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evaluation - Some _atomic elements' TreeForm looks confusing with Level in appearance


In[1]:= Level[1/2,{-1}]
Out[1]= {1/2}


TreeForm[1/2]

enter image description here




In[2]:= Level[1/2,{-1}]
Out[2]= {1/2}

In[3]:= Level[Unevaluated[1/2],{-1}]
Out[3]= {1,2,-1}


In[4]:= 1/2//FullForm
Out[5]//FullForm= Rational[1,2]

Rational[1,2] in TreeForm,but Times[1,Power[2,-1]] when Level.


In[5]:= Level[Unevaluated[1/2],{-1},Heads->True]
Out[5]= {Times,1,Power,2,-1}

How to comprehend this? How to obtain TreeForm[Hold@Unevaluated[1/2]] without Hold and Uevaluated in whole TreeForm's graph or TreeForm@{{{Hold[1/2],b}},b,c} with out hold? enter image description here


And How to get {1,2} from Level[1/2, {-1}]?




Answer



There is an evaluation leak in TreeForm that requires a double-Unevaluated to circumvent:


TreeForm[Unevaluated @ Unevaluated[1/2]]

enter image description here


The second question is more troublesome. Because Rational is an atomic object Level does not extract its conceptual sub-parts. This is true of other atomic objects as well:


sa = SparseArray @ Range @ 5;
Level[sa, {-1}]



{SparseArray[<5>,{5}]}

The only thing I can think of is a conversion to held FullForm as follows:


Level[MakeExpression @ ToBoxes @ FullForm[1/2], {-1}]


{1, 2}

Level[MakeExpression @ ToBoxes @ FullForm[sa], {-1}]



{Automatic, 5, 0, 1, 0, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5}

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