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PCM20210728_SICP_1.1.3_Evaluating_Combinations
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### A Pluto.jl notebook ###
# v0.20.0
using Markdown
using InteractiveUtils
# ╔═╡ 2016a90d-6ef5-4142-861d-6c68ffd202e1
begin
using Pluto
using Plots
using GraphRecipes
#----------------------------------------------------------------
println("pkgversion(Pluto) = ", pkgversion(Pluto))
println("pkgversion(Plots) = ", pkgversion(Plots))
println("pkgversion(GraphRecipes) = ", pkgversion(GraphRecipes))
end # begin
# ╔═╡ 749c8c80-f126-11eb-33a6-b72ce370f20f
md"
===================================================================================
### SICP: [1.1.3 Evaluating Combinations](https://sarabander.github.io/sicp/html/1_002e1.xhtml#g_t1_002e1_002e3)
###### file: PCM20210728\_SICP\_1.1.3\_Evaluating\_Combinations
###### Julia/Pluto.jl-code (1.11.2/0.20.3) by PCM *** 2024/12/07 ****
===================================================================================
"
# ╔═╡ 8c18c58a-632b-499e-a227-9900ddfba434
md"
##### 0. Introduction
First we try to be as close as possible to the *functional* style of SICP in [*MIT-Scheme*](https://en.wikipedia.org/wiki/MIT/GNU_Scheme), then we introduce *idiomatic* Julia elements.
In case of any doubt you can consult the [Julia doc](https://docs.julialang.org/en/v1/).
"
# ╔═╡ 16d2b971-b57f-4e4a-bb44-f4cf92ff1b19
md"
---
##### 1. Topics
*Topics* dealt are:
- Expressions
- Combinations
- Kantorovic Tree
- Data Flow Tree
- Evaluation order
"
# ╔═╡ 141b0dc2-c23f-47b9-8ab1-95adb1a0cf07
md"
---
##### 2. Libraries
"
# ╔═╡ 6bbc8d28-5c9e-4a91-9aaa-7f72cda4917d
md"
---
##### 3. SICP-Scheme-like *functional* Julia: *Evaluation* of *Expressions*
According to [SICP (ch.1.1.3)](https://mitp-content-server.mit.edu/books/content/sectbyfn/books_pres_0/6515/sicp.zip/full-text/book/book-Z-H-4.html#%_toc_%_sec_1.1.3]) the process of evaluation is:
*To evaluate a combination, do the following:*
- 1. *Evaluate the subexpressions of the combination.*
- 2. *Apply the procedure that is the value of the leftmost subexpression (the operator) to the arguments that are the values of the other subexpressions (the operands).*
This same *evaluation scheme* can be used to interpret the value of *Julia* combinations. More precisely the evaluation order is a *partial order* which can be described by a *Kantorovic tree* (Fig. 1.1.3.2) or a *data flow tree* (Fig. 1.1.3.2).
"
# ╔═╡ 850f51da-f320-4c40-955d-fd0e4f6ae6ad
md"
SICP presents an example:
(* (+ 2 (* 4 6))
(+ 3 5 7)).
This can be easily tranpiled to Julia:
"
# ╔═╡ 17bcdc6b-48f5-4fb9-b260-dd6a93998520
*( +( 2, *( 4, 6)),
+( 3, 5, 7)) # ==> 390 --> :)
# ╔═╡ aef5c84c-c764-4489-a927-12538ae5181c
*( +( 2, *( 4, 6)), +( 3, 5, 7)) # ==> 390 --> :)
# ╔═╡ 86c99cbd-9e4c-4d92-aab3-4e9c2df21dbe
md"
A nonlinear tree of subexpressions and corresponding values is presented in Fig. 1.1.1.3.1. The order of operand evaluation is undetermined.
