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PCM20221217_SICP_2.5.2.4_Inadequacies_of_Hierarchies.jl
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### A Pluto.jl notebook ###
# v0.19.12
using Markdown
using InteractiveUtils
# ╔═╡ 82dab45d-a94b-41fb-87c1-f5fe3d8cf300
using Plots
# ╔═╡ ac1f2b50-7e0a-11ed-0185-57234c8c876d
md"
===================================================================================
#### SICP\_2.5.2.4\_[Inadequacies\_of\_Hierarchies]()
##### file: PCM20221217\_SICP\_2.5.2.4\_Inadequacies\_of\_Hierarchies.jl
##### Julia/Pluto.jl-code (1.8.3/0.19.14) by PCM *** 2022/12/23 ***
===================================================================================
"
# ╔═╡ 10385c82-54cd-4df0-afea-2706b821175f
md"
##### Concept hierarchy of 2D-Polygons
SICP presents an informal example of a concept hierarchy with *mixed* types. We refine their concept nodes by a partion into *abstract* and *concrete* concepts. This is shown in Fig. 2.5.2.4.1 (below). Alternative and more formal hierarchies with the same set or subset of figures are [known](https://en.wikipedia.org/wiki/Quadrilateral). These hierarchies were constructed with [*Euler*](https://en.wikipedia.org/wiki/Quadrilateral#/media/File:Euler_diagram_of_quadrilateral_types.svg) or [*Hasse*](https://en.wikipedia.org/wiki/Quadrilateral#/media/File:Symmetries_of_square.svg) diagrams.
"
# ╔═╡ e7ee86ea-28aa-48b0-8ff6-c5bb66fec663
let
xMax = 20.0
yMax = 16.0
arrow = :head
width11 = 11.0
width10 = 10.0
width5 = 5.0
#===============================================================================#
function plotUnaryTree!(markOfLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; heightOfTree=2, fontSize=9, arrow=nothing, rootIsTop=false)
plot!([ # of vertical bar or arrow '|'
(coordinateXOfRootMark,
rootIsTop ? # leaf
coordinateYOfRootMark-heightOfTree+heightOfTree/8 :
coordinateYOfRootMark+heightOfTree-heightOfTree/8),
(coordinateXOfRootMark,
rootIsTop ? # root
coordinateYOfRootMark-heightOfTree/8 :
coordinateYOfRootMark+heightOfTree/8)],
lw=1, linecolor=:black, arrow=arrow)
annotate!( # mark of leaf 'x'
(coordinateXOfRootMark,
rootIsTop ?
coordinateYOfRootMark-heightOfTree :
coordinateYOfRootMark+heightOfTree,
text(markOfLeaf, fontSize, :blue)))
annotate!( # mark of root 'x'
(coordinateXOfRootMark,
coordinateYOfRootMark, text(markOfRoot, fontSize, :blue)))
end # function plotUnaryTree!
#------------------------------------------------------------------------------
function plotBinaryTree!(markOfLeftLeaf, markOfRightLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=1.5, heightOfTree=2, fontSize=9, arrow=nothing, rootIsTop=false)
annotate!( # mark of left leaf 'x'
(coordinateXOfRootMark-widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark - heightOfTree :
coordinateYOfRootMark + heightOfTree,
text(markOfLeftLeaf, fontSize, :blue)))
plot!([ # plot of left vertical bar '|'
(coordinateXOfRootMark-widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark - heightOfTree + heightOfTree/8 :
coordinateYOfRootMark + heightOfTree - heightOfTree/8),
(coordinateXOfRootMark-widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark-heightOfTree/2 :
coordinateYOfRootMark+heightOfTree/2)],
lw=1, linecolor=:black, arrow=arrow)
annotate!( # mark of right leaf 'x'
(coordinateXOfRootMark+widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark - heightOfTree :
coordinateYOfRootMark + heightOfTree,
text(markOfRightLeaf, fontSize, :blue)))
plot!([ # plot of left vertical bar '|'
(coordinateXOfRootMark+widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark - heightOfTree + heightOfTree/8 :
coordinateYOfRootMark + heightOfTree - heightOfTree/8),
(coordinateXOfRootMark+widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark-heightOfTree/2 :
coordinateYOfRootMark+heightOfTree/2)],
lw=1, linecolor=:black, arrow=arrow)
plot!([ # plot horizontal bar '-'
(coordinateXOfRootMark-widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark-heightOfTree/2 :
coordinateYOfRootMark+heightOfTree/2),
(coordinateXOfRootMark+widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark-heightOfTree/2 :
coordinateYOfRootMark+heightOfTree/2)],
lw=1, linecolor=:black)
plot!([ # plot of middle vertical bar '|'
(coordinateXOfRootMark,
rootIsTop ?
coordinateYOfRootMark-heightOfTree/2 :
coordinateYOfRootMark+heightOfTree/2),
(coordinateXOfRootMark,
rootIsTop ?
coordinateYOfRootMark-heightOfTree/8 :
coordinateYOfRootMark+heightOfTree/8)],
lw=1, linecolor=:black, arrow=arrow) # plot of middle vertical bar '|'
annotate!(
(coordinateXOfRootMark, coordinateYOfRootMark, text(markOfRoot, fontSize, :blue))) # mark of root 'x'
end # function plotBinaryTree!
