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PCM20210730_SICP_1.1.4_Compound_Procedures.jl
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### A Pluto.jl notebook ###
# v0.20.0
using Markdown
using InteractiveUtils
# ╔═╡ 3d323fd6-b7a2-427d-a058-6dfe9ab04289
begin
using Pluto
using Plots
using GraphRecipes
#----------------------------------------------------------------
println("pkgversion(Pluto) = ", pkgversion(Pluto))
println("pkgversion(Plots) = ", pkgversion(Plots))
println("pkgversion(GraphRecipes) = ", pkgversion(GraphRecipes))
end # begin
# ╔═╡ e4ea9712-f127-11eb-1ce4-e9286638b6cf
md"
===================================================================================
#### SICP: [1.1.4 Compound Procedures](https://mitp-content-server.mit.edu/books/content/sectbyfn/books_pres_0/6515/sicp.zip/full-text/book/book-Z-H-10.html#%_sec_1.1.4)
###### file: PCM20210730\_SICP\_1.1.4\_Compound\_Procedures.jl
###### Julia/Pluto.jl-code (1.11.2/0.20.3) by PCM *** 2024/12/10 ***
===================================================================================
"
# ╔═╡ 506915e1-15ef-43b6-aaf4-c3074e6c08ba
md"
##### 0. Introduction
"
# ╔═╡ 9b9a9365-f17d-4e98-b6d2-360d417781b6
md"
---
##### 1. Topics
- *generic* function
- *dynamic* vs *static* types
- *methods* of *function*
- *infix* operator, *iuxtaposition* of operands
- *definition* of function with *keyword* $function$
- *definition* of function with *anonymous* function with operator $\textit{->}$
- *String* as *argument*
- *typifying* of arguments
- *dispatch* of function calls
- *multiple dispatch*
"
# ╔═╡ f6741d7a-4cbe-442a-b508-73085eed5ecf
md"
---
##### 2. Libraries
"
# ╔═╡ 4e1efa4a-cb44-4913-a35f-0a779ee0ee2a
md"
##### 3. SICP-Scheme-like *functional* Julia: Compound Procedures
*Compound procedures* are *functions* with a *body* consisting of one or more *expressions*.
"
# ╔═╡ 73339eae-4754-49b1-938a-5ceae1c0f6a3
md"
###### 3.1 *Definition* and *Application* of *Function* $square$
"
# ╔═╡ d39b8c94-18a2-4ddd-ae82-1e05bfcc5c85
md"
###### 1st *untyped, generic method* of function $square$
A *generic* function is an *untyped* function. This means that *input* and *output* are *not* constrained by *static* types (e.g.: Int64, Float64). Before the *binding* of arguments to parameters arguments possess the default *generic* type $Any$. At *binding time* the generic type $Any$ is *constrained* *dynamically* to the type of the argument.
"
# ╔═╡ ece77425-0b83-4a9a-b2ef-757bfaa60891
md"
###### To square something, multiply it by itself* (SICP, 1996, ch. 1.1.4)
| |
v v
square(x) = *(x, x)
"
# ╔═╡ 150ad79c-42b4-4981-8711-1ef426725ca0
square(x) = *(x, x) # ==> square
# ╔═╡ 7e97208a-d1b0-435e-8756-f0b468b1c795
md"
---
###### 3.2 *Definition* and *Application* of *Generic* Function $sumOfSquares$
$sumOfSquares : \mathbb R \times \mathbb R \rightarrow \mathbb R$
$sumOfSquares: (x, y) \mapsto sumOfSquares(x, y)$
$sumOfSquares(x, y) := x^2 + y^2$
$\;$
"
# ╔═╡ b6fda0b6-2ea2-4f2f-961b-65936c050852
md"
---
###### 3.3 *Definition* and *Application* of *Generic* Function $f$
$f : \mathbb R \times \mathbb R \rightarrow \mathbb R$
$f : a \mapsto f(a)$
$f(a) := sumOfSquares(a+1, 2a)$
$\;$
"
# ╔═╡ 1cf1668b-220e-4813-af3b-fef0f938e29b
md"
---
##### 4. Idiomatic *functional* Julia ...
###### ... with *infix* operator, *keyword* $function$, *anonymous* function with operator $->$
"
# ╔═╡ 51f99623-1572-4c05-b9d9-1cd4393c31e0
typeof(Function)
# ╔═╡ 780b9896-21d5-4acd-a878-86a3670ccaaf
md"
---
###### 4.1 Alternatives for Defining Functions
"
# ╔═╡ 7c8b7c1d-1e23-49c6-be97-32c9f2e38041
md"
---
###### 4.2 More *typed* Methods for Function $square$
###### 2nd *typed* method of function $square$
$square : \mathbb R \rightarrow \mathbb R$
$square : x \mapsto x * x$
$square(x) := *(x, x)$
$\;$
"
# ╔═╡ 9410ff1c-daf0-48de-be8a-f31c5a76dbed
square(x::Real)::Real = x * x # specialized definition function 'square'
# ╔═╡ f9b0181b-c988-4d93-85e9-1a7bc41ecee4
md"""
---
###### 3rd *typed* method of function $square$
The need for a third method $square$ is clear. If we would call $square("oh,\ no! ")$ we would get the *concatenated* string $oh, no!\ oh, no! $. This happens because the $*$-operator is multiple times *overloaded* and defined not only for the multiplation of *numbers* but also for *concatenation* of *strings*. When we want to suppress the latter behavior, we have to define a special *3rd method* for $square$ with a typed argument $square(x::String)$.
