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# Intersecting Number Wheels

Intersecting Number Wheels
You are encouraged to solve this task according to the task description, using any language you may know.

A number wheel has:

• A name which is an uppercase letter.
• A set of ordered values which are either numbers or names.

A number is generated/yielded from a named wheel by:

1. Starting at the first value of the named wheel and advancing through subsequent values and wrapping around to the first value to form a "wheel":
1.a If the value is a number, yield it.
1.b If the value is a name, yield the next value from the named wheel
1.c Advance the position of this wheel.

Given the wheel

`A: 1 2 3`

the number 1 is first generated, then 2, then 3, 1, 2, 3, 1, ...

Note: When more than one wheel is defined as a set of intersecting wheels then the first named wheel is assumed to be the one that values are generated from.

Examples

Given the wheels:

```   A: 1 B 2
B: 3 4
```

The series of numbers generated starts:

```   1, 3, 2, 1, 4, 2, 1, 3, 2, 1, 4, 2, 1, 3, 2...
```

The intersections of number wheels can be more complex, (and might loop forever), and wheels may be multiply connected.

Note: If a named wheel is referenced more than once by one or many other wheels, then there is only one position of the wheel that is advanced by each and all references to it.

E.g.

``` A:  1 D D
D:  6 7 8
Generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...
```

Generate and show the first twenty terms of the sequence of numbers generated from these groups:

```   Intersecting Number Wheel group:
A:  1 2 3

Intersecting Number Wheel group:
A:  1 B 2
B:  3 4

Intersecting Number Wheel group:
A:  1 D D
D:  6 7 8

Intersecting Number Wheel group:
A:  1 B C
B:  3 4
C:  5 B
```

## ALGOL 68

`BEGIN    # a number wheel element                                                  #    MODE NWELEMENT = UNION( CHAR # wheel name #, INT # wheel value # );    # a number wheel                                                          #    MODE NW = STRUCT( CHAR name, REF INT position, FLEX[ 1 : 0 ]NWELEMENT values );    # get the next value from a number wheel in an array of number wheels     #    # note: invalid wheel names will cause subscript range errors             #    OP   NEXT = ( []NW wheels )INT:         BEGIN            INT  result;            BOOL found := FALSE;            INT  w     := LWB wheels; # start with the first wheel            #            WHILE NOT found DO                IF position OF wheels[ w ] > UPB values OF wheels[ w ] THEN                    # passed the end of the wheel, go back to the start       #                    position OF wheels[ w ] := LWB values OF wheels[ w ]                FI;                NWELEMENT e = ( values OF wheels[ w ] )[ position OF wheels[ w ] ];                position OF wheels[ w ] +:= 1;                CASE e                  IN ( INT  n ): BEGIN result := n; found := TRUE END                   , ( CHAR c ): BEGIN                                     w := LWB wheels;                                     WHILE name OF wheels[ w ] /= c DO w +:= 1 OD                                 END                ESAC            OD;            result         END # NEXT # ;    # prints the first n values from an array of wheels                       #    PROC show = ( INT n, []NW wheels )VOID:         BEGIN            print( ( "First ", whole( n, 0 ), " values from the Intersecting Number Wheels:" ) );            FOR i FROM LWB wheels TO UPB wheels DO                print( ( newline, "    ", name OF wheels[ i ], ":" ) );                FOR v FROM LWB values OF wheels[ i ] TO UPB values OF wheels[ i ] DO                    CASE ( values OF wheels[ i ] )[ v ]                      IN ( INT  n ): print( ( " ", whole( n, 0 ) ) )                       , ( CHAR c ): print( ( " ", c ) )                    ESAC                OD            OD;            print( ( newline, "        " ) );            FOR i TO n DO print( ( " ", whole( NEXT wheels, 0 ) ) ) OD;            print( ( newline, newline ) )         END # show # ;    # show some wheels in action                                              #    show( 20, ( NW( "A", LOC INT := 1, (  1,   2,   3  ) ) ) );    show( 20, ( NW( "A", LOC INT := 1, (  1,  "B",  2  ) )              , NW( "B", LOC INT := 1, (  3,   4       ) ) ) );    show( 20, ( NW( "A", LOC INT := 1, (  1,  "D", "D" ) )              , NW( "D", LOC INT := 1, (  6,   7,   8  ) ) ) );    show( 20, ( NW( "A", LOC INT := 1, (  1,  "B", "C" ) )              , NW( "B", LOC INT := 1, (  3,   4       ) )              , NW( "C", LOC INT := 1, (  5,  "B"      ) ) ) )END`
Output:
```First 20 values from the Intersecting Number Wheels:
A: 1 2 3
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2

First 20 values from the Intersecting Number Wheels:
A: 1 B 2
B: 3 4
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3

First 20 values from the Intersecting Number Wheels:
A: 1 D D
D: 6 7 8
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6

First 20 values from the Intersecting Number Wheels:
A: 1 B C
B: 3 4
C: 5 B
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

