Xah Talk Show 2025-08-16 Ep693 Xah Wolfram Mode Demo, and Determine Symbol is Function or Option

• https://youtu.be/ItviluS5ays

• computer science.
• Deep dive on an esoteric topic, Wolfram language symbols.
• Not a practical topic for coders or engineers.
• But kinda related to programing language design on identifiers, especially lisp family or symbolic languages, introspection feature.

• demo WolframScript
• Wolfram: Download Wolfram Engine
• demo of Emacs: Xah Wolfram Mode 📦

• show problem of completion of function vs option

• Wolfram: Symbol
• Wolfram Language for Programers

• ai answer
• https://x.com/xah_lee/status/1956768900852703234
• https://x.com/i/grok/share/gDj9k8IYONamHWdej2G1wG5tT

ParametricPlot3D[
{Cos[x], Sin[x], t},
{x, 0, 2 Pi 2},
{t, 0, 5}
]

ParametricPlot3D[
{Cos[x], Sin[x], x},
{x, 0, 2 Pi 2}
]

(* HHHH------------------------------ *)

Table[ {x, x^2}, {x, 1, 5}]
(* {{1, 1}, {2, 4}, {3, 9}, {4, 16}, {5, 25}} *)

Table[ x, {x, 1, 5}]
(* {1, 2, 3, 4, 5} *)

Table[ f[x,y], {x, 1, 2}, {y, 1, 3}]
(* 
{
{f[1, 1], f[1, 2], f[1, 3]},
{f[2, 1], f[2, 2], f[2, 3]}
}
 *)

(* HHHH------------------------------ *)

ParametricPlot3D[
{Cos[x], Sin[x], x},
{x, 0, 2 Pi 2},
Background -> Red
]

Options[ParametricPlot3D]

(* 
{AlignmentPoint -> Center,
 AspectRatio -> Automatic,
 AutomaticImageSize -> False,
 Axes -> True,
 AxesEdge -> Automatic,
 AxesLabel -> None,
 AxesOrigin -> Automatic,
 AxesStyle -> {},
 Background -> None,
 BaselinePosition -> Automatic,
 BaseStyle -> {},
 BoundaryStyle -> None,
 Boxed -> True,
 BoxRatios -> Automatic,
 BoxStyle -> {},
 ClipPlanes -> None,
 ClipPlanesStyle -> Automatic,
 ColorFunction -> Automatic,
 ColorFunctionScaling -> True,
 ColorOutput -> Automatic,
 ContentSelectable -> Automatic,
 ControllerLinking -> False,
 ControllerMethod -> Automatic,
 ControllerPath -> Automatic,
 CoordinatesToolOptions -> Automatic,
 DisplayFunction :> $DisplayFunction,
 Epilog -> {},
 Evaluated -> Automatic,
 EvaluationMonitor -> None,
 Exclusions -> Automatic,
 ExclusionsStyle -> None,
 FaceGrids -> None,
 FaceGridsStyle -> {},
 FormatType :> TraditionalForm,
 ImageMargins -> 0.,
 ImagePadding -> All,
 ImageSize -> Automatic,
 ImageSizeRaw -> Automatic,
 LabelingSize -> Automatic,
 LabelStyle -> {},
 Lighting -> Automatic,
 MaxRecursion -> Automatic,
 Mesh -> Automatic,
 MeshFunctions -> Automatic,
 MeshShading -> None,
 MeshStyle -> Automatic,
 Method -> Automatic,
 NormalsFunction -> Automatic,
 PerformanceGoal :> $PerformanceGoal,
 PlotLabel -> None,
 PlotLabels -> None,
 PlotLegends -> None,
 PlotPoints -> Automatic,
 PlotRange -> Automatic,
 PlotRangePadding -> Automatic,
 PlotRegion -> Automatic,
 PlotStyle -> Automatic,
 PlotTheme :> $PlotTheme,
 PreserveImageOptions -> Automatic,
 Prolog -> {},
 RegionFunction -> (True & ),
 RotationAction -> Fit,
 ScalingFunctions -> None,
 SphericalRegion -> Automatic,
 TargetUnits -> Automatic,
 TextureCoordinateFunction -> Automatic,
 TextureCoordinateScaling -> Automatic,
 Ticks -> Automatic,
 TicksStyle -> {},
 TouchscreenAutoZoom -> False,
 ViewAngle -> Automatic,
 ViewCenter -> Automatic,
 ViewMatrix -> Automatic,
 ViewPoint -> {1.3,
 -2.4,
 2.},
 ViewProjection -> Automatic,
 ViewRange -> All,
 ViewVector -> Automatic,
 ViewVertical -> {0,
 0,
 1},
 WorkingPrecision -> MachinePrecision}
 *)

classifySymbol[sym_Symbol] :=
 Module[
{usage = sym::usage,
name = SymbolName[sym]},
  If[! StringQ[usage], "Undefined or no usage",
   If[StringStartsQ[usage, name <> " is an option"], "Option",
    If[StringContainsQ[usage, name <> "["], "Function",
     "Other"]]]

]

(* HHHH------------------------------ *)

Table::usage

"DisplayForm[
RowBox[{Table, [, RowBox[{StyleBox[expr, TI], ,, StyleBox[n, TI]}], ]}]] generates a list of DisplayForm[StyleBox[n, TI]] copies of DisplayForm[StyleBox[expr, TI]].

