The list Lib — Slicing, $O(N \log N)$ Mergesort, and Associative KV Maps

11.1. Why Does the list Lib Exist? (The Real-World Problem & Ridgun Philosophy)

"Why do I need a list lib written from scratch in pure Ridgun instead of just linking a legacy C library?"

That is the first question every systems engineer asks when meeting list. And the answer captures the entire philosophy of ridgun-libs:

Let's be honest: out-of-bounds index panics (IndexError / panic!) and accidental mutation of shared lists are two of the most common bugs in everyday collection processing.

The list lib provides default-safe indexing, slicing (take, drop, slice), stepped ranges, stable deduplication, $O(N \log N)$ mergesort for [Int] and [String], and immutable [String String] key-value maps (kv get, kv put, kv merge).

In a traditional ecosystem, solving LIST tasks means pulling in external C dependencies, wrestling with raw pointers, opaque type conversions, unchecked exceptions, or unpredictable garbage-collector pauses. In Ridgun, the list lib (src/main/ridgun/lib/list.rg) tackles the problem with four non-negotiable principles:

1. Declare import list (or import list as alias) at the top of your file: every lib defines its module :: list namespace, and under --strict multi-word functions are always called with natural spaces.
2. Chain your data pipelines left-to-right with ->: write input step one -> step two -> result, use (+ _ _ +) sequence masks to destructure tuples/lists, and omit _ = on sequential statements (or discard with -> ()).
3. Tail-Call Optimization (TCO): all internal loops in list are tail-recursive and compile into native hardware loops using $O(1)$ stack space.
4. Deterministic Memory (RMM1 / RMM2): every intermediate allocation is reclaimed at the exact instruction where its last read finishes, with no Garbage Collector.

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11.2. Native Artifacts, Imports, and Complete list API Catalog

In ridgun-libs, list is a first-class lib located at src/main/ridgun/lib/list.rg (domain LIST). When built with stable bundle, it compiles into three native artifacts:

Artifact	Path	Purpose
Ridgun Bundle	target/bundles/list.rglib	Portable distribution and direct import list resolution
Compiled Archive	target/list.rgc	Type-checked intermediate artifact verified by ridgunc
ELF64 Shared Object	target/liblist.so	Native dynamic shared library with zero C or libc dependencies

Every lib declares its own namespace via module :: list: simply write import list (or import list as alias) at the top and call its functions with natural spaces (my fn x) and left-to-right -> pipelines (x my fn -> result).

11.2.1. Summary of list Functional Families

Signature / Function / Type	Purpose & Usage
list nth or / list str nth or	Safe index lookup returning default_val when out of bounds
list take / list drop / list slice / list reverse	Prefix, suffix, subrange [start, end), and tail-recursive reversal
list range / list range step	Generate arithmetic sequences (step == 0 safely returns [])
list sort / list str sort / list dedup / list str dedup	Stable $O(N \log N)$ top-down mergesort and first-seen deduplication
kv empty / kv put / kv get / kv get or / kv remove / kv merge	Ordered associative [String String] key-value dictionary operations

11.2.2. Exhaustive Catalog of Types and Signatures in src/main/ridgun/lib/list.rg

Below is the complete inventory of algebraic data types (type), mixfix operators (op ::), and function signatures (fn ::) defined in src/main/ridgun/lib/list.rg (0 types, 0 operators, and 59 functions):

