]



      a[b[c[d[e[f[g]]]]]]




      deCompose @ exp



      a[b][c][d][e][f][g]







      share|improve this answer











      $endgroup$


















        10












        $begingroup$

        Operate[#[[0]], First@#] &[a[b[c]]]



        a[b][c]




        ClearAll[deCompose]
        
deCompose = Nest[Operate[#[[0]], First@#] &, #, Depth[#] - 2] &;
        

        
deCompose@a[b[c]]



        a[b][c]




        exp = Compose[a, b, c, d, e, f, g]



        a[b[c[d[e[f[g]]]]]]




        deCompose @ exp



        a[b][c][d][e][f][g]







        share|improve this answer











        $endgroup$
















          10












          10








          10





          $begingroup$

          Operate[#[[0]], First@#] &[a[b[c]]]



          a[b][c]




          ClearAll[deCompose]
          
deCompose = Nest[Operate[#[[0]], First@#] &, #, Depth[#] - 2] &;
          

          
deCompose@a[b[c]]



          a[b][c]




          exp = Compose[a, b, c, d, e, f, g]



          a[b[c[d[e[f[g]]]]]]




          deCompose @ exp



          a[b][c][d][e][f][g]







          share|improve this answer











          $endgroup$



          Operate[#[[0]], First@#] &[a[b[c]]]



          a[b][c]




          ClearAll[deCompose]
          
deCompose = Nest[Operate[#[[0]], First@#] &, #, Depth[#] - 2] &;
          

          
deCompose@a[b[c]]



          a[b][c]




          exp = Compose[a, b, c, d, e, f, g]



          a[b[c[d[e[f[g]]]]]]




          deCompose @ exp



          a[b][c][d][e][f][g]








          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited Jan 23 at 6:52

























          answered Jan 23 at 6:45









          kglrkglr

          185k10202421




          185k10202421























              23












              $begingroup$

              test = a[b[c[d]]];
              

              
Fold[
              
  Construct,   (* or Compose, see [1] *)
              
  Level[test, {-1}, Heads -> True]
              
]
              




              a[b][c][d]



              [1] - Is there a name for #1@#2&?



              Alternatively, thanks to OP and Mr.Wizard:



              HeadCompose @@ Level[test, {-1}, Heads -> True]





              share|improve this answer











              $endgroup$









              • 1




                $begingroup$
                No Operate, No # and no _, a clear winner here :P
                $endgroup$
                – Kuba♦
                Jan 23 at 9:20












              • $begingroup$
                Oh A+ that's slick
                $endgroup$
                – b3m2a1
                Jan 23 at 9:20






              • 3




                $begingroup$
                One issue is that this will die on nested stuff like my example case, but I still like how clean this is. You could even get away with HeadCompose @@ Level[test, {-1}, Heads -> True]
                $endgroup$
                – b3m2a1
                Jan 23 at 9:22






              • 1




                $begingroup$
                @evanb Compose will do as well.
                $endgroup$
                – Kuba♦
                Jan 23 at 9:37






              • 3




                $begingroup$
                +1, ++clever. yet another variant: Level[test, {-1}, HeadCompose, Heads -> True]
                $endgroup$
                – WReach
                Jan 23 at 22:49
















              23












              $begingroup$

              test = a[b[c[d]]];
              

              
Fold[
              
  Construct,   (* or Compose, see [1] *)
              
  Level[test, {-1}, Heads -> True]
              
]
              




              a[b][c][d]



              [1] - Is there a name for #1@#2&?



