Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 MergeTree

Source Notebook

Merge subtrees of a tree into a graph

Contributed by: Nikolay Murzin

ResourceFunction["MergeTree"][tree]

returns a directed acyclic graph (DAG) representation of tree with identical subtrees merged together.

ResourceFunction["MergeTree"][tree, f]

merges tree based on applying the function f to each of its subtrees.

ResourceFunction["MergeTree"][f]

represents an operator form of ResourceFunction["MergeTree"].

Details and Options

ResourceFunction["MergeTree"] works on Tree objects.
ResourceFunction["MergeTree"] works on trees with Head Graph (i.e. objects for which TreeGraphQ is True) by using GraphTree to convert them to Tree objects.
The default merging function is Hash.
EdgeTags of a resulting graph contain original tree edge information as a tagged DirectedEdge object whose tag is the node's child index.
ResourceFunction["MergeTree"] accepts the same options as Graph.
ResourceFunction["MergeTree"] takes the following additional options:
"VertexLabelFunction"Automaticfunction applied to an association of tree positions and tree data values to label vertices, default is Row[Values[#],","]&

Examples

Basic Examples (2) 

Merge identical subtrees of a tree:

In[1]:=
ResourceFunction["MergeTree"][\!\(\* GraphicsBox[ NamespaceBox["Trees", DynamicModuleBox[{Typeset`tree = HoldComplete[ Tree[$CellContext`f, { Tree[$CellContext`g, { Tree[$CellContext`a, None]}], Tree[$CellContext`g, { Tree[$CellContext`a, None]}], Tree[$CellContext`g, { Tree[$CellContext`b, None]}]}]]}, NamespaceBox[{ {RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1], Opacity[0.7], LineBox[{{0.8660254037844387, 1.7320508075688774`}, {0., 0.8660254037844387}}], LineBox[{{0.8660254037844387, 1.7320508075688774`}, { 0.8660254037844387, 0.8660254037844387}}], LineBox[{{0.8660254037844387, 1.7320508075688774`}, { 1.7320508075688774`, 0.8660254037844387}}], LineBox[{{0., 0.8660254037844387}, {0., 0.}}], LineBox[{{0.8660254037844387, 0.8660254037844387}, { 0.8660254037844387, 0.}}], LineBox[{{1.7320508075688774`, 0.8660254037844387}, { 1.7320508075688774`, 0.}}]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], TagBox[InsetBox[ FrameBox["f", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.8660254037844387, 1.7320508075688774}], "DynamicName", BoxID -> "VertexID$1"], TagBox[InsetBox[ FrameBox["g", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0., 0.8660254037844387}], "DynamicName", BoxID -> "VertexID$2"], TagBox[InsetBox[ FrameBox["a", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0., 0.}], "DynamicName", BoxID -> "VertexID$3"], TagBox[InsetBox[ FrameBox["g", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.8660254037844387, 0.8660254037844387}], "DynamicName", BoxID -> "VertexID$4"], TagBox[InsetBox[ FrameBox["a", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0.8660254037844387, 0.}], "DynamicName", BoxID -> "VertexID$5"], TagBox[InsetBox[ FrameBox["g", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.7320508075688774, 0.8660254037844387}], "DynamicName", BoxID -> "VertexID$6"], TagBox[InsetBox[ FrameBox["b", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.7320508075688774, 0.}], "DynamicName", BoxID -> "VertexID$7"]}}]]], AlignmentPoint->Center, Axes->False, AxesLabel->None, AxesOrigin->Automatic, AxesStyle->{}, Background->None, BaseStyle->Directive[ FrontEnd`GraphicsHighlightColor -> RGBColor[ 0.403921568627451, 0.8705882352941177, 0.7176470588235294]], BaselinePosition->Automatic, ContentSelectable->Automatic, Epilog->{}, FormatType->StandardForm, Frame->False, FrameLabel->FormBox["False", StandardForm], FrameStyle->{}, FrameTicks->None, FrameTicksStyle->{}, GridLines->None, GridLinesStyle->{}, ImageMargins->0., ImagePadding->All, ImageSize->Automatic, LabelStyle->{}, PlotLabel->None, PlotRange->All, PlotRangeClipping->False, PlotRangePadding->Automatic, PlotRegion->Automatic, Prolog->{}, RotateLabel->True, Ticks->Automatic, TicksStyle->{}]\)]
Out[1]=

