How to obtain a list of all build-in system level Heads?

Question

I am writing a small Mathematical expression parser and need a list of all Mathematica build-in Heads (system context?) so I can check the type of input.

Such as List,Integer,Times,Plus,Rational,Symbol,Real,Sin,Cos ,Power,Equal, and so on. i.e. those names which return from the command Head[..]. This does not include user level expressions ofcourse. Only system level Heads, obtained from Fresh kernel.

I googled and could not find an answer. May be this is something that can be obtained WolframLanguageData ? But I never used this, and when I looked at it, I did not see how to ask it for this.

Answer 1

You can generate a list with

Select[
 Names["System`*"],
 Quiet[
   With[{
     dv = ToExpression[#, InputForm, DownValues],
     expr = ToExpression[#, InputForm]
     },
    dv =!= {} && MemberQ[dv, HoldPattern[expr[__]], \[Infinity]]
    ]
   ] &
 ]

I am not entirely sure if this is complete, but it is a starting point.

Alternatively you can hope that the usage string of any function starts with "f[...] ...". There is no guarantee, but it seems to be this way. Then you can use

Table[
 With[{usage = WolframLanguageData[sym, "PlaintextUsage"]},
  If[
   StringQ[usage],
   If[StringMatchQ[usage, sym ~~ "[" ~~ Except["]"] ~~ __], sym, 
    Nothing],
   Nothing
   ]
  ],
 {sym, Names["System`*"]}
 ]

Note, however, that this is very slow! I have done it with the first 200 symbols from Names["System`*"] and it took about 20 seconds.