$square : \mathbb S \rightarrow \mathbb E$
$square : x \mapsto error(.)$
$square(x) := error(.)$
where:
$\mathbb S = \text{domain of }\textit{strings}$
$\mathbb E = \text{domain of }\textit{errors}$
$\;$
"""
# ╔═╡ 7693444c-efe8-4698-b979-787b03bb8d29
*("oh, ", "no !") # operator $*$ is defined for strings !
# ╔═╡ bd99f22b-51f2-48fe-8391-b1e37498e7ff
square(x::String) = error("Strings should not be squared!")
# ╔═╡ 2ef23512-6a23-4d2d-86fa-db9c1743c529
square
# ╔═╡ 8db7e80c-a877-44ff-aa15-48841c035aeb
square(21) # ==> 441 --> :)
# ╔═╡ 95f00b9b-646c-4ac5-b6fd-16f84a89d7b9
square( +(2, 5)) # ==> 49 --> :)
# ╔═╡ 731aa7ca-d4af-4be8-8a40-2eec5522ad99
square(square(3)) # ==> 81 --> :)
# ╔═╡ d263c3dd-f20b-4de2-b42b-ea88475d63ac
square(square(3.)) # ==> 81.0 --> :)
# ╔═╡ 7254bd30-87b7-48e9-99f8-56159dc78ad4
sumOfSquares(x, y) = +(square(x), square(y))
# ╔═╡ 714e9893-f609-4a24-a020-0041f5361a2d
typeof(square)
# ╔═╡ c97d34e3-3ace-48a2-8044-24758947fdc1
typeof(square) <: Function # true --> :)
# ╔═╡ 6bf0a86b-2d41-49e1-bea9-bf82cddcbc7a
square
# ╔═╡ 4462e7ca-18f7-4f9d-8198-0196dac76c7d
typeof(square)
# ╔═╡ bc018df0-02ea-4011-ad6e-2176e4a1b232
square(21) # square2 : Integer --> Integer
# ╔═╡ 965efc63-8dac-4397-8052-312bccd4e736
square(21.0) # square : Float --> Float
# ╔═╡ 7ff29624-964a-435c-a909-550484a527c6
md"
---
###### 4.3 *Multiple Dispatch*
*Multiple dispatch* of function calls is possible when there are several *methods* with differently *typed parameters* of the same function symbol. In a function *call* first *more narrow* methods are tried then the *next less narrow* methods, etc. What is more or less narrow is defined by the relevant type hierarchy. This is called *muliple dispatch* of function calls.
"
# ╔═╡ fa90b927-c58c-4307-8524-28bb6927423c
square("oh, no! ") # ==> error --> :)
# ╔═╡ d78a705e-bf07-4af9-919a-a2b2de73cf6c
md"
---
###### *Methods* as targets for *multiple dispatch*
"
# ╔═╡ 13b98b93-a478-4e4a-b4a2-423d6af45369
methods(square)
# ╔═╡ 3454c059-533a-4f06-b72e-7deb61c0aedf
typejoin(Real, String) # ==> Any
# ╔═╡ 58c6ef37-5ca5-4e89-b96f-dc2fea19447c
typejoin(Int64, Float64, String) # ==> Any
# ╔═╡ ccdbeff9-c398-417b-b933-61662f406ad0
function makeMyTypeTreeAny()
g = [
0 0 0 0 0 0; # Any
1 0 0 0 0 0; # Real -> Any
0 1 0 0 0 0; # Int64 -> Real
0 1 0 0 0 0; # Float64 -> Real
0 1 0 0 0 0; # Irrational -> Real
1 0 0 0 0 0] # String -> Any
names = [" Any ", " Real ", " Int64 ", " Float64 ", " Irrational ", " String "]
edgelabels = Dict{Tuple, String}((2, 1) => "supertype", (3, 2) => "supertype", (4, 2) => "supertype", (5, 2) => "supertype", (6, 1) => "supertype")
graphplot(g, x=[5.0, 4.0, 2.0, 4.0, 6.0, 8.0], y = [3, 1.5, 0, 0, 0, 0], edgelabel=edgelabels, nodeshape=:rect, nodecolor=:aqua, names=names, lw=2, nodesize=0.3, fontsize=8, size=(600, 300), title="Fig. 1.1.4.1 Excerpt of Type Tree: Any", titlefontsize=12)
end # makeMyTypeTreeAny()
# ╔═╡ 4bb8fae0-d70b-47a0-a551-851d478275a2
makeMyTypeTreeAny()
# ╔═╡ 21650888-8948-4fe6-8b08-08472a84ad32
function makeMyTypeTreeSquare()
g = [
0 0 0;
1 0 0;
1 0 0]
names = ["square(x)", "square(x::Real)", "square(x::String)"]