"
# ╔═╡ dc826433-95e3-48cf-b451-75fa78af5a8a
let
#------------------------------------------------------------------------------
function plotUnaryTree!(markOfLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; heightOfTree=2, fontSize=9)
plot!([ # plot of middle vertical arm '|'
(coordinateXOfRootMark, coordinateYOfRootMark+heightOfTree/8),
(coordinateXOfRootMark, coordinateYOfRootMark+heightOfTree-heightOfTree/8)],
lw=1, linecolor=:black)
annotate!( # mark of leaf 'x'
(coordinateXOfRootMark, 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)
annotate!( # mark of left leaf 'x'
(coordinateXOfRootMark-widthOfTree/2,
coordinateYOfRootMark+heightOfTree,
text(markOfLeftLeaf, fontSize, :blue)))
plot!([ # plot of left vertical arm '|'
(coordinateXOfRootMark-widthOfTree/2,
coordinateYOfRootMark + heightOfTree-heightOfTree/8),
(coordinateXOfRootMark-widthOfTree/2, coordinateYOfRootMark+heightOfTree/2)],
lw=1, linecolor=:black)
annotate!( # mark of right leaf 'x'
(coordinateXOfRootMark+widthOfTree/2,
coordinateYOfRootMark+heightOfTree,
text(markOfRightLeaf, fontSize, :blue)))
plot!([ # plot of right vertical arm '|'
(coordinateXOfRootMark+widthOfTree/2,
coordinateYOfRootMark+heightOfTree-heightOfTree/8),
(coordinateXOfRootMark+widthOfTree/2, coordinateYOfRootMark+heightOfTree/2)],
lw=1, linecolor=:black)
plot!([ # plot of horizontal bar '-'
(coordinateXOfRootMark-widthOfTree/2, coordinateYOfRootMark+heightOfTree/2),
(coordinateXOfRootMark+widthOfTree/2, coordinateYOfRootMark+heightOfTree/2)],
lw=1, linecolor=:black)
plot!([ # plot of middle vertical arm '|'
(coordinateXOfRootMark, coordinateYOfRootMark+heightOfTree/2),
(coordinateXOfRootMark, coordinateYOfRootMark+heightOfTree/8)],
lw=1, linecolor=:black)
annotate!( # mark of root 'x'
(coordinateXOfRootMark, coordinateYOfRootMark, text(markOfRoot, fontSize, :blue)))
end # function plotBinaryTree!
#------------------------------------------------------------------------------
function plotTernaryTree!(markOfLeftLeaf, markOfMiddleLeaf, markOfRightLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=3.0,
heightOfTree=2, fontSize=9)
#---------------------------------------------------------
plotBinaryTree!(markOfLeftLeaf, markOfRightLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=widthOfTree, heightOfTree=heightOfTree, fontSize=fontSize)
#---------------------------------------------------------
plotUnaryTree!(markOfMiddleLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; heightOfTree=heightOfTree, fontSize=fontSize)
end # function plotTernaryTree!
#------------------------------------------------------------------------------
function plotQuaternyTree!(markOfLeftMostLeaf, markOfLeftLeaf, markOfRightLeaf, markOfRightMostLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=4.0, heightOfTree=2, fontSize=9)
#---------------------------------------------------------
plotBinaryTree!(markOfLeftMostLeaf, markOfRightMostLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=widthOfTree, heightOfTree=heightOfTree, fontSize=fontSize)
#---------------------------------------------------------
plotBinaryTree!(markOfLeftLeaf, markOfRightLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=widthOfTree/3, heightOfTree=heightOfTree, fontSize=fontSize)
end # function plotQuaternyTree!
#------------------------------------------------------------------------------
plot(xlim=(-2, 11), ylim=(3, 11), legend=:false, ticks=:none)
plotTernaryTree!( "*", "4", "6", "24", 4.5, 8.0; widthOfTree=2.0)
plotTernaryTree!( "+", "2", "24", "26", 3.5, 6.0; widthOfTree=2.0)
plotQuaternyTree!("+", "3", "5", "7", "15", 7.5, 6.0; widthOfTree=3.0)
plotTernaryTree!( "*", "26", "15", "390", 3.5, 4.0; widthOfTree=8.0)
#------------------------------------------------------------------------------
end # let
# ╔═╡ ef763055-54f9-4399-8120-e111b03decfc
md"
**Fig. 1.1.3.1** Nonlinear tree of (sub-)expression and *values* (cf. SICP, 1966, Figure 1.1, p.10)
---
"
# ╔═╡ b5fef8cf-4117-4145-a2af-829b1ae3e691
md"
The *linear* combination can be transpiled to a *nonlinear* *Kantorovic* tree (Fig. 1.1.3.1) and a *data flow tree* (Fig. 1.1.3.2), which describe the *partial order* of evaluation.
