# Generator/Exponential

(Redirected from Generator)
You are encouraged to solve this task according to the task description, using any language you may know.

A generator is an executable entity (like a function or procedure) that contains code that yields a sequence of values, one at a time, so that each time you call the generator, the next value in the sequence is provided.

Generators are often built on top of coroutines or objects so that the internal state of the object is handled “naturally”.

Generators are often used in situations where a sequence is potentially infinite, and where it is possible to construct the next value of the sequence with only minimal state.

• Create a function that returns a generation of the m'th powers of the positive integers starting from zero, in order, and without obvious or simple upper limit. (Any upper limit to the generator should not be stated in the source but should be down to factors such as the languages natural integer size limit or computational time/size).
• Use it to create a generator of:
•   Squares.
•   Cubes.
• Create a new generator that filters all cubes from the generator of squares.
• Drop the first 20 values from this last generator of filtered results, and then show the next 10 values.

Note that this task requires the use of generators in the calculation of the result.

Also see

## 11l

Translation of: C++
```T Generator
F.virtual.abstract next() -> Float

T PowersGenerator(Generator)
i = 0.0
Float e

F (e)
.e = e

F.virtual.assign next() -> Float
V r = .i ^ .e
.i++
R r

T Filter
Generator gen, filter
Float lastG, lastF

F (Generator gen, filter)
.gen = gen
.filter = filter
.lastG = .gen.next()
.lastF = .filter.next()

F ()()
L .lastG >= .lastF
I .lastG == .lastF
.lastG = .gen.next()
.lastF = .filter.next()

V out = .lastG
.lastG = .gen.next()
R out

V gen = Filter(PowersGenerator(2), PowersGenerator(3))

L 20
gen()
L 10
print(gen(), end' ‘ ’)```
Output:
```529 576 625 676 784 841 900 961 1024 1089
```

To modify the internal state, the function uses an access parameter. For a different approach, see the Random packages of the Ada compiler, which use the so-called "Rosen trick". With the next release of Ada 2012 functions are allowed to have in-out parameters, which would solve this problem, too. You could also use procedures instead of functions.

```package Generator is

type Generator is tagged private;
procedure Reset (Gen : in out Generator);
function Get_Next (Gen : access Generator) return Natural;

type Generator_Function is access function (X : Natural) return Natural;
procedure Set_Generator_Function (Gen  : in out Generator;
Func : Generator_Function);

procedure Skip (Gen : access Generator'Class; Count : Positive := 1);

private

function Identity (X : Natural) return Natural;

type Generator is tagged record
Last_Source : Natural := 0;
Last_Value  : Natural := 0;
Gen_Func    : Generator_Function := Identity'Access;
end record;

end Generator;
```

```package Generator.Filtered is

type Filtered_Generator is new Generator with private;
procedure Reset (Gen : in out Filtered_Generator);
function Get_Next (Gen : access Filtered_Generator) return Natural;

procedure Set_Source (Gen    : in out Filtered_Generator;
Source : access Generator);
procedure Set_Filter (Gen    : in out Filtered_Generator;
Filter : access Generator);

private

type Filtered_Generator is new Generator with record
Last_Filter : Natural := 0;
Source, Filter : access Generator;
end record;

end Generator.Filtered;
```

```package body Generator is

--------------
-- Identity --
--------------

function Identity (X : Natural) return Natural is
begin
return X;
end Identity;

----------
-- Skip --
----------

procedure Skip (Gen : access Generator'Class; Count : Positive := 1) is
Val : Natural;
pragma Unreferenced (Val);
begin
for I in 1 .. Count loop
Val := Gen.Get_Next;
end loop;
end Skip;

-----------
-- Reset --
-----------

procedure Reset (Gen : in out Generator) is
begin
Gen.Last_Source := 0;
Gen.Last_Value := 0;
end Reset;

--------------
-- Get_Next --
--------------

function Get_Next (Gen : access Generator) return Natural is
begin
Gen.Last_Source := Gen.Last_Source + 1;
Gen.Last_Value := Gen.Gen_Func (Gen.Last_Source);
return Gen.Last_Value;
end Get_Next;

----------------------------
-- Set_Generator_Function --
----------------------------

procedure Set_Generator_Function
(Gen  : in out Generator;
Func : Generator_Function)
is
begin
if Func = null then
Gen.Gen_Func := Identity'Access;
else
Gen.Gen_Func := Func;
end if;
end Set_Generator_Function;

end Generator;
```

```package body Generator.Filtered is

-----------
-- Reset --
-----------

procedure Reset (Gen : in out Filtered_Generator) is
begin
Reset (Generator (Gen));
Gen.Source.Reset;
Gen.Filter.Reset;
Gen.Last_Filter := 0;
end Reset;

--------------
-- Get_Next --
--------------

function Get_Next (Gen : access Filtered_Generator) return Natural is
Next_Source : Natural := Gen.Source.Get_Next;
Next_Filter : Natural := Gen.Last_Filter;
begin
loop
if Next_Source > Next_Filter then
Gen.Last_Filter := Gen.Filter.Get_Next;
Next_Filter := Gen.Last_Filter;
elsif Next_Source = Next_Filter then
Next_Source := Gen.Source.Get_Next;
else
return Next_Source;
end if;
end loop;
end Get_Next;

----------------
-- Set_Source --
----------------

procedure Set_Source
(Gen    : in out Filtered_Generator;
Source : access Generator)
is
begin
Gen.Source := Source;
end Set_Source;

----------------
-- Set_Filter --
----------------

procedure Set_Filter
(Gen    : in out Filtered_Generator;
Filter : access Generator)
is
begin
Gen.Filter := Filter;
end Set_Filter;

end Generator.Filtered;
```

example use:

```with Ada.Text_IO;
with Generator.Filtered;

procedure Generator_Test is

function Square (X : Natural) return Natural is
begin
return X * X;
end Square;

function Cube (X : Natural) return Natural is
begin
return X * X * X;
end Cube;

G1, G2 : aliased Generator.Generator;
F : aliased Generator.Filtered.Filtered_Generator;

begin

G1.Set_Generator_Function (Func => Square'Unrestricted_Access);
G2.Set_Generator_Function (Func => Cube'Unrestricted_Access);

F.Set_Source (G1'Unrestricted_Access);
F.Set_Filter (G2'Unrestricted_Access);

F.Skip (20);

for I in 1 .. 10 loop
Ada.Text_IO.Put (", F:" & Integer'Image (F.Get_Next));
end loop;

end Generator_Test;
```
Output:
```I: 1, F: 529
I: 2, F: 576
I: 3, F: 625
I: 4, F: 676
I: 5, F: 784
I: 6, F: 841
I: 7, F: 900
I: 8, F: 961
I: 9, F: 1024
I: 10, F: 1089```

