PCM20210822_SICP_2.2.1_RepresentingSequences.jl

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

using Markdown
using InteractiveUtils

# ╔═╡ 373a14a0-036b-11ec-3063-73539b537973
md"
======================================================================================
#### SICP: [2.2.1 Representing Sequences](https://sarabander.github.io/sicp/html/2_002e2.xhtml#g_t2_002e2_002e1) 

###### file: PCM20210822\_SICP\_2.2.1\_RepresentingSequences.jl

###### Julia/Pluto.jl-code (1.8.5/...) by PCM *** 2023/03/01 ***
======================================================================================
"

# ╔═╡ 278e3d83-0583-459a-adec-95843b3314fd
md"
##### 2.2.1.1 SICP-Scheme-like *functional* Julia
"

# ╔═╡ 15d15f7e-ae79-4f36-87ca-0363ea9f598e
md"
---
##### Introduction
"

# ╔═╡ b2eb614e-8369-40f1-a7df-2551a3e20c9d
md"
###### 1st (default) untyped *method* of Scheme-like *constructor* function $$cons$$ implemented as Julia's $$namedTuple$$
"

# ╔═╡ ecbb360b-42d8-4ee8-8356-2028b1e5ccba
# (default) *untyped* constructor 'cons' with named fields 'car' and 'cdr'
cons(car, cdr) = (car=car, cdr=cdr)  
#                  ^--------^------------- named fields
#     ^-----^----------^--------^--------- parameter

# ╔═╡ 76b9bc7c-8afd-4e1d-a727-7646f377b09d
md"
###### 1st (default) *untyped* method of Scheme-like *selector* function $$car$$
"

# ╔═╡ f7000508-5beb-4d1f-8d9f-ca0dd98d94af
car(cons) = cons.car          # definition of selector 'car'
# ^--------------------------- function name
#     ^-------^--------------- parameter
#                 ^----------- field name

# ╔═╡ 100ac0a5-9f7d-4563-9fac-03967cb82e17
md"
###### 1st (default) *untyped* method of Scheme-like *selector* function $$cdr$$
"

# ╔═╡ e4bc1b01-7e3f-41ad-b054-e52912c9357c
cdr(cons) = cons.cdr          # definition of selector 'cdr'
# ^--------------------------- function name
#     ^-------^--------------- parameter 
#                 ^----------- field name

# ╔═╡ 5a6d3aa0-cd51-4c8a-a5cd-4cb1082b5135
md""" 
---


                      +-----+-----+      +-------+
                ----->|  o  |  o--|----->| "two" |
                      +--|--+-----+      +-------+
                         |
                         |
                     +---+--+
                     | :one |
                     +------+


**Fig 2.2.1**:  *Latent* box-and-pointer structure generated by $$cons(:one,\text{"two"})$$ (cf. Fig. 2.2, SICP, 1996)

---
"""

# ╔═╡ b4ef7e20-499d-4019-a694-f5e88c3e0d67
md""" 
---


                      +-----+-----+      +-----+-----+
                ----->|  o  |  o--|----->|  o  |  o  |
                      +--|--+-----+      +--|--+--|--+
                         |                  |     |
                   +-----+-----+        +-----+ +-----+
                   |  o  |  o  |        |  3  | | 4.0 |
                   +--|--+--|--+        +-----+ +-----+
                      |     |
                 +------+ +-------+
                 | :one | | "two" |
                 +------+ +-------+


**Fig 2.2.2**:  *Latent* box-and-pointer structure generated by $$cons(cons(:one, \text{"two"}), cons(3, 4.0))$$ (s.a. Fig. 2.3.left, SICP, 1996)

---
"""

# ╔═╡ 49d36791-24d6-4c7e-bec6-7593e8889478
md""" 
---


                      +-----+-----+      +-------+
                ----->|  o  |  o--|----->|  4.0  | 
                      +--|--+-----+      +-------+
                         |
                   +-----+-----+        +-----+-----+
                   |  o  |  o--|------->|  o  |  o  |
                   +--|--+-----+        +--|--+--|--+
                      |                    |     |
                 +------+            +-------+ +-------+
                 | :one |            | "two" | |   3   |
                 +------+            +-------+ +-------+


**Fig 2.2.3** *Latent* box-and-pointer structure generated by $$cons(cons(:one, cons(\text{"two"}, 3)), 4.0)$$ (s.a. Fig. 2.3.right, SICP, 1996)

---
"""