```

## C

`#include <stdio.h>#include <stdlib.h>#include <string.h> struct Wheel {    char *seq;    int len;    int pos;}; struct Wheel *create(char *seq) {    struct Wheel *w = malloc(sizeof(struct Wheel));    if (w == NULL) {        return NULL;    }     w->seq = seq;    w->len = strlen(seq);    w->pos = 0;     return w;} char cycle(struct Wheel *w) {    char c = w->seq[w->pos];    w->pos = (w->pos + 1) % w->len;    return c;} struct Map {    struct Wheel *v;    struct Map *next;    char k;}; struct Map *insert(char k, struct Wheel *v, struct Map *head) {    struct Map *m = malloc(sizeof(struct Map));    if (m == NULL) {        return NULL;    }     m->k = k;    m->v = v;    m->next = head;     return m;} struct Wheel *find(char k, struct Map *m) {    struct Map *ptr = m;     while (ptr != NULL) {        if (ptr->k == k) {            return ptr->v;        }        ptr = ptr->next;    }     return NULL;} void printOne(char k, struct Map *m) {    struct Wheel *w = find(k, m);    char c;     if (w == NULL) {        printf("Missing the wheel for: %c\n", k);        exit(1);    }     c = cycle(w);    if ('0' <= c && c <= '9') {        printf(" %c", c);    } else {        printOne(c, m);    }} void exec(char start, struct Map *m) {    struct Wheel *w;    int i;     if (m == NULL) {        printf("Unable to proceed.");        return;    }     for (i = 0; i < 20; i++) {        printOne(start, m);    }    printf("\n");} void group1() {    struct Wheel *a = create("123");     struct Map *m = insert('A', a, NULL);     exec('A', m);} void group2() {    struct Wheel *a = create("1B2");    struct Wheel *b = create("34");     struct Map *m = insert('A', a, NULL);    m = insert('B', b, m);     exec('A', m);} void group3() {    struct Wheel *a = create("1DD");    struct Wheel *d = create("678");     struct Map *m = insert('A', a, NULL);    m = insert('D', d, m);     exec('A', m);} void group4() {    struct Wheel *a = create("1BC");    struct Wheel *b = create("34");    struct Wheel *c = create("5B");     struct Map *m = insert('A', a, NULL);    m = insert('B', b, m);    m = insert('C', c, m);     exec('A', m);} int main() {    group1();    group2();    group3();    group4();     return 0;}`
Output:
``` 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4```

## C#

`using System;using System.Collections.Generic;using System.Linq; public static class IntersectingNumberWheels{    public static void Main() {        TurnWheels(('A', "123")).Take(20).Print();        TurnWheels(('A', "1B2"), ('B', "34")).Take(20).Print();        TurnWheels(('A', "1DD"), ('D', "678")).Take(20).Print();        TurnWheels(('A', "1BC"), ('B', "34"), ('C', "5B")).Take(20).Print();    }     static IEnumerable<char> TurnWheels(params (char name, string values)[] wheels) {        var data = wheels.ToDictionary(wheel => wheel.name, wheel => wheel.values.Loop().GetEnumerator());        var primary = data[wheels[0].name];        while (true) {            yield return Turn(primary);        }         char Turn(IEnumerator<char> sequence) {            sequence.MoveNext();            char c = sequence.Current;            return char.IsDigit(c) ? c : Turn(data[c]);        }    }     static IEnumerable<T> Loop<T>(this IEnumerable<T> seq) {        while (true) {            foreach (T element in seq) yield return element;        }    }     static void Print(this IEnumerable<char> sequence) => Console.WriteLine(string.Join(" ", sequence));}`
Output:
```1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4```

## C++

Translation of: D
`#include <initializer_list>#include <iostream>#include <map>#include <vector> struct Wheel {private:    std::vector<char> values;    size_t index; public:    Wheel() : index(0) {        // empty    }     Wheel(std::initializer_list<char> data) : values(data), index(0) {        //values.assign(data);        if (values.size() < 1) {            throw new std::runtime_error("Not enough elements");        }    }     char front() {        return values[index];    }     void popFront() {        index = (index + 1) % values.size();    }}; struct NamedWheel {private:    std::map<char, Wheel> wheels; public:    void put(char c, Wheel w) {        wheels[c] = w;    }     char front(char c) {        char v = wheels[c].front();        while ('A' <= v && v <= 'Z') {            v = wheels[v].front();        }        return v;    }     void popFront(char c) {        auto v = wheels[c].front();        wheels[c].popFront();         while ('A' <= v && v <= 'Z') {            auto d = wheels[v].front();            wheels[v].popFront();            v = d;        }    }}; void group1() {    Wheel w({ '1', '2', '3' });    for (size_t i = 0; i < 20; i++) {        std::cout << ' ' << w.front();        w.popFront();    }    std::cout << '\n';} void group2() {    Wheel a({ '1', 'B', '2' });    Wheel b({ '3', '4' });     NamedWheel n;    n.put('A', a);    n.put('B', b);     for (size_t i = 0; i < 20; i++) {        std::cout << ' ' << n.front('A');        n.popFront('A');    }    std::cout << '\n';} void group3() {    Wheel a({ '1', 'D', 'D' });    Wheel d({ '6', '7', '8' });     NamedWheel n;    n.put('A', a);    n.put('D', d);     for (size_t i = 0; i < 20; i++) {        std::cout << ' ' << n.front('A');        n.popFront('A');    }    std::cout << '\n';} void group4() {    Wheel a({ '1', 'B', 'C' });    Wheel b({ '3', '4' });    Wheel c({ '5', 'B' });     NamedWheel n;    n.put('A', a);    n.put('B', b);    n.put('C', c);     for (size_t i = 0; i < 20; i++) {        std::cout << ' ' << n.front('A');        n.popFront('A');    }    std::cout << '\n';} int main() {    group1();    group2();    group3();    group4();     return 0;}`
Output:
``` 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4```

## D

`import std.exception;import std.range;import std.stdio; struct Wheel {    private string[] values;    private uint index;     invariant {        enforce(index < values.length, "index out of range");    }     this(string[] value...) in {        enforce(value.length > 0, "Cannot create a wheel with no elements");    } body {        values = value;    }     enum empty = false;     auto front() {        return values[index];    }     void popFront() {        index = (index + 1) % values.length;    }} struct NamedWheel {    private Wheel[char] wheels;    char m;     this(char c, Wheel w) {        add(c, w);        m = c;    }     void add(char c, Wheel w) {        wheels[c] = w;    }     enum empty = false;     auto front() {        auto v = wheels[m].front;        char c = v[0];        while ('A' <= c && c <= 'Z') {            v = wheels[c].front;            c = v[0];        }        return v;    }     void popFront() {        auto v = wheels[m].front;        wheels[m].popFront;         char c = v[0];        while ('A' <= c && c <= 'Z') {            auto d = wheels[c].front;            wheels[c].popFront;            c = d[0];        }    }} void group1() {    auto a = Wheel("1", "2", "3");    a.take(20).writeln;} void group2() {    auto a = Wheel("1", "B", "2");    auto b = Wheel("3", "4");     auto n = NamedWheel('A', a);    n.add('B', b);     n.take(20).writeln;} void group3() {    auto a = Wheel("1", "D", "D");    auto d = Wheel("6", "7", "8");     auto n = NamedWheel('A', a);    n.add('D', d);     n.take(20).writeln;} void group4() {    auto a = Wheel("1", "B", "C");    auto b = Wheel("3", "4");    auto c = Wheel("5", "B");     auto n = NamedWheel('A', a);    n.add('B', b);    n.add('C', c);     n.take(20).writeln;} void main() {    group1();    group2();    group3();    group4();}`
Output:
```["1", "2", "3", "1", "2", "3", "1", "2", "3", "1", "2", "3", "1", "2", "3", "1", "2", "3", "1", "2"]
["1", "3", "2", "1", "4", "2", "1", "3", "2", "1", "4", "2", "1", "3", "2", "1", "4", "2", "1", "3"]
["1", "6", "7", "1", "8", "6", "1", "7", "8", "1", "6", "7", "1", "8", "6", "1", "7", "8", "1", "6"]
["1", "3", "5", "1", "4", "3", "1", "4", "5", "1", "3", "4", "1", "3", "5", "1", "4", "3", "1", "4"]```