## ALGOL 68

Translation of: Python
Works with: ALGOL 68 version Revision 1 - with currying of functions and PRAGMA READ extensions
Works with: ALGOL 68G version Any - tested with release algol68g-2.3.5.
File: Template.Generator.a68
```MODE YIELDVALUE = PROC(VALUE)VOID;
MODE GENVALUE = PROC(YIELDVALUE)VOID;

PROC gen filtered = (GENVALUE gen candidate, gen exclude, YIELDVALUE yield)VOID: (
VALUE candidate; SEMA have next exclude = LEVEL 0;
VALUE exclude;   SEMA get next exclude  = LEVEL 0;
BOOL initialise exclude := TRUE;

PAR ( # run each generator in a different thread #
# FOR VALUE next exclude IN # gen exclude( # ) DO #
##   (VALUE next exclude)VOID: (
DOWN get next exclude; exclude := next exclude;
IF candidate <= exclude THEN
UP have next exclude
ELSE
UP get next exclude
FI
# OD #)),
# FOR VALUE next candidate IN # gen candidate( # ) DO #
##   (VALUE next candidate)VOID: (
candidate := next candidate;
IF initialise exclude ORF candidate > exclude THEN
UP get next exclude;
DOWN have next exclude; # wait for result #
initialise exclude := FALSE
FI;
IF candidate < exclude THEN
yield(candidate)
FI
# OD #))
)
);

PROC gen slice = (GENVALUE t, VALUE start, stop, YIELDVALUE yield)VOID: (
INT index := 0;
# FOR VALUE i IN # t( # ) DO #
##   (VALUE i)VOID: (
IF   index >= stop THEN done
ELIF index >= start THEN yield(i) FI;
index +:= 1
# OD # ));
done: SKIP
);

PROC get list = (GENVALUE gen)[]VALUE: (
INT upb := 0;
INT ups := 2;
FLEX [ups]VALUE out;
# FOR VALUE i IN # gen( # ) DO #
##   (VALUE i)VOID:(
upb +:= 1;
IF upb > ups THEN # dynamically grow the array 50% #
[ups +:= ups OVER 2]VALUE append; append[:upb-1] := out; out := append
FI;
out[upb] := i
# OD # ))
out[:upb]
);

PROC powers = (VALUE m, YIELDVALUE yield)VOID:
FOR n FROM 0 DO yield(n ** m) OD;```
File: test.Generator.a68
```#!/usr/local/bin/a68g --script #

MODE VALUE = INT;

GENVALUE squares = powers(2,), cubes = powers(3,);
GENVALUE fil = gen filtered(squares, cubes,);

printf((\$g(0)x\$, get list(gen slice(fil, 20, 30, )) ))```
Output:
```529 576 625 676 784 841 900 961 1024 1089
```

## AppleScript

Composable generators can be constructed from the methods and persistent properties of script objects:

Translation of: JavaScript
Translation of: Python
```----------------- EXPONENTIAL / GENERATOR ----------------

-- powers :: Gen [Int]
on powers(n)
script f
on |λ|(x)
x ^ n as integer
end |λ|
end script
fmapGen(f, enumFrom(0))
end powers

--------------------------- TEST -------------------------
on run
take(10, ¬
drop(20, ¬
differenceGen(powers(2), powers(3))))

--> {529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089}
end run

------------------------- GENERIC ------------------------

-- Just :: a -> Maybe a
on Just(x)
{type:"Maybe", Nothing:false, Just:x}
end Just

-- Nothing :: Maybe a
on Nothing()
{type:"Maybe", Nothing:true}
end Nothing

-- Tuple (,) :: a -> b -> (a, b)
on Tuple(a, b)
{type:"Tuple", |1|:a, |2|:b, length:2}
end Tuple

-- differenceGen :: Gen [a] -> Gen [a] -> Gen [a]
on differenceGen(ga, gb)
-- All values of ga except any
script
property g : zipGen(ga, gb)
property bs : {}
property xy : missing value
on |λ|()
set xy to g's |λ|()
if missing value is xy then
xy
else
set x to |1| of xy
set y to |2| of xy
set bs to {y} & bs
if bs contains x then
|λ|() -- Next in series.
else
x
end if
end if
end |λ|
end script
end differenceGen

-- drop :: Int -> [a] -> [a]
-- drop :: Int -> String -> String
on drop(n, xs)
set c to class of xs
if script is not c then
if string is not c then
if n < length of xs then
items (1 + n) thru -1 of xs
else
{}
end if
else
if n < length of xs then
text (1 + n) thru -1 of xs
else
""
end if
end if
else
take(n, xs) -- consumed
return xs
end if
end drop

-- enumFrom :: Int -> [Int]
on enumFrom(x)
script
property v : missing value
on |λ|()
if missing value is not v then
set v to 1 + v
else
set v to x
end if
return v
end |λ|
end script
end enumFrom

-- fmapGen <\$> :: (a -> b) -> Gen [a] -> Gen [b]
on fmapGen(f, gen)
script
property g : mReturn(f)
on |λ|()
set v to gen's |λ|()
if v is missing value then
v
else
g's |λ|(v)
end if
end |λ|
end script
end fmapGen

-- length :: [a] -> Int
on |length|(xs)
set c to class of xs
if list is c or string is c then
length of xs
else
(2 ^ 29 - 1) -- (maxInt - simple proxy for non-finite)
end if
end |length|

-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
if script is class of f then
f
else
script
property |λ| : f
end script
end if
end mReturn

-- take :: Int -> [a] -> [a]
-- take :: Int -> String -> String
on take(n, xs)
set c to class of xs
if list is c then
if 0 < n then
items 1 thru min(n, length of xs) of xs
else
{}
end if
else if string is c then
if 0 < n then
text 1 thru min(n, length of xs) of xs
else
""
end if
else if script is c then
set ys to {}
repeat with i from 1 to n
set v to xs's |λ|()
if missing value is v then
return ys
else
set end of ys to v
end if
end repeat
return ys
else
missing value
end if
end take

-- uncons :: [a] -> Maybe (a, [a])
on uncons(xs)
set lng to |length|(xs)
if 0 = lng then
Nothing()
else
if (2 ^ 29 - 1) as integer > lng then
if class of xs is string then
set cs to text items of xs
Just(Tuple(item 1 of cs, rest of cs))
else
Just(Tuple(item 1 of xs, rest of xs))
end if
else
set nxt to take(1, xs)
if {} is nxt then
Nothing()
else
Just(Tuple(item 1 of nxt, xs))
end if
end if
end if
end uncons

-- zipGen :: Gen [a] -> Gen [b] -> Gen [(a, b)]
on zipGen(ga, gb)
script
property ma : missing value
property mb : missing value
on |λ|()
if missing value is ma then
set ma to uncons(ga)
set mb to uncons(gb)
end if
if Nothing of ma or Nothing of mb then
missing value
else
set ta to Just of ma
set tb to Just of mb
set x to Tuple(|1| of ta, |1| of tb)
set ma to uncons(|2| of ta)
set mb to uncons(|2| of tb)
return x
end if
end |λ|
end script
end zipGen
```
Output:
`{529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089}`

