PCM20210818_SICP_1.3.2_ConstructingProceduresUsingLambda.jl

### A Pluto.jl notebook ###
# v0.19.12

using Markdown
using InteractiveUtils

# ╔═╡ a46a671b-a813-4ab6-872f-0bbc29b1ee39
using Plots

# ╔═╡ 0bdc1f22-be80-11ed-1491-69cfe2382d1b
md"
=====================================================================================
#### SICP: 1.3.2 Constructing Procedures Using Lambda
##### file: PCM20210818\_SICP\_1.3.2\_ConstructingProceduresUsingLambda.jl
##### Julia/Pluto.jl-code (1.8.5/19.11) by PCM *** 2023/03/10 ***

=====================================================================================
"

# ╔═╡ 84db3c33-49f2-4045-a407-f21361b2cb37
md"
---
#### 1.3.2.1 SICP-SCHEME-like functional Julia ...
###### ... with anonomous $\lambda$-function $\mapsto$

"


# ╔═╡ f2c97a28-f1b7-43d7-a91f-272bcd886a12
md"
---
$\lambda: x \mapsto x+4$
"

# ╔═╡ 60e849eb-c960-4ad2-86d9-1d8065e26e69
function(x) +(x, 4) end                     # definition with 'function ... end'

# ╔═╡ a3e85937-1fd7-411b-b620-16ceb8d051af
(function(x) +(x, 4) end)(2)                # application to argument '2'

# ╔═╡ 313274ed-fb9b-48c5-8bee-a3db4df8d297
x -> +(x, 4)                                # definition with '->'

# ╔═╡ cb99f6fd-bb69-4e98-b379-48069e778f70
(x -> +(x, 4))(2)                           # application

# ╔═╡ bb7e8e2f-94cf-4713-b36c-92e7816b6a34
md"
---
$\lambda: x \mapsto \frac{1}{x\cdot(x+2)}$
"

# ╔═╡ 704e5679-36d6-43cf-9d5b-253d93aa29e2
function(x) /(1.0, *(x, +(x, 2))) end       # definition with 'function ... end'

# ╔═╡ e883c51e-1c3f-4d40-a13f-9af39d5e08e9
(function(x) /(1.0, *(x, +(x, 2))) end)(2)  # application with '2'

# ╔═╡ 1ae10bc5-b8eb-41d0-89c7-d80c9cc598e8
x -> /(1.0, *(x, +(x, 2)))                  # definition with '->'

# ╔═╡ dd2922e7-ea2c-4457-bedd-6ae3885a42ac
(x -> /(1.0, *(x, +(x, 2))))(2)             # application with '2'

# ╔═╡ 9c27049a-3c48-4d69-b181-be7acc4772e4
function sum1(term, a, next, b)
	>(a, b) ? 
		0 :
		+(term(a), sum1(term, next(a), next, b))
end # function sum1

# ╔═╡ 433ed93c-2c05-4bed-826e-eca8153bd30b
function pi_sum1(a, b)
	sum1(function(x) /(1.0, *(x, +(x, 2))) end, a, x -> +(x, 4), b)
end

# ╔═╡ 962ca66e-ffe4-4625-b5ed-a2dc29072c15
function integral1(f, a, b, dx)
	*(sum1(f, +(a, /(dx, 2.0)), x -> +(x, dx), b), dx)
end # function pi_sum1

# ╔═╡ 9754ae8a-180d-4da6-90ef-13e660f05dd1
8 * pi_sum1(1, 1E5)

# ╔═╡ 617b5094-bd33-455b-b1e4-87c214f21d60
md"
---
$\int_0^1 x^3 dx = \left[\frac{x^4}{4}\right]_0^1=\frac{1^4}{4}-\frac{1^0}{4}=\frac{1}{4}$
" 

# ╔═╡ 4d3d47f5-f6ec-40d8-9907-6b75cfa55547
integral1(x->^(x, 3), 0, 1, 0.001)  # ==> 0.25 -->  :)

# ╔═╡ 6132d02f-7bd8-4e1d-aea5-212fefc2d355
plot(x->^(x, 3), 0, 1, size=(700, 300), xlim=(0.0, 1.1), ylim=(0.0, 1.2), line=:darkblue, fill=(0, :lightblue), aspect_ratio=1, framestyle=:semi, title="f: x->x^3", xguide="x", yguide="f: x^3")