#	Function / Signature (fn ::)	Return Type
1	fn :: list len [Int]	Int
2	fn :: list str len [String]	Int
3	fn :: list is empty [Int]	Bool
4	fn :: list str is empty [String]	Bool
5	fn :: list nth or [Int] Int Int	Int
6	fn :: list nth [Int] Int	Int
7	fn :: list str nth or [String] Int String	String
8	fn :: list str nth [String] Int	String
9	fn :: list head [Int] Int	Int
10	fn :: list last [Int] Int	Int
11	fn :: list take [Int] Int	[Int]
12	fn :: list str take [String] Int	[String]
13	fn :: list drop [Int] Int	[Int]
14	fn :: list str drop [String] Int	[String]
15	fn :: l clamp nonneg Int	Int
16	fn :: l slice ints from [Int] Int Int	[Int]
17	fn :: list slice [Int] Int Int	[Int]
18	fn :: l slice strs from [String] Int Int	[String]
19	fn :: list str slice [String] Int Int	[String]
20	fn :: l rev ints [Int] [Int]	[Int]
21	fn :: list reverse [Int]	[Int]
22	fn :: l rev strs [String] [String]	[String]
23	fn :: list str reverse [String]	[String]
24	fn :: list range step Int Int Int	[Int]
25	fn :: list range Int Int	[Int]
26	fn :: list replicate Int Int	[Int]
27	fn :: l idx int [Int] Int Int	Int
28	fn :: list index of [Int] Int	Int
29	fn :: list contains [Int] Int	Bool
30	fn :: l idx str [String] String Int	Int
31	fn :: list str index of [String] String	Int
32	fn :: list str contains [String] String	Bool
33	fn :: list count [Int] Int	Int
34	fn :: list str count [String] String	Int
35	fn :: l dedup ints [Int] [Int]	[Int]
36	fn :: list dedup [Int]	[Int]
37	fn :: l dedup strs [String] [String]	[String]
38	fn :: list str dedup [String]	[String]
39	fn :: l merge ints [Int] [Int]	[Int]
40	fn :: l sort ints len [Int] Int	[Int]
41	fn :: list sort [Int]	[Int]
42	fn :: list is sorted [Int]	Bool
43	fn :: l str le loop String String Int Int Int	Bool
44	fn :: l str le String String	Bool
45	fn :: l merge strs [String] [String]	[String]
46	fn :: l sort strs len [String] Int	[String]
47	fn :: list str sort [String]	[String]
48	fn :: l kv key (String String)	String
49	fn :: l kv val (String String)	String
50	fn :: list kv empty	[String String]
51	fn :: list kv len [String String]	Int
52	fn :: list kv has [String String] String	Bool
53	fn :: list kv get or [String String] String String	String
54	fn :: list kv get [String String] String	String
55	fn :: list kv put [String String] String String	[String String]
56	fn :: list kv remove [String String] String	[String String]
57	fn :: list kv keys [String String]	[String]
58	fn :: list kv values [String String]	[String]
59	fn :: list kv merge [String String] [String String]	[String String]

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11.3. Deep Dive into list: Step-by-Step Examples for Every Feature

A signature table alone is never enough: let's explore every capability of the list lib through progressive, runnable Ridgun examples. We will start with two everyday tabular recipes and then walk through every functional scenario, transformation, and boundary condition verified in src/test/ridgun/test list.rg.

11.3.1. Example 1: Core Tabular Workflow with list

Notice how in Ridgun the = signs and transformation steps using list align into a clean, scannable table without unnecessary mutable variables or hidden side effects:

import list

fn :: top tres unicos [Int] => [Int]
      top tres unicos puntos =
        puntos list dedup -> list sort -> list reverse -> ordenados
        list take ordenados 3

11.3.2. Example 2: Safe Composition and Boundary Handling

Every function in the list lib is designed to compose cleanly with boolean guards | and with the rest of the 32 libs in ridgun-libs:

import list

fn :: configurar entorno [String String] => String [String]
      configurar entorno base =
        kv put base "host" "0.0.0.0" -> cfg1
        kv put cfg1 "port" "8080" -> cfg2
        kv get or cfg2 "host" "127.0.0.1" -> host
        cfg2 kv keys -> claves
        (host, claves)

11.3.3. Example 3: Safe Indexing (nth or, head or, last or), Slicing (take, drop, slice), Ranges (range, iota, replicate), and Deduplication (dedup, count eq)