# ╔═╡ 4f343982-2aba-40ff-9d9d-f630ed4673f7
md"""
---


          +-----+-----+      +-----+-----+      +-----+-----+      +-----+-----+
    ----->|  o  |  o--|----->|  o  |  o--|----->|  o  |  o--|----->|  o  |  /  |
          +--|--+-----+      +--|--+-----+      +--|--+-----+      +--|--+-----+
             |                  |                  |                  |     
         +------+           +-------+           +-----+            +-----+
         | :one |           | "two" |           |  3  |            | 4.0 |
         +------+           +-------+           +-----+            +-----+


          
**Fig 2.2.4**:  The *latent* box-and-pointer structure of a *chain* (= *list*) of pairs generated by $$cons(:one, cons(\text{ "two" },cons(3, cons(4.0, :nil))))$$ (cf. Fig. 2.4, SICP, 1996)

---
"""

# ╔═╡ 04a3c30a-ccce-469c-9fa5-2b451082be8a
md"
###### function $$pp$$ ($$pp$$ = *pretty print*)
converts a *latent* box-pointer structure in a *manifest* *list* representation with parentheses $$(...)$$
"

# ╔═╡ b491dcdb-e51b-4438-8a26-e975e2a50533
md"
###### Testing $pp$
"

# ╔═╡ 47ff8a5c-4682-48c7-8080-272a73f38c3d
md"
---
##### Sequences
"

# ╔═╡ 54b14609-6552-40e9-9410-cbf8b8694a04
md"
###### 1st (default) untyped *method* of *constructor* function 'list' ...
###### ... *conceptualization* as *latent* box-pointer structure (=cons-cells) and *implementation* as Julia's $$NamedTuple$$
"

# ╔═╡ 531f20b7-7205-4c84-a0eb-63ddddc41180
md"
*(<par>...)* means *slurping*: *many* arguments are slurped into *one* parameter

*(<arg>...)* means *splatting*: *one* argument is splatted into *many* parameters
"

# ╔═╡ 79733f7a-fc76-4dff-9f2c-5774b334ce36
md"""
---
    one_through_four
         |
         |
         |     +-----+-----+      +-----+-----+      +-----+-----+      +-----+-----+
         +---->|  o  |  o--|----->|  o  |  o--|----->|  o  |  o--|----->|  o  |  /  |
               +--|--+-----+      +--|--+-----+      +--|--+-----+      +--|--+-----+
                  |                  |                  |                  |     
              +------+           +-------+           +-----+            +-----+
              | :one |           | "two" |           |  3  |            | 4.0 |
              +------+           +-------+           +-----+            +-----+


        
**Fig. 2.2.5** *sequence* or *list* $$one\_through\_four$$ = $$list(:one, \text{"two"}, 3, 4.0)$$ (cf. Fig.2.4, SICP, 1996)

---
"""

# ╔═╡ 702449f7-20c2-43c9-a9a0-5be31ce61c4f
md"""
---


                +---+---+    +---+---+    +---+---+    +---+---+    +---+---+
      myList--->| o | o-|--->| o | o-|--->| o | o-|--->| o | o-|--->| o | / |
                +---+---+    +---+---+    +---+---+    +---+---+    +---+---+
                  |             |           |            |            |
               +-----+       +-----+     +-----+      +-----+      +-----+
               |  a  |       |  b  |     |  3  |      |  4  |      | foo |
               +-----+       +-----+     +-----+      +-----+      +-----+


 
**Fig. 2.2.6** Different types of elements in myList = list(:a, :b, 3, 4, "foo")

---
"""

# ╔═╡ a5ba5446-2f0e-4bba-8b36-77bcffd83c0e
md"
###### 1st (default) *untyped* method of combined *selector* function $$cadr$$ ...
"

# ╔═╡ 1428e283-676a-4553-8987-25eeb97d904a
md"
---
##### List operations
"

# ╔═╡ 7ac3bbee-5b12-4f0e-b2ef-b7244fb793fc
md"
###### 1st (default) untyped *method* of function $$list\_ref$$
"

# ╔═╡ af79cdc3-a4bf-4343-9371-9258da74be2b
md"
for $$n=0$$, $$list\_ref$$ should be the $$car$$ of the list
"

# ╔═╡ 20a4cca9-dd1b-4f60-82ef-ad50d13de35c
md"
###### 1st (default) *untyped* method of function $$length$$
"

# ╔═╡ a802dec0-ed35-468d-b4e2-a36a6405ec0d
md"
###### 2nd untyped *linear-recursive* variant method of function $$length$$
"