              Alternatively, thanks to OP and Mr.Wizard:



              HeadCompose @@ Level[test, {-1}, Heads -> True]





              share|improve this answer











              $endgroup$









              • 1




                $begingroup$
                No Operate, No # and no _, a clear winner here :P
                $endgroup$
                – Kuba♦
                Jan 23 at 9:20












              • $begingroup$
                Oh A+ that's slick
                $endgroup$
                – b3m2a1
                Jan 23 at 9:20






              • 3




                $begingroup$
                One issue is that this will die on nested stuff like my example case, but I still like how clean this is. You could even get away with HeadCompose @@ Level[test, {-1}, Heads -> True]
                $endgroup$
                – b3m2a1
                Jan 23 at 9:22






              • 1




                $begingroup$
                @evanb Compose will do as well.
                $endgroup$
                – Kuba♦
                Jan 23 at 9:37






              • 3




                $begingroup$
                +1, ++clever. yet another variant: Level[test, {-1}, HeadCompose, Heads -> True]
                $endgroup$
                – WReach
                Jan 23 at 22:49














              23












              23








              23





              $begingroup$

              test = a[b[c[d]]];
              

              
Fold[
              
  Construct,   (* or Compose, see [1] *)
              
  Level[test, {-1}, Heads -> True]
              
]
              




              a[b][c][d]



              [1] - Is there a name for #1@#2&?



              Alternatively, thanks to OP and Mr.Wizard:



              HeadCompose @@ Level[test, {-1}, Heads -> True]





              share|improve this answer











              $endgroup$



              test = a[b[c[d]]];
              

              
Fold[
              
  Construct,   (* or Compose, see [1] *)
              
  Level[test, {-1}, Heads -> True]
              
]
              




              a[b][c][d]



              [1] - Is there a name for #1@#2&?



              Alternatively, thanks to OP and Mr.Wizard:



              HeadCompose @@ Level[test, {-1}, Heads -> True]






              share|improve this answer














              share|improve this answer



              share|improve this answer








              edited Jan 23 at 21:59

























              answered Jan 23 at 9:18









              Kuba♦Kuba

              106k12204526




              106k12204526








              • 1




                $begingroup$
                No Operate, No # and no _, a clear winner here :P
                $endgroup$
                – Kuba♦
                Jan 23 at 9:20












              • $begingroup$
                Oh A+ that's slick
                $endgroup$
                – b3m2a1
                Jan 23 at 9:20






              • 3




                $begingroup$
                One issue is that this will die on nested stuff like my example case, but I still like how clean this is. You could even get away with HeadCompose @@ Level[test, {-1}, Heads -> True]
                $endgroup$
                – b3m2a1
                Jan 23 at 9:22






              • 1




                $begingroup$
                @evanb Compose will do as well.
                $endgroup$
                – Kuba♦
                Jan 23 at 9:37






              • 3




                $begingroup$
                +1, ++clever. yet another variant: Level[test, {-1}, HeadCompose, Heads -> True]
                $endgroup$
                – WReach
                Jan 23 at 22:49














              • 1




                $begingroup$
                No Operate, No # and no _, a clear winner here :P
                $endgroup$
                – Kuba♦
                Jan 23 at 9:20












              • $begingroup$
                Oh A+ that's slick
                $endgroup$
                – b3m2a1
                Jan 23 at 9:20






              • 3




                $begingroup$
                One issue is that this will die on nested stuff like my example case, but I still like how clean this is. You could even get away with HeadCompose @@ Level[test, {-1}, Heads -> True]
                $endgroup$
                – b3m2a1
                Jan 23 at 9:22






              • 1




                $begingroup$
                @evanb Compose will do as well.
                $endgroup$
                – Kuba♦
                Jan 23 at 9:37






              • 3




                $begingroup$
                +1, ++clever. yet another variant: Level[test, {-1}, HeadCompose, Heads -> True]
                $endgroup$
                – WReach
                Jan 23 at 22:49








              1




              1




              $begingroup$
              No Operate, No # and no _, a clear winner here :P
              $endgroup$
              – Kuba♦
              Jan 23 at 9:20






              $begingroup$
              No Operate, No # and no _, a clear winner here :P
              $endgroup$
              – Kuba♦
              Jan 23 at 9:20














              $begingroup$
              Oh A+ that's slick
              $endgroup$
              – b3m2a1
              Jan 23 at 9:20




              $begingroup$
              Oh A+ that's slick
              $endgroup$
              – b3m2a1
              Jan 23 at 9:20