## F#

` // Wheels within wheels. Nigel Galloway: September 30th., 2019. let N(n)=fun()->nlet wheel(n:(unit->int)[])=let mutable g= -1 in (fun()->g<-(g+1)%n.Length; n.[g]())let A1=wheel[|N(1);N(2);N(3)|]for n in 0..20 do printf "%d " (A1())printfn ""let B2=wheel[|N(3);N(4)|]let A2=wheel[|N(1);B2;N(2)|]for n in 0..20 do printf "%d " (A2())printfn ""let D3=wheel[|N(6);N(7);N(8)|]let A3=wheel[|N(1);D3;D3|]for n in 0..20 do printf "%d " (A3())printfn ""let B4=wheel[|N(3);N(4)|]let C4=wheel[|N(5);B4|]let A4=wheel[|N(1);B4;C4|]for n in 0..20 do printf "%d " (A4())printfn "" `
Output:
```1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 2
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 7
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 5
```

## Factor

An attempt has been made to simplify the interface as much as possible by creating a natural literal syntax for number wheel groups. This should be useful for exploring these types of sequences in the future. `nw-parser` is an EBNF grammar that turns

```"A: 1 B C\nB: 3 4\nC: 5 B"
```

into

```{
{ "A" T{ number-wheel { seq T{ circular { seq { 1 "B" "C" } } } } { i 0 } } }
{ "B" T{ number-wheel { seq T{ circular { seq { 3 4 } } } } { i 0 } } }
{ "C" T{ number-wheel { seq T{ circular { seq { 5 "B" } } } } { i 0 } } }
}
```

⁠— a dictionary-like structure that is transformed into a lazy list which yields the expected sequence elements.

Works with: Factor version 0.99 2019-07-10
`USING: accessors assocs circular io kernel lists lists.lazy mathmath.parser multiline peg.ebnf prettyprint prettyprint.customsequences strings ;IN: rosetta-code.number-wheels TUPLE: group pretty list ; C: <group> group M: group pprint* pretty>> write ; TUPLE: number-wheel seq i ; : <number-wheel> ( seq -- number-wheel )    <circular> 0 number-wheel boa ; : yield ( assoc -- n )    dup first first [ dup integer? ]    [ dupd of [ i>> ] [ [ 1 + ] change-i seq>> nth ] bi ] until    nip ; : number-wheel>lazy ( assoc -- list )    0 lfrom swap [ yield nip ] curry lmap-lazy ; EBNF: nw-parser [=[    num   = [0-9]+ => [[ >string string>number ]]    name  = [a-zA-Z]+ => [[ >string ]]    wheel = (" "~ (num | name))+ "\n"?          => [[ but-last first <number-wheel> ]]    group = (name ":"~ wheel)+ => [[ number-wheel>lazy ]]]=] SYNTAX: NUMBER-WHEELS: parse-here dup nw-parser <group> suffix! ; : .take ( n group -- )    list>> ltake list>array [ pprint bl ] each "..." print ;`

Now the interface defined above may be used:

`USING: generalizations io kernel prettyprintrosetta-code.number-wheels ; NUMBER-WHEELS:A: 1 2 3; NUMBER-WHEELS:A: 1 B 2B: 3 4; NUMBER-WHEELS:A: 1 D DD: 6 7 8; NUMBER-WHEELS:A: 1 B CB: 3 4C: 5 B; [     "Intersecting number wheel group:" print    [ . ] [ "Generates:" print 20 swap .take nl ] bi] 4 napply`
Output:
```Intersecting number wheel group:
A: 1 2 3
Generates:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ...

Intersecting number wheel group:
A: 1 B 2
B: 3 4
Generates:
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 ...

Intersecting number wheel group:
A: 1 D D
D: 6 7 8
Generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Intersecting number wheel group:
A: 1 B C
B: 3 4
C: 5 B
Generates:
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 ...
```

## Go

`package main import (    "fmt"    "sort"    "strconv") type wheel struct {    next   int    values []string} type wheelMap = map[string]wheel func generate(wheels wheelMap, start string, maxCount int) {    count := 0    w := wheels[start]    for {        s := w.values[w.next]        v, err := strconv.Atoi(s)        w.next = (w.next + 1) % len(w.values)        wheels[start] = w        if err == nil {            fmt.Printf("%d ", v)            count++            if count == maxCount {                fmt.Println("...\n")                return            }        } else {            for {                w2 := wheels[s]                ss := s                s = w2.values[w2.next]                w2.next = (w2.next + 1) % len(w2.values)                wheels[ss] = w2                v, err = strconv.Atoi(s)                if err == nil {                    fmt.Printf("%d ", v)                    count++                    if count == maxCount {                        fmt.Println("...\n")                        return                    }                    break                }            }        }    }} func printWheels(wheels wheelMap) {    var names []string    for name := range wheels {        names = append(names, name)    }    sort.Strings(names)    fmt.Println("Intersecting Number Wheel group:")    for _, name := range names {        fmt.Printf("  %s: %v\n", name, wheels[name].values)    }    fmt.Print("  Generates:\n    ")} func main() {    wheelMaps := []wheelMap{        {            "A": {0, []string{"1", "2", "3"}},        },        {            "A": {0, []string{"1", "B", "2"}},            "B": {0, []string{"3", "4"}},        },        {            "A": {0, []string{"1", "D", "D"}},            "D": {0, []string{"6", "7", "8"}},        },        {            "A": {0, []string{"1", "B", "C"}},            "B": {0, []string{"3", "4"}},            "C": {0, []string{"5", "B"}},        },    }    for _, wheels := range wheelMaps {        printWheels(wheels)        generate(wheels, "A", 20)    }}`
Output:
```Intersecting Number Wheel group:
A: [1 2 3]
Generates:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ...

Intersecting Number Wheel group:
A: [1 B 2]
B: [3 4]
Generates:
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 ...

Intersecting Number Wheel group:
A: [1 D D]
D: [6 7 8]
Generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Intersecting Number Wheel group:
A: [1 B C]
B: [3 4]
C: [5 B]
Generates:
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 ...
```

Defining a unit movement of the interlocking wheels as a recursive descent, terminating at the first digit found, and printing a map-accumulation of that recursion over a list of given length but arbitrary content.