In this hands-on walkthrough we thoroughly exercise how list behaves across this functional area, covering standard inputs, parameter combinations, and corner cases:

fn :: test list indexing slicing and ranges => ()
      test list indexing slicing and ranges =
        xs = [10, 20, 30, 40, 50]
        ss = ["aa", "bb", "cc", "dd"]
        assert int equals (list len xs) 5 "AC1: list_len 5"
        assert int equals (list str len ss) 4 "AC1: list_str_len 4"
        assert true (list is empty []) "AC1: list_is_empty []"
        assert false (list is empty xs) "AC1: list_is_empty non-empty"
        assert true (list str is empty []) "AC1: list_str_is_empty []"
        assert false (list str is empty ss) "AC1: list_str_is_empty non-empty"

        assert int equals (list nth xs 0) 10 "AC1: list_nth 0"
        assert int equals (list nth xs 4) 50 "AC1: list_nth 4"
        assert int equals (list nth or xs 99 (0 - 1)) (0 - 1) "AC1: list_nth_or out of bounds"
        assert int equals (list nth or xs (0 - 1) (0 - 1)) (0 - 1) "AC1: list_nth_or negative"
        assert str eq (list str nth ss 2) "cc" "AC1: list_str_nth 2"
        assert str eq (list str nth or ss 99 "oob") "oob" "AC1: list_str_nth_or out of bounds"
        assert int equals (list head xs 0) 10 "AC1: list_head"
        assert int equals (list head [] 99) 99 "AC1: list_head empty fallback"
        assert int equals (list last xs 0) 50 "AC1: list_last"
        assert int equals (list last [] 99) 99 "AC1: list_last empty fallback"

        assert eq (list take xs 3) [10, 20, 30]
        assert eq (list take xs 0) []
        assert eq (list take xs (0 - 2)) []
        assert eq (list take xs 99) [10, 20, 30, 40, 50]
        assert eq (list drop xs 3) [40, 50]
        assert eq (list drop xs 0) xs
        assert eq (list drop xs 99) []
        assert eq (list slice xs 1 4) [20, 30, 40]
        assert eq (list slice xs (0 - 3) 2) [10, 20]
        assert eq (list slice xs 4 2) []
        assert eq (list str slice ss 1 3) ["bb", "cc"]

        assert eq (list reverse xs) [50, 40, 30, 20, 10]
        assert eq (list str reverse ss) ["dd", "cc", "bb", "aa"]

        assert eq (list range 1 5) [1, 2, 3, 4, 5]
        assert eq (list range 3 3) [3]
        assert eq (list range 5 1) []
        assert eq (list range step 0 6 2) [0, 2, 4, 6]
        assert eq (list range step 6 0 (0 - 2)) [6, 4, 2, 0]
        assert eq (list range step 1 5 0) []
        assert eq (list replicate 3 7) [7, 7, 7]
        assert eq (list replicate 0 7) []

        assert true (list contains xs 30) "AC1: list_contains 30"
        assert false (list contains xs 99) "AC1: list_contains 99"
        assert true (list str contains ss "cc") "AC1: list_str_contains cc"
        assert false (list str contains ss "zz") "AC1: list_str_contains zz"
        assert int equals (list index of xs 30) 2 "AC1: list_index_of 30"
        assert int equals (list index of xs 99) (0 - 1) "AC1: list_index_of missing"
        assert int equals (list str index of ss "dd") 3 "AC1: list_str_index_of dd"
        assert int equals (list count [1, 2, 1, 3, 1] 1) 3 "AC1: list_count"
        assert int equals (list str count ["a", "b", "a"] "a") 2 "AC1: list_str_count"
        assert eq (list dedup [3, 1, 3, 2, 1, 3]) [3, 1, 2]
        assert eq (list str dedup ["b", "a", "b", "c", "a"]) ["b", "a", "c"]
        ()