# ╔═╡ 49338ccd-1767-4fac-b7db-3ba7e04492ee
md"
###### 1st (default) *untyped* method of function $$append$$
"

# ╔═╡ 4ae3bca1-94a5-4464-92d8-1b76e710a652
md"
---
##### Mapping over lists
"

# ╔═╡ 5b9d814c-0878-44ef-913e-00cc89ad4639
md"
###### 1st (default) *untyped* method of function $$scale\_list$$
"

# ╔═╡ 005c006a-697c-4f6f-9f18-78c99af79e7b
md"
###### 1st (default) *untyped* method of function $$myMap$$
"

# ╔═╡ 8a462e3e-cbfb-47bc-8f4d-7f147c4e2cdd
md"
---
##### 2.2.1.2 Idiomatic *imperative* or *typed* Julia
"

# ╔═╡ 31576ae3-a89a-413a-92cd-6fe1eaba2d08
md"
###### 2nd (specialized) *typed variant* method of function $$list$$ ...
 - implemented as Julia *Array* and ...
 - the $$xs$$ parameter in $$list2$$ is *slurping* and ...
 - the $$xs$$ argument in $$[xs::Any...]$$ is *splatting*
"

# ╔═╡ 3cd07141-0ed6-485b-8cd5-40aa615b5d8e
list2(xs::Any...)::Array = [xs::Any...]::Array # slurping (left) = spitting (right)

# ╔═╡ 9dc33f4f-33a3-4855-b0a2-f908a163ebf7
md"
---
    
    
                            +------->+---->+---->+---->+
                            |        |     |     |     |
      one_through_four2 --->|     +-----+-----+-----+-----+      
                            +---->|  1  |  2  |  3  |  4  |
                                  +-----+-----+-----+-----+
                    

        
Fig. 2.2.7 *sequence* or *list* $$one\_through\_four2$$ = $$list2(1,2,3,4)$$ implemented as an Julia *array*

---
"

# ╔═╡ 224d8870-bb45-4ace-86eb-200e1a7868f9
one_through_four2 = list2(1,2,3,4)

# ╔═╡ 966d3379-43f3-45f2-b90f-b69739f0a53e
Tuple(one_through_four2)

# ╔═╡ 41a0e04c-d9ec-465c-922c-dca7e37d13a0
typeof(one_through_four2)

# ╔═╡ eefc868f-a339-4499-b450-e1dfbbbed481
md"""
---
    
    
                            +------->+---->+---->+---->+---->+
                            |        |     |     |     |     |
                myList2 --->|     +-----+-----+-----+-----+-----+      
                            +---->| :a  | :b  |  3  |  4  |"foo"|
                                  +-----+-----+-----+-----+-----+
                    

         
Fig. 2.2.8 $$myList2 = list2(:a, :b, 3, 4, \text{"foo"})$$ implemented as a Julia *array*

---
"""

# ╔═╡ 1d4cf0a0-187d-4c62-8589-0184d21e8ee1
myList2 = list2(:a, :b, 3, 4, "foo")

# ╔═╡ bf9ff18e-4ce0-405e-958b-d521f463a4c8
Tuple(myList2)

# ╔═╡ de40c17b-3fce-4abf-ba77-df817ae9dedf
typeof(myList2)

# ╔═╡ a5bda10e-20e7-4cd9-877a-f392a8c1c44b
md"
###### 2nd (specialized) *typed* method of *constructor* function $$cons$$ ...
######  ... implemented with Julia's *Array*
"

# ╔═╡ c1645190-174d-424a-abbd-c2abb488b7ba
# definition of a second variant for function 'cons'
cons(car::Any, list::Array)::Array = pushfirst!(list[1:end], car)

# ╔═╡ 9abffca7-23c0-4287-8b54-f69d1f95a19f
cons(:one, "two")              # similar to SICP, 1996, Fig 2.2

# ╔═╡ e980b7d8-1c8b-4354-9bbd-313539b5c6ec
# Fig 2.2.2, similar to SICP, 1996, Fig. 2.3.left
cons(
	cons(:one, "two"), 
	cons(3, 4.0))  

# ╔═╡ 8203d83e-9ba8-40c2-8fb1-1f0f1f4a508c
# Fig 2.2.3, similar to SICP, 1996, Fig. 2.3.right
cons(
	cons(1, 
		cons(2, 3)), 
	4)                        

# ╔═╡ 77a6bc9b-6948-40f7-85f4-862e1824d436
# Fig 2.2.4, similar to SICP, 1996, Fig. 2.4
cons(:one, 
	cons("two",
		cons(3, 
			cons(4.0, :nil))))          

# ╔═╡ b5d38b3c-8033-4898-af30-e385cb24cdd8
typeof(cons(:nil, :nil))  # ==> NamedTuple{(:car, :cdr), Tuple{Symbol, Symbol}}

