Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 FindHeadArities

Source Notebook

Find the distinct heads that occur in an expression and their corresponding arities

Contributed by: Stephen Wolfram, Jan Mangaldan and Nikolay Murzin

ResourceFunction["FindHeadArities"][expr]

gives an Association whose keys are the distinct heads in expr and whose values are the arities of those heads.

Details and Options

ResourceFunction["FindHeadArities"] has the attributes HoldFirst and SequenceHold.
With the default option setting "IncludeAtoms"→False, ResourceFunction["FindHeadArities"] includes only the heads of non-atomic expressions. With "IncludeAtoms"→True, heads of atomic expressions are included.

Examples

Basic Examples (1) 

Find the arities of various heads in the given expression:

In[1]:=
ResourceFunction["FindHeadArities"][f[f[a, b], c] == g[f[b, c]]]
Out[1]=

Scope (1) 

FindHeadArities lists all the arities found for a head:

In[2]:=
ResourceFunction["FindHeadArities"][f[x, f[x, y, z], u, f[v, w]]]
Out[2]=

Options (2) 

IncludeAtoms (2) 

By default, FindHeadArities ignores atomic expressions:

In[3]:=
ResourceFunction["FindHeadArities"][b[] == c[a, b]]
Out[3]=

Use "IncludeAtoms"→True to account for atomic expressions:

In[4]:=
ResourceFunction["FindHeadArities"][b[] == c[a, b], "IncludeAtoms" -> True]
Out[4]=

Possible Issues (2) 

FindHeadArities operates on the evaluated form of expressions:

In[5]:=
ResourceFunction["FindHeadArities"][(1 + 2 5) + 3 5 7]
Out[5]=
In[6]:=
ResourceFunction["FindHeadArities"][Sequence[2, 3]]
Out[6]=

Wrap expressions in Unevaluated to work with unevaluated versions:

In[7]:=
ResourceFunction["FindHeadArities"][Unevaluated[(1 + 2 5) + 3 5 7]]
Out[7]=
In[8]:=
ResourceFunction["FindHeadArities"][Unevaluated[Sequence[2, 3]]]
Out[8]=

Publisher

N. Murzin

Version History

  • 2.0.0 – 11 September 2020
  • 1.0.0 – 09 September 2020

Related Resources

License Information