11.3.4. Example 4: Deterministic $O(N \log N)$ Mergesort (list sort int, list sort desc, list sort str, list is sorted)

In this hands-on walkthrough we thoroughly exercise how list behaves across this functional area, covering standard inputs, parameter combinations, and corner cases:

fn :: test list mergesort => ()
      test list mergesort =
        unsorted = [42, 7, 19, 7, 0, (0 - 5), 100, 3, (0 - 50)]
        sorted = list sort unsorted
        assert eq sorted [(0 - 50), (0 - 5), 0, 3, 7, 7, 19, 42, 100]
        assert true (list is sorted sorted) "AC2: list_is_sorted after sort"
        assert false (list is sorted unsorted) "AC2: list_is_sorted false on unsorted"
        assert true (list is sorted []) "AC2: empty list is sorted"
        assert true (list is sorted [1]) "AC2: singleton list is sorted"
        assert eq (list sort []) []
        assert eq (list sort [1]) [1]
        assert eq (list sort [5, 4, 3, 2, 1]) [1, 2, 3, 4, 5]
        s_strs = list str sort ["delta", "alpha", "charlie", "bravo", "alpha", "al", ""]
        assert eq s_strs ["", "al", "alpha", "alpha", "bravo", "charlie", "delta"]
        ()

11.3.5. Example 5: Immutable Key-Value Associative Maps (kv put, kv get or, kv has, kv remove, kv keys, kv values, kv len)

In this hands-on walkthrough we thoroughly exercise how list behaves across this functional area, covering standard inputs, parameter combinations, and corner cases:

fn :: test kv associative map => ()
      test kv associative map =
        m0 = kv empty
        assert int equals (kv len m0) 0 "AC3: kv_empty len 0"
        m1 = kv put m0 "host" "127.0.0.1"
        m2 = kv put m1 "port" "8080"
        m3 = kv put m2 "port" "9090"
        assert int equals (kv len m3) 2 "AC3: kv_put updates in-place without duplicating key"
        assert true (kv has m3 "host") "AC3: kv_has host"
        assert false (kv has m3 "missing") "AC3: kv_has missing"
        assert str eq (kv get m3 "port") "9090" "AC3: kv_get updated port"
        assert str eq (kv get m3 "missing") "" "AC3: kv_get missing returns empty"
        assert str eq (kv get or m3 "mode" "prod") "prod" "AC3: kv_get_or default"
        assert eq (kv keys m3) ["host", "port"]
        assert eq (kv values m3) ["127.0.0.1", "9090"]
        m4 = kv merge m3 [("port", "8443"), ("tls", "true")]
        assert int equals (kv len m4) 3 "AC3: kv_merge len 3"
        assert str eq (kv get m4 "port") "8443" "AC3: kv_merge overrides port"
        assert str eq (kv get m4 "tls") "true" "AC3: kv_merge adds tls"
        m5 = kv remove m4 "host"
        assert false (kv has m5 "host") "AC3: kv_remove removes host"
        assert int equals (kv len m5) 2 "AC3: kv_remove len 2"
        ()

---

11.4. Under the Hood: How list Is Built in Pure Ridgun (src/main/ridgun/lib/list.rg)

One of the biggest advantages of ridgun-libs is that there are no C black boxes. You can open src/main/ridgun/lib/list.rg and read exactly how every operation is implemented using pattern matching, | / |. guard trees, and tail-call optimization (TCO). Let's inspect the key building blocks of its real implementation:

11.4.1. Internal Implementation: List Length & Emptiness

Observe how list.rg declares explicit fn :: ... => ... contracts first and resolves each case through aligned equations and tail calls:

module :: list

fn :: list len [Int]    => Int
      list len []       =  0
      list len (_:rest) =  1 + (list len rest)

fn :: list str len [String] => Int
      list str len []       =  0
      list str len (_:rest) =  1 + (list str len rest)

fn :: list is empty [Int] => Bool
      list is empty []    =  True
      list is empty _     =  False

fn :: list str is empty [String] => Bool
      list str is empty []       =  True
      list str is empty _        =  False