"
# ╔═╡ e67ab7e1-b26f-49a6-afce-fe4a1f1e37cb
begin
#------------------------------------------------------------------------------
function plotUnaryTree!(markOfLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; heightOfTree=2, fontSize=10)
plot!([ # plot of middle vertical arm '|'
(coordinateXOfRootMark, coordinateYOfRootMark + heightOfTree/4),
(coordinateXOfRootMark, coordinateYOfRootMark+heightOfTree-heightOfTree/4)],
lw=1, linecolor=:black)
annotate!( # mark of leaf 'x'
(coordinateXOfRootMark, 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=10)
annotate!( # mark of left leaf 'x'
(coordinateXOfRootMark-widthOfTree/2,
coordinateYOfRootMark+heightOfTree,
text(markOfLeftLeaf, fontSize, :blue)))
plot!([ # plot of left vertical arm '|'
(coordinateXOfRootMark-widthOfTree/2,
coordinateYOfRootMark + heightOfTree-heightOfTree/6),
(coordinateXOfRootMark-widthOfTree/2, coordinateYOfRootMark+heightOfTree/2)],
lw=1, linecolor=:black)
annotate!( # mark of right leaf 'x'
(coordinateXOfRootMark+widthOfTree/2,
coordinateYOfRootMark+heightOfTree,
text(markOfRightLeaf, fontSize, :blue)))
plot!([ # plot of right vertical arm '|'
(coordinateXOfRootMark+widthOfTree/2,
coordinateYOfRootMark+heightOfTree-heightOfTree/6),
(coordinateXOfRootMark+widthOfTree/2, coordinateYOfRootMark+heightOfTree/2)],
lw=1, linecolor=:black)
plot!([ # plot of horizontal bar '-'
(coordinateXOfRootMark-widthOfTree/2, coordinateYOfRootMark+heightOfTree/2),
(coordinateXOfRootMark+widthOfTree/2, coordinateYOfRootMark+heightOfTree/2)],
lw=1, linecolor=:black)
plot!([ # plot of middle vertical arm '|'
(coordinateXOfRootMark, coordinateYOfRootMark+heightOfTree/2),
(coordinateXOfRootMark, coordinateYOfRootMark+heightOfTree/6)],
lw=1, linecolor=:black)
annotate!( # mark of root 'x'
(coordinateXOfRootMark, coordinateYOfRootMark, text(markOfRoot, fontSize, :blue)))
end # function plotBinaryTree!
#------------------------------------------------------------------------------
function plotTernaryTree!(markOfLeftLeaf, markOfMiddleLeaf, markOfRightLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=3.0,
heightOfTree=2, fontSize=10)
#-----------------------------------------------------------------------
plotBinaryTree!(markOfLeftLeaf, markOfRightLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=widthOfTree, heightOfTree=heightOfTree, fontSize=fontSize)
#-----------------------------------------------------------------------
plotUnaryTree!(markOfMiddleLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; heightOfTree=heightOfTree, fontSize=fontSize)
end # function plotTernaryTree!
#------------------------------------------------------------------------------
function plotQuaternyTree!(markOfLeftMostLeaf, markOfLeftLeaf, markOfRightLeaf, markOfRightMostLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=4.0, heightOfTree=2, fontSize=10)
#---------------------------------------------------------------------
plotBinaryTree!(markOfLeftMostLeaf, markOfRightMostLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=widthOfTree, heightOfTree=heightOfTree, fontSize=fontSize)
#---------------------------------------------------------------------
plotBinaryTree!(markOfLeftLeaf, markOfRightLeaf, markOfRoot, coordinateXOfRootMark, coordinateYOfRootMark; widthOfTree=widthOfTree/3, heightOfTree=heightOfTree, fontSize=fontSize)
end # function plotQuaternyTree!