Merge subtrees by a given function:

In[2]:=
ResourceFunction["MergeTree"][\!\(\* GraphicsBox[ NamespaceBox["Trees", DynamicModuleBox[{Typeset`tree = HoldComplete[ Tree[2, { Tree[6, { Tree[5, None], Tree[3, None], Tree[1, { Tree[4, None]}]}]}]]}, NamespaceBox[{ {RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1], Opacity[0.7], LineBox[{{0.8451542547285166, 2.53546276418555}, { 0.8451542547285166, 1.6903085094570334`}}], LineBox[{{0.8451542547285166, 1.6903085094570334`}, {0., 0.8451542547285167}}], LineBox[{{0.8451542547285166, 1.6903085094570334`}, { 0.8451542547285166, 0.8451542547285167}}], LineBox[{{0.8451542547285166, 1.6903085094570334`}, { 1.6903085094570331`, 0.8451542547285167}}], LineBox[{{1.6903085094570331`, 0.8451542547285167}, { 1.6903085094570331`, 0.}}]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], TagBox[InsetBox[ FrameBox["2", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.8451542547285166, 2.53546276418555}], "DynamicName", BoxID -> "VertexID$1"], TagBox[InsetBox[ FrameBox["6", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.8451542547285166, 1.6903085094570334}], "DynamicName", BoxID -> "VertexID$2"], TagBox[InsetBox[ FrameBox["5", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0., 0.8451542547285167}], "DynamicName", BoxID -> "VertexID$3"], TagBox[InsetBox[ FrameBox["3", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0.8451542547285166, 0.8451542547285167}], "DynamicName", BoxID -> "VertexID$4"], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.6903085094570331, 0.8451542547285167}], "DynamicName", BoxID -> "VertexID$5"], TagBox[InsetBox[ FrameBox["4", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.6903085094570331, 0.}], "DynamicName", BoxID -> "VertexID$6"]}}]]], AlignmentPoint->Center, Axes->False, AxesLabel->None, AxesOrigin->Automatic, AxesStyle->{}, Background->None, BaseStyle->Directive[ FrontEnd`GraphicsHighlightColor -> RGBColor[ 0.403921568627451, 0.8705882352941177, 0.7176470588235294]], BaselinePosition->Automatic, ContentSelectable->Automatic, Epilog->{}, FormatType->StandardForm, Frame->False, FrameLabel->FormBox["False", StandardForm], FrameStyle->{}, FrameTicks->None, FrameTicksStyle->{}, GridLines->None, GridLinesStyle->{}, ImageMargins->0., ImagePadding->All, ImageSize->Automatic, LabelStyle->{}, PlotLabel->None, PlotRange->All, PlotRangeClipping->False, PlotRangePadding->Automatic, PlotRegion->Automatic, Prolog->{}, RotateLabel->True, Ticks->Automatic, TicksStyle->{}]\), OddQ@*TreeData]
Out[2]=

Scope (3) 

Use TreeFold to merge subtrees after folding them:

In[3]:=
ResourceFunction["MergeTree"][\!\(\* GraphicsBox[ NamespaceBox["Trees", DynamicModuleBox[{Typeset`tree = HoldComplete[ Tree[1, { Tree[2, None], Tree[3, { Tree[1, None], Tree[2, None]}], Tree[6, None]}]]}, NamespaceBox[{ {RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1], Opacity[0.7], LineBox[{{0.8164965809277261, 1.6329931618554523`}, {0., 0.8164965809277261}}], LineBox[{{0.8164965809277261, 1.6329931618554523`}, { 0.8164965809277261, 0.8164965809277261}}], LineBox[{{0.8164965809277261, 1.6329931618554523`}, { 1.6329931618554523`, 0.8164965809277261}}], LineBox[{{0.8164965809277261, 0.8164965809277261}, { 0.4082482904638631, 0.}}], LineBox[{{0.8164965809277261, 0.8164965809277261}, { 1.2247448713915892`, 0.}}]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.8164965809277261, 1.6329931618554523}], "DynamicName", BoxID -> "VertexID$1"], TagBox[InsetBox[ FrameBox["2", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0., 0.8164965809277261}], "DynamicName", BoxID -> "VertexID$2"], TagBox[InsetBox[ FrameBox["3", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.8164965809277261, 0.8164965809277261}], "DynamicName", BoxID -> "VertexID$3"], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0.4082482904638631, 0.}], "DynamicName", BoxID -> "VertexID$4"], TagBox[InsetBox[ FrameBox["2", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.2247448713915892, 0.}], "DynamicName", BoxID -> "VertexID$5"], TagBox[InsetBox[ FrameBox["6", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.6329931618554523, 0.8164965809277261}], "DynamicName", BoxID -> "VertexID$6"]}}]]], AlignmentPoint->Center, Axes->False, AxesLabel->None, AxesOrigin->Automatic, AxesStyle->{}, Background->None, BaseStyle->Directive[ FrontEnd`GraphicsHighlightColor -> RGBColor[ 0.403921568627451, 0.8705882352941177, 0.7176470588235294]], BaselinePosition->Automatic, ContentSelectable->Automatic, Epilog->{}, FormatType->StandardForm, Frame->False, FrameLabel->FormBox["False", StandardForm], FrameStyle->{}, FrameTicks->None, FrameTicksStyle->{}, GridLines->None, GridLinesStyle->{}, ImageMargins->0., ImagePadding->All, ImageSize->Automatic, LabelStyle->{}, PlotLabel->None, PlotRange->All, PlotRangeClipping->False, PlotRangePadding->Automatic, PlotRegion->Automatic, Prolog->{}, RotateLabel->True, Ticks->Automatic, TicksStyle->{}]\), TreeFold[#1 + Total[#2] &]]
Out[3]=

Annotate a graph with edge tags showing original tree hierarchy:

In[4]:=
ResourceFunction["MergeTree"][\!\(\* GraphicsBox[ NamespaceBox["Trees", DynamicModuleBox[{Typeset`tree = HoldComplete[ Tree[1, { Tree[2, None], Tree[3, { Tree[1, None], Tree[2, None]}], Tree[6, None]}]]}, NamespaceBox[{ {RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1], Opacity[0.7], LineBox[{{0.8164965809277261, 1.6329931618554523`}, {0., 0.8164965809277261}}], LineBox[{{0.8164965809277261, 1.6329931618554523`}, { 0.8164965809277261, 0.8164965809277261}}], LineBox[{{0.8164965809277261, 1.6329931618554523`}, { 1.6329931618554523`, 0.8164965809277261}}], LineBox[{{0.8164965809277261, 0.8164965809277261}, { 0.4082482904638631, 0.}}], LineBox[{{0.8164965809277261, 0.8164965809277261}, { 1.2247448713915892`, 0.}}]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.8164965809277261, 1.6329931618554523}], "DynamicName", BoxID -> "VertexID$1"], TagBox[InsetBox[ FrameBox["2", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0., 0.8164965809277261}], "DynamicName", BoxID -> "VertexID$2"], TagBox[InsetBox[ FrameBox["3", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.8164965809277261, 0.8164965809277261}], "DynamicName", BoxID -> "VertexID$3"], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0.4082482904638631, 0.}], "DynamicName", BoxID -> "VertexID$4"], TagBox[InsetBox[ FrameBox["2", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.2247448713915892, 0.}], "DynamicName", BoxID -> "VertexID$5"], TagBox[InsetBox[ FrameBox["6", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.6329931618554523, 0.8164965809277261}], "DynamicName", BoxID -> "VertexID$6"]}}]]], AlignmentPoint->Center, Axes->False, AxesLabel->None, AxesOrigin->Automatic, AxesStyle->{}, Background->None, BaseStyle->Directive[ FrontEnd`GraphicsHighlightColor -> RGBColor[ 0.403921568627451, 0.8705882352941177, 0.7176470588235294]], BaselinePosition->Automatic, ContentSelectable->Automatic, Epilog->{}, FormatType->StandardForm, Frame->False, FrameLabel->FormBox["False", StandardForm], FrameStyle->{}, FrameTicks->None, FrameTicksStyle->{}, GridLines->None, GridLinesStyle->{}, ImageMargins->0., ImagePadding->All, ImageSize->Automatic, LabelStyle->{}, PlotLabel->None, PlotRange->All, PlotRangeClipping->False, PlotRangePadding->Automatic, PlotRegion->Automatic, Prolog->{}, RotateLabel->True, Ticks->Automatic, TicksStyle->{}]\), TreeFold[#1 + Total[#2] &], EdgeLabels -> Placed["EdgeTag", {.5, {0, 1}}], VertexLabels -> Placed[Automatic, Center], VertexSize -> 0.1]
Out[4]=