DisplayForm[RowBox[{Table, [, RowBox[{StyleBox[expr, TI], ,, RowBox[{{, RowBox[{StyleBox[i, TI], ,, SubscriptBox[StyleBox[i, TI], StyleBox[max, TI]]}], }}]}], ]}]] generates a list of the values of DisplayForm[StyleBox[expr, TI]] when DisplayForm[StyleBox[i, TI]] runs from 1 to DisplayForm[SubscriptBox[StyleBox[i, TI], StyleBox[max, TI]]].

DisplayForm[RowBox[{Table, [, RowBox[{StyleBox[expr, TI], ,, RowBox[{{, RowBox[{StyleBox[i, TI], ,, SubscriptBox[StyleBox[i, TI], StyleBox[min, TI]], ,, SubscriptBox[StyleBox[i, TI], StyleBox[max, TI]]}], }}]}], ]}]] starts with DisplayForm[RowBox[{StyleBox[i, TI], =, SubscriptBox[StyleBox[i, TI], StyleBox[min, TI]]}]].

DisplayForm[RowBox[{Table, [, RowBox[{StyleBox[expr, TI], ,, RowBox[{{, RowBox[{StyleBox[i, TI], ,, SubscriptBox[StyleBox[i, TI], StyleBox[min, TI]], ,, SubscriptBox[StyleBox[i, TI], StyleBox[max, TI]], ,, StyleBox[di, TI]}], }}]}], ]}]] uses steps DisplayForm[StyleBox[di, TI]].

DisplayForm[RowBox[{Table, [, RowBox[{StyleBox[expr, TI], ,, RowBox[{{, RowBox[{StyleBox[i, TI], ,, RowBox[{{, RowBox[{SubscriptBox[StyleBox[i, TI], StyleBox[1, TR]], ,, SubscriptBox[StyleBox[i, TI], StyleBox[2, TR]], ,, StyleBox[..., TR]}], }}]}], }}]}], ]}]] uses the successive values DisplayForm[SubscriptBox[StyleBox[i, TI], StyleBox[1, TR]]], DisplayForm[SubscriptBox[StyleBox[i, TI], StyleBox[2, TR]]], ....
DisplayForm[RowBox[{Table, [, RowBox[{StyleBox[expr, TI], ,, RowBox[{{, RowBox[{StyleBox[i, TI], ,, SubscriptBox[StyleBox[i, TI], StyleBox[min, TI]], ,, SubscriptBox[StyleBox[i, TI], StyleBox[max, TI]]}], }}], ,, RowBox[{{, RowBox[{StyleBox[j, TI], ,, SubscriptBox[StyleBox[j, TI], StyleBox[min, TI]], ,, SubscriptBox[StyleBox[j, TI], StyleBox[max, TI]]}], }}], ,, StyleBox[..., TR]}], ]}]] gives a nested list. The list associated with DisplayForm[StyleBox[i, TI]] is outermost."

(* HHHH------------------------------ *)

StringQ[Table::usage]
(* True *)

(* HHHH------------------------------ *)

TextForm[Information[ "Table" ]] // StringQ

StringForm[Information[ "Table" ]] // StringQ
(* False *)

ToString[Information[ "Table" ]] // StringQ
True

ToString[Information[ "Table" ]]

Table[expr, n] generates a list of n copies of expr. Table[expr, {i, i   }] generates a list of the values of expr when i runs from 1 to i   . Table[expr, {i, i   , i   }] starts with i = i   . Table[expr, {i, i   , i   , di}] uses steps di. Table[expr, {i, {i , i , ...}}] uses the successive values i , i , ....Table[expr, {i, i   , i   }, {j, j   , j   }, ...] gives a nested list. The list associated with i is outermost.
                                                                      max                                                                 max                   min   max                    min                   min   max                                        1   2                                   1   2                     min   max        min   max

Attributes[Table]={HoldAll, Protected}

Table[expr, n] generates a list of n copies of expr. Table[expr, {i, i   }] generates a list of the values of expr when i runs from 1 to i   . Table[expr, {i, i   , i   }] starts with i = i   . Table[expr, {i, i   , i   , di}] uses steps di. Table[expr, {i, {i , i , ...}}] uses the successive values i , i , ....Table[expr, {i, i   , i   }, {j, j   , j   }, ...] gives a nested list. The list associated with i is outermost.
                                                                      max                                                                 max                   min   max                    min                   min   max                                        1   2                                     1   2                       min   max        min   max

Attributes[Table]={HoldAll, Protected}

(* HHHH------------------------------ *)

Clear[classifySymbol]

classifySymbol[xsym_Symbol] :=
 Block[
{xdocstr = ToString[Information[ xsym ]],
xname = SymbolName[xsym]},
  If[
! StringQ[xdocstr], "Undefined or no xdocstr",
   If[
     StringStartsQ[xdocstr, xname <> " is an option"], "Option",
      If[ StringContainsQ[xdocstr, xname <> "["], "Function",
     "Other"]]]
]

Map[classifySymbol, Names["*"]]

Map[
Function[x, classifySymbol[Symbol[x]]]
, Names["t*"]]

(* HHHH------------------------------ *)

classifySymbol[Table]
(* Function *)
classifySymbol[Background]
(* Option *)