# ╔═╡ 23e0515e-8023-41e0-b6d7-dd416d9db9a7
md"
---
$\int_0^1 (6 - 6x^5) dx = \int_0^1 6\;dx - 6\int_0^1 x^5 dx= \left[6x - \frac{6x^6}{6}\right]_0^1 = \left[6-\frac{6}{6}\right]-\left[0-\frac{0}{6}\right]=5.$
"

# ╔═╡ 3514b2a0-5dfa-4c0c-926c-7dcce3e12a2c
integral1(x->-(6, *(6, ^(x, 5))), 0.0, 1.0, 1.0E-4) # ==> 5.0  --> :)

# ╔═╡ a0f823ca-0a55-482a-9675-3c82fc86bd56
plot(x->-(6, *(6, ^(x, 5))), 0, 1, size=(500, 400), xlim=(0.0, 1.2), ylim=(0.0, 6.2), line=:darkblue, fill=(0, :lightblue), framestyle=:semi, title="f: x->(6-6x^5)", xguide="x", yguide="f: x->(6-6x^5)")

# ╔═╡ f062cf19-6507-4382-b450-57cf91c9d3a4
md"
---
###### Using $let$ to create local variables

$f(x,y)=x(1+xy)^2+y(1-y)+(1+xy)(1-y)$

"

# ╔═╡ 0c7b960d-35cf-4391-9496-7088b5a54326
f1(x, y) =                            # präfix operators
	+(*(x,(+(1, *(x, y))^2)),         # x(1+xy)^2
	  *(y, -(1, y)),                  # y(1-y)
	  *(+(1, *(x, y)), -(1, y)))      # (1+xy)(1-y)

# ╔═╡ 42c074af-0452-458b-aae6-0eb22507883b
f1(1, 2)

# ╔═╡ 371c282e-4fc2-4939-8d7f-46ebb66a24a5
f2(x, y) =                            # infix operators
	x*(1+x*y)^2 + y*(1-y) + (1+x*y)*(1-y)

# ╔═╡ 28e864e5-8fdd-4bd0-bc62-97cdc79e0c7e
f2(1, 2)

# ╔═╡ 14369a73-db5d-417e-a605-e31894b53a9c
md"
---
###### Using $let$ to create local variables

$f(x,y)=x(1+xy)^2+y(1-y)+(1+xy)(1-y) \equiv f(x,y)=xa^2+yb+ab$

with *local* variables

$a=(1+xy)$

and

$b=(1-y).$

"

# ╔═╡ b90a1a90-2e74-48cd-a34c-268d7bf4805f
function f3(x, y)
	function f_helper(a, b)
		square(x) = *(x, x)
		+(  *(x, square(a)),
			*(y, b),
			*(a, b))
	end # function f_helper
	f_helper(+(1, *(x, y)), -(1, y))
end # function f3

# ╔═╡ 2c0b827b-6c7b-4f12-9ab3-3ada545d7287
f3(1, 2)

# ╔═╡ 900bc14e-f097-46cd-9c6b-5784a5b37347
function f4(x, y)
	((a, b) -> 
		+(*(x,a^2),*(y,b),*(a,b)))(+(1,*(x,y)),-(1,y)) # λ, arg must be inline !
end # function f4

# ╔═╡ bc5e9381-8162-481f-80bb-12324c692cea
f4(1, 2)

# ╔═╡ 1aab0c44-8270-4a34-963c-11855b3d030b
function f5(x, y)
	(function (a, b)
		+(*(x,a^2),*(y,b),*(a,b)) 
	end)(+(1, *(x,y)), -(1, y)) # args must be close to '...end) !
end # function f5

# ╔═╡ 0b218a78-c5fc-4bf1-8fca-ab76f410bc0f
f5(1, 2)

# ╔═╡ fbda6639-bb4c-4aad-9880-8f87c6b0c3de
function f6(x, y)
	let a = +(1, *(x, y)), b = -(1, y) 
		+(*(x,a^2),*(y,b),*(a,b))      # body of let
	end # let
end # function f6