              3




              3




              $begingroup$
              One issue is that this will die on nested stuff like my example case, but I still like how clean this is. You could even get away with HeadCompose @@ Level[test, {-1}, Heads -> True]
              $endgroup$
              – b3m2a1
              Jan 23 at 9:22




              $begingroup$
              One issue is that this will die on nested stuff like my example case, but I still like how clean this is. You could even get away with HeadCompose @@ Level[test, {-1}, Heads -> True]
              $endgroup$
              – b3m2a1
              Jan 23 at 9:22




              1




              1




              $begingroup$
              @evanb Compose will do as well.
              $endgroup$
              – Kuba♦
              Jan 23 at 9:37




              $begingroup$
              @evanb Compose will do as well.
              $endgroup$
              – Kuba♦
              Jan 23 at 9:37




              3




              3




              $begingroup$
              +1, ++clever. yet another variant: Level[test, {-1}, HeadCompose, Heads -> True]
              $endgroup$
              – WReach
              Jan 23 at 22:49




              $begingroup$
              +1, ++clever. yet another variant: Level[test, {-1}, HeadCompose, Heads -> True]
              $endgroup$
              – WReach
              Jan 23 at 22:49











              10












              $begingroup$

              This works on any level:



              a[b[c]] //. x_[s : _[_]] :> Operate[x, s]
              
(* a[b][c] *)
              

              
a[b[c[d[e[f[g[h]]]]]]] //. x_[s : _[_]] :> Operate[x, s]
              
(* a[b][c][d][e][f][g][h] *)


              simpler syntax but same thing:



              a[b[c[d[e[f[g[h]]]]]]] //. x_[y_[z_]] -> x[y][z]
              
(* a[b][c][d][e][f][g][h] *)


              Of course, if the components a, b, c etc. have such complicated internal structure that they match the pattern x_[s:_[_]] (equivalent to x_[y_[z_]]), then this proposed solution will fail by over-matching. This could be remedied by constraining the pattern and fixing which elements must be atomic with _?AtomQ. It all depends on the use case.



              This way of pattern matching can also be expanded to specific other situations like a[b[c],d[e]] etc., depending on what result is desired.






              share|improve this answer











              $endgroup$













              • $begingroup$
                For your terribly nested example, what characterizes the composition is that none of the components are atomic. With NotAtomQ[x_] := !AtomQ[x] we have blehm == bleh //. x_?NotAtomQ[s : _?NotAtomQ[_?NotAtomQ]] :> Operate[x, s]. This breaks the a[b[c]] example though. I find that pattern matching gives more fine-grained control than Level in this situation.
                $endgroup$
                – Roman
                Jan 23 at 10:19










              • $begingroup$
                Or perhaps a[b[c[d[e[f]]]]] //. a_[b_[c_]] :> a[b][c].
                $endgroup$
                – march
                Jan 23 at 16:51










              • $begingroup$
                @march that's exactly the same as I wrote, just using a slightly different syntax. Yes maybe your version is clearer, sorry for being so cryptic.
                $endgroup$
                – Roman
                Jan 23 at 17:47
















              10












              $begingroup$

              This works on any level:



              a[b[c]] //. x_[s : _[_]] :> Operate[x, s]
              
(* a[b][c] *)
              

              
a[b[c[d[e[f[g[h]]]]]]] //. x_[s : _[_]] :> Operate[x, s]
              
(* a[b][c][d][e][f][g][h] *)


              simpler syntax but same thing:



              a[b[c[d[e[f[g[h]]]]]]] //. x_[y_[z_]] -> x[y][z]
              
(* a[b][c][d][e][f][g][h] *)


              Of course, if the components a, b, c etc. have such complicated internal structure that they match the pattern x_[s:_[_]] (equivalent to x_[y_[z_]]), then this proposed solution will fail by over-matching. This could be remedied by constraining the pattern and fixing which elements must be atomic with _?AtomQ. It all depends on the use case.