# ╔═╡ 3c1528ac-63ed-4944-9afb-6e10b9b26793
typeof(cons(:nil, :nil))  <: NamedTuple 

# ╔═╡ 1627b84f-d538-4d11-bd1e-2e2f3082e779
typeof(cons(:nil, :nil))  <: Tuple  # ==> false -->  :(

# ╔═╡ df60c1a7-3f91-4370-8232-135bfff959d1
cons(:one,                          # latent box-pointer structure of Fig. 2.2.4
	cons("two",
		cons(3, 
			cons(4.0, :nil))))

# ╔═╡ 413f608d-5bf5-4f93-9ef0-a9d6d7f8583b
list(elements...) =                        # parameter 'elements' slurps arguments
	if ==(elements, ())
		cons(:nil, :nil)
	elseif ==(lastindex(elements), 1)
		cons(elements[1], :nil)
	else                                   # 'elements[2:end]...' splatts its elements
		cons(elements[1], list(elements[2:end]...))
	end #if

# ╔═╡ be432d3e-6f08-4344-bee1-f2eeb9718fb4
list((:a, :b))                             # ==> NamedTuple

# ╔═╡ 19dfb768-a350-4e70-a6fe-0d1f8eae96c4
one_through_four =             # nested named tuples
	list(:one, "two", 3, 4.0)

# ╔═╡ 1efc3f69-28f7-46fb-ba00-2dc1c434234b
myList = list(:a, :b, 3, 4, "foo")     # nested named tuples

# ╔═╡ 0bf35cab-4249-4984-be04-cffb3aab352d
squares = list(1, 4, 9, 16, 25)           # nested named tuples

# ╔═╡ b5fb717e-2988-4492-aa46-ac835b2099b5
odds = list(1, 3, 5, 7)

# ╔═╡ 606fa931-1420-4df3-b0c2-c903d161fb6b
cons(10, one_through_four)     # nested named tuples

# ╔═╡ 88b6b567-3fc1-4af1-aecb-f1f1c0c1e75f
cons(5, one_through_four)      # nested named tuples

# ╔═╡ 74d753ce-50a6-4075-9108-eec2aca841c1
md"
###### 2nd (specialized) *typed* method of *selector* function $$car$$
"

# ╔═╡ 8812f55d-1d06-49bd-a967-24077b720a39
car(list::Array)::Any = first(list::Array)

# ╔═╡ 3049ab44-f2a2-4baf-9765-301392337c3f
car(one_through_four)

# ╔═╡ efb2cdf0-b929-4b91-8ebf-22df244e577c
car(myList)

# ╔═╡ 3c6644b3-003a-44d1-b8f7-bc41edd467b3
md"
###### 2nd (specialized) *typed* method of *selector* function $$cdr$$
"

# ╔═╡ a66e8fe3-9f44-4d02-9e21-439cca73cd89
cdr(list::Array)::Array = list[2:end]::Array

# ╔═╡ 6f28288b-0cd9-4d32-b80b-1145a582a562
# iterative pp a box-pointer structure as tuple
function pp(consStruct::NamedTuple)::Tuple  
	#--------------------------------------------------------------------------------
	function pp_iter(ppArray, consStruct::NamedTuple)
		if consStruct == cons(:nil, :nil)
			(Tuple(ppArray),)
		elseif (car(consStruct) !== :nil) && (cdr(consStruct) == :nil)
			Tuple(push!(ppArray, car(consStruct)))
		else
			pp_iter(push!(ppArray, car(consStruct)), cdr(consStruct))
		end # if
	end # pp_iter
	#-----------------------------------------------------------------
	pp_iter([], consStruct)
end # function pp

# ╔═╡ 78829665-5360-4c7a-ae09-b664560e4749
pp(cons(:one, "two"))   # ==> dotted pair ==> *no* list structure ! *no* pp !

# ╔═╡ d404efa1-dc5f-40bb-8f10-bfb93dbd09ed
pp(cons(:one, cons("two", :nil)))

# ╔═╡ 25ae5618-cbc6-4325-bfb9-7be558102b9e
pp(cons(:nil, :nil))                # ==> (:nil) ==> (()) because :nil == ()

# ╔═╡ 04de1c1f-7c2c-4a07-89ad-f7fadc11d04a
typeof(pp(cons(:nil, :nil)))        

# ╔═╡ cb1bd172-6e08-42d2-beb1-7278e5961f83
pp(cons(:a, :nil))                  # ==> (:a, ()) ==> (:a)  -->    :)

# ╔═╡ 165c5ded-6f9f-42cd-9ece-d54a40e847e3
pp(cons(:a, cons(:b, :nil)))        # ==> cons(:a, (:b)) ==> (:a, :b)

# ╔═╡ 5cec6d4d-4124-46a4-9400-d3c7bfeaa2b2
pp(cons(:one,                       # Scheme-like list of Fig. 2.2.4
	cons("two",
		cons(3, 
			cons(4.0, :nil)))))