edgelabels = Dict{Tuple, String}((2, 1) => "less narrow argument's type", (3, 1) => "less narrow argument's type")
graphplot(g, x=[1.0, 0.0, 2.0], y = [0.7, 0, 0], edgelabel=edgelabels, nodeshape=:rect, nodecolor=:aqua, names=names, lw=2, nodesize=0.1, fontsize=8, title="Fig. 1.1.4.2 Dispatch of Methods of Function: square(.)", titlefontsize=12, size=(800, 300))
end # function makeMyTypeTreeSquare()
# ╔═╡ 93bf2d55-ca89-436c-802e-8e3f26e7d65c
makeMyTypeTreeSquare()
# ╔═╡ c44ce267-d9d7-46ea-a6f2-54170cda5409
md"
---
###### 2nd (specialized) *typed* method of function 'sumOfSquares'
"
# ╔═╡ abd380fc-5018-462c-8641-3fc269e0d2cb
sumOfSquares(x::Real, y::Real)::Real = square(x) + square(y)
# ╔═╡ e6a69b7f-dfb5-45db-a0fc-e4d24229f6c3
sumOfSquares(3, 5)
# ╔═╡ 706e727c-f29b-4cdb-ae08-cddd5725cdae
f1(a) = sumOfSquares(+(a, 1), *(a, 2))
# ╔═╡ 2b7d0b48-70de-40fd-bf43-660e70f2416e
f1(5) # (5 + 1)^2 + (5 * 2)^2 = 6^2 + 10^2 = 36 + 100 = 136
# ╔═╡ 358250f0-94b7-48a8-acde-1c1f2734c967
# alternative function definition of f1 with 'function'
f2 = function(a)
sumOfSquares((a + 1), 2a) # infix '+' and iuxtapositioned '2a'
end
# ╔═╡ 538f4130-f6e1-43c2-8020-f7f2488e2442
f2(5)
# ╔═╡ 3766c9b6-0ff5-4b0d-bc85-2c9bfe0a1d50
# 2nd alternative function definition of f1 with anonymous function '->'
f3 = a -> sumOfSquares((a + 1), 2a)
# ╔═╡ 84bb8887-9df3-4ff0-ab50-eb144cd2f118
f3(5)
# ╔═╡ 8a67cb77-a84f-4750-9099-56b5ef8ae038
sumOfSquares(3.0, 4.0)
# ╔═╡ d0fac6ee-0507-4a55-907c-a86136e48e65
f4(a::Real)::Real =
sumOfSquares(a + 1::Real, 2a::Real)::Real
# ╔═╡ f29a4f6f-d090-4be8-9d0f-14369c35b6b3
f4(5)
# ╔═╡ 863f12ad-c33c-4888-ba69-2c69f55edd07
f4(5.0)
# ╔═╡ 1752aa11-635b-4179-86fa-736305434312
md"
---
##### 5. Summary
First we defined *generic* functions. These are the *first* method of that *function symbol*. Then we *specialized* the *generic* function by *typing* the function's *arguments*. This assures the correct *dispatch* of function calls. In a function call first *more narrow* methods are tried then the *next less narrow* methods, etc.
This is called *muliple dispatch* of function calls.
"
# ╔═╡ 20f492e1-1b1b-4852-8e40-37d4bd96c2a3
md"
---
##### 6. References
- **Abelson, H., Sussman, G.J. & Sussman, J.**, [*Structure and Interpretation of Computer Programs*](https://mitp-content-server.mit.edu/books/content/sectbyfn/books_pres_0/6515/sicp.zip/full-text/book/book-Z-H-10.html#%_sec_1.1.4), Cambridge, Mass.: MIT Press, (2/e), 1996, last visit 2024/12/08
"
# ╔═╡ 923f3c7d-9b17-4458-9ee3-8dd0e36f8452
md"
---
##### end of ch. 1.1.4
===================================================================================
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**
===================================================================================
"
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
GraphRecipes = "bd48cda9-67a9-57be-86fa-5b3c104eda73"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
Pluto = "c3e4b0f8-55cb-11ea-2926-15256bba5781"
[compat]
GraphRecipes = "~0.5.13"
Plots = "~1.35.8"
Pluto = "~0.20.3"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised
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