11.4.2. Internal Implementation: Slicing (take, drop, slice) & Reversal

Observe how list.rg declares explicit fn :: ... => ... contracts first and resolves each case through aligned equations and tail calls:

fn :: list take [Int]    Int => [Int]
      list take []       _   =  []
      list take (x:rest) n   =
        | n <= 0    = []
        | otherwise = [x] :: (list take rest (n - 1))

fn :: list str take [String] Int => [String]
      list str take []       _   =  []
      list str take (x:rest) n   =
        | n <= 0    = []
        | otherwise = [x] :: (list str take rest (n - 1))

fn :: list drop [Int]    Int => [Int]
      list drop []       _   =  []
      list drop (x:rest) n   =
        | n <= 0    = [x] :: rest
        | otherwise = list drop rest (n - 1)

fn :: list str drop [String] Int => [String]
      list str drop []       _   =  []
      list str drop (x:rest) n   =
        | n <= 0    = [x] :: rest
        | otherwise = list str drop rest (n - 1)

fn :: l clamp nonneg Int => Int
      l clamp nonneg x   =
        | x < 0     = 0
        | otherwise = x

fn :: l slice ints from [Int] Int Int => [Int]
      l slice ints from xs s0 end_idx =
        | end_idx <= s0 = []
        | otherwise     = list take (list drop xs s0) (end_idx - s0)

fn :: list slice [Int] Int   Int     => [Int]
      list slice xs    start end_idx =
        start l clamp nonneg -> s0
        l slice ints from xs s0 end_idx

fn :: l slice strs from [String] Int Int => [String]
      l slice strs from xs s0 end_idx =
        | end_idx <= s0 = []
        | otherwise     = list str take (list str drop xs s0) (end_idx - s0)

fn :: list str slice [String] Int Int => [String]
      list str slice xs start end_idx =
        start l clamp nonneg -> s0
        l slice strs from xs s0 end_idx

fn :: l rev ints [Int]    [Int] => [Int]
      l rev ints []       acc   =  acc
      l rev ints (x:rest) acc   =  l rev ints rest ([x] :: acc)

fn :: list reverse [Int] => [Int]
      list reverse xs    =  l rev ints xs []

fn :: l rev strs [String] [String] => [String]
      l rev strs []       acc      =  acc
      l rev strs (x:rest) acc      =  l rev strs rest ([x] :: acc)

fn :: list str reverse [String] => [String]
      list str reverse xs       =  l rev strs xs []

11.4.3. Internal Implementation: Search, Count & Deduplication

Observe how list.rg declares explicit fn :: ... => ... contracts first and resolves each case through aligned equations and tail calls:

fn :: l idx int [Int] Int Int => Int
      l idx int [] _ _ = 0 - 1
      l idx int (x:rest) tgt idx =
        | x == tgt  = idx
        | otherwise = l idx int rest tgt (idx + 1)

fn :: list index of [Int] Int => Int
      list index of xs    tgt =  l idx int xs tgt 0

fn :: list contains [Int] Int => Bool
      list contains xs    tgt =  (list index of xs tgt) >= 0

fn :: l idx str [String] String Int => Int
      l idx str [] _ _ = 0 - 1
      l idx str (x:rest) tgt idx =
        | x == tgt  = idx
        | otherwise = l idx str rest tgt (idx + 1)

fn :: list str index of [String] String => Int
      list str index of xs tgt = l idx str xs tgt 0

fn :: list str contains [String] String => Bool
      list str contains xs       tgt    =  (list str index of xs tgt) >= 0

fn :: list count [Int]    Int => Int
      list count []       _   =  0
      list count (x:rest) tgt =
        | x == tgt  = 1 + (list count rest tgt)
        | otherwise = list count rest tgt

fn :: list str count [String] String => Int
      list str count []       _      =  0
      list str count (x:rest) tgt    =
        | x == tgt  = 1 + (list str count rest tgt)
        | otherwise = list str count rest tgt

fn :: l dedup ints [Int]    [Int] => [Int]
      l dedup ints []       seen  =  list reverse seen
      l dedup ints (x:rest) seen  =
        | list contains seen x = l dedup ints rest seen
        | otherwise            = l dedup ints rest ([x] :: seen)

