13
$\begingroup$

Is there a built in function that distinguishes between different kinds of variables? I mean something like:

VariableType[ 123 ]

Number

VariableType[ f[x] ]

Function

VariableType[ x ]

Variable

A={{a,b},{c,d}};
VariableType[ A ]

List

Etc.? Please let me know how this function is actually called. Or maybe one can implement it?

| improve this question | |
$\endgroup$
  • 7
    $\begingroup$ What you want is Head, although it cannot distinguish functions, because they are usual symbols in Mathematica. Try Head[{a,b,c}] or Head[1] or Head[1.0] $\endgroup$ – halirutan♦ Oct 8 '14 at 15:51
  • 2
    $\begingroup$ Depending on what you are doing, you may also be interested in Blank with a Head specified, like _Integer, _String, _a $\endgroup$ – mfvonh Oct 8 '14 at 15:54
  • 1
    $\begingroup$ See also: (22449), (59671) $\endgroup$ – Mr.Wizard♦ Oct 8 '14 at 18:07
  • $\begingroup$ @Mr.Wizard It's a duplicate of the first link you provided. On the other hand, to find this link, you already have to know Head - of which the OP apparently wasn't aware of. To close or not to close ... $\endgroup$ – eldo Oct 8 '14 at 18:20
13
$\begingroup$

A few examples 

fun[x_] := x^2

sphere = Graphics3D[{Sphere[{0, 0, 0}, 0.01]}, Boxed -> False, ImageSize -> 30];

str =
  {"1", "Pi", "{f}", "f", "f[x]", "f+f", "Inactivate[f+f,Plus]",
   "Hold[1+2+3]", "{1,{2,{3}}}", "fun[2]", "fun[x]", "Cos[Exp[x]]",
   "Red", "sphere", "DateObject[{2014,10}]"};

table =
  With[{exp = ToExpression /@ str},
   Prepend[
    Transpose[{
      str,
      exp,
      Head /@ exp,
      LeafCount /@ exp,
      Map[TreeForm[#,
         AspectRatio -> 1,
         ImageSize -> 40,
         PlotStyle -> PointSize[Medium],
         VertexRenderingFunction -> Function[{p}, Point[p]]] &,
       exp]}],
    Style[#, Bold, 16] & /@ {"Input", "Output", "Head", "Leaves", "Graph"}]];

Framed[
 Grid[table,
  Alignment -> Left,
  Dividers -> All,
  Spacings -> {{2, 2, 2, 2, 2}, 2},
  BaseStyle -> {FontFamily -> "Helvetica"},
  Background -> {None, {{Hue[.6, .15, .9], GrayLevel[.9]}}},
  FrameStyle -> Directive[Thick, White]],
 FrameMargins -> 0.5,
 FrameStyle -> GrayLevel[.7]]

enter image description here

Grid[
 Partition[
  Map[TreeForm[#,
     AspectRatio -> 1,
     ImageSize -> 200,
     EdgeRenderingFunction -> ({Black, Arrow[#, 0.2]} &)] &,
   {1, {f}, f + f,
    fun[x], Red, DateObject[{2014, 10}],
    Hold[1 + 2 + 3], {1, {2, {3}}}, sphere}],
  3],
 Background -> GrayLevel@0.95,
 Dividers -> All]

enter image description here

See the documentation for Head and read the tutorials linked therein:

Just for fun

a[b] + c[d] /. head_[_] :> head

a + c

a[b] + c[d] /. head_[_, _] :> head

Plus

| improve this answer | |
$\endgroup$
  • 2
    $\begingroup$ Great answer, but very complex... any possibility to have a brief explanation of the results? is the sort answer the function Head[]? Thanks!! $\endgroup$ – Matifou Nov 25 '16 at 23:04

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.