## ATS

```(* "Generators" *)

(* I implement "generators" as non-linear closures. *)

#define NIL list_nil ()
#define ::  list_cons

(* Integer powers where base and power are of any unsigned integer
types. *)
fn {tk_b, tk_p : tkind}
g1uint_ipow
(base  : g1uint tk_b,
power : g1uint tk_p)
:<> g1uint tk_b =
let
fun
loop {p : nat}
.<p>.
(b     : g1uint tk_b,
p     : g1uint (tk_p, p),
accum : g1uint tk_b)
:<> g1uint tk_b =
let
val ph = half p
val accum = (if ph + ph = p then accum else accum * b)
in
if ph = g1i2u 0 then
accum
else
loop (b * b, ph, accum)
end

prval () = lemma_g1uint_param base
prval () = lemma_g1uint_param power
in
loop (base, power, g1i2u 1)
end

overload ipow with g1uint_ipow of 100

(* Some unit tests of ipow. *)
val- 0U = ipow (0U, 100U)
val- 1U = ipow (0U, 0U)         (* Sometimes a convenient result. *)
val- 9UL = ipow (3UL, 2ULL)
val- 81ULL = ipow (3ULL, 4U)

typedef generator (tk : tkind) =
() -<cloref1> g1uint tk

typedef option_generator (tk : tkind) =
() -<cloref1> Option (g1uint tk)

fn {tk_b : tkind}
{tk_p : tkind}
make_powers_generator
(power : g1uint tk_p)
:<!wrt> generator tk_b =
let
val base : ref (g1uint tk_b) = ref (g1i2u 0)
in
lam () =>
let
val b = !base
val result = ipow (b, power)
in
!base := succ b;
result
end
end

fn {tk : tkind}
make_generator_of_1_that_are_not_also_2
(gen1 : generator tk,
gen2 : generator tk)
:<!wrt> generator tk =
let
val initialized : ref bool = ref false
val x2 : ref (g1uint tk) = ref (g1i2u 0)

fn
check (x1 : g1uint tk)
:<1> bool =
let
fun
loop ()
:<1> bool =
if x1 <= !x2 then
(x1 <> !x2)
else
begin
!x2 := gen2 ();
loop ()
end
in
loop ()
end
in
lam () =>
let
var result : g1uint tk = g1i2u 0
var found_one : bool = false
in
if ~(!initialized) then
begin
!x2 := gen2 ();
!initialized := true
end;
while (~found_one)
let
val next1 = gen1 ()
in
if check next1 then
begin
result := next1;
found_one := true
end
end;
result
end
end

fn {tk : tkind}
make_dropper
(n   : size_t,
gen : generator tk)
:<!wrt> generator tk =
let
val counter : ref size_t = ref n
in
lam () =>
begin
while (isneqz (!counter))
let
val _ = gen ()
in
!counter := pred (!counter)
end;
gen ()
end
end

fn {tk : tkind}
make_taker
(n   : size_t,
gen : generator tk)
:<!wrt> option_generator tk =
let
val counter : ref size_t = ref n
in
lam () =>
if iseqz (!counter) then
None ()
else
begin
!counter := pred (!counter);
Some (gen ())
end
end

implement
main0 () =
let
macdef filter = make_generator_of_1_that_are_not_also_2<tk>

val squares_generator = make_powers_generator<tk> 2U
val cubes_generator = make_powers_generator<tk> 3U
val gen = filter (squares_generator, cubes_generator)
val gen = make_dropper<tk> (i2sz 20, gen)
val gen = make_taker<tk> (i2sz 10, gen)

var done : bool = false
in
while (~done)
begin
case+ gen () of
| None () => done := true
| Some x => print! (" ", x)
end;
println! ()
end```
Output:
```\$ patscc -DATS_MEMALLOC_GCBDW generator-exponential.dats -lgc && ./a.out
529 576 625 676 784 841 900 961 1024 1089```

## C

### Library: libco

libco is a tiny library that adds cooperative multithreading, also known as coroutines, to the C language. Its co_switch(x) function pauses the current cothread and resumes the other cothread x.

This example provides next64() and yield64(), to generate 64-bit integers. next64() switches to a generator. Then the generator passes some 64-bit integer to yield64(), which switches to the first cothread, where next64() returns this 64-bit integer.

```#include <inttypes.h>	/* int64_t, PRId64 */
#include <stdlib.h>	/* exit() */
#include <stdio.h>	/* printf() */

#include <libco.h>	/* co_{active,create,delete,switch}() */

/* A generator that yields values of type int64_t. */
struct gen64 {
int64_t given;
void (*free)(struct gen64 *);
void *garbage;
};

/* Yields a value. */
inline void
yield64(struct gen64 *gen, int64_t value)
{
gen->given = value;
co_switch(gen->taker);
}

/* Returns the next value that the generator yields. */
inline int64_t
next64(struct gen64 *gen)
{
gen->taker = co_active();
co_switch(gen->giver);
return gen->given;
}

static void
gen64_free(struct gen64 *gen)
{
co_delete(gen->giver);
}

struct gen64 *entry64;

/*
* Creates a cothread for the generator. The first call to next64(gen)
* will enter the cothread; the entry function must copy the pointer
* from the global variable struct gen64 *entry64.
*
* Use gen->free(gen) to free the cothread.
*/
inline void
gen64_init(struct gen64 *gen, void (*entry)(void))
{
if ((gen->giver = co_create(4096, entry)) == NULL) {
/* Perhaps malloc() failed */
exit(1);
}
gen->free = gen64_free;
entry64 = gen;
}

/*
* Generates the powers 0**m, 1**m, 2**m, ....
*/
void
powers(struct gen64 *gen, int64_t m)
{
int64_t base, exponent, n, result;

for (n = 0;; n++) {
/*
* This computes result = base**exponent, where
* exponent is a nonnegative integer. The result
* is the product of repeated squares of base.
*/
base = n;
exponent = m;
for (result = 1; exponent != 0; exponent >>= 1) {
if (exponent & 1) result *= base;
base *= base;
}
yield64(gen, result);
}
/* NOTREACHED */
}

/* stuff for squares_without_cubes() */
#define ENTRY(name, code) static void name(void) { code; }
ENTRY(enter_squares, powers(entry64, 2))
ENTRY(enter_cubes, powers(entry64, 3))

struct swc {
struct gen64 cubes;
struct gen64 squares;
void (*old_free)(struct gen64 *);
};

static void
swc_free(struct gen64 *gen)
{
struct swc *f = gen->garbage;
f->cubes.free(&f->cubes);
f->squares.free(&f->squares);
f->old_free(gen);
}

/*
* Generates the squares 0**2, 1**2, 2**2, ..., but removes the squares
* that equal the cubes 0**3, 1**3, 2**3, ....
*/
void
squares_without_cubes(struct gen64 *gen)
{
struct swc f;
int64_t c, s;

gen64_init(&f.cubes, enter_cubes);
c = next64(&f.cubes);

gen64_init(&f.squares, enter_squares);
s = next64(&f.squares);

/* Allow other cothread to free this generator. */
f.old_free = gen->free;
gen->garbage = &f;
gen->free = swc_free;

for (;;) {
while (c < s)
c = next64(&f.cubes);
if (c != s)
yield64(gen, s);
s = next64(&f.squares);
}
/* NOTREACHED */
}

ENTRY(enter_squares_without_cubes, squares_without_cubes(entry64))

/*
* Look at the sequence of numbers that are squares but not cubes.
* Drop the first 20 numbers, then print the next 10 numbers.
*/
int
main()
{
struct gen64 gen;
int i;

gen64_init(&gen, enter_squares_without_cubes);

for (i = 0; i < 20; i++)
next64(&gen);
for (i = 0; i < 9; i++)
printf("%" PRId64 ", ", next64(&gen));
printf("%" PRId64 "\n", next64(&gen));

gen.free(&gen); /* Free memory. */
return 0;
}
```

```\$ libco=/home/kernigh/park/libco
\$ cc -I\$libco -o main main.c \$libco/libco.c
\$ ./main
529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089```

### Using struct to store state

```#include <stdio.h>
#include <stdlib.h>
#include <math.h>

typedef int (*seq_func)(void *);
#define SEQ_BASE seq_func f; int output

/* sort of polymorphing data structure */
typedef struct { SEQ_BASE; } gen_t;

int seq_next(void *state)
{
return ((gen_t*)state)->output = (*(seq_func*)state)(state);
}

typedef struct {
SEQ_BASE;
int pos, n;
} power_gen_t;

int power_next(void *s)
{
return (int)pow(++((power_gen_t*)s)->pos, ((power_gen_t*)s)->n);
}

void *power_seq(int n)
{
power_gen_t *s = malloc(sizeof(power_gen_t));
s->output = -1;
s->f = power_next;
s->n = n;
s->pos = -1;
return s;
}

typedef struct {
SEQ_BASE;
void *in, *without;
} filter_gen_t;

int filter_next(void *s)
{
gen_t *in = ((filter_gen_t*)s)->in, *wo = ((filter_gen_t*)s)->without;

do{
seq_next(in);
while (wo->output < in->output)
seq_next(wo);
} while(wo->output == in->output);

return in->output;
}

void* filter_seq(gen_t *in, gen_t *without)
{
filter_gen_t *filt = malloc(sizeof(filter_gen_t));
filt->in = in;
filt->without = without;
filt->f = filter_next;
filt->output = -1;
return filt;
}

int main()
{
int i;
void *s = filter_seq(power_seq(2), power_seq(3));

for (i = 0; i < 20; i++) seq_next(s);
for (i = 0; i < 10; i++)
printf("%d\n", seq_next(s));

return 0;
}
```
Output:
```529
576
625
676
784
841
900
961
1024

1089```

## C#

```using System;
using System.Collections.Generic;
using System.Linq;

static class Program {
static void Main() {
Func<int, IEnumerable<int>> ms = m => Infinite().Select(i => (int)Math.Pow(i, m));
var squares = ms(2);
var cubes = ms(3);
var filtered = squares.Where(square => cubes.First(cube => cube >= square) != square);
var final = filtered.Skip(20).Take(10);
foreach (var i in final) Console.WriteLine(i);
}

static IEnumerable<int> Infinite() {
var i = 0;
while (true) yield return i++;
}
}
```