`import qualified Data.Map.Strict as Mimport Data.Maybe (fromMaybe)import Data.List (mapAccumL)import Data.Char (isDigit)import Data.Bool (bool)  clockWorkTick :: M.Map Char String -> (M.Map Char String, Char)clockWorkTick = flip click 'A'  where    click wheels name =      let wheel = fromMaybe ['?'] (M.lookup name wheels)          v = head wheel      in bool           click           (,)           (isDigit v || '?' == v)           (M.insert name (leftRotate wheel) wheels)           v leftRotate :: [a] -> [a]leftRotate = take . length <*> (tail . cycle)  -- TEST ---------------------------------------------------main :: IO ()main = do  let wheelSets =        [ [('A', "123")]        , [('A', "1B2"), ('B', "34")]        , [('A', "1DD"), ('D', "678")]        , [('A', "1BC"), ('B', "34"), ('C', "5B")]        ]  putStrLn "State of each wheel-set after 20 clicks:\n"  mapM_ print \$    fmap      (flip (mapAccumL (const . clockWorkTick)) (replicate 20 ' ') . M.fromList)      wheelSets  putStrLn "\nInitial state of the wheel-sets:\n"  mapM_ print wheelSets`
Output:
```State of each wheel-set after 20 clicks:

(fromList [('A',"312")],"12312312312312312312")
(fromList [('A',"21B"),('B',"43")],"13214213214213214213")
(fromList [('A',"D1D"),('D',"786")],"16718617816718617816")
(fromList [('A',"C1B"),('B',"34"),('C',"5B")],"13514314513413514314")

Initial state of the wheel-sets:

[('A',"123")]
[('A',"1B2"),('B',"34")]
[('A',"1DD"),('D',"678")]
[('A',"1BC"),('B',"34"),('C',"5B")]```

## Java

` package intersectingNumberWheels;import java.util.ArrayList;import java.util.HashMap;import java.util.List;import java.util.Map;import java.util.stream.IntStream; public class WheelController {	private static final String IS_NUMBER = "[0-9]";	private static final int TWENTY = 20;	private static Map<String, WheelModel> wheelMap; 	public static void advance(String wheel) {		WheelModel w = wheelMap.get(wheel);		if (w.list.get(w.position).matches(IS_NUMBER)) {			w.printThePosition();			w.advanceThePosition();		} else {			String wheelName = w.list.get(w.position);			advance(wheelName);			w.advanceThePosition();		}	} 	public static void run() {		System.out.println(wheelMap);		IntStream.rangeClosed(1, TWENTY).forEach(i -> advance("A"));		System.out.println();		wheelMap.clear();	} 	public static void main(String[] args) {		wheelMap = new HashMap<>();		wheelMap.put("A", new WheelModel("A", "1", "2", "3"));		run();		wheelMap.put("A", new WheelModel("A", "1", "B", "2"));		wheelMap.put("B", new WheelModel("B", "3", "4"));		run();		wheelMap.put("A", new WheelModel("A", "1", "D", "D"));		wheelMap.put("D", new WheelModel("D", "6", "7", "8"));		run();		wheelMap.put("A", new WheelModel("A", "1", "B", "C"));		wheelMap.put("B", new WheelModel("B", "3", "4"));		wheelMap.put("C", new WheelModel("C", "5", "B"));		run();	} } class WheelModel {	String name;	List<String> list;	int position;	int endPosition;	private static final int INITIAL = 0; 	public WheelModel(String name, String... values) {		super(); 		this.name = name.toUpperCase();		this.list = new ArrayList<>();		for (String value : values) {			list.add(value);		}		this.position = INITIAL;		this.endPosition = this.list.size() - 1;	} 	@Override	public String toString() {		return list.toString();	} 	public void advanceThePosition() {		if (this.position == this.endPosition) {			this.position = INITIAL;// new beginning		} else {			this.position++;// advance position		}	} 	public void printThePosition() {		System.out.print(" " + this.list.get(position));	}} `

Output: {A=[1, 2, 3]}

```1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
```

{A=[1, B, 2], B=[3, 4]}

```1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
```

{A=[1, D, D], D=[6, 7, 8]}

```1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
```

{A=[1, B, C], B=[3, 4], C=[5, B]}

```1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4
```

## JavaScript

Map-accumulation of a recursive digit-search, over an array of given length and arbitrary contents.

Translation of: Python
`(() => {    'use strict';     // main :: IO ()    const main = () => {         // clockWorkTick :: Dict -> (Dict, Char)        const clockWorkTick = wheelMap => {            // The new configuration of the wheels, tupled with            // a digit found by recursive descent from a single            // click of the first wheel.            const click = wheels => wheelName => {                const                    wheel = wheels[wheelName] || ['?'],                    v = wheel[0];                return bool(click)(Tuple)(isDigit(v) || '?' === v)(                    insertDict(wheelName)(                        leftRotate(wheel)                    )(wheels)                )(v);            };            return click(wheelMap)('A');        };         // leftRotate ::[a] -> [a]        const leftRotate = xs =>            // The head of the list appended            // to the tail of of the list.            0 < xs.length ? (                xs.slice(1).concat(xs[0])            ) : [];          // TEST -------------------------------------------        // State of each wheel-set after 20 clicks,        // paired with the resulting series of characters.         const tuple = uncurry(Tuple);        const wheelLists = [            [tuple('A', '123')],            [tuple('A', '1B2'), tuple('B', '34')],            [tuple('A', '1DD'), tuple('D', '678')],            [tuple('A', '1BC'), tuple('B', '34'), tuple('C', '5B')]        ];         console.log([            'Series and state of each wheel-set after 20 clicks:\n',            unlines(                map(tuples => showWheels(                    mapAccumL(                        compose(constant, clockWorkTick)                    )(dictFromList(tuples))(replicate(20)(''))                ))(wheelLists)            ),            '\nInitial state of each wheel-set:\n',            map(map(compose(                JSON.stringify,                dictFromList,                x => [Array.from(x)]            )))(wheelLists).join('\n')        ].join('\n'));    };     // DISPLAY FORMATTING ---------------------------------     // showWheels :: (Dict, [Char]) -> String    const showWheels = tpl =>        JSON.stringify(            Array.from(secondArrow(concat)(tpl))        );     // GENERIC FUNCTIONS ----------------------------------     // Tuple (,) :: a -> b -> (a, b)    const Tuple = a => b => ({        type: 'Tuple',        '0': a,        '1': b,        length: 2    });     // bool :: a -> a -> Bool -> a    const bool = f => t => p =>        p ? t : f;     // compose (<<<) :: (b -> c) -> (a -> b) -> a -> c    const compose = (...fs) =>        x => fs.reduceRight((a, f) => f(a), x);     // concat :: [[a]] -> [a]    // concat :: [String] -> String    const concat = xs =>        0 < xs.length ? (() => {            const unit = 'string' !== typeof xs[0] ? (                []            ) : '';            return unit.concat.apply(unit, xs);        })() : [];     // constant :: a -> b -> a    const constant = k => _ => k;     // dictFromList :: [(k, v)] -> Dict    const dictFromList = kvs =>        Object.fromEntries(kvs);     // secondArrow :: (a -> b) -> ((c, a) -> (c, b))    const secondArrow = f => xy =>        // A function over a simple value lifted        // to a function over a tuple.        // f (a, b) -> (a, f(b))        Tuple(xy[0])(            f(xy[1])        );     // insertDict :: String -> a -> Dict -> Dict    const insertDict = k => v => dct =>        Object.assign({}, dct, {            [k]: v        });     // isDigit :: Char -> Bool    const isDigit = c => {        const n = c.codePointAt(0);        return 48 <= n && 57 >= n;    };     // map :: (a -> b) -> [a] -> [b]    const map = f => xs =>        (Array.isArray(xs) ? (            xs        ) : xs.split('')).map(f);     // Map-accumulation is a combination of map and a catamorphism;    // it applies a function to each element of a list, passing an    // accumulating parameter from left to right, and returning a final    // value of this accumulator together with the new list.     // mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])    const mapAccumL = f => acc => xs =>        xs.reduce((a, x) => {            const pair = f(a[0])(x);            return Tuple(pair[0])(a[1].concat(pair[1]));        }, Tuple(acc)([]));     // replicate :: Int -> a -> [a]    const replicate = n => x =>        Array.from({            length: n        }, () => x);     // uncurry :: (a -> b -> c) -> ((a, b) -> c)    const uncurry = f =>        (x, y) => f(x)(y);     // unlines :: [String] -> String    const unlines = xs => xs.join('\n');     // MAIN ---    return main();})();`
Output:
```Series and state of each wheel-set after 20 clicks:

[{"A":"312"},"12312312312312312312"]
[{"A":"21B","B":"43"},"13214213214213214213"]
[{"A":"D1D","D":"786"},"16718617816718617816"]
[{"A":"C1B","B":"34","C":"5B"},"13514314513413514314"]

Initial state of each wheel-set:

{"A":"123"}
{"A":"1B2"},{"B":"34"}
{"A":"1DD"},{"D":"678"}
{"A":"1BC"},{"B":"34"},{"C":"5B"}```

## Julia

`const d1 = Dict("A" => [["1", "2", "3"], 1])const d2 = Dict("A" => [["1", "B", "2"], 1], "B" => [["3", "4"], 1])const d3 = Dict("A" => [["1", "D", "D"], 1], "D" => [["6", "7", "8"], 1])const d4 = Dict("A" => [["1", "B", "C"], 1], "B" => [["3", "4"], 1],    "C" => [["5", "B"], 1]) function getvalue!(wheelname, allwheels)    wheel = allwheels[wheelname]    s = wheel[1][wheel[2]]    wheel[2] = mod1(wheel[2] + 1, length(wheel[1]))    return haskey(allwheels, s) ? getvalue!(s, allwheels) : send function testwheels(wheels, numterms = 20, firstwheel = "A")    println("\nNumber Wheels:")    for k in sort(collect(keys(wheels)))        print("\$k: [")        for s in wheels[k][1]            print(s, " ")        end        println("\b]")    end    print("Output: ")    for _ in 1:numterms        print(getvalue!(firstwheel, wheels), " ")    end    println("...")end foreach(testwheels, [d1, d2, d3, d4]) `
Output:
```Number Wheels:
A: [1 2 3]
Output: 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ...

Number Wheels:
A: [1 B 2]
B: [3 4]
Output: 1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 ...

Number Wheels:
A: [1 D D]
D: [6 7 8]
Output: 1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Number Wheels:
A: [1 B C]
B: [3 4]
C: [5 B]
Output: 1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 ...
```

## Kotlin

Translation of: Java
`import java.util.Collectionsimport java.util.stream.IntStream object WheelController {    private val IS_NUMBER = "[0-9]".toRegex()    private const val TWENTY = 20    private var wheelMap = mutableMapOf<String, WheelModel>()     private fun advance(wheel: String) {        val w = wheelMap[wheel]        if (w!!.list[w.position].matches(IS_NUMBER)) {            w.printThePosition()        } else {            val wheelName = w.list[w.position]            advance(wheelName)        }        w.advanceThePosition()    }     private fun run() {        println(wheelMap)        IntStream.rangeClosed(1, TWENTY)            .forEach { advance("A") }        println()        wheelMap.clear()    }     @JvmStatic    fun main(args: Array<String>) {        wheelMap["A"] = WheelModel("1", "2", "3")        run()        wheelMap["A"] = WheelModel("1", "B", "2")        wheelMap["B"] = WheelModel("3", "4")        run()        wheelMap["A"] = WheelModel("1", "D", "D")        wheelMap["D"] = WheelModel("6", "7", "8")        run()        wheelMap["A"] = WheelModel("1", "B", "C")        wheelMap["B"] = WheelModel("3", "4")        wheelMap["C"] = WheelModel("5", "B")        run()    }} internal class WheelModel(vararg values: String?) {    var list = mutableListOf<String>()    var position: Int    private var endPosition: Int     override fun toString(): String {        return list.toString()    }     fun advanceThePosition() {        if (position == endPosition) {            position = INITIAL // new beginning        } else {            position++ // advance position        }    }     fun printThePosition() {        print(" \${list[position]}")    }     companion object {        private const val INITIAL = 0    }     init {        Collections.addAll<String>(list, *values)        position = INITIAL        endPosition = list.size - 1    }}`
Output:
```{A=[1, 2, 3]}
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
{A=[1, B, 2], B=[3, 4]}
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
{A=[1, D, D], D=[6, 7, 8]}
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
{A=[1, B, C], B=[3, 4], C=[5, B]}
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4```

## Maple

` with(ArrayTools): module Wheel() option object; local spokes := Array([1,2,3]); local currentSpoke := 1;  export currentValue::static := proc(self::Wheel)  local valueOut;  if type(self:-spokes[self:-currentSpoke], integer) then   valueOut := self:-spokes[self:-currentSpoke]:  else   valueOut := currentValue(self:-spokes[self:-currentSpoke]):  end if:  rotate(self):  return valueOut; end proc:  export rotate::static := proc(self::Wheel)  if self:-currentSpoke = ArrayNumElems(self:-spokes) then self:-currentSpoke := 1:  else self:-currentSpoke += 1: end if: end proc:  export ModuleApply::static := proc()  Object(Wheel, _passed); end proc:  export ModuleCopy::static := proc(new::Wheel, proto::Wheel, spo::Array, curr::integer, \$)  new:-spokes := spo:  new:-currentSpoke := curr: end proc:end module: A := Wheel(Array([1,2,3]), 1): seq(currentValue(A), 1..20); A := Wheel(Array([1,B,2]), 1):B := Wheel(Array([3,4]), 1): seq(currentValue(A), 1..20); A := Wheel(Array([1,d,d]), 1):d := Wheel(Array([6,7,8]), 1): seq(currentValue(A), 1..20); A := Wheel(Array([1,b,C]), 1):b := Wheel(Array([3,4]), 1):C := Wheel(Array([5,b]), 1): seq(currentValue(A), 1..20); `
Output:
```
1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2