Use the operator form of MergeTree:

In[5]:=
ResourceFunction["MergeTree"][Mod[TreeData[#], 5] &]@ BlockRandom[RandomTree[10], RandomSeeding -> 10]
Out[5]=

Options (1) 

VertexLabelFunction (1) 

Use a custom function to label vertices:

In[6]:=
ResourceFunction["MergeTree"][\!\(\* GraphicsBox[ NamespaceBox["Trees", DynamicModuleBox[{Typeset`tree = HoldComplete[ Tree[1, { Tree[2, None], Tree[3, { Tree[1, None], Tree[2, None]}], Tree[6, None]}]]}, NamespaceBox[{ {RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1], Opacity[0.7], LineBox[{{0.8164965809277261, 1.6329931618554523`}, {0., 0.8164965809277261}}], LineBox[{{0.8164965809277261, 1.6329931618554523`}, { 0.8164965809277261, 0.8164965809277261}}], LineBox[{{0.8164965809277261, 1.6329931618554523`}, { 1.6329931618554523`, 0.8164965809277261}}], LineBox[{{0.8164965809277261, 0.8164965809277261}, { 0.4082482904638631, 0.}}], LineBox[{{0.8164965809277261, 0.8164965809277261}, { 1.2247448713915892`, 0.}}]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.8164965809277261, 1.6329931618554523}], "DynamicName", BoxID -> "VertexID$1"], TagBox[InsetBox[ FrameBox["2", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0., 0.8164965809277261}], "DynamicName", BoxID -> "VertexID$2"], TagBox[InsetBox[ FrameBox["3", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.8164965809277261, 0.8164965809277261}], "DynamicName", BoxID -> "VertexID$3"], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0.4082482904638631, 0.}], "DynamicName", BoxID -> "VertexID$4"], TagBox[InsetBox[ FrameBox["2", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.2247448713915892, 0.}], "DynamicName", BoxID -> "VertexID$5"], TagBox[InsetBox[ FrameBox["6", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameStyle->Directive[ RGBColor[0.6588235294117647, 0.7294117647058823, 0.7058823529411765], AbsoluteThickness[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.6329931618554523, 0.8164965809277261}], "DynamicName", BoxID -> "VertexID$6"]}}]]], AlignmentPoint->Center, Axes->False, AxesLabel->None, AxesOrigin->Automatic, AxesStyle->{}, Background->None, BaseStyle->Directive[ FrontEnd`GraphicsHighlightColor -> RGBColor[ 0.403921568627451, 0.8705882352941177, 0.7176470588235294]], BaselinePosition->Automatic, ContentSelectable->Automatic, Epilog->{}, FormatType->StandardForm, Frame->False, FrameLabel->FormBox["False", StandardForm], FrameStyle->{}, FrameTicks->None, FrameTicksStyle->{}, GridLines->None, GridLinesStyle->{}, ImageMargins->0., ImagePadding->All, ImageSize->Automatic, LabelStyle->{}, PlotLabel->None, PlotRange->All, PlotRangeClipping->False, PlotRangePadding->Automatic, PlotRegion->Automatic, Prolog->{}, RotateLabel->True, Ticks->Automatic, TicksStyle->{}]\), TreeFold[#1 + Total[#2] &], "VertexLabelFunction" -> f]
Out[6]=

Applications (1) 

Make a graph representation of AxiomaticTheory formulas:

In[7]:=
ResourceFunction["MergeTree"][ ExpressionTree@AxiomaticTheory["BooleanAxioms"], "VertexLabelFunction" -> First]
Out[7]=

Version History

  • 1.0.0 – 24 January 2022

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