32
$\begingroup$

I was surprised to see Graph objects are atomic. Is there a way (through documentation or programmatically) to find all atomic heads?

The ones I know of are:

Integer Rational Real Complex Symbol String SparseArray StructuredArray SymmetrizedArray Image (* since v9 *) Image3D Graph ColorProfileData Association MeshRegion BoundaryMeshRegion Language`ArrayObject ByteArray NumericArray QuantityArray RawArray RawData Audio Video

Are there any others?

Special Structured Matrices

VandermondeMatrix CauchyMatrix ToeplitzMatrix HankelMatrix FourierMatrix HilbertMatrix

Others mentioned in the comments

Internal`Bag System`Utilities`HashTable System`RawArray BooleanFunction Dispatch (* since v10 *) Dataset

Neural net functionality

AggregationLayer BasicRecurrentLayer BatchNormalizationLayer CatenateLayer ConstantArrayLayer ConstantPlusLayer ConstantTimesLayer ContrastiveLossLayer ConvolutionLayer CrossEntropyLossLayer DeconvolutionLayer DotLayer DropoutLayer ElementwiseLayer EmbeddingLayer FlattenLayer GatedRecurrentLayer ImageAugmentationLayer InstanceNormalizationLayer LinearLayer LocalResponseNormalizationLayer LongShortTermMemoryLayer MeanAbsoluteLossLayer MeanSquaredLossLayer NetChain NetDecoder NetEncoder NetEvaluationMode NetExtract NetFoldOperator NetGraph NetInitialize NetMapOperator NetModel NetNestOperator NetPairEmbeddingOperator NetPort NetPortGradient NetReplacePart PaddingLayer PartLayer PoolingLayer ReplicateLayer ReshapeLayer ResizeLayer SequenceAttentionLayer SequenceLastLayer SequenceMostLayer SequenceRestLayer SequenceReverseLayer SoftmaxLayer SpatialTransformationLayer SummationLayer ThreadingLayer TotalLayer TransposeLayer UnitVectorLayer
Improve this question
$\endgroup$
19
  • 7
    $\begingroup$ Strangely, SparseArrays are actually not atomic, but just treated for most purposes as if they were. They are the only non-atomic atoms, though, as far as I know. And in addition to your list, there are several other undocumented atomic objects as well, such as the Internal`Bag, the System`Utilities`HashTable, the System`RawArray, and probably others besides. Several objects that should be atomic (by the standards of the SparseArray) aren't, such as CompiledFunction and LibraryFunction. $\endgroup$ Commented Apr 27, 2014 at 3:38
  • 5
    $\begingroup$ The same question on Stack Overflow: (5964469) $\endgroup$ Commented Apr 28, 2014 at 19:19
  • 6
    $\begingroup$ What is atomic and what isn't changes with versions. Image isn't atomic in v7 and v8. $\endgroup$ Commented Apr 29, 2014 at 16:54
  • 4
    $\begingroup$ @ChipHurst AtomQ is defined as "an expression which cannot be divided into subexpressions", and has notes such as "You can use AtomQ in a recursive procedure to tell when you have reached the bottom of the tree corresponding to an expression." and "AtomQ gives True for any object whose subparts cannot be accessed using functions like Map". Clearly Association should not be AtomQ by these measures. But as you point out, it is also not NormalQ (which would mean that it behaves like its FullForm), if we had such a thing. AtomQ and NormalQ are currently "mixed together", we should separate them. $\endgroup$ Commented Jul 17, 2014 at 18:20
  • 3
    $\begingroup$ @TaliesinBeynon ... With[{a = Association[1 -> 2]}, Hold[a]]. But it doesn't, there are differences (again, part extraction, pattern matching). Also consider SparseArray, which also has parts, but again doesn't behave identically to its FullForm. SparseArray is also marked as AtomQ for this reason. Perhaps you could consider changing the description of AtomQ in the documentation instead of letting AtomQ return False for associations. What AtomQ really means is a bit complicated, but it's valuable to have it, and changing it would break either consistency ... $\endgroup$ Commented Aug 5, 2014 at 14:39

2 Answers 2

Reset to default
17
$\begingroup$

You can executive the code in mma 10 or above version

EntityClass["WolframLanguageSymbol", "Atomic"]//EntityList

But is not all atomic function,as I know.

Improve this answer
$\endgroup$
6
  • $\begingroup$ Wow, very nice! $\endgroup$ Commented Sep 23, 2015 at 22:23
  • $\begingroup$ I'm accepting this because only a few (documented System heads) are missing: Integer, String, Symbol, QuantityArray. The first three make sense I think. For example you can't create an integer using the head Integer. $\endgroup$ Commented Nov 17, 2017 at 15:36
  • 1
    $\begingroup$ Tell me how to. :) $\endgroup$ Commented Nov 17, 2017 at 15:39
  • $\begingroup$ @yode You can create a true symbol still: a = Symbol["s"];s === a $\endgroup$ Commented Nov 17, 2017 at 16:37
  • $\begingroup$ @user18792 Ah, right. I guess Integer and String are the only 2 then. $\endgroup$ Commented Nov 17, 2017 at 20:52
6
$\begingroup$

Since it's the only "answer" I can see to post (as CW) there is also BooleanFunction as originally pointed out by Sasha.

In version 10 Dispatch tables are atomic.(1)

Array[# -> 2 # &, 5] // Dispatch // AtomQ 
True
Improve this answer
$\endgroup$
2
  • $\begingroup$ The same as association. <|a -> 1|> // AtomQ gives True. $\endgroup$ Commented Jul 14, 2014 at 15:55
  • $\begingroup$ @YiWang Association is already mentioned in the Question body above, but yes. $\endgroup$ Commented Jul 14, 2014 at 23:36

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.