1, 3, 2, 1, 4, 2, 1, 3, 2, 1, 4, 2, 1, 3, 2, 1, 4, 2, 1, 3

1, 6, 7, 1, 8, 6, 1, 7, 8, 1, 6, 7, 1, 8, 6, 1, 7, 8, 1, 6

1, 3, 5, 1, 4, 3, 1, 4, 5, 1, 3, 4, 1, 3, 5, 1, 4, 3, 1, 4

```

## Perl

Translation of: Julia
`use strict;use warnings;use feature 'say'; sub get_next {    my(\$w,%wheels) = @_;    my \$wh = \@{\$wheels{\$w}}; # reference, not a copy    my \$value = \$\$wh[0][\$\$wh[1]];    \$\$wh[1] = (\$\$wh[1]+1) % @{\$\$wh[0]};    defined \$wheels{\$value} ? get_next(\$value,%wheels) : \$value;} sub spin_wheels {    my(%wheels) = @_;    say "\$_: " . join ', ', @{\${\$wheels{\$_}}[0]} for sort keys %wheels;    print get_next('A', %wheels) . ' ' for 1..20; print "\n\n";} spin_wheels(%\$_) for( {'A' => [['1', '2', '3'], 0]}, {'A' => [['1', 'B', '2'], 0], 'B' => [['3', '4'], 0]}, {'A' => [['1', 'D', 'D'], 0], 'D' => [['6', '7', '8'], 0]}, {'A' => [['1', 'B', 'C'], 0], 'B' => [['3', '4'], 0], 'C' => [['5', 'B'], 0]},);`
Output:
```A: 1, 2, 3
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2

A: 1, B, 2
B: 3, 4
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3

A: 1, D, D
D: 6, 7, 8
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6

A: 1, B, C
B: 3, 4
C: 5, B
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4```

## Phix

`function terms(sequence wheels, integer n)    sequence res = repeat(' ',n),             pos = repeat(2,length(wheels)),             wvs = vslice(wheels,1)    integer wheel = 1, rdx = 1    while rdx<=n do        integer p = pos[wheel],                c = wheels[wheel][p]        p = iff(p=length(wheels[wheel])?2:p+1)        pos[wheel] = p        if c>'9' then            wheel = find(c,wvs)        else            res[rdx] = c            rdx += 1            wheel = 1        end if    end while    return resend function constant wheels = {{"A123"},                   {"A1B2","B34"},                   {"A1DD","D678"},                   {"A1BC","B34","C5B"}} for i=1 to length(wheels) do    ?terms(wheels[i],20)end for`
Output:
```"12312312312312312312"
"13214213214213214213"
"16718617816718617816"
"13514314513413514314"
```

## Python

### Python: Original class and generator based

`from itertools import islice class INW():    """    Intersecting Number Wheels    represented as a dict mapping    name to tuple of values.    """     def __init__(self, **wheels):        self._wheels = wheels        self.isect = {name: self._wstate(name, wheel)                       for name, wheel in wheels.items()}     def _wstate(self, name, wheel):        "Wheel state holder"        assert all(val in self._wheels for val in wheel if type(val) == str), \               f"ERROR: Interconnected wheel not found in {name}: {wheel}"        pos = 0        ln = len(wheel)        while True:            nxt, pos = wheel[pos % ln], pos + 1            yield next(self.isect[nxt]) if type(nxt) == str else nxt     def __iter__(self):        base_wheel_name = next(self.isect.__iter__())        yield from self.isect[base_wheel_name]     def __repr__(self):        return f"{self.__class__.__name__}({self._wheels})"     def __str__(self):        txt = "Intersecting Number Wheel group:"        for name, wheel in self._wheels.items():            txt += f"\n  {name+':':4}" + ' '.join(str(v) for v in wheel)        return txt def first(iter, n):    "Pretty print first few terms"    return ' '.join(f"{nxt}" for nxt in islice(iter, n)) if __name__ == '__main__':    for group in[      {'A': (1, 2, 3)},      {'A': (1, 'B', 2),       'B': (3, 4)},      {'A': (1, 'D', 'D'),       'D': (6, 7, 8)},      {'A': (1, 'B', 'C'),       'B': (3, 4),       'C': (5, 'B')}, # 135143145...     ]:        w = INW(**group)        print(f"{w}\n  Generates:\n    {first(w, 20)} ...\n")`
Output:
```Intersecting Number Wheel group:
A:  1 2 3
Generates:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ...

Intersecting Number Wheel group:
A:  1 B 2
B:  3 4
Generates:
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 ...

Intersecting Number Wheel group:
A:  1 D D
D:  6 7 8
Generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Intersecting Number Wheel group:
A:  1 B C
B:  3 4
C:  5 B
Generates:
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 ...```

### Python: Simplified procedural

`def nextfrom(w, name):    while True:        nxt, w[name] = w[name][0], w[name][1:] + w[name][:1]        if '0' <= nxt[0] <= '9':            return nxt        name = nxt if __name__ == '__main__':    for group in '''A: 1 2 3A: 1 B 2; B: 3 4A: 1 D D; D: 6 7 8A: 1 B C; B: 3 4; C: 5 B'''.strip().split('\n'):        print(f"Intersecting Number Wheel group:\n  {group}")        wheel, first = {}, None        for w in group.strip().split(';'):            name, *values = w.strip().split()            wheel[name[:-1]] = values            first = name[:-1] if first is None else first        gen = ' '.join(nextfrom(wheel, first) for i in range(20))        print(f"  Generates:\n    {gen} ...\n")`
Output:
```Intersecting Number Wheel group:
A: 1 2 3
Generates:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ...

Intersecting Number Wheel group:
A: 1 B 2; B: 3 4
Generates:
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 ...

Intersecting Number Wheel group:
A: 1 D D; D: 6 7 8
Generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Intersecting Number Wheel group:
A: 1 B C; B: 3 4; C: 5 B
Generates:
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 ...```

And Again

This time the `nextfromr` function is recursive and it will only work for single character names and numbers due to character string rotation being used.
Input is just a list of Python dicts, and depends on c-python dicts being odered by key insertion order.

