Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 CombinatorBracketsPlot

Source Notebook

Visualize matched brackets of a combinator

Contributed by: Wolfram Research

ResourceFunction["CombinatorBracketsPlot"][expr]

visualizes the pairing of the brackets in the combinator expr.

Details and Options

ResourceFunction["CombinatorBracketsPlot"] has the same options as Graphics, with the following additions:
AppearanceAutomaticoverall appearance
"BracketCharacters"Automaticcharacters used to represent the brackets
ColorRulesAutomaticcolor rules for points corresponding to the symbols present
"IncludeTextForm"Truewhether to display the brackets of the combinator
PlotStyleAutomaticstyle to use
Possible settings for the Appearance option include "Bush", "Mountain", "Tree" and "Vee".

Examples

Basic Examples (5) 

Visualize a particular combinator:

In[1]:=
ResourceFunction["CombinatorBracketsPlot"][ s[k[s]][k][s[s[k[s]][k]][s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]]][ s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]][s][k], Appearance -> "Vee"]
Out[1]=

Do not display brackets:

In[2]:=
ResourceFunction["CombinatorBracketsPlot"][ s[k[s]][k][s[s[k[s]][k]][s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]]][ s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]][s][k], Appearance -> "Vee", "IncludeTextForm" -> False]
Out[2]=

Use a "Mountain" appearance:

In[3]:=
ResourceFunction["CombinatorBracketsPlot"][ s[k[s]][k][s[s[k[s]][k]][s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]]][ s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]][s][k], Appearance -> "Mountain"]
Out[3]=

Without brackets:

In[4]:=
ResourceFunction["CombinatorBracketsPlot"][ s[k[s]][k][s[s[k[s]][k]][s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]]][ s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]][s][k], Appearance -> "Mountain", "IncludeTextForm" -> False]
Out[4]=

Use a "Bush" appearance:

In[5]:=
ResourceFunction["CombinatorBracketsPlot"][ s[k[s]][k][s[s[k[s]][k]][s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]]][ s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]][s][k], Appearance -> "Bush"]
Out[5]=

Without brackets:

In[6]:=
ResourceFunction["CombinatorBracketsPlot"][ s[k[s]][k][s[s[k[s]][k]][s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]]][ s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]][s][k], Appearance -> "Bush", "IncludeTextForm" -> False]
Out[6]=

Use a "Tree" appearance:

In[7]:=
ResourceFunction["CombinatorBracketsPlot"][ s[k[s]][k][s[s[k[s]][k]][s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]]][ s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]][s][k], Appearance -> "Tree"]
Out[7]=

Without brackets:

In[8]:=
ResourceFunction["CombinatorBracketsPlot"][ s[k[s]][k][s[s[k[s]][k]][s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]]][ s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]][s][k], Appearance -> "Tree", "IncludeTextForm" -> False]
Out[8]=

Scope (1) 

Use any symbol:

In[9]:=
ResourceFunction[ "CombinatorBracketsPlot"][\[ScriptE][\[ScriptE][\[ScriptE]][\ \[ScriptE]]][\[ScriptE]][\[ScriptE]]]
Out[9]=

Options (5) 

Appearance (1) 

Show various visualization styles for a combinator:

In[10]:=
GraphicsGrid[ Partition[ Table[ResourceFunction["CombinatorBracketsPlot"][ s[k[s]][k][s[s[k[s]][k]][s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]]][ s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]][s][k], Appearance -> ap, "BracketCharacters" -> {"[", "]"}, PlotLabel -> ap], {ap, {"Bush", "Mountain", "Tree", "Vee"}}], 2]]
Out[10]=

BracketCharacters (1) 

Use different bracketing characters:

In[11]:=
ResourceFunction["CombinatorBracketsPlot"][ s[k[s]][k][s[s[k[s]][k]][s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]]][ s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]][s][k], "BracketCharacters" -> {"\[LeftAngleBracket]", "\[RightAngleBracket]"}]
Out[11]=

ColorRules (1) 

Specify color rules for points corresponding to the symbols present:

In[12]:=
GraphicsGrid[ Partition[ Table[ResourceFunction["CombinatorBracketsPlot"][ s[k[s]][k][s[s[k[s]][k]][s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]]][ s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]][s][k], Appearance -> ap, ColorRules -> {s -> Red, k -> Blue}, PlotLabel -> ap], {ap, {"Bush", "Mountain", "Tree", "Vee"}}], 2]]
Out[12]=

IncludeTextForm (1) 

Show with and without brackets:

In[13]:=
GraphicsRow[ ResourceFunction["CombinatorBracketsPlot"][ s[k[s]][k][s[s[k[s]][k]][s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]]][ s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]][s][k], "IncludeTextForm" -> #] & /@ {True, False}]
Out[13]=

PlotStyle (1) 

Change the styling:

In[14]:=
ResourceFunction["CombinatorBracketsPlot"][ s[k[s]][k][s[s[k[s]][k]][s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]]][ s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]][s][k], "IncludeTextForm" -> False, PlotStyle -> Directive[RGBColor[0.711529, 0.181058, 0.], Thick]]
Out[14]=
In[15]:=
ResourceFunction["CombinatorBracketsPlot"][ s[k[s]][k][s[s[k[s]][k]][s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]]][ s[s[k[s]][k]][s[s[k[s]][k]][s[k]]]][s][k], Appearance -> "Mountain", "IncludeTextForm" -> False, PlotStyle -> Directive[RGBColor[0.8505, 0.4275, 0.13185], AbsolutePointSize[4], AbsoluteThickness[1]]]
Out[15]=

Version History

  • 1.0.0 – 03 December 2020

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