# ╔═╡ 8d03375c-77a5-4b92-9ec7-16ba347d5dc7
f6(1, 2)

# ╔═╡ 9f1a394d-2cca-42d1-bb03-5e9be765261e
let x = 5
	let x = 3
		+(x, *(x, 10))
	end + x        # to add the value of inner let '+ x' must be inline with 'end' !
end

# ╔═╡ 9102f937-b02d-4d5d-9fd6-f83643e27cdd
let x = 2   # semantics of Julia 'let' is different from Scheme's 'let' semantics !
	let x = 3, y = +(x, 2)
		*(x, y)
	end
end

# ╔═╡ 634d23d2-df73-404c-9e19-145ca6b47305
function f7(x, y)
	a = +(1, *(x, y))
	b = -(1, y)
	+(*(x,a^2),*(y,b),*(a,b))
end # function f7

# ╔═╡ 8a59bf14-0dc5-471c-bc0e-ec7c53e6ded6
f7(1, 2)

# ╔═╡ c2228ed7-7062-4810-aef2-b269845c26b0
md"
---
###### Nonterminating Lambda-Expression

in Scheme with tail-call optimization is

$((lambda (x) (x\;x))(lambda(x)(x\;x)))$


"

# ╔═╡ 9642417f-981c-4346-8a6f-3b1c69b862c8
try
	(x -> x(x))(x -> x(x)) 
catch
    @warn "lambda-expression is not terminating, so stack overflow"
end

# ╔═╡ 0013515a-fc8a-45df-8c08-3c7b7de17cb8
md"
---
##### CPS (= [Continuation Passing Style](https://en.wikipedia.org/wiki/Continuation-passing_style))
"

# ╔═╡ e230ec99-56b8-416a-9f47-9feaf46dab1b
md"
###### Basic CPS-Operators
"

# ╔═╡ 857a21e8-dc2f-415c-9669-aff2e1b30343
cpsAdd(x, y, k)  = k(+(x, y))

# ╔═╡ cb84a330-6c45-4da2-8ac3-a9e843129573
cpsMult(x, y, k) = k(*(x, y))

# ╔═╡ dcd3061b-b54b-41a0-a218-1304c2559b1b
cpsExp(x, y, k)  = k(^(x, y))

# ╔═╡ 697d7b63-cba6-4569-950e-10d3f7bbdff1
cpsEq(x, y, k)   = k(==(x, y))

# ╔═╡ 70cec50e-6c07-460c-99a0-e3e9c582b155
cpsSub(x, y, k)  = k(-(x, y))

# ╔═╡ 8cfe5793-265b-4e5c-8ae4-6b49f7c9c7b4
cpsIfThenElse(trueValue, FalseValue, condition, kTrue, kFalse) = 
	condition ? 
	kTrue(trueValue) :           # application of true-Continuation
	kFalse(FalseValue)           # application of false-Continuation

# ╔═╡ 22c29e5f-9512-4460-9678-22f3d3efb4df
md"
---
###### Tests of Basic CPS-Operators
"


# ╔═╡ 4b6f4f18-d867-463b-80d7-51a9dddfcc51
cpsAdd(3, 4, xAddY -> print("x + y is $xAddY"))

# ╔═╡ 9fd6c383-c3b8-4b8b-957f-b8e458054a3d
cpsSub(1, 2, xSubY -> print("x == y is $xSubY"))

# ╔═╡ 12a0195e-3038-4f1d-968a-9631b59c41f4
cpsMult(3, 4, xMultY -> print("x * y is $xMultY"))

# ╔═╡ 8353921c-ec1c-4896-9ffa-91e06009a725
cpsExp(3, 4, xExpY -> print("x^y is $xExpY"))

# ╔═╡ a09663da-e08d-4866-9927-4fea1c9ac11c
cpsEq(1, 1, xEqY -> print("x == y is $xEqY"))

# ╔═╡ 28ecdc1f-291f-4dca-a0fa-22d66fef2fc2
cpsEq(1, 2, xEqY -> print("x == y is $xEqY"))

# ╔═╡ dbfffd66-2ecb-4e8c-89ff-cf6e635f2ac9
cpsIfThenElse( 0, 0, ==(0, 0), 
	value -> print("true case: value = $value "),     # true-Continuation
	value -> print("false case: value = $value "))    # false-Continuation