## C++

A templated solution.

```#include <iostream>
using namespace std;

template<class T>
class Generator
{
public:
virtual T operator()() = 0;
};

// Does nothing unspecialized
template<class T, T P>
class PowersGenerator: Generator<T> {};

// Specialize with other types, or provide a generic version of pow
template<int P>
class PowersGenerator<int, P>: Generator<int>
{
public:
int i;
PowersGenerator() { i = 1; }
virtual int operator()()
{
int o = 1;
for(int j = 0; j < P; ++j) o *= i;
++i;
return o;
}
};

// Only works with non-decreasing generators
template<class T, class G, class F>
class Filter: Generator<T>
{
public:
G gen;
F filter;
T lastG, lastF;

Filter() { lastG = gen(); lastF = filter(); }

virtual T operator()()
{
while(lastG >= lastF)
{
if(lastG == lastF)
lastG = gen();
lastF = filter();
}

T out = lastG;
lastG = gen();
return out;
}
};

int main()
{
Filter<int, PowersGenerator<int, 2>, PowersGenerator<int, 3>> gen;

for(int i = 0; i < 20; ++i)
gen();

for(int i = 20; i < 30; ++i)
cout << i << ": " << gen() << endl;
}
```
Output:
```20: 529
21: 576
22: 625
23: 676
24: 784
25: 841
26: 900
27: 961
28: 1024
29: 1089
```

## Clojure

In Clojure, the role that generator functions take in some other languages is generally filled by sequences. Most of the functions that produce sequences produce lazy sequences, many of the standard functions deal with sequences, and their use in Clojure is extremely idiomatic. Thus we can define squares and cubes as lazy sequences:

```(defn powers [m] (for [n (iterate inc 1)] (reduce * (repeat m n)))))
(def squares (powers 2))
(take 5 squares) ; => (1 4 9 16 25)
```

The definition here of the squares-not-cubes lazy sequence uses the loop/recur construct, which isn't lazy. So we use lazy-seq explicity:

```(defn squares-not-cubes
([] (squares-not-cubes (powers 2) (powers 3)))
([squares cubes]
(loop [[p2first & p2rest :as p2s] squares, [p3first & p3rest :as p3s] cubes]
(cond
(= p2first p3first) (recur p2rest p3rest)
(> p2first p3first) (recur p2s p3rest)
:else (cons p2first (lazy-seq (squares-not-cubes p2rest p3s)))))))

(->> (squares-not-cubes) (drop 20) (take 10))
; => (529 576 625 676 784 841 900 961 1024 1089)
```

If we really need a generator function for some reason, any lazy sequence can be turned into a stateful function. (The inverse of seq->fn is the standard function repeatedly.)

```(defn seq->fn [sequence]
(let [state (atom (cons nil sequence))]
(fn [] (first (swap! state rest)))

(def f (seq->fn (squares-not-cubes)))
[(f) (f) (f)] ; => [4 9 16]
```

## Common Lisp

```(defun take (seq &optional (n 1))
(values-list (loop repeat n collect (funcall seq))))

(defun power-seq (n)
(let ((x 0))
(lambda () (expt (incf x) n))))

(defun filter-seq (s1 s2) ;; remove s2 from s1
(let ((x1 (take s1)) (x2 (take s2)))
(lambda ()
(tagbody g
(if (= x1 x2)
(progn (setf x1 (take s1) x2 (take s2)) (go g)))
(if (> x1 x2)
(progn (setf x2 (take s2)) (go g))))

(prog1 x1 (setf x1 (take s1))))))

(let ((2not3 (filter-seq (power-seq 2) (power-seq 3))))
(take 2not3 20) ;; drop 20
(princ (multiple-value-list (take 2not3 10))))
```

## D

### Efficient Standard Version

```void main() {
import std.stdio, std.bigint, std.range, std.algorithm;

auto squares = 0.sequence!"n".map!(i => i.BigInt ^^ 2);
auto cubes = 0.sequence!"n".map!(i => i.BigInt ^^ 3);

squares.setDifference(cubes).drop(20).take(10).writeln;
}
```
Output:
`[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]`

### Simple Ranges-Based Implementation

Translation of: C#
```void main() {
import std.stdio, std.bigint, std.range, std.algorithm;

auto squares = 0.sequence!"n".map!(i => i.BigInt ^^ 2);
auto cubes = 0.sequence!"n".map!(i => i.BigInt ^^ 3);

squares
.filter!(s => cubes.find!(c => c >= s).front != s)
.drop(20)
.take(10)
.writeln;
}
```

The output is the same.

### More Efficient Ranges-Based Version

```import std.stdio, std.bigint, std.range, std.algorithm;

struct Filtered(R1, R2) if (is(ElementType!R1 == ElementType!R2)) {
R1 s1;
R2 s2;
alias ElementType!R1 T;
T front, source, filter;

this(R1 r1, R2 r2) {
s1 = r1;
s2 = r2;
source = s1.front;
filter = s2.front;
popFront;
}

static immutable empty = false;

void popFront() {
while (true) {
if (source > filter) {
s2.popFront;
filter = s2.front;
continue;
} else if (source < filter) {
front = source;
s1.popFront;
source = s1.front;
break;
}
s1.popFront;
source = s1.front;
}
}
}

auto filtered(R1, R2)(R1 r1, R2 r2) // Helper function.
if (isInputRange!R1 && isInputRange!R2 &&
is(ElementType!R1 == ElementType!R2)) {
return Filtered!(R1, R2)(r1, r2);
}

void main() {
auto squares = 0.sequence!"n".map!(i => i.BigInt ^^ 2);
auto cubes = 0.sequence!"n".map!(i => i.BigInt ^^ 3);
filtered(squares, cubes).drop(20).take(10).writeln;
}
```

The output is the same.

### Closures-Based Version

Translation of: Go
```import std.stdio;

auto powers(in double e) pure nothrow {
double i = 0;
return () => i++ ^^ e;
}

auto filter2(D)(D af, D bf) {
double a = af(), b = bf();

return {
double r;
while (true) {
if (a < b) {
r = a;
a = af();
break;
}
if (b == a)
a = af();
b = bf();
}
return r;
};
}

void main() {
auto fgen = filter2(2.powers, 3.powers);
foreach (immutable i; 0 .. 20)
fgen();
foreach (immutable i; 0 .. 10)
write(fgen(), " ");
writeln;
}
```
Output:
`529 576 625 676 784 841 900 961 1024 1089 `

### Generator Range Version

```import std.stdio, std.range, std.algorithm, std.concurrency, std.bigint;

auto powers(in uint m) pure nothrow @safe {
return 0.sequence!"n".map!(i => i.BigInt ^^ m);
}

auto filtered(R1, R2)(R1 r1, R2 r2) /*@safe*/
if (isForwardRange!R1 && isForwardRange!R2 &&
is(ElementType!R1 == ElementType!R2)) {
return new Generator!(ElementType!R1)({
auto v = r1.front; r1.popFront;
auto f = r2.front; r2.popFront;

while (true) {
if (v > f) {
f = r2.front; r2.popFront;
continue;
} else if (v < f)
yield(v);
v = r1.front; r1.popFront;
}
});
}

void main() {
auto squares = 2.powers, cubes = 3.powers;
filtered(squares, cubes).drop(20).take(10).writeln;
}
```
Output:
`[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]`