# ╔═╡ d0518c8e-12b0-45c8-aae6-cbd5cdd82e00
pp(list())                                 # the empty list                           

# ╔═╡ 44db31bc-5b6b-4809-9464-97e09b1160cf
pp(one_through_four)           # Scheme-like list

# ╔═╡ dee2d0c4-3431-4355-9c02-c15b8e335256
pp(cons(10, one_through_four)) # Scheme-like list

# ╔═╡ 143b00c0-8418-4ca2-b840-403bd7ca5faf
pp(cons(5, one_through_four))  # Scheme-like list

# ╔═╡ e0181f07-538d-489c-81bb-6ac2c779989e
pp(myList)                             # Scheme-like list

# ╔═╡ e13349e0-3a7a-4245-b6f7-5b8ea019053a
pp(squares)                               # # Scheme-like list

# ╔═╡ 52391fbc-87ac-42b1-8790-8dda0d3e1008
pp(odds)

# ╔═╡ be65d3f7-84cf-4d9d-9f8e-171f09745d23
cdr(one_through_four)          # nested named tuples

# ╔═╡ 062906e4-1e1c-4d3d-8d18-ba3689c82b67
pp(cdr(one_through_four))      # Scheme-like list

# ╔═╡ 8c47ee7a-7bb5-44e3-aeb1-12f2f9f368eb
car(cdr(one_through_four))

# ╔═╡ 4439e6b7-27c1-4a8f-adc9-9de9b4efcc82
cdr(myList)                            # nested named tuples

# ╔═╡ 18a9bb82-0943-4fad-844f-da3878efb4bc
pp(cdr(myList))                        # Scheme-like list

# ╔═╡ 2b2963a1-9db2-46f4-89b4-26b502cfc9a7
cadr(consCell) = car(cdr(consCell)) 

# ╔═╡ 95836205-128f-489e-b767-303adf325916
# according SICP first element should have index == 0
function list_ref(items, n)
	if ==(n, 0)
		car(items)
	else
		list_ref(cdr(items), -(n, 1))
	end
end

# ╔═╡ c5c02c4f-6676-4a73-92a5-0d8a4c49330f
function length(list)
	#--------------------------------------------------------------
	null(list) = (car(list) == :nil) && (cdr(list) == :nil)
	singleItem(list) = (car(list) !== :nil) && (cdr(list) == :nil)
	#--------------------------------------------------------------
	if null(list) 
		0
	elseif singleItem(list)
		1
	else
		+(1, length(cdr(list)))
	end # if
end

# ╔═╡ 550ec189-2017-4489-b301-865986b6a8cf
function length2(list)
	#--------------------------------------------------------------
	null(list) = (car(list) == :nil) && (cdr(list) == :nil)
	singleItem(list) = (car(list) !== :nil) && (cdr(list) == :nil)
	#--------------------------------------------------------------
	function length_iter(temp_list, count)
		if null(temp_list) 
			count
		elseif singleItem(temp_list)
			count + 1
		else
			length_iter(cdr(temp_list), +(1, count))
		end # if
	end
	#--------------------------------------------------------------
	length_iter(list, 0)
end

# ╔═╡ 9e453d79-4c54-4c6c-bf4d-7b982fed5a18
length2(list())

# ╔═╡ c234ab19-8fa7-4963-bd88-3077c3924502
length2(list(:a))

# ╔═╡ 501ea091-049c-4bfc-86bf-d820dd59ecf7
length2(list(:a, :b))

# ╔═╡ 7ce00f81-566a-414d-9feb-b25907f5443d
length2(odds)

# ╔═╡ 589badfa-1f1c-4f1e-8ca2-06f98c34b53b
function append(list1, list2) 
	#--------------------------------------------------------------
	null(list) = (car(list) == :nil) && (cdr(list) == :nil)
	singleItem(list) = (car(list) !== :nil) && (cdr(list) == :nil)
	#--------------------------------------------------------------
	if null(list1)
		list2
	elseif singleItem(list1)
		cons(car(list1), list2)
	else
		cons(car(list1), append(cdr(list1), list2))
	end # if
end