# ╔═╡ c1637306-5454-4e24-ac87-4555abebd7c7
cpsIfThenElse( 0, 5, ==(5, 0), 
	value -> print("true case: value = $value "),     # true-Continuation
	value -> print("false case: value = $value "))    # false-Continuation

# ╔═╡ 3a9b96f5-abe3-4140-807e-f05c0adc53f7
md"
---
##### Application of CPS-Style Functions
"

# ╔═╡ 2c4031b1-b1f2-47fc-ba72-7a3390445c79
md"
###### Nonrecursive Example: *Pythagoras*

$c=\sqrt{a^2+b^2}= (a^2+b^2)^{1/2}$
"

# ╔═╡ 973f5f48-040b-4552-9528-1e3dee12b49c
md"
---
###### DST (=*Direct* STyle)
"

# ╔═╡ e0f8d9f6-62a2-47d4-9fac-10672738b90b
function pythagorasDST(a, b)                 # DSt = Direct Style
	^( +( *( a, a), *( b, b)), 1/2)
end # function pythagorasDSt

# ╔═╡ b850208d-49d7-489c-9867-2acbd366041d
let a = 3
	b = 4
	c = pythagorasDST(a, b)
end # let

# ╔═╡ eaad7fad-c313-482f-920d-5d2885876ee7
md"
---
###### ISS (= Imperative Sequential Style)
"

# ╔═╡ 8ebef2b8-3c45-4257-abae-6f7e4916a5c5
function pythagorasISS(a, b)                 # ISS = Imperative Sequential Style
	let bSquare = *(b, b)
		let aSquare = *(a, a)
			let cSquare = +(bSquare, aSquare)
				let c 		= ^(cSquare, 1/2)
					print("c = sqrt(a^2 + b^2) = $c")
				end # let
			end # let
		end # let
	end # let
end # function pythagorasDSt

# ╔═╡ d9b274db-37d3-47cb-be5e-07f487fe13aa
pythagorasISS(3, 4)

# ╔═╡ e01734b4-c51e-4c9c-b3cb-c87f556e97cc
md"
---
###### NLS (= Nested Lambdas Style)
"

# ╔═╡ 81f36bde-b59a-4066-b5eb-21a6741a2b86
function pythagorasNLS(a, b)                 # NLS = Nested Lambdas Style
	(bSquare -> 
		(aSquare ->
			(cSquare ->
				(c -> 
					print("c = sqrt(a^2 + b^2) = $c"))(^(cSquare, 1/2)))(+(bSquare, aSquare)))(*(a, a)))(*(b, b))
end # function pythagorasNLS

# ╔═╡ 2860e077-f4cb-441b-af25-6c11f3613e35
pythagorasNLS(3, 4)

# ╔═╡ 02dc74fa-d530-490e-ae86-b63da5466392
md"
---
##### CPS (= Continuation Passing Style)
"

# ╔═╡ c8c956c6-0b86-4d97-9840-4252ae571523
function pythagorasCPS(a, b, k)             # CPS = Continuation Passing Style
	cpsMult(b, b, bSquare -> 
		cpsMult(a, a, aSquare -> 
			cpsAdd(bSquare, aSquare, cSquare -> 
				cpsExp(cSquare, 1/2, k))))
end # function pythagorasCPS

# ╔═╡ 9c8df1cb-5e0e-4120-b6c9-a50e4ad305e6
let a = 3
	b = 4
	k = c -> print("c = sqrt(a^2 + b^2) = $c")
	c = pythagorasCPS(a, b, k)
end # let

# ╔═╡ e03464fb-cfbe-402a-a6fc-1fa764fd20a3
md"
---
##### Linear Recursive Example: Factorial
"

# ╔═╡ 3e7759d5-bbb1-473d-a775-5fcd406ad9b6
md"
$n!=
\begin{cases}
1, & \text{ if } n = 0 \\
n \cdot(n-1)!, & \text{ if } n \gt 0 \\
\end{cases}$
"