## Delphi

Works with: Delphi version 6.0

This program demostrates hierarchial object structure. It starts with a base generator object that has all the basic features need by a generator. Child objects are then created which customized the behavior to generate squares, cubes and filtered squares. Once the base object is created, any variation can be created with just a few lines of code. This is the power of polymorphism and inheritance.

```{Custom object forms basic generator}

type TCustomGen = class(TObject)
private
FNumber: integer;
FExponent: integer;
FStart: integer;
protected
property Exponent: integer read FExponent write FExponent;
public
constructor Create; virtual;
procedure Reset;
function Next: integer; virtual;
procedure Skip(Count: integer);
property Start: integer read FStart write FStart;
end;

{Child object specifically for generating Squares}

type TSquareGen = class(TCustomGen)
public
constructor Create; override;
end;

{Child object specifically for generating cubes}

type TCubeGen = class(TCustomGen)
public
constructor Create; override;
end;

{Child object specifically for filtering squares}

type TFilterSquareGen = class(TSquareGen)
private
function IsCube(N: integer): boolean;
public
function Next: integer; override;
end;

{ TCustomGen }

constructor TCustomGen.Create;
begin
Start:=0;
{Default to returning X^1}
Exponent:=1;
Reset;
end;

function TCustomGen.Next: integer;
{Find next number in sequence}
var I: integer;
begin
Result:=FNumber;
{Raise to specified power}
for I:=1 to FExponent-1 do Result:=Result * Result;
{Get next base}
Inc(FNumber);
end;

procedure TCustomGen.Reset;
begin
FNumber:=Start;
end;

procedure TCustomGen.Skip(Count: integer);
{Skip specified number of items}
var I: integer;
begin
for I:=1 to Count do Next;
end;

{ TSquareGen }

constructor TSquareGen.Create;
begin
inherited;
Exponent:=2;
end;

{ TCubeGen }

constructor TCubeGen.Create;
begin
inherited;
Exponent:=3;
end;

{ TFilterSquareGen }

function TFilterSquareGen.IsCube(N: integer): boolean;
{Test if number is perfect cube}
var I: integer;
begin
I:=Round(Power(N,1/3));
Result:=I*I*I = N;
end;

function TFilterSquareGen.Next: integer;
begin
{Gets inherited next square, rejects cubes}
repeat Result:=inherited Next
until not IsCube(Result);
end;

{-----------------------------------------------------------}

procedure DoTest(Memo: TMemo; Gen: TCustomGen; SkipCnt: integer; Title: string);
{Carry out TGenerators tests. "Gen" is a TCustomGen which is the parent of}
{all generators. That means "DoTest" can work with any type of generator}
var S: string;
var I,V: integer;
begin
Gen.Reset;
Gen.Skip(SkipCnt);
S:='[';
for I:=1 to 10 do S:=S+Format(' %d',[Gen.Next]);
end;

procedure TestGenerators(Memo: TMemo);
{Tests all three types of generators}
var SquareGen: TSquareGen;
var CubeGen: TCubeGen;
var Filtered: TFilterSquareGen;
begin
SquareGen:=TSquareGen.Create;
try
CubeGen:=TCubeGen.Create;
try
Filtered:=TFilterSquareGen.Create;
try
DoTest(Memo,SquareGen,0,'Testing Square Generator');
DoTest(Memo,CubeGen,0,'Testing Cube Generator');
DoTest(Memo,Filtered,20,'Testing Squares with cubes removed');

finally Filtered.Free; end;
finally CubeGen.Free; end;
finally SquareGen.Free; end;
end;
```
Output:
```Testing Square Generator
[ 0 1 4 9 16 25 36 49 64 81]
Testing Cube Generator
[ 0 1 16 81 256 625 1296 2401 4096 6561]
Testing Squares with cubes removed
[ 529 576 625 676 784 841 900 961 1024 1089]
```

## E

E does not provide coroutines on the principle that interleaving of execution of code should be explicit to avoid unexpected interactions. However, this problem does not especially require them. Each generator here is simply a function that returns the next value in the sequence when called.

```def genPowers(exponent) {
var i := -1
return def powerGenerator() {
return (i += 1) ** exponent
}
}

def filtered(source, filter) {
var fval := filter()
return def filterGenerator() {
while (true) {
def sval := source()
while (sval > fval) {
fval := filter()
}
if (sval < fval) {
return sval
}
}
}
}

def drop(n, gen) {
for _ in 1..n { gen() }
}

def squares := genPowers(2)
def cubes := genPowers(3)
def squaresNotCubes := filtered(squares, cubes)
drop(20, squaresNotCubes)
for _ in 1..10 {
print(`\${squaresNotCubes()} `)
}
println()```

## EchoLisp

```(lib 'tasks) ;; for make-generator

;; generator of generators
(define (gen-power power)
(make-generator
(lambda(n) (yield (expt n power)) (1+ n))  1))

(define powers-2 (gen-power 2))
(define powers-3 (gen-power 3))

(take powers-3 10)
→ (1 8 27 64 125 216 343 512 729 1000)

;; generators substraction
;; input : two generators ga, gb - Sequences must be increasing
;; output : new generator  = ga sequence minus gb sequence

(define (gen-substract ga gb)
(define (substract b (a))
(set! a (next ga))
(while (>= a b) ; avance b until > a
(when (= a b) (set! a (next ga)))
(set! b (next gb)))
(yield a)
b ) ;; b := next state
(make-generator substract (next gb)))

;; application
(define task    (gen-substract (gen-power 2) (gen-power 3)))

→ (529 576 625 676 784 841 900 961 1024 1089)

; inspect
```

## Elixir

Translation of: Erlang
```defmodule Generator do
def filter( source_pid, remove_pid ) do
first_remove = next( remove_pid )
spawn( fn -> filter_loop(source_pid, remove_pid, first_remove) end )
end

def next( pid ) do
send(pid, {:next, self})
x -> x
end
end

def power( m ), do: spawn( fn -> power_loop(m, 0) end )

squares_pid = power( 2 )
cubes_pid = power( 3 )
filter_pid = filter( squares_pid, cubes_pid )
for _x <- 1..20, do: next(filter_pid)
for _x <- 1..10, do: next(filter_pid)
end

defp filter_loop( pid1, pid2, n2 ) do
{:next, pid} ->
{n, new_n2} = filter_loop_next( next(pid1), n2, pid1, pid2 )
send( pid, n )
filter_loop( pid1, pid2, new_n2 )
end
end

defp filter_loop_next( n1, n2, pid1, pid2 ) when n1 > n2, do:
filter_loop_next( n1, next(pid2), pid1, pid2 )
defp filter_loop_next( n, n, pid1, pid2 ), do:
filter_loop_next( next(pid1), next(pid2), pid1, pid2 )
defp filter_loop_next( n1, n2, _pid1, _pid2 ), do: {n1, n2}

defp power_loop( m, n ) do
{:next, pid} -> send( pid, round(:math.pow(n, m) ) )
end
power_loop( m, n + 1 )
end
end

```
Output:
```[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
```

## Emacs Lisp

This code requires generator library which was introduced in Emacs 25.2

```;; lexical-binding: t
(require 'generator)

(iter-defun exp-gen (pow)
(let ((i -1))
(while
(setq i (1+ i))
(iter-yield (expt i pow)))))

(iter-defun flt-gen ()
(let* ((g (exp-gen 2))
(f (exp-gen 3))
(i (iter-next g))
(j (iter-next f)))
(while
(setq i (iter-next g))
(while (> i j)
(setq j (iter-next f)))
(unless (= i j)
(iter-yield i)))))

(let ((g (flt-gen))
(o 'nil))
(dotimes (i 29)
(setq o (iter-next g))
(when (>= i 20)
(print o))))
```

## Erlang

```-module( generator ).