#------------------------------------------------------------------------------
function plotTernaryTree!(markOfLeftLeaf, markOfMiddleLeaf, markOfRightLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=3.0,
heightOfTree=2, fontSize=9, arrow=nothing, rootIsTop=false)
#---------------------------------------------------------
plotBinaryTree!(markOfLeftLeaf, markOfRightLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=widthOfTree, heightOfTree=heightOfTree, fontSize=fontSize, arrow=arrow, rootIsTop=rootIsTop)
#---------------------------------------------------------
plotUnaryTree!(markOfMiddleLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; heightOfTree=heightOfTree, fontSize=fontSize, arrow=arrow, rootIsTop=rootIsTop)
end # function plotTernaryTree!
#------------------------------------------------------------------------------
function plotQuaternyTree!(markOfLeftMostLeaf, markOfLeftLeaf, markOfRightLeaf, markOfRightMostLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=4.0, heightOfTree=2, fontSize=9, arrow=nothing, rootIsTop=false)
#---------------------------------------------------------
plotBinaryTree!(markOfLeftMostLeaf, markOfRightMostLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=widthOfTree, heightOfTree=heightOfTree, fontSize=fontSize, arrow=arrow, rootIsTop=rootIsTop)
#---------------------------------------------------------
plotBinaryTree!(markOfLeftLeaf, markOfRightLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=widthOfTree/3, heightOfTree=heightOfTree, fontSize=fontSize, arrow=arrow, rootIsTop=rootIsTop)
end # function plotQuaternyTree!
#===============================================================================#
plot(xlim=(-1.5, xMax), ylim=(1, yMax), legend=:false, ticks=:none)
#-------------------------------------------------------------------------------
plotBinaryTree!("Triangle(s)", "Quadrilateral(s)", "Polygon(s)", xMax-11.0, yMax-0.0; widthOfTree=width10, heightOfTree=3.0, fontSize=8, arrow=arrow, rootIsTop=true)
#------------------------------------------------------------------------------
plotBinaryTree!("Isoscele(s)", "Right(s)", "Triangle(s)", xMax-16.0, yMax-3.0; widthOfTree=width5, heightOfTree=4.5, fontSize=8, arrow=arrow, rootIsTop=true)
#------------------------------------------------------------------------------
plotBinaryTree!("Trapezoid(s)", "Kite(s)", "Quadrilateral(s)", xMax-6.0, yMax-3.0; widthOfTree=width5, heightOfTree=3.0, fontSize=8, arrow=arrow, rootIsTop=true)
#------------------------------------------------------------------------------
plotBinaryTree!("Isoscele(s)", "Right(s)", "IsoscelesRight(s)", xMax-16.0, yMax-11.0; widthOfTree=width5, heightOfTree=3.5, fontSize=8, arrow=:tail, rootIsTop=false)
#------------------------------------------------------------------------------
plotUnaryTree!("Isoscele(s)", "Equilateral(s)", xMax-18.5, yMax-13.0; heightOfTree=5.5, fontSize=8, arrow=nothing, rootIsTop=false)
#------------------------------------------------------------------------------
plotBinaryTree!("Rectangle(s)", "Rhomb(us|i)", "Square(s)", xMax-6.0, yMax-13.0; widthOfTree=5.0, heightOfTree=3.0, fontSize=8, arrow=:tail, rootIsTop=false)
#------------------------------------------------------------------------------
plotUnaryTree!("Trapezoid(s)", "Parallelogram(s)", xMax-8.5, yMax-8.0; heightOfTree=2, fontSize=8, arrow=:tail, rootIsTop=false)
#------------------------------------------------------------------------------
plotUnaryTree!("Kite(s)", "", xMax-3.5, yMax-10.5; heightOfTree=4.5, fontSize=8, arrow=:tail, rootIsTop=false)
#------------------------------------------------------------------------------
plotUnaryTree!("", "", xMax-8.5, yMax-10.0; heightOfTree=2, fontSize=8, arrow=:tail, rootIsTop=false) # Parallelogram <--> Rectangle
#------------------------------------------------------------------------------
plot!([(11.5, 7.7), (16.4, 6.2)], lw=1, linecolor=:black, arrow=:tail)
#===============================================================================#
end # let
# ╔═╡ 41c792b6-4884-41b1-b3cd-573a19bf7842
md"
**Fig. 2.5.2.4.1**: *Mixed* concept hierarchy of *abstract* and *concrete* types of 2D-polygons (cf. Fig.2.26, p.199, SICP, 2/e, 1996); *plural* form of concept names (like: Polgon*s*) denotes *abstract* and *singular* form (like: Square) *concrete* types; *arrows* denote the *sub-/supertype* relation.