# ╔═╡ 6c7029d1-d512-410e-953c-497601fc0ea6
md"
---
###### DST (=*Direct* STyle)
"

# ╔═╡ 03084fc1-4bb5-4fc2-8cd2-fa73b923b923
function factorialDST(n)
	if ==(n, 0)
		1
	else 
		*(n, factorialDST(-(n, 1)))
	end # if
end # function factorialDST

# ╔═╡ a4396645-8990-425f-94df-32e0ccfa7425
factorialDST(5)

# ╔═╡ 67cd2551-e8c9-4c0b-938e-5618d4b94339
md"
---
###### ISS (= Imperative Sequential Style)
"

# ╔═╡ def785ce-6ad1-4cf2-a3f2-cabd7cb0c33b
function factorialISS(n)
	let isZero = ==(n, 0)
		let result =
			if isZero
				1
			else
				let nSub1 = -(n, 1)
					let facValNSub1 = factorialISS(nSub1)
						*(n, facValNSub1)
					end # let facValNSub1
				end # let nSub1
			end # if boolean
			result
		end # let result
	end # let boolean
end # function factorialISS

# ╔═╡ 37e84a60-fe11-4687-b7be-7e1cfa39081c
factorialISS(5)

# ╔═╡ ebbcabe4-3ca7-456e-82e5-f93f816ecba2
md"
---
###### CPS-(= Continuation Passing)-Style

###### $factorialCPS1$ is a mixture of *DST* and *CPS*-Style:
The condition $if...then...else$ in $factorialCPS1$ is a relict of direct-style coding. This relict has to be removed to get a pure CPS-styled . This has been achieved in $factorialCPS2$. 
"

# ╔═╡ e7e1a162-7450-4329-9cbb-2457a813076c
function factorialCPS1(n, k)
	cpsEq(n, 0, isZero -> 
					if isZero
						k(1) 
					else
						cpsSub(n, 1, nSub1 ->
									factorialCPS1(nSub1, 
													facValNSub1 ->
																	cpsMult(n, facValNSub1, k)))
					end # if
	) # end cpsEq
end # function factorialCPS1

# ╔═╡ d73f1ae9-f0d0-4c02-b6c2-6a9a19fdc238
factorialCPS1(0, result -> result)

# ╔═╡ d284b83d-ee52-4285-b005-16a2f9098e0b
factorialCPS1(0, result -> result)

# ╔═╡ a9958ad9-2092-4893-bdae-e31584b1fed8
factorialCPS1(5, result -> result)

# ╔═╡ 6c90570d-4a73-4cb6-8137-a8512d2b6736
factorialCPS1(6, result -> result)

# ╔═╡ a867dff9-f922-4214-88e2-cde3037ae9d6
md"
---
###### NLS (Nested Lambda Style)): $factorialCPS2$ 
"

# ╔═╡ 2d7e5950-a472-4ff8-80d6-317a8cec04be
function factorialNLS2(n)
	let isNEqZero = n == 0
		let 
			isNEqZero ? 1 : 
				let 
					nSub1 = n - 1
						let facValNSub1 = factorialNLS2(nSub1)
							n * facValNSub1
						end # let
				end # let
		end # let
	end # let
end # function factorialNLS2

# ╔═╡ fa36ac19-b792-455d-8667-e4b22013a493
factorialNLS2(0)

# ╔═╡ 75793fe4-9d5e-4ff9-b32e-a589e9722937
factorialNLS2(1)

# ╔═╡ 85e61913-b8a1-4a80-9bb5-d7b756a209cb
factorialNLS2(5)

# ╔═╡ 744f1453-d321-46f0-ba5d-cef4ea8b08c1
factorialNLS2(6)

# ╔═╡ 7293c431-85eb-40e0-ab74-0b3db732066d
md"
---
###### $factorialCPS2$ is a *pure* CPS-styled Recursive Factorial
The condition $if...then...else$ has been replaced by the function $cpsIfThenElse$ with Two Continuations

$trueContinuation$
and

$falseContinuation.$

"