-export( [filter/2, next/1, power/1, task/0] ).

filter(	Source_pid, Remove_pid ) ->
First_remove = next( Remove_pid	),
erlang:spawn( fun() -> filter_loop(Source_pid, Remove_pid, First_remove) end ).

next( Pid ) ->
Pid ! {next, erlang:self()},

power( M ) -> erlang:spawn( fun() -> power_loop(M, 0) end ).

Squares_pid = power( 2 ),
Cubes_pid = power( 3 ),
Filter_pid = filter( Squares_pid, Cubes_pid ),
[next(Filter_pid) || _X <- lists:seq(1, 20)],
[next(Filter_pid) || _X <- lists:seq(1, 10)].

filter_loop( Pid1, Pid2, N2 ) ->
{next, Pid} ->
{N, New_N2} = filter_loop_next( next(Pid1), N2, Pid1, Pid2 ),
Pid ! N
end,
filter_loop( Pid1, Pid2, New_N2 ).

filter_loop_next( N1, N2, Pid1, Pid2 ) when N1 > N2 -> filter_loop_next( N1, next(Pid2), Pid1, Pid2 );
filter_loop_next( N, N, Pid1, Pid2 ) -> filter_loop_next( next(Pid1), next(Pid2), Pid1, Pid2 );
filter_loop_next( N1, N2, _Pid1, _Pid2 ) -> {N1, N2}.

power_loop( M, N ) ->
receive	{next, Pid} -> Pid ! erlang:round(math:pow(N, M) ) end,
power_loop( M, N + 1 ).
```
Output:
```31> generator:task().
[529,576,625,676,784,841,900,961,1024,1089]
```

## F#

Translation of: C#
```let m n = Seq.unfold(fun i -> Some(bigint.Pow(i, n), i + 1I)) 0I

let squares = m 2
let cubes = m 3

let (--) orig veto = Seq.where(fun n -> n <> (Seq.find(fun m -> m >= n) veto)) orig

let ``squares without cubes`` = squares -- cubes

Seq.take 10 (Seq.skip 20 (``squares without cubes``))
|> Seq.toList |> printfn "%A"
```
Output:
`[529; 576; 625; 676; 784; 841; 900; 961; 1024; 1089]`

## Factor

Using lazy lists for our generators:

```USING: fry kernel lists lists.lazy math math.functions
prettyprint ;
IN: rosetta-code.generator-exponential

: mth-powers-generator ( m -- lazy-list )
[ 0 lfrom ] dip [ ^ ] curry lmap-lazy ;

: lmember? ( elt list -- ? )
over '[ unswons dup _ >= ] [ drop ] until nip = ;

: 2-not-3-generator ( -- lazy-list )
2 mth-powers-generator
[ 3 mth-powers-generator lmember? not ] <lazy-filter> ;

10 2-not-3-generator 20 [ cdr ] times ltake list>array .
```
Output:
```{ 529 576 625 676 784 841 900 961 1024 1089 }
```

## Fantom

Using closures to implement generators.

```class Main
{
// Create and return a function which generates mth powers when called
|->Int| make_generator (Int m)
{
current := 0
return |->Int|
{
current += 1
return (current-1).pow (m)
}
}

|->Int| squares_without_cubes ()
{
squares := make_generator (2)
cubes := make_generator (3)
c := cubes.call
return |->Int|
{
while (true)
{
s := squares.call
while (c < s) { c = cubes.call }
if (c != s) return s
}
return 0
}
}

Void main ()
{
swc := squares_without_cubes ()
20.times { swc.call } // drop 20 values
10.times // display the next 10
{
echo (swc.call)
}
}
}```
Output:
```529
576
625
676
784
841
900
961
1024
1089
```

## Forth

```\ genexp-rcode.fs   Generator/Exponential for RosettaCode.org

\ Generator/filter implementation using return stack as continuations stack
: ENTER         ( cont.addr --  ;borrowed from M.L.Gasanenko papers)
>R
;
: |             ( f --  ;true->go ahead, false->return into generator )
IF EXIT THEN R> DROP
;
: GEN           ( --  ;generate forever what is between 'GEN' and ';' )
BEGIN R@ ENTER AGAIN
;
: STOP          ( f --  ;return to caller of word that contain 'GEN' )
IF R> DROP R> DROP R> DROP THEN
;

\ Problem at hand
: square        ( n -- n^2 )    dup * ;
: cube          ( n -- n^3 )    dup square * ;

\ Faster tests using info that tested numbers are monotonic growing
VARIABLE Sqroot         \ last square root
VARIABLE Cbroot         \ last cubic  root
: square?       ( u -- f  ;test U for square number)
BEGIN
Sqroot @ square over <
WHILE
1 Sqroot +!
REPEAT
Sqroot @ square =
;
: cube?         ( u -- f  ;test U for cubic  number)
BEGIN
Cbroot @ cube over <
WHILE
1 Cbroot +!
REPEAT
Cbroot @ cube =
;
VARIABLE Counter
: (go)  ( u -- u' )
GEN 1+ Counter @ 30 >= STOP
dup square? | dup cube? 0= | Counter @ 20 >= 1 Counter +! | dup .
;
:noname 0 Counter ! 1 Sqroot ! 1 Cbroot ! 0 (go) drop ;
execute cr bye
```
Output:
```\$ gforth -e "include genexp-rcode.fs"
529 576 625 676 784 841 900 961 1024 1089
\$
```

## FreeBASIC

Translation of: VBA
```Dim Shared As Long lastsquare, nextsquare, lastcube, midcube, nextcube

Function squares() As Long
lastsquare += nextsquare
nextsquare += 2
squares = lastsquare
End Function

Function cubes() As Long
lastcube += nextcube
nextcube += midcube
midcube += 6
cubes = lastcube
End Function

lastsquare = 1 : nextsquare = -1 : lastcube = -1 : midcube = 0 : nextcube = 1
Dim As Long cube, square
cube = cubes

For i As Byte = 1 To 30
Do
square = squares
Do While cube < square
cube = cubes
Loop
If square <> cube Then Exit Do
Loop
If i > 20 Then Print square;
Next i
Sleep
```
Output:
```Igual que la entrada de VBA.
```

## FunL

(for the powers function)
Translation of: Scala
(for the filter)
```def powers( m ) = map( (^ m), 0.. )

def
filtered( s@sh:_, ch:ct ) | sh > ch = filtered( s, ct )
filtered( sh:st, c@ch:_ ) | sh < ch = sh # filtered( st, c )
filtered( _:st, c ) = filtered( st, c )

println( filtered(powers(2), powers(3)).drop(20).take(10) )```
Output:
```[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
```

## Go

Most direct and most efficient on a single core is implementing generators with closures.

```package main

import (
"fmt"
"math"
)

// note: exponent not limited to ints
func newPowGen(e float64) func() float64 {
var i float64
return func() (r float64) {
r = math.Pow(i, e)
i++
return
}
}

// given two functions af, bf, both monotonically increasing, return a
// new function that returns values of af not returned by bf.
func newMonoIncA_NotMonoIncB_Gen(af, bf func() float64) func() float64 {
a, b := af(), bf()
return func() (r float64) {
for {
if a < b {
r = a
a = af()
break
}
if b == a {
a = af()
}
b = bf()
}
return
}
}

func main() {
fGen := newMonoIncA_NotMonoIncB_Gen(newPowGen(2), newPowGen(3))
for i := 0; i < 20; i++ {
fGen()
}
for i := 0; i < 10; i++ {
fmt.Print(fGen(), " ")
}
fmt.Println()
}
```
Output:
```529 576 625 676 784 841 900 961 1024 1089
```

Alternatively, generators can be implemented in Go with goroutines and channels. There are tradeoffs however, and often one technique is a significantly better choice.

Goroutines can run concurrently, but there is overhead associated with thread scheduling and channel communication. Flow control is also different. A generator implemented as a closure is a function with a single entry point fixed at the beginning. On repeated calls, execution always starts over at the beginning and ends when a value is returned. A generator implemented as a goroutine, on the other hand, "returns" a value by sending it on a channel, and then the goroutine continues execution from that point. This allows more flexibility in structuring code.