# ╔═╡ b33110e1-8a30-4831-908e-833104b37494
function scale_list(list, factor)
	#--------------------------------------------------------------
	null(list) = (car(list) == :nil) && (cdr(list) == :nil)
	singleItem(list) = (car(list) !== :nil) && (cdr(list) == :nil)
	#--------------------------------------------------------------
	if null(list)
		list
	elseif singleItem(list)
		cons(car(list) * factor, :nil)
	else
		cons(car(list) * factor, scale_list(cdr(list), factor))
	end
end

# ╔═╡ f62445fd-e6c0-4e3a-bc49-5f213a7f2192
function myMap(proc, list)
	#--------------------------------------------------------------
	null(list) = (car(list) == :nil) && (cdr(list) == :nil)
	singleItem(list) = (car(list) !== :nil) && (cdr(list) == :nil)
	#--------------------------------------------------------------
	if null(list)
		list
	elseif singleItem(list)
		cons(proc(car(list)), :nil)
	else
		cons(proc(car(list)), myMap(proc, (cdr(list))))
	end # if
end

# ╔═╡ 74057de4-cf91-413d-b4f6-5e10ea2d5ece
myMap(abs, list(-10, 2.5, -11.6, 17))          # named nested tuple

# ╔═╡ 1a387789-4234-4a4b-80ae-1de62ca7162b
pp(myMap(abs, list(-10, 2.5, -11.6, 17)))      # Scheme-like list

# ╔═╡ 06f3b046-2650-4755-aada-3865688fa612
myMap(x -> *(x, x), list(1, 2, 3, 4))          # named nested tuple

# ╔═╡ 7df7fc3c-5408-48ba-9a27-08bab8eebc8c
pp(myMap(x -> *(x, x), list(1, 2, 3, 4)))

# ╔═╡ b5054052-cb2d-4486-9b24-cdeb4eaf6aef
function scale_list2(list, factor)
	myMap(x -> *(x, factor), list)
end

# ╔═╡ 4c522af5-eea5-458c-8c1c-b6403d4d9e69
scale_list2(list(), 10)

# ╔═╡ d01d3225-4bf0-4a94-9c08-155a137876f0
scale_list2(list(1, 2, 3, 4, 5), 10)

# ╔═╡ e07aa3d4-549e-4158-b1e7-8419872e8cc9
pp(scale_list2(list(1, 2, 3, 4, 5), 10))

# ╔═╡ 01d68de9-95f9-4c61-aa2d-8f4697dfcf8f
Tuple(cons(10, one_through_four2))

# ╔═╡ 621dbe13-519e-4ef1-8be8-258b3bbd9fc2
car(one_through_four2)

# ╔═╡ 7ae797c1-9dd8-499a-97fb-0d84001051e3
Tuple(cdr(one_through_four2))

# ╔═╡ 7f77a89d-e662-4857-aa4c-47d162fc09a0
car(cdr(one_through_four2))

# ╔═╡ e196666e-3a31-4f64-8ee6-caa9de9b0853
md"
###### 2nd (specialized) *typed* method of combined *selector* function $$cadr$$ ...
"

# ╔═╡ 273c3c3e-8f5f-4924-ac2f-1b3f7a17e5a0
cadr(list::Array) = car(cdr(list::Array))

# ╔═╡ 96e38418-c4e3-4563-aee8-fe75f8f7df9c
cadr(myList)

# ╔═╡ a9ffe340-608b-402b-b5bd-bc0b1e086528
cadr(one_through_four)

# ╔═╡ d5e77221-31e5-469b-99af-38953626bb77
cadr(one_through_four2)

# ╔═╡ bec12008-cf9e-4768-bccc-b39d83634617
md"
###### 3rd (default) *typed variant* method of *function* $$length$$ ...
######  ... implemented with $$while$$ and type $$NamedTuple{(:car, :cdr)}$$
"

# ╔═╡ a02680a3-5457-4e3d-ba31-54b257e2bd90
function length3(list::NamedTuple{(:car, :cdr)})::Signed
	#-------------------------------------------------------------
	null(list) = (car(list) == :nil) && (cdr(list) == :nil)
	singleItem(list) = (car(list) !== :nil) && (cdr(list) == :nil)
	#-------------------------------------------------------------
	temp_list, count = list, 0
	if null(temp_list) 
			count
	else 
		while !singleItem(temp_list)
			temp_list, count = cdr(temp_list), count + 1
		end # while
		count + 1
	end # if
	#-------------------------------------------------------------
end