# ╔═╡ e370bc78-e2ce-4db7-aefb-5678c9080977
function factorialCPS2(n, k)
	cpsEq(n, 0, isNEqZero -> 
		cpsIfThenElse(1, n, isNEqZero, 
			stopValue -> k(stopValue),                # true continuation
			n -> cpsSub(n, 1, nSub1 ->                # false continuation
						factorialCPS2(nSub1, 
								facValNSub1 -> 
										cpsMult(n, facValNSub1, k)))))
end # function factorialCPS2

# ╔═╡ a028b140-6b8f-4303-8d45-9989e0d9163c
factorialCPS2(0, result -> result)

# ╔═╡ 4a912f72-0bd3-4678-819e-0ca3f34e7e59
factorialCPS2(1, result -> result)

# ╔═╡ 83e548b4-7f37-46bc-9ab4-e935ce201e16
factorialCPS2(5, result -> result)

# ╔═╡ a1910a28-207f-49dc-925e-9c61c1939304
factorialCPS2(6, result -> result)

# ╔═╡ c2c2b482-64ac-4306-94e2-1e79c82d9ac9
md"
---
##### Linear Iterative Example: Tail-Recursive Factorial
"

# ╔═╡ 6e2d6f64-b00b-4c4b-8408-215c5d58628c
md"
$n!=
\begin{cases}
product, & \text{ if } n \lt counter \\
iter(product, counter) ;= iter(counter * product, counter + 1), & \text{ if } n \ge counter \\
\end{cases}$
"

# ╔═╡ 42da07de-5508-4757-8ced-39cb8e67950a
md"
---
###### DST (=*Direct* STyle)
"

# ╔═╡ 48799cb6-d61c-4eda-aa29-c1e93c8a0302
function factorial2DST(n)
	function iter(product, counter)
		if counter == 0
			product
		else
			iter( product * counter, counter - 1)
		end # if
	end # function iter
	iter(1, n)
end # function factorial2DST

# ╔═╡ 2113e9c5-c003-4980-a8bd-6af6b5ee37ed
factorial2DST(0)

# ╔═╡ 7c87a7c4-7451-4bdd-a73e-6cf7c0184a9d
factorial2DST(1)

# ╔═╡ e93267e3-da0b-4794-9d28-3f56d0524a57
factorial2DST(5)

# ╔═╡ 78353412-675f-424d-a476-85fd38ad4cf8
factorial2DST(6)

# ╔═╡ 7e622eec-37ac-43e9-9483-fc114fed1d9b
md"
---
###### CPS-(= Continuation Passing)-Style

###### $factorial2CPS1$ is a mixture of *DST* and *CPS*-Style:
The condition $if...then...else$ in $factorial2CPS1$ is a relict of direct-style coding. This relict has to be removed to get a pure CPS-styled . This has been achieved in $factorial2CPS2$. 
"

# ╔═╡ 97eeed7e-34c2-40a4-bfae-bbb3c4f53638
function factorial2CPS1(n, k)
	function iter(product, counter, k)
		cpsEq(counter, 0, isCounterZero -> 
					if isCounterZero
						k(product)       # unmodified continuation
					else 
						cpsSub(counter, 1, counterSub1 -> 
								cpsMult(counter, product, countMultProd -> 					iter(countMultProd, counterSub1, k)))
					end # if
		)
	end # function iter
	iter(1, n, k)
end # function factorial2CPS1

# ╔═╡ 964dcb14-0373-4a15-a677-0e7cc683bf12
factorial2CPS1(0, result -> result)

# ╔═╡ 8ec93546-22c3-4cfa-933c-ffebec8917b4
factorial2CPS1(1, result -> result)

# ╔═╡ 319a46c2-f17b-4cb9-a581-48d33008e0d2
factorial2CPS1(5, result -> result)

# ╔═╡ 8ab5f711-7610-4d81-bb7a-fa218c0d9922
factorial2CPS1(6, result -> result)

# ╔═╡ c8a0352a-21b0-49e2-a0c6-857b06bcdf81
md"
---
###### $factorial2CPS2$ is a *pure* CPS-styled Recursive Factorial
The condition $if...then...else$ has been replaced by the function $cpsIfThenElse$ with Two Continuations