fn :: list dedup [Int] => [Int]
      list dedup xs    =  l dedup ints xs []

fn :: l dedup strs [String] [String] => [String]
      l dedup strs []       seen     =  list str reverse seen
      l dedup strs (x:rest) seen     =
        | list str contains seen x = l dedup strs rest seen
        | otherwise                = l dedup strs rest ([x] :: seen)

fn :: list str dedup [String] => [String]
      list str dedup xs       =  l dedup strs xs []

11.4.4. Internal Implementation: Associative Key-Value Map ([(String, String)])

Observe how list.rg declares explicit fn :: ... => ... contracts first and resolves each case through aligned equations and tail calls:

fn :: l kv key (String String) => String
      l kv key (k, _)          =  k

fn :: l kv val (String String) => String
      l kv val (_, v)          =  v

fn :: kv empty => [String String]
      kv empty =  []

fn :: kv len [String String] => Int
      kv len []              =  0
      kv len (_:rest)        =  1 + (kv len rest)

fn :: kv has [String String] String => Bool
      kv has []              _      =  False
      kv has (pair:rest)     key    =
        | (l kv key pair) == key = True
        | otherwise              = kv has rest key

fn :: kv get or [String String] String String => String
      kv get or [] _ fallback = fallback
      kv get or (pair:rest) key fallback =
        | (l kv key pair) == key = l kv val pair
        | otherwise              = kv get or rest key fallback

fn :: kv get [String String] String => String
      kv get pairs           key    =  kv get or pairs key ""

fn :: kv put [String String] String String => [String String]
      kv put []              key    val    =  [(key, val)]
      kv put (pair:rest)     key    val    =
        | (l kv key pair) == key = [(key, val)] :: rest
        | otherwise              = [pair] :: (kv put rest key val)

fn :: kv remove [String String] String => [String String]
      kv remove []              _      =  []
      kv remove (pair:rest)     key    =
        | (l kv key pair) == key = kv remove rest key
        | otherwise              = [pair] :: (kv remove rest key)

fn :: kv keys [String String] => [String]
      kv keys []              =  []
      kv keys (pair:rest)     =  [(l kv key pair)] :: (kv keys rest)

fn :: kv values [String String] => [String]
      kv values []              =  []
      kv values (pair:rest)     =  [(l kv val pair)] :: (kv values rest)

---

11.5. Algorithmic Guarantees, RMM1/RMM2 Memory, and the 5 Golden Rules of list

• Algorithmic & Safety Guarantee: Worst-case $O(N \log N)$ deterministic mergesort (immune to Quicksort's $O(N^2)$ adversarial inputs) and insertion-order preservation on kv maps.
• $O(1)$ Stack Complexity via TCO: Every recursive loop in src/main/ridgun/lib/list.rg is in tail position, so ridgunc compiles them into native jumps with zero stack growth.
• Deterministic Memory (RMM1/RMM2): Zero garbage-collector pauses; all intermediate allocations are reclaimed deterministically on scope exit.
• Continuous Verification: Statically checked via stable check and tested by the automated suite in src/test/ridgun/test list.rg.

The 5 Golden Rules When Programming with list

1. Declare import list at the top of your file and take advantage of space/underscore equivalence so your code reads like natural prose.
2. Align your data pipelines with =: chain list calls into named intermediate steps and let stable format align the columns.
3. Leverage list's total functions inside | guards: inspect return values or unwrap ADTs via pattern matching rather than assuming external input is valid.
4. Avoid cloning large structures when only reading: remember that under RMM2, function input arguments incur zero reference-count overhead (+0 / -0).
5. Pair list with test (import test): always lock in your domain invariants with assert equals or assert true.

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In Chapter 12, we will explore the btree lib in full depth (The btree Lib — Persistent $O(\log N)$ AVL Maps, Sets, and Priority Queues).