---
"
# ╔═╡ f431d55b-5f3c-440e-91ec-90c6ca87606f
md"
Fig. 2.5.2.4.1 is an example of an *informal* concept hierarchy with *multiple* inheritance. Each *abstract* concept is mapped to a Julian *abstract type*. The same is done with *concrete* versions. A *type* is defined as a set of possible values. Because of semantic ambiguities for certain concepts (here: IsoscelesRightTriangle(s), Rhomb(us|i), and Square(s)) we have to *demix* this *multiple* inheritance hierarchy into one with *single* inheritance (Fig. 2.5.2.4.2, below).
"
# ╔═╡ 081bbd02-5b10-48d0-be04-d434708549c5
let
xMax = 20.0
yMax = 16.0
arrow = :head
#===============================================================================#
function plotUnaryTree!(markOfLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; heightOfTree=2, fontSize=9, arrow=nothing, rootIsTop=false)
plot!([ # of vertical bar or arrow '|'
(coordinateXOfRootMark,
rootIsTop ? # leaf
coordinateYOfRootMark-heightOfTree+heightOfTree/8 :
coordinateYOfRootMark+heightOfTree-heightOfTree/8),
(coordinateXOfRootMark,
rootIsTop ? # root
coordinateYOfRootMark-heightOfTree/8 :
coordinateYOfRootMark+heightOfTree/8)],
lw=1, linecolor=:black, arrow=arrow)
annotate!( # mark of leaf 'x'
(coordinateXOfRootMark,
rootIsTop ?
coordinateYOfRootMark-heightOfTree :
coordinateYOfRootMark+heightOfTree,
text(markOfLeaf, fontSize, :blue)))
annotate!( # mark of root 'x'
(coordinateXOfRootMark,
coordinateYOfRootMark, text(markOfRoot, fontSize, :blue)))
end # function plotUnaryTree!
#------------------------------------------------------------------------------
function plotBinaryTree!(markOfLeftLeaf, markOfRightLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=1.5, heightOfTree=2, fontSize=9, arrow=nothing, rootIsTop=false)
annotate!( # mark of left leaf 'x'
(coordinateXOfRootMark-widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark - heightOfTree :
coordinateYOfRootMark + heightOfTree,
text(markOfLeftLeaf, fontSize, :blue)))
plot!([ # plot of left vertical bar '|'
(coordinateXOfRootMark-widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark - heightOfTree + heightOfTree/8 :
coordinateYOfRootMark + heightOfTree - heightOfTree/8),
(coordinateXOfRootMark-widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark-heightOfTree/2 :
coordinateYOfRootMark+heightOfTree/2)],
lw=1, linecolor=:black, arrow=arrow)
annotate!( # mark of right leaf 'x'
(coordinateXOfRootMark+widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark - heightOfTree :
coordinateYOfRootMark + heightOfTree,
text(markOfRightLeaf, fontSize, :blue)))
plot!([ # plot of left vertical bar '|'
(coordinateXOfRootMark+widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark - heightOfTree + heightOfTree/8 :
coordinateYOfRootMark + heightOfTree - heightOfTree/8),
(coordinateXOfRootMark+widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark-heightOfTree/2 :
coordinateYOfRootMark+heightOfTree/2)],
lw=1, linecolor=:black, arrow=arrow)
plot!([ # plot horizontal bar '-'
(coordinateXOfRootMark-widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark-heightOfTree/2 :
coordinateYOfRootMark+heightOfTree/2),
(coordinateXOfRootMark+widthOfTree/2,
rootIsTop ?
coordinateYOfRootMark-heightOfTree/2 :
coordinateYOfRootMark+heightOfTree/2)],
lw=1, linecolor=:black)
plot!([ # plot of middle vertical bar '|'
(coordinateXOfRootMark,
rootIsTop ?
coordinateYOfRootMark-heightOfTree/2 :
coordinateYOfRootMark+heightOfTree/2),
(coordinateXOfRootMark,
rootIsTop ?
coordinateYOfRootMark-heightOfTree/8 :
coordinateYOfRootMark+heightOfTree/8)],
lw=1, linecolor=:black, arrow=arrow) # plot of middle vertical bar '|'
annotate!(
(coordinateXOfRootMark, coordinateYOfRootMark, text(markOfRoot, fontSize, :blue))) # mark of root 'x'
end # function plotBinaryTree!