```package main

import (
"fmt"
"math"
)

func newPowGen(e float64) chan float64 {
ch := make(chan float64)
go func() {
for i := 0.; ; i++ {
ch <- math.Pow(i, e)
}
}()
return ch
}

// given two input channels, a and b, both known to return monotonically
// increasing values, supply on channel c values of a not returned by b.
func newMonoIncA_NotMonoIncB_Gen(a, b chan float64) chan float64 {
ch := make(chan float64)
go func() {
for va, vb := <-a, <-b; ; {
switch {
case va < vb:
ch <- va
fallthrough
case va == vb:
va = <-a
default:
vb = <-b

}
}
}()
return ch
}

func main() {
ch := newMonoIncA_NotMonoIncB_Gen(newPowGen(2), newPowGen(3))
for i := 0; i < 20; i++ {
<-ch
}
for i := 0; i < 10; i++ {
fmt.Print(<-ch, " ")
}
fmt.Println()
}
```

Generators in most cases can be implemented using infinite lists in Haskell. Because Haskell is lazy, only as many elements as needed is computed from the infinite list:

```import Data.List.Ordered

powers :: Int -> [Int]
powers m = map (^ m) [0..]

squares :: [Int]
squares = powers 2

cubes :: [Int]
cubes = powers 3

foo :: [Int]
foo = filter (not . has cubes) squares

main :: IO ()
main = print \$ take 10 \$ drop 20 foo
```
Output:
`[529,576,625,676,784,841,900,961,1024,1089]`

## Icon and Unicon

Generators are close to the heart and soul of Icon/Unicon. Co-expressions let us circumvent the normal backtracking mechanism and get results where we need them.

```procedure main()

write("Non-cube Squares (21st to 30th):")
every (k := 0, s := noncubesquares()) do
if(k +:= 1) > 30 then break
else write(20 < k," : ",s)
end

procedure mthpower(m)   #: generate i^m for i = 0,1,...
while (/i := 0) | (i +:= 1) do suspend i^m
end

procedure noncubesquares()  #: filter for squares that aren't cubes
cu := create mthpower(3)    # co-expressions so that we can
sq := create mthpower(2)    # ... get our results where we need

repeat {
if c === s then  ( c := @cu , s := @sq )
else if s > c then c := @cu
else {
suspend s
s := @sq
}
}
end
```

Note: The task could be written without co-expressions but would be likely be ugly. If there is an elegant non-co-expression version please add it as an alternate example.

Output:
```Non-cube Squares (21st to 30th):
21 : 529
22 : 576
23 : 625
24 : 676
25 : 784
26 : 841
27 : 900
28 : 961
29 : 1024
30 : 1089```

## J

Generators are not very natural, in J, because they avoid the use of arrays and instead rely on sequential processing.

Here is a generator for mth powers of a number:

```coclass 'mthPower'
N=: 0
create=: 3 :0
M=: y
)
next=: 3 :0
n=. N
N=: N+1
n^M
)
```

And, here are corresponding square and cube generators

```stateySquare=: 2 conew 'mthPower'
stateyCube=: 3 conew 'mthPower'
```

Here is a generator for squares which are not cubes:

```coclass 'uncubicalSquares'
N=: 0
next=: 3 :0"0
while. (-: <.) 3 %: *: n=. N do. N=: N+1 end. N=: N+1
*: n
)
```

And here is an example of its use:

```   next__g i.10 [ next__g i.20 [ g=: conew 'uncubicalSquares'
529 576 625 676 784 841 900 961 1024 1089
```

That said, here is a more natural approach, for J.

```mthPower=: 1 :'^&m@i.'
squares=: 2 mthPower
cubes=: 3 mthPower
uncubicalSquares=: squares -. cubes
```

The downside of this approach is that it is computing independent sequences. And for the "uncubicalSquares" verb, it is removing some elements from that sequence. So you must estimate how many values to generate. However, this can be made transparent to the user with a simplistic estimator:

```uncubicalSquares=: {. squares@<.@p.~&3 1.1 -. cubes
```

Example use:

```20 }. uncubicalSquares 30 NB. the 21st through 30th uncubical square
529 576 625 676 784 841 900 961 1024 1089
```

## Java

Works with: java version 8
```import java.util.function.LongSupplier;
import static java.util.stream.LongStream.generate;

public class GeneratorExponential implements LongSupplier {
private LongSupplier source, filter;
private long s, f;

public GeneratorExponential(LongSupplier source, LongSupplier filter) {
this.source = source;
this.filter = filter;
f = filter.getAsLong();
}

@Override
public long getAsLong() {
s = source.getAsLong();

while (s == f) {
s = source.getAsLong();
f = filter.getAsLong();
}

while (s > f) {
f = filter.getAsLong();
}

return s;
}

public static void main(String[] args) {
generate(new GeneratorExponential(new SquaresGen(), new CubesGen()))
.skip(20).limit(10)
.forEach(n -> System.out.printf("%d ", n));
}
}

class SquaresGen implements LongSupplier {
private long n;

@Override
public long getAsLong() {
return n * n++;
}
}

class CubesGen implements LongSupplier {
private long n;

@Override
public long getAsLong() {
return n * n * n++;
}
}
```
`529 576 625 676 784 841 900 961 1024 1089`

## JavaScript

### Procedural

```function PowersGenerator(m) {
var n=0;
while(1) {
yield Math.pow(n, m);
n += 1;
}
}

function FilteredGenerator(g, f){
var value = g.next();
var filter = f.next();

while(1) {
if( value < filter ) {
yield value;
value = g.next();
} else if ( value > filter ) {
filter = f.next();
} else {
value = g.next();
filter = f.next();
}
}
}

var squares = PowersGenerator(2);
var cubes = PowersGenerator(3);

var filtered = FilteredGenerator(squares, cubes);

for( var x = 0; x < 20; x++ ) filtered.next()
for( var x = 20; x < 30; x++ ) console.logfiltered.next());
```

#### ES6

```function* nPowerGen(n) {
let e = 0;
while (1) { e++ && (yield Math.pow(e, n)); }
}

function* filterGen(gS, gC, skip=0) {
let s = 0; // The square value
let c = 0; // The cube value
let n = 0; // A skip counter

while(1) {
s = gS.next().value;
s > c && (c = gC.next().value);
s == c ?
c = gC.next().value :
n++ && n > skip && (yield s);
}
}

const filtered = filterGen(nPowerGen(2), nPowerGen(3), skip=20);
```
```// Generate the first 10 values
for (let n = 0; n < 10; n++) {
console.log(filtered.next().value)
}
```
```529
576
625
676
784
841
900
961
1024
1089```

### Functional

#### ES6

Compositional derivation of custom generators:

Translation of: Python
```(() => {
'use strict';

// main :: IO()
const main = () => {

// powers :: Gen [Int]
const powers = n =>
fmapGen(
x => Math.pow(x, n),
enumFrom(0)
);

// xs :: [Int]
const xs = take(10, drop(20,
differenceGen(
powers(2),
powers(3)
)
));

console.log(xs);
// -> [529,576,625,676,784,841,900,961,1024,1089]
};

// GENERIC FUNCTIONS ----------------------------------

// Just :: a -> Maybe a
const Just = x => ({
type: 'Maybe',
Nothing: false,
Just: x
});

// Nothing :: Maybe a
const Nothing = () => ({
type: 'Maybe',
Nothing: true,
});

// Tuple (,) :: a -> b -> (a, b)
const Tuple = (a, b) => ({
type: 'Tuple',
'0': a,
'1': b,
length: 2
});