# ╔═╡ cd34304a-8cc9-465d-bccc-18a9f5b9c121
length3(list())

# ╔═╡ 614c56ac-09a5-4f35-b92f-1d8cabbf6ecb
length3(list(:a))

# ╔═╡ 8728a302-43ab-468c-a051-6b0491674a88
length3(list(:a, :b))

# ╔═╡ ffe04f45-008e-4465-aeec-1c5c18f2157e
length3(odds)

# ╔═╡ 9d0e664d-8758-4b7a-bee7-6d077e70fe1e
# idiomatic Julia with broadcasting '.^2'
squares2 = list2(1,2,3,4,5).^2      # broadcasting over arrays does work

# ╔═╡ 812d7392-eca3-44fb-af0d-612b1534e961
Tuple(squares2)

# ╔═╡ bcc67c53-de8b-462e-b5d3-5825740e1b92
md"
###### 2nd (specialized) *typed method* of function $$list\_ref$$
"

# ╔═╡ 7177cb33-9202-4394-a1b2-89255bbdfcd4
function list_ref(list::Array, n)::Any
	list[n+1]
end

# ╔═╡ 2844c5a8-b20d-4979-a3e5-533e6b83e7fc
list_ref(squares, 0)                      # for index == 0 it's the first element 

# ╔═╡ 8c855187-3f21-47bf-93d8-4c1400674bf6
list_ref(squares, 0) == car(squares)

# ╔═╡ b022a613-510f-4f9b-9540-94718884b3f4
list_ref(squares, 3)                      # for index == 3 it's the 4th element 

# ╔═╡ cf8956ba-61d3-4027-9d49-ad8cbfed97b4
list_ref(squares2, 3)

# ╔═╡ d1b4d1b1-7d6d-4059-b451-a97d798c4dd6
list_ref(squares2, 0)

# ╔═╡ 39d7227c-3586-4f62-875f-d72c08aa455a
list_ref(squares2, 3)

# ╔═╡ 8705f9e7-bffd-4ac0-a01b-7ce32f976c8c
odds2 = list2(1, 3, 5, 7)

# ╔═╡ cd5dd465-2084-483c-bcea-f508c6aead84
Tuple(odds2)

# ╔═╡ 8ee31694-4e27-49a2-9570-a586cd998d91
md"
###### 2nd (specialized) *typed* method of function $$length$$ ...
######  ... implemented with Julia's $$Array$$
"

# ╔═╡ 8b8671fd-2af1-4b59-beca-1ce8ac51dbc7
function length(list::Array)::Int
	lastindex(list)
end

# ╔═╡ 54fa7582-ca53-495c-bcfc-73b57c01d9a8
length(odds)

# ╔═╡ 97d8ea55-d515-4eb2-a907-17cdc9be51d4
length(odds2)

# ╔═╡ b12de1c2-bfef-4679-975b-141ad169e11a
md"
###### 2nd (specialized) *typed* method of function $$append$$ ...
######  ... implemented with Julia's $$Array$$
"

# ╔═╡ 9ddf31fb-8fed-42f9-9e0d-c0c75f008cee
function append(list1::Array, list2::Array)::Array
	#------------------------------------
	null(list::Array)::Bool = list == []
	#------------------------------------
	if null(list1)
		list2
	else 
		cons(car(list1), append(cdr(list1), list2))
	end	
end

# ╔═╡ 6048f7e3-5570-4449-9c60-de2f44794b2a
append(squares, odds)

# ╔═╡ 0e0d818b-d998-4a8b-b4bf-f8a88ab7dc4c
pp(append(squares, odds))

# ╔═╡ 00414b7f-b1d9-424e-ab38-2a1a1d64da8f
append(odds, squares)


# ╔═╡ eb27d136-d979-43d9-b102-600f82870792
pp(append(odds, squares))

# ╔═╡ 8741dc08-700c-4d7e-a94d-2cfdbe48cf1e
Tuple(append(squares2, odds2))

# ╔═╡ d601bdb9-f736-450c-b1e9-fe291f13b2b6
Tuple(append(odds2, squares2))

# ╔═╡ 8060aeae-6cbc-4b26-b9f1-29d572b7bab3
first(odds2)

# ╔═╡ 87e8768c-d562-444d-be5a-176fa08a393d
last(odds2)

# ╔═╡ 811ca574-a55c-44e0-890f-388877804f4e
Tuple(copy(odds2[1:3]))

# ╔═╡ 3108621b-98a7-4c97-9a33-445b766e04f5
function append2(list1::Array, list2::Array)::Array
	#------------------------------------
	null(list::Array)::Bool = list == []
	#------------------------------------
	function append_iter(list1::Array, list1_list2::Array)
		if 	null(list1)
			list1_list2
		else 
			append_iter(list1[1:end-1], cons(last(list1),list1_list2))
		end
	end
	append_iter(list1, list2)
end