`def nextfromr(w, name):    nxt, w[name] = w[name][0], w[name][1:] + w[name][:1]    return nxt if '0' <= nxt[0] <= '9' else nextfromr(w, nxt) if __name__ == '__main__':    for group in [{'A': '123'},                  {'A': '1B2', 'B': '34'},                  {'A': '1DD', 'D': '678'},                  {'A': '1BC', 'B': '34', 'C': '5B'},]:        print(f"Intersecting Number Wheel group:\n  {group}")        first = next(group.__iter__())        gen = ' '.join(nextfromr(group, first) for i in range(20))        print(f"  Generates:\n   {gen} ...\n")`
Output:
```Intersecting Number Wheel group:
{'A': '123'}
Generates:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ...

Intersecting Number Wheel group:
{'A': '1B2', 'B': '34'}
Generates:
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 ...

Intersecting Number Wheel group:
{'A': '1DD', 'D': '678'}
Generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Intersecting Number Wheel group:
{'A': '1BC', 'B': '34', 'C': '5B'}
Generates:
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 ...```

### Python: Functional composition

Defining a unit rotation of the wheel-set as a recursive descent, and taking a map-accumulation of this recursion over a list of specific length and arbitrary content.

Works with: Python version 3.7
`'''Intersecting number wheels''' from functools import reducefrom itertools import cycle, islice  # clockWorkTick :: Dict -> (Dict, Char)def clockWorkTick(wheelMap):    '''The new state of the wheels, tupled with a       digit found by recursive descent from a single       click of the first wheel.'''    def click(wheels):        def go(wheelName):            wheel = wheels.get(wheelName, ['?'])            v = wheel[0]            return (Tuple if v.isdigit() or '?' == v else click)(                insertDict(wheelName)(leftRotate(wheel))(wheels)            )(v)        return lambda name: go(name)    return click(wheelMap)('A')  # leftRotate :: [a] -> Stringdef leftRotate(xs):    ''' A string shifted cyclically towards        the left by one position.    '''    return ''.join(islice(cycle(xs), 1, 1 + len(xs)))  # TEST ----------------------------------------------------# main :: IO ()def main():    '''First twenty values from each set of test wheels.'''     wheelMaps = [dict(kvs) for kvs in [        [('A', "123")],        [('A', "1B2"), ('B', "34")],        [('A', "1DD"), ('D', "678")],        [('A', "1BC"), ('B', "34"), ('C', "5B")]    ]]    print('New state of wheel sets, after 20 clicks of each:\n')    for wheels, series in [            mapAccumL(compose(const)(clockWorkTick))(                dct            )(' ' * 20) for dct in wheelMaps    ]:        print((wheels, ''.join(series)))     print('\nInital states:')    for x in wheelMaps:        print(x)  # GENERIC ------------------------------------------------- # Tuple (,) :: a -> b -> (a, b)def Tuple(x):    '''Constructor for a pair of values,       possibly of two different types.    '''    return lambda y: (        x + (y,)    ) if isinstance(x, tuple) else (x, y)  # compose (<<<) :: (b -> c) -> (a -> b) -> a -> cdef compose(g):    '''Right to left function composition.'''    return lambda f: lambda x: g(f(x))  # const :: a -> b -> adef const(k):    '''The latter of two arguments,       with the first discarded.    '''    return lambda _: k  # insertDict :: String -> a -> Dict -> Dictdef insertDict(k):    '''A dictionary updated with a (k, v) pair.'''    def go(v, dct):        dup = dict(dct)        dup.update({k: v})        return dup    return lambda v: lambda dct: go(v, dct)  # mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])def mapAccumL(f):    '''A tuple of an accumulation and a list derived by a       combined map and fold,       with accumulation from left to right.    '''    def go(a, x):        tpl = f(a[0])(x)        return (tpl[0], a[1] + [tpl[1]])    return lambda acc: lambda xs: (        reduce(go, xs, (acc, []))    )  # MAIN ---if __name__ == '__main__':    main()`
Output:
```New state of wheel sets, after 20 clicks of each:

({'A': '312'}, '12312312312312312312')
({'A': '21B', 'B': '43'}, '13214213214213214213')
({'A': 'D1D', 'D': '786'}, '16718617816718617816')
({'A': 'C1B', 'B': '34', 'C': '5B'}, '13514314513413514314')

Inital states:
{'A': '123'}
{'A': '1B2', 'B': '34'}
{'A': '1DD', 'D': '678'}
{'A': '1BC', 'B': '34', 'C': '5B'}```

## Raku

(formerly Perl 6) A succinct Raku example using a few additional language features. Wheels are implemented as infinite repeating sequences, allowing a single iterator to keep track of the current position. This means the code contains no position tracking whatsoever.

` #| advance rotates a named wheel \$n by consuming an item from an infinite sequence. It is called#| from within a gather block and so can use take in order to construct an infinite, lazy sequence#| of result valuessub advance(\$g, \$n) {	given \$g{\$n}.pull-one {		when /\d/ { take \$_ }		default   { samewith \$g, \$_ } # samewith re-calls this function with new parameters	}} #| Input groups are a hash containing each wheel name as the key, and a list of values constructed#| using <> to split on whitespace. They are transformed using xx * to repeat the list infinitely.#| We then retrieve the underlying iterator in order for wheel position to be persistent. Each group#| is then aggregated into a lazy output sequence using an infinite loop inside a gather block.[	{A => <1 2 3>},	{A => <1 B 2>, B => <3 4>},	{A => <1 D D>, D => <6 7 8>},	{A => <1 B C>, B => <3 4>, C => <5 B>},]	#| %() converts a list of pairs produced by map into a hash. \$^k and \$^v are implicit variables.	#| They are processed in alphabetical order and make the block arity 2, called with two vars.	#| .kv gets the list of wheel names and wheel values from the input entry	==> map({ %(.kv.map: { \$^k => (|\$^v xx *).iterator }) })	#| gather constructs a lazy sequence, in which we infinitely loop advancing wheel A	==> map({ gather { loop { advance \$_, 'A' }} })	#| state variables are only initialised once, and are kept between invocations.	==> map({ state \$i = 1; say "Group {\$i++}, First 20 values: \$_[^20]" }) `
Output:
```Group 1, First 20 values: 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
Group 2, First 20 values: 1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
Group 3, First 20 values: 1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
Group 4, First 20 values: 1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4
```

## REXX

Quite a bit of the REXX code deals with detecting of errors   (and issuing error messages)   in the specification and
generation/construction of the wheel sets.

This REXX program uses   numbers   (any form),   not   digits   (for the values on the wheels).