#------------------------------------------------------------------------------
function plotTernaryTree!(markOfLeftLeaf, markOfMiddleLeaf, markOfRightLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=3.0,
heightOfTree=2, fontSize=9, arrow=nothing, rootIsTop=false)
#---------------------------------------------------------
plotBinaryTree!(markOfLeftLeaf, markOfRightLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=widthOfTree, heightOfTree=heightOfTree, fontSize=fontSize, arrow=arrow, rootIsTop=rootIsTop)
#---------------------------------------------------------
plotUnaryTree!(markOfMiddleLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; heightOfTree=heightOfTree, fontSize=fontSize, arrow=arrow, rootIsTop=rootIsTop)
end # function plotTernaryTree!
#------------------------------------------------------------------------------
function plotQuaternyTree!(markOfLeftMostLeaf, markOfLeftLeaf, markOfRightLeaf, markOfRightMostLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=4.0, heightOfTree=2, fontSize=9, arrow=nothing, rootIsTop=false)
#---------------------------------------------------------
plotBinaryTree!(markOfLeftMostLeaf, markOfRightMostLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=widthOfTree, heightOfTree=heightOfTree, fontSize=fontSize, arrow=arrow, rootIsTop=rootIsTop)
#---------------------------------------------------------
plotBinaryTree!(markOfLeftLeaf, markOfRightLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=widthOfTree/3, heightOfTree=heightOfTree, fontSize=fontSize, arrow=arrow, rootIsTop=rootIsTop)
end # function plotQuaternyTree!
#===============================================================================#
plot(xlim=(-1.5, xMax), ylim=(1, yMax), legend=:false, ticks=:none)
#-------------------------------------------------------------------------------
plotBinaryTree!("Triangle(s)", "Quadrilateral(s)", "Polygon(s)", xMax-11.0, yMax-2.0; widthOfTree=10.0, heightOfTree=3.0, fontSize=8, arrow=arrow, rootIsTop=true)
#------------------------------------------------------------------------------
plotBinaryTree!("Isoscele(s)", "Right(s)", "Triangle(s)", xMax-16.0, yMax-5.0; widthOfTree=5.0, heightOfTree=4.5, fontSize=8, arrow=arrow, rootIsTop=true)
#------------------------------------------------------------------------------
plotBinaryTree!("Trapezoid(s)", "Kite(s)", "Quadrilateral(s)", xMax-6.0, yMax-5.0; widthOfTree=9.0, heightOfTree=3.0, fontSize=8, arrow=arrow, rootIsTop=true)
#------------------------------------------------------------------------------
plotUnaryTree!("", "IsoscelesRight(s)", xMax-16.0, yMax-11.0; heightOfTree=4.5, fontSize=8, arrow=:tail, rootIsTop=false)
#------------------------------------------------------------------------------
plotUnaryTree!("Isoscele(s)", "Equilateral(s)", xMax-18.5, yMax-13.0; heightOfTree=3.5, fontSize=8, arrow=:tail, rootIsTop=false)
#------------------------------------------------------------------------------
plotBinaryTree!("Square(s)", "Rhomb(us|i)", "", xMax-6.0, yMax-4.6; widthOfTree=3.0, heightOfTree=6.0, fontSize=8, arrow=:head, rootIsTop=true)
#------------------------------------------------------------------------------
plotUnaryTree!("Trapezoid(s)", "Parallelogram(s)", xMax-10.5, yMax-10.0; heightOfTree=2, fontSize=8, arrow=:tail, rootIsTop=false)
#------------------------------------------------------------------------------
plotUnaryTree!("", "Rectangle(s)", xMax-10.5, yMax-12.0; heightOfTree=2, fontSize=8, arrow=:tail, rootIsTop=false) # Parallelogram <--> Rectangle
#===============================================================================#
end # let
# ╔═╡ adf35063-d418-4013-80c4-a2510b5d1f68
md"
**Fig. 2.5.2.4.2**: *Demixed* super-/subtype hierarchy of *abstract* and *concrete* types of 2D-polygons; *super-/sub*type relations are denoted by *up-arrows*.
---
"
# ╔═╡ d85e5bf0-d529-4c57-86e2-32f254182bc3
md"""
In a footnote SICP gives a resumé on hierarchies with *multiple* inheritance: "*... much of the complexity of object-oriented programming languages - and the subtle and confusing differences among contemporary object-oriented languages - centers on the treatment of generic operations on interrelated types.*"(SICP, 1996, p.200)
"""
# ╔═╡ f4bea9bb-da9b-49de-86bd-7ea63e8c9237
md"
---
##### end of ch. 2.5.2.4
"
# ╔═╡ fe37adb6-46e7-4d1e-9ed8-5ca2079e7b04
md"
====================================================================================
This is a **draft** under the Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) license. Comments, suggestions for improvement and bug reports are welcome: **claus.moebus(@)uol.de**
====================================================================================
"
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
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[compat]
Plots = "~1.38.0"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
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