              This way of pattern matching can also be expanded to specific other situations like a[b[c],d[e]] etc., depending on what result is desired.






              share|improve this answer











              $endgroup$













              • $begingroup$
                For your terribly nested example, what characterizes the composition is that none of the components are atomic. With NotAtomQ[x_] := !AtomQ[x] we have blehm == bleh //. x_?NotAtomQ[s : _?NotAtomQ[_?NotAtomQ]] :> Operate[x, s]. This breaks the a[b[c]] example though. I find that pattern matching gives more fine-grained control than Level in this situation.
                $endgroup$
                – Roman
                Jan 23 at 10:19










              • $begingroup$
                Or perhaps a[b[c[d[e[f]]]]] //. a_[b_[c_]] :> a[b][c].
                $endgroup$
                – march
                Jan 23 at 16:51










              • $begingroup$
                @march that's exactly the same as I wrote, just using a slightly different syntax. Yes maybe your version is clearer, sorry for being so cryptic.
                $endgroup$
                – Roman
                Jan 23 at 17:47














              10












              10








              10





              $begingroup$

              This works on any level:



              a[b[c]] //. x_[s : _[_]] :> Operate[x, s]
              
(* a[b][c] *)
              

              
a[b[c[d[e[f[g[h]]]]]]] //. x_[s : _[_]] :> Operate[x, s]
              
(* a[b][c][d][e][f][g][h] *)


              simpler syntax but same thing:



              a[b[c[d[e[f[g[h]]]]]]] //. x_[y_[z_]] -> x[y][z]
              
(* a[b][c][d][e][f][g][h] *)


              Of course, if the components a, b, c etc. have such complicated internal structure that they match the pattern x_[s:_[_]] (equivalent to x_[y_[z_]]), then this proposed solution will fail by over-matching. This could be remedied by constraining the pattern and fixing which elements must be atomic with _?AtomQ. It all depends on the use case.



              This way of pattern matching can also be expanded to specific other situations like a[b[c],d[e]] etc., depending on what result is desired.






              share|improve this answer











              $endgroup$



              This works on any level:



              a[b[c]] //. x_[s : _[_]] :> Operate[x, s]
              
(* a[b][c] *)
              

              
a[b[c[d[e[f[g[h]]]]]]] //. x_[s : _[_]] :> Operate[x, s]
              
(* a[b][c][d][e][f][g][h] *)


              simpler syntax but same thing:



              a[b[c[d[e[f[g[h]]]]]]] //. x_[y_[z_]] -> x[y][z]
              
(* a[b][c][d][e][f][g][h] *)


              Of course, if the components a, b, c etc. have such complicated internal structure that they match the pattern x_[s:_[_]] (equivalent to x_[y_[z_]]), then this proposed solution will fail by over-matching. This could be remedied by constraining the pattern and fixing which elements must be atomic with _?AtomQ. It all depends on the use case.



              This way of pattern matching can also be expanded to specific other situations like a[b[c],d[e]] etc., depending on what result is desired.







              share|improve this answer














              share|improve this answer



              share|improve this answer








              edited Jan 29 at 23:14

























              answered Jan 23 at 9:12









              RomanRoman

              1,756614




              1,756614












              • $begingroup$
                For your terribly nested example, what characterizes the composition is that none of the components are atomic. With NotAtomQ[x_] := !AtomQ[x] we have blehm == bleh //. x_?NotAtomQ[s : _?NotAtomQ[_?NotAtomQ]] :> Operate[x, s]. This breaks the a[b[c]] example though. I find that pattern matching gives more fine-grained control than Level in this situation.
                $endgroup$
                – Roman
                Jan 23 at 10:19










              • $begingroup$
                Or perhaps a[b[c[d[e[f]]]]] //. a_[b_[c_]] :> a[b][c].
                $endgroup$
                – march
                Jan 23 at 16:51










              • $begingroup$
                @march that's exactly the same as I wrote, just using a slightly different syntax. Yes maybe your version is clearer, sorry for being so cryptic.
                $endgroup$
                – Roman
                Jan 23 at 17:47


















