11

Since everything is an expression in Mathematica, why must a string object be formed by "abc" but not by a String[abc] expression?

You can look at a string's head by:

Head["abc"]

String

But you can not produce the same string by String

String[abc]

which, from my point of view, seems inconsistent with the principle that Everything Is an Expression.

However, I noticed that the basic Symbol object, on the other hand, can be formed by something like Symbol["a"].

The same question goes for four number objects (Integer, Real, Rational, and Complex). You can't say an integer 1 by something like Integer[1], can you?

Edit:Rational and Complex can be produced by their respective heads. So The question is valid only for String and two number objects, i.e. Integer and Real.

Naitree
  • 1,235
  • 9
  • 20

1 Answers1

10

String and Integer are what I termed "implicit heads" while writing:

Rather than being part of the standard expression itself, at least as I understand it, these implicit heads instead serve the purpose of providing a "type" for pattern matching. (With a pattern _String, _Integer, etc.) The atomic expressions themselves are stored in a low-level format and handled transparently behind the scenes.

Of the heads you list Rational and Complex are exceptions as these are a kind of hybrid head: you can use them to enter data:

{Complex[1, 2], Rational[5, 8]}

{1 + 2 I, 5/8}

Critically you can also match patterns within these heads:

{1 + 2 I, 5/8} /. {Complex[a_, b_] :> foo[a, b], Rational[n_, m_] :> bar[n, m]}

{foo[1, 2], bar[5, 8]}

Nevertheless these expressions are considered "atomic" and they cannot be manipulated other ways that apply to standard expressions:

AtomQ /@ {1 + 2 I, 5/8}
foo @@@ {1 + 2 I, 5/8}

{True, True}

{1 + 2 I, 5/8}
Community
  • 1
Mr.Wizard
  • 271,378
  • 34
  • 587
  • 1,371
  • 1
    I'm sorry for misleadingly including the Rational and Complex. I just got a bit "unconscious" for forgetting that they are not the same case. I have excluded them from my descriptive details to avoid possible misguidance. – Naitree Sep 14 '14 at 13:16
  • 1
    @Naitree I found them an interesting aspect of the question and took a large portion of my answer to address them. Unless you feel that my answer is inadequate (which the Accept indicates against) I prefer that you restore your question to its original form. – Mr.Wizard Sep 14 '14 at 13:42
  • 1
    After reading your answer, I thought it might be misleading for other readers to include a stated fact which is actually false. That's the reason I removed them. I will now re-include them for consistency and add additional comments for avoiding misguidance for other readers. – Naitree Sep 14 '14 at 13:58