#------------------------------------------------------------------------------
end # begin
# ╔═╡ 188ac878-77af-4d8c-9106-e1a8a98f6787
function plotMyKantorovicTree(; title="")
#-----------------------------------------------------------------------------
plot(xlim=(-2, 7), ylim=(4.5, 8.5), legend=:false, ticks=:none, title=title)
plotBinaryTree!( "4", "6", "*", 1.5, 7.0, heightOfTree=1, fontSize=10)
plotBinaryTree!( "2", "*", "+", 0.75, 6.0, heightOfTree=1, fontSize=10)
plotTernaryTree!("3", "5", "7", "+", 4.0, 6.0; widthOfTree=2.0, heightOfTree=1, fontSize=10)
plotBinaryTree!( "+", "+", "*", 2.36, 5.0; widthOfTree=3.25, heightOfTree=1, fontSize=10)
#------------------------------------------------------------------------------
end # function plotMyKantorovicTree
# ╔═╡ febe0c4a-fe1f-4f07-be71-b4e611cbe697
plotMyKantorovicTree(title="Kantorovic tree of *( +( 2, *( 4, 6)), +( 3, 5, 7))")
# ╔═╡ b82526ad-6917-4a25-b16e-e007a3037be9
md"
**Fig 1.1.3.2** *Nonlinear* *Kantorovic* tree (Bauer & Wösnner, 1982, p.21) of
- *prefix*-expression (from root to leaves):
$$*( +( 2, *( 4, 6)), +( 3, 5, 7))$$
- *infix*-expression (from leaf to root to leaf):
$$(2 + 4*6)*(3 + 5 + 7)$$
- *postfix*-expression (from leaves to root):
$$((2, (4, 6)*)+,(3,5,7)+)*$$
---
"
# ╔═╡ dec89253-b421-4057-991b-eca2096cf7d8
function plotMyDataFlowTree(; title="")
#-----------------------------------------------------------------------------
plot(xlim=(-2, 7), ylim=(0.5, 14), legend=:false, ticks=:none, title=title)
plotBinaryTree!( "4", "6", "*", 1.5, 11, heightOfTree=2, fontSize=10)
plotUnaryTree!("", "", 1.5, 9.0, heightOfTree=2.0, fontSize=10)
plotBinaryTree!( "2", "24", "+", 0.75, 7, heightOfTree=2, fontSize=10)
plotTernaryTree!("3", "5", "7", "+", 4.0, 7; widthOfTree=2.0, heightOfTree=2, fontSize=10)
plotUnaryTree!("", "", 0.75, 5, heightOfTree=2, fontSize=10)
plotUnaryTree!("", "", 4.0, 5, heightOfTree=2, fontSize=10)
plotBinaryTree!( "26", "15", "*", 2.375, 3; widthOfTree=3.25, heightOfTree=2, fontSize=10)
plotUnaryTree!("", "390", 2.375, 1.5, heightOfTree=2, fontSize=10)
#------------------------------------------------------------------------------
end # function plotMyDataFlowTree()
# ╔═╡ 44285bc5-4f21-4e60-80ba-04efe09fde26
plotMyDataFlowTree(title="Data Flow Tree of *( +( 2, *( 4, 6)), +( 3, 5, 7))")
# ╔═╡ d123c0f1-dd19-4fc8-9fad-b5a3f766aa34
md"
**Fig 1.1.3.3** nonlinear *Data Flow* Tree of *Prefix* Expression *( +( 2, *( 4, 6)), +( 3, 5, 7))
"
# ╔═╡ d12f3b54-52d2-4dba-89ba-9722a47798fd
*( +( 2, *( 4, 6)),
+( 3, 5, 7)) # ==> 390 --> :)
# ╔═╡ db698f35-cd91-469b-92ad-f6c86b55b16b
md"
---
##### 4. Idiomatic Julia ...
###### ... with *infix* operators
"
# ╔═╡ e2443252-7c22-4385-87a4-caf4eec72d60
(2 + (4 * 6)) * (3 + 5 + 7)
# ╔═╡ fec0b277-1847-4552-96d3-c05f11a43fbd
(2 + 4 * 6) * (3 + 5 + 7)
# ╔═╡ b2e91e77-0dc4-4d59-8578-e473d0caf993
md"
---
##### 5. Summary
*Linear* Expressions can be transferred to *nonlinear Kantorovic* trees. When they are decorated with *value nodes* they become *data flow* trees. All evaluation orders of *linear* expressions which are consistent with these trees are semantically o.k.
"
# ╔═╡ d42c001d-a772-430e-a4b8-19f5e09acee4
md"
---
#### References
- **Abelson, H., Sussman, G.J. & Sussman, J.**, Structure and Interpretation of Computer Programs, Cambridge, Mass.: MIT Press, (2/e), 1996, [https://sarabander.github.io/sicp/](https://sarabander.github.io/sicp/), last visit 2022/08/23
- **Bauer, F.L. & Wössner, H.**; Algorithmic Language and Program Development; Heidelberg: Springer, 1982
"
# ╔═╡ c0e324a0-da15-424a-935f-e62b8ca990be
md"
---
##### end of ch. 1.1.3
====================================================================================
This is a **draft** under the [Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)](https://creativecommons.org/licenses/by-nc-sa/4.0/) license. Comments, suggestions for improvement and bug reports are welcome: **claus.moebus(@)uol.de**
====================================================================================
"
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