`/*REXX program  expresses numbers  from  intersecting number wheels  (or wheel sets).   */@.=                                              /*initialize array to hold the wheels. */parse arg lim @.1                                /*obtain optional arguments from the CL*/if lim='' | lim=","  then lim= 20                /*Not specified?  Then use the default.*/if @.1='' | @.1=","  then do;  @.1= ' A:  1 2 3 '                               @.2= ' A:  1 B 2,    B:  3 4 '                               @.3= ' A:  1 D D,    D:  6 7 8 '                               @.4= ' A:  1 B C,    B:  3 4,    C:  5 B '                          end       do i=1  while @.i\='';  call build        /*construct the wheel set  (gear sets).*/                               call run          /*execute    "    "    "      "    "   */       end   /*i*/exit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/error: say;   say;   say '***error***'  arg(1);   say;   say;   exit 12isLet: return datatype( arg(1), 'M')  &  length( arg(1) )==1isNum: return datatype( arg(1), 'N')/*──────────────────────────────────────────────────────────────────────────────────────*/build: @wn= 'wheel name';     first=;      @wnnfbac= 'wheel name not followed by a colon:'       @gn= 'gear name' ;     gear.=;      say copies('═', 79)       say 'building wheel group for: '    @.i;    wheels= space(@.i);        upper wheels          do y=1  while wheels\='';  parse var wheels  w gears ',' wheels;    L= length(w)          if L==2  then do;  !.y= left(w, 1)              /*obtain the 1-char gear name.*/                             if right(w, 1)\==':'  then call error @wnnfbac  w                             if \isLet(!.y)        then call error @wn "not a letter:"  w                        end                   else                       call error "first token isn't a" @wn':'   w          if y==1  then first= !.1               /*Is this is the 1st wheel set?  Use it*/          if first==''                   then call error "no wheel name was specified."          n= !.y                                 /*obtain the name of the 1st wheel set.*/          gear.n.0= 1                            /*initialize default 1st gear position.*/          say '   setting gear.name:'  n   '    gears=' gears             do g=1  for words(gears);         _= word(gears, g)             if isNum(_) | isLet(_)  then do;  gear.n.g= _;  iterate;  end             call error  @gn  "isn't a number or a gear name:"  _             end   /*g*/          end      /*y*/;        return/*──────────────────────────────────────────────────────────────────────────────────────*/run: say;       say center(' running the wheel named '   first" ", 79, "─");           \$=        do #=0  by 0  until words(\$)==lim;           n= first        z= gear.n.0;               x= gear.n.z;      z= z + 1        gear.n.0= z;      if gear.n.z==''  then gear.n.0= 1        if isNum(x)  then do;      \$= \$ x;    iterate;    end  /*found a number, use it.*/        xx= x                                  /*different gear, keep switching until #.*/           do forever;            nn= xx           if gear.nn.0==''  then call error "a gear is using an unknown gear name:"   x           zz= gear.nn.0;         xx= gear.nn.zz           zz= zz + 1;  gear.nn.0= zz;  if gear.nn.zz==''  then gear.nn.0= 1           if isNum(xx)  then do; \$= \$ xx;  iterate #;  end           end                                 /* [↑]  found a number,  now use  FIRST. */        end   /*until*/     say '('lim "results): " strip(\$);         say;          say;          return`
output   when using the default inputs:
```═══════════════════════════════════════════════════════════════════════════════
building wheel group for:   A:  1 2 3
setting gear.name: A     gears= 1 2 3

───────────────────────── running the wheel named  A ──────────────────────────
(20 results):  1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2

═══════════════════════════════════════════════════════════════════════════════
building wheel group for:   A:  1 B 2,    B:  3 4
setting gear.name: A     gears= 1 B 2
setting gear.name: B     gears= 3 4

───────────────────────── running the wheel named  A ──────────────────────────
(20 results):  1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3

═══════════════════════════════════════════════════════════════════════════════
building wheel group for:   A:  1 D D,    D:  6 7 8
setting gear.name: A     gears= 1 D D
setting gear.name: D     gears= 6 7 8

───────────────────────── running the wheel named  A ──────────────────────────
(20 results):  1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6

═══════════════════════════════════════════════════════════════════════════════
building wheel group for:   A:  1 B C,    B:  3 4,    C:  5 B
setting gear.name: A     gears= 1 B C
setting gear.name: B     gears= 3 4
setting gear.name: C     gears= 5 B

───────────────────────── running the wheel named  A ──────────────────────────
(20 results):  1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4
```

## Visual Basic .NET

Translation of: C#
`Imports System.Runtime.CompilerServices Module Module1     <Extension()>    Iterator Function Loopy(Of T)(seq As IEnumerable(Of T)) As IEnumerable(Of T)        While True            For Each element In seq                Yield element            Next        End While    End Function     Iterator Function TurnWheels(ParamArray wheels As (name As Char, values As String)()) As IEnumerable(Of Char)        Dim data = wheels.ToDictionary(Function(wheel) wheel.name, Function(wheel) wheel.values.Loopy.GetEnumerator)        Dim primary = data(wheels(0).name)         Dim Turn As Func(Of IEnumerator(Of Char), Char) = Function(sequence As IEnumerator(Of Char))                                                              sequence.MoveNext()                                                              Dim c = sequence.Current                                                              Return If(Char.IsDigit(c), c, Turn(data(c)))                                                          End Function         While True            Yield Turn(primary)        End While    End Function     <Extension()>    Sub Print(sequence As IEnumerable(Of Char))        Console.WriteLine(String.Join(" ", sequence))    End Sub     Sub Main()        TurnWheels(("A", "123")).Take(20).Print()        TurnWheels(("A", "1B2"), ("B", "34")).Take(20).Print()        TurnWheels(("A", "1DD"), ("D", "678")).Take(20).Print()        TurnWheels(("A", "1BC"), ("B", "34"), ("C", "5B")).Take(20).Print()    End Sub End Module`
Output:
```1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4```

## zkl

`fcn intersectingNumberWheelsW(wheels){ // ("A":(a,b,"C"), "C":(d,e) ...)   ws:=wheels.pump(Dictionary(),fcn([(k,v)]){ return(k,Walker.cycle(v)) });  // new Dictionary   Walker.zero().tweak(fcn(w,wheels){      while(1){	 w=wheels[w].next();	// increment wheel w	 if(Int.isType(w)) return(w);      }         }.fp("A",ws))	// assume wheel A exists and is always first}`
`wheelSets:=T( Dictionary("A",T(1,2,3)),	      Dictionary("A",T(1,"B",2),   "B",T(3,4)),	      Dictionary("A",T(1,"D","D"), "D",T(6,7,8)),	      Dictionary("A",T(1,"B","C"), "C",T(5,"B"),  "B",T(3,4)) );foreach ws in (wheelSets){   println("Wheel set:");   ws.pump(String,fcn([(k,v)]){ "  %s: %s\n".fmt(k,v.concat(" ")) }).print();   println("-->",intersectingNumberWheelsW(ws).walk(20).concat(" "));}`
Output:
```Wheel set:
A: 1 2 3
-->1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
Wheel set:
A: 1 B 2
B: 3 4
-->1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
Wheel set:
A: 1 D D
D: 6 7 8
-->1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
Wheel set:
A: 1 B C
C: 5 B
B: 3 4
-->1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4
```