              • $begingroup$
                For your terribly nested example, what characterizes the composition is that none of the components are atomic. With NotAtomQ[x_] := !AtomQ[x] we have blehm == bleh //. x_?NotAtomQ[s : _?NotAtomQ[_?NotAtomQ]] :> Operate[x, s]. This breaks the a[b[c]] example though. I find that pattern matching gives more fine-grained control than Level in this situation.
                $endgroup$
                – Roman
                Jan 23 at 10:19










              • $begingroup$
                Or perhaps a[b[c[d[e[f]]]]] //. a_[b_[c_]] :> a[b][c].
                $endgroup$
                – march
                Jan 23 at 16:51










              • $begingroup$
                @march that's exactly the same as I wrote, just using a slightly different syntax. Yes maybe your version is clearer, sorry for being so cryptic.
                $endgroup$
                – Roman
                Jan 23 at 17:47
















              $begingroup$
              For your terribly nested example, what characterizes the composition is that none of the components are atomic. With NotAtomQ[x_] := !AtomQ[x] we have blehm == bleh //. x_?NotAtomQ[s : _?NotAtomQ[_?NotAtomQ]] :> Operate[x, s]. This breaks the a[b[c]] example though. I find that pattern matching gives more fine-grained control than Level in this situation.
              $endgroup$
              – Roman
              Jan 23 at 10:19




              $begingroup$
              For your terribly nested example, what characterizes the composition is that none of the components are atomic. With NotAtomQ[x_] := !AtomQ[x] we have blehm == bleh //. x_?NotAtomQ[s : _?NotAtomQ[_?NotAtomQ]] :> Operate[x, s]. This breaks the a[b[c]] example though. I find that pattern matching gives more fine-grained control than Level in this situation.
              $endgroup$
              – Roman
              Jan 23 at 10:19












              $begingroup$
              Or perhaps a[b[c[d[e[f]]]]] //. a_[b_[c_]] :> a[b][c].
              $endgroup$
              – march
              Jan 23 at 16:51




              $begingroup$
              Or perhaps a[b[c[d[e[f]]]]] //. a_[b_[c_]] :> a[b][c].
              $endgroup$
              – march
              Jan 23 at 16:51












              $begingroup$
              @march that's exactly the same as I wrote, just using a slightly different syntax. Yes maybe your version is clearer, sorry for being so cryptic.
              $endgroup$
              – Roman
              Jan 23 at 17:47




              $begingroup$
              @march that's exactly the same as I wrote, just using a slightly different syntax. Yes maybe your version is clearer, sorry for being so cryptic.
              $endgroup$
              – Roman
              Jan 23 at 17:47











              5












              $begingroup$

              Not particularly "clean," but it works:



              Operate[Head[#], Level[#, 2][[2]]] & @ a[b[c]]


              For the full generalization:



              Nest[Operate[Head[#], Level[#, 2][[2]]] & , #, Depth[#] -2] & @
              
 a[b[c[d[e]]]]





              share|improve this answer











              $endgroup$


















                5












                $begingroup$

                Not particularly "clean," but it works:



                Operate[Head[#], Level[#, 2][[2]]] & @ a[b[c]]


                For the full generalization:



                Nest[Operate[Head[#], Level[#, 2][[2]]] & , #, Depth[#] -2] & @
                
 a[b[c[d[e]]]]





                share|improve this answer











                $endgroup$
















                  5












                  5








                  5





                  $begingroup$

                  Not particularly "clean," but it works:



                  Operate[Head[#], Level[#, 2][[2]]] & @ a[b[c]]


                  For the full generalization:



                  Nest[Operate[Head[#], Level[#, 2][[2]]] & , #, Depth[#] -2] & @
                  
 a[b[c[d[e]]]]





                  share|improve this answer











                  $endgroup$



                  Not particularly "clean," but it works:



                  Operate[Head[#], Level[#, 2][[2]]] & @ a[b[c]]


                  For the full generalization:



                  Nest[Operate[Head[#], Level[#, 2][[2]]] & , #, Depth[#] -2] & @
                  
 a[b[c[d[e]]]]






                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited Jan 23 at 6:53

























                  answered Jan 23 at 6:28









                  David G. StorkDavid G. Stork

                  24.4k22153




                  24.4k22153






























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