$trueContinuation$
and

$falseContinuation.$

"

# ╔═╡ ae12f10b-623d-49f2-bfeb-c7e646db832f
function factorial2CPS2(n, k)
	function iter(product, counter, k)
		cpsEq(counter, 0, isCounterZero -> 
			cpsIfThenElse(product, counter, isCounterZero, 
				product ->                               # true continuation
					k(product),                   
				counter ->                               # false continuation
					cpsSub(counter, 1, counterSub1 ->    
								cpsMult(counter, product, countMultProd -> 						iter(countMultProd, counterSub1, k)))))
	end # function iter
	iter(1, n, k)
end # function factorial2CPS2

# ╔═╡ dd3a3675-b32c-4f1c-ae82-16109218f6c1
factorial2CPS2(0, result -> result)

# ╔═╡ 80653648-c27a-455e-b736-3f1e5bd80b15
factorial2CPS2(1, result -> result)

# ╔═╡ c8cc03ec-ce99-479f-bc1c-0eaecccf1a8a
factorial2CPS2(5, result -> result)

# ╔═╡ 972d5841-5c9f-4f82-b921-0061411eb8d0
factorial2CPS2(6, result -> result)

# ╔═╡ 5f25a438-fadf-4e9c-8234-7d668e797298
md"
---
#### 1.3.2.2 idiomatic imperative Julia ...
###### ... with while, Function, self-defined FloatOrSigned
"

# ╔═╡ f179f2cd-bb71-49ca-a3a4-c3ee48ef28c3
FloatOrSigned = Union{AbstractFloat, Signed}

# ╔═╡ 13138a8d-f944-4941-9372-57c7cb5ae76d
# idiomatic Julia-code with '::Function', '::Real', 'while', '+='
function sum2(term::Function, a::FloatOrSigned, next::Function, b::FloatOrSigned)::FloatOrSigned
	sum = 0
	while !(a > b)
		sum += term(a)
		a = next(a)
	end # while
	sum
end # function sum2

# ╔═╡ 066538f0-0a85-4763-97aa-85caaaf9fd6e
function pi_sum2(a::FloatOrSigned, b::FloatOrSigned)::FloatOrSigned
	sum2(function(x) 1.0 / (x * (x + 2)) end , a, function(x) x+4 end, b)
end

# ╔═╡ 1b92beeb-8d34-45cd-807d-8b3aef90526c
8 * pi_sum2(1, 1E5)

# ╔═╡ 00b2e013-5134-4181-8e0e-e07babc4bf46
deviation = abs(8 * pi_sum2(1, 1E5) - pi)

# ╔═╡ 986c3531-565a-48eb-8ffe-20411ac119dc
function integral2(f::Function, a::FloatOrSigned, b::FloatOrSigned, dx::FloatOrSigned)::FloatOrSigned
	sum2(f, a+dx/2.0, function(x) x+dx end, b) * dx
end # function integral2

# ╔═╡ 96e52bd7-bda8-41e6-8560-1e85dbd275b1
integral2(x->x^3, 0, 1, 0.001)

# ╔═╡ 94a7ffea-8915-4880-9e31-b6b01c6d27b8
integral2(x->-6x^5+6, 0.0, 1.0, 1.0E-4) # should be 5.0

# ╔═╡ 45c4441e-3a4f-4813-92ad-1b9744181661
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 2022/08/25

- **Stark, P.A.**; *Introduction to Numerical Methods*, NY: Macmillan Company, 1970

- **Wikipedia**; *Continuation Passing Style*; [https://en.wikipedia.org/wiki/Continuation-passing_style](https://en.wikipedia.org/wiki/Continuation-passing_style) - last visit 2023/03/07 -

"


# ╔═╡ cc754c67-4e7c-4b34-abf3-4919ebf99386
md"
---
##### end of ch. 1.3.2
"

# ╔═╡ 965d0b6b-90cb-49d5-a482-d5982be4e264
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
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[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.12+3"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "c6edfe154ad7b313c01aceca188c05c835c67360"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.4+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.29.0+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.1.1+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+0"
"""

# ╔═╡ Cell order:
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