// differenceGen :: Gen [a] -> Gen [a] -> Gen [a]
function* differenceGen(ga, gb) {
// All values of generator stream a except any
// already seen in generator stream b.
const
stream = zipGen(ga, gb),
sb = new Set([]);
let xy = take(1, stream);
while (0 < xy.length) {
const [x, y] = Array.from(xy);
if (!sb.has(x)) yield x;
xy = take(1, stream);
}
};

// drop :: Int -> [a] -> [a]
// drop :: Int -> Generator [a] -> Generator [a]
// drop :: Int -> String -> String
const drop = (n, xs) =>
Infinity > length(xs) ? (
xs.slice(n)
) : (take(n, xs), xs);

// enumFrom :: Enum a => a -> [a]
function* enumFrom(x) {
let v = x;
while (true) {
yield v;
v = 1 + v;
}
}

// fmapGen <\$> :: (a -> b) -> Gen [a] -> Gen [b]
function* fmapGen(f, gen) {
let v = take(1, gen);
while (0 < v.length) {
yield(f(v))
v = take(1, gen)
}
}

// fst :: (a, b) -> a
const fst = tpl => tpl;

// Returns Infinity over objects without finite length.
// This enables zip and zipWith to choose the shorter
// argument when one is non-finite, like cycle, repeat etc

// length :: [a] -> Int
const length = xs =>
(Array.isArray(xs) || 'string' === typeof xs) ? (
xs.length
) : Infinity;

// snd :: (a, b) -> b
const snd = tpl => tpl;

// take :: Int -> [a] -> [a]
// take :: Int -> String -> String
const take = (n, xs) =>
'GeneratorFunction' !== xs.constructor.constructor.name ? (
xs.slice(0, n)
) : [].concat.apply([], Array.from({
length: n
}, () => {
const x = xs.next();
return x.done ? [] : [x.value];
}));

// uncons :: [a] -> Maybe (a, [a])
const uncons = xs => {
const lng = length(xs);
return (0 < lng) ? (
lng < Infinity ? (
Just(Tuple(xs, xs.slice(1))) // Finite list
) : (() => {
const nxt = take(1, xs);
return 0 < nxt.length ? (
Just(Tuple(nxt, xs))
) : Nothing();
})() // Lazy generator
) : Nothing();
};

// zipGen :: Gen [a] -> Gen [b] -> Gen [(a, b)]
const zipGen = (ga, gb) => {
function* go(ma, mb) {
let
a = ma,
b = mb;
while (!a.Nothing && !b.Nothing) {
let
ta = a.Just,
tb = b.Just
yield(Tuple(fst(ta), fst(tb)));
a = uncons(snd(ta));
b = uncons(snd(tb));
}
}
return go(uncons(ga), uncons(gb));
};

// MAIN ---
return main();
})();
```
Output:
`[529,576,625,676,784,841,900,961,1024,1089]`

## jq

Works with: jq version 1.4

Part 1: i^m, 2^m and 3^m

jq is a purely functional language and so does not have generators with state. To generate a sequence of values one-by-one therefore requires a "next-value" function, the input of which must include relevant state information. For convenience, a counter is usually included. For generating i^m, therefore, we would have:

```# Compute self^m where m is a non-negative integer:
def pow(m): . as \$in | reduce range(0;m) as \$i (1; .*\$in);

# state: [i, i^m]
def next_power(m): . + 1 | [., pow(m) ];```

To make such generators easier to use, we shall define filters to skip and to emit a specified number of items:

```# skip m states, and return the next state
def skip(m; next):
if m <= 0 then . else next | skip(m-1; next) end;

# emit m states including the initial state
def emit(m; next):
if m <= 0 then empty else ., (next | emit(m-1; next)) end;```

Examples:

```# Generate the first 4 values in the sequence i^2:
[0,0] | emit(4; next_power(2)) | .

# Generate all the values in the sequence i^3 less than 100:
[0,0] | recurse(next_power(3) | if . < 100 then . else empty end) | .```

An aside on streams

Since the release of version jq 1.4, enhancements for processing streams of values have been added, notably "foreach" and "limit". If your version of jq has these enhancements, then it is often preferable to use them in conjunction with functions that emit streams of values rather than the "next-value" functions that are the focus of this page.

Part 2: selection from 2 ^ m

```# Infrastructure:
def last(f): reduce f as \$i (null; \$i);

# emit the last value that satisfies condition, or null
def while(condition; next):
def w: if condition then ., (next|w) else empty end;
last(w);

# Powers of m1 that are not also powers of m2.
# filtered_next_power(m1;m2) produces [[i, i^m1], [j, j^m1]] where i^m1
# is not a power of m2 and j^m2 < i^m1
#
def filtered_next_power(m1; m2):
if . then . else [[0,0],[0,0]] end
| (. | next_power(m1)) as \$next1
| (. | while( . <= \$next1; next_power(m2))) as \$next2
| if \$next1 == \$next2
then [\$next1, \$next2] | filtered_next_power(m1;m2)
else [\$next1, \$next2]
end ;

# Emit ten powers of 2 that are NOT powers of 3,
# skipping the first 20 integers satisfying the condition, including 0.
filtered_next_power(2;3)
| skip(20; filtered_next_power(2;3))
| emit(10; filtered_next_power(2;3))
| .```
Output:
```\$ jq -n -f generators.jq
529
576
625
676
784
841
900
961
1024
1089
```

## Julia

The task can be achieved by using closures, iterators or tasks. Here is a solution using anonymous functions and closures.

```drop(gen::Function, n::Integer) = (for _ in 1:n gen() end; gen)
take(gen::Function, n::Integer) = collect(gen() for _ in 1:n)

function pgen(n::Number)
x = 0
return () -> (x += 1) ^ n
end

function genfilter(g1::Function, g2::Function)
local r1
local r2 = g2()
return () -> begin
r1 = g1()
while r2 <  r1 r2 = g2() end
while r1 == r2 r1 = g1() end
return r1
end
end

@show take(drop(genfilter(pgen(2), pgen(3)), 20), 10)
```
Output:
`take(drop(genfilter(pgen(2), pgen(3)), 20), 10) = [529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]`

## Kotlin

Coroutines were introduced in version 1.1 of Kotlin but, as yet, are an experimental feature:

```// version 1.1.0
// compiled with flag -Xcoroutines=enable to suppress 'experimental' warning

import kotlin.coroutines.experimental.buildSequence

fun generatePowers(m: Int) =
buildSequence {
var n = 0
val mm = m.toDouble()
while (true) yield(Math.pow((n++).toDouble(), mm).toLong())
}

fun generateNonCubicSquares(squares: Sequence<Long>, cubes: Sequence<Long>) =
buildSequence {
val iter2 = squares.iterator()
val iter3 = cubes.iterator()
var square = iter2.next()
var cube = iter3.next()
while (true) {
if (square > cube) {
cube = iter3.next()
continue
} else if (square < cube) {
yield(square)
}
square = iter2.next()
}
}

fun main(args: Array<String>) {
val squares = generatePowers(2)
val cubes = generatePowers(3)
val ncs = generateNonCubicSquares(squares, cubes)
print("Non-cubic squares (21st to 30th) : ")
ncs.drop(20).take(10).forEach { print("\$it ") } // print 21st to 30th items
println()
}
```
Output:
```Non-cubic squares (21st to 30th) : 529 576 625 676 784 841 900 961 1024 1089
```

## Lingo

Lingo neither supports coroutines nor first-class functions, and also misses syntactic sugar for implementing real generators. But in the context of for or while loops, simple pseudo-generator objects that store states internally and manipulate data passed by reference can be used to implement generator-like behavior and solve the given task.

```squares = script("generator.power").new(2)
cubes   = script("generator.power").new(3)
filter  = script("generator.filter").new(squares, cubes)
filter.