# ╔═╡ 8d40ce9b-55ec-48fb-a6c1-74cbf640a44d
Tuple(append2(squares2, odds2))

# ╔═╡ c5ea6612-8793-49c8-b8db-f033f9bedfff
Tuple(append2(odds2, squares2))

# ╔═╡ 96fdc3f7-e75a-4697-b48a-ee7dac5301c8
function append3(list1::Array, list2::Array)::Array
	#------------------------------------
	null(list::Array)::Bool = list == []
	#------------------------------------
	list1_list2 = list2
	while !null(list1)
		list1, list1_list2 = list1[1:end-1], cons(last(list1),list1_list2)
	end
	list1_list2
end

# ╔═╡ 56863dba-89b3-4e14-b627-d79874cc477b
Tuple(append3(squares2, odds2))

# ╔═╡ df552faa-0cb4-427c-a1e2-3c274e107c68
Tuple(append3(odds2, squares2))

# ╔═╡ 53388b16-6443-4aac-b6b6-d23a8e8b7c9d
function append4(list1::Array, list2::Array)::Array
	vcat(list1, list2)
end

# ╔═╡ bff34be8-d69f-4c32-8355-bff70babd128
Tuple(append4(squares2, odds2))

# ╔═╡ 2e4b1c5c-a6b1-447b-986f-6209cd74a9c3
Tuple(append4(odds2, squares2))

# ╔═╡ 5f38b665-766a-4032-a26b-036b476790a2
md"
##### Mapping over lists
"

# ╔═╡ af1109e0-47ad-4ab2-8209-27bb8f880bb5
md"
###### 2nd (specialized) *typed* method of function $$scale\_list$$ ...
######  ... implemented with Julia's *broadcasting* over $$Array$$s
"

# ╔═╡ 50b38ed0-84c2-4dac-b2ec-9f21e6ae1333
function scale_list(list::Array, factor::Number)::Array
	list.*factor
end

# ╔═╡ 0b7050d5-1824-407a-b14e-42e2b96c367b
scale_list(list(), 10)

# ╔═╡ 689180cf-ab0d-4488-a272-ca960a37c3f4
pp(scale_list(list(), 10))                     # pretty print

# ╔═╡ ac560a9b-faac-47d1-948c-88d94fee7fcc
scale_list(list(1, 2, 3, 4, 5), 10)            # named nested tuple

# ╔═╡ 6daa1278-575f-4b8e-bd2f-0db8e6ccf7f3
pp(scale_list(list(1, 2, 3, 4, 5), 10))

# ╔═╡ 878d99ae-14e3-46e5-b31a-74af7df6e039
Tuple(scale_list(list2(1, 2, 3, 4, 5), 10))

# ╔═╡ f5af7525-2be7-48a5-b938-c2344b6f2bff
typeof(scale_list(list2(1, 2, 3, 4, 5), 10))

# ╔═╡ 7ef4344c-2049-49eb-882b-10239ce9ec3b
Tuple(list2(-10, 2.5, -11.6, 17))

# ╔═╡ 2a76cc50-c918-45b8-ab64-8d03228f113e
Tuple(map(abs, list2(-10, 2.5, -11.6, 17)))

# ╔═╡ 7a1d9398-453b-4616-97c2-c6e463f78b25
map(list2(-10, 2.5, -11.6, 17)) do item
	abs(item)
end

# ╔═╡ 89e4b01a-1ad7-486a-994c-f53061de9f04
map(x -> x^2, list2(1, 2, 3, 4))

# ╔═╡ 17aaf21c-d037-45a9-bbbf-63218db57adf
map(list2(1, 2, 3, 4)) do item
	item^2
end

# ╔═╡ 454a1c03-7353-4909-b244-13ffd61fd9ea
function scale_list3(list::Array, factor::Number)::Array
	map(list) do item
		item*factor
	end # map
end

# ╔═╡ 17180638-2950-4f62-801a-b6eeedda28ef
scale_list3(list2(1, 2, 3, 4, 5), 10)

# ╔═╡ a43f0bce-8507-4b33-9862-f11999071a59
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 2022/09/04
"

# ╔═╡ 41e8c05a-fd5e-4d94-a14c-ed60b6570d59
md"
---
##### end of ch. 2.2.1
====================================================================================

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]
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

julia_version = "1.8.5"
manifest_format = "2.0"
project_hash = "da39a3ee5e6b4b0d3255bfef95601890afd80709"

[deps]
"""

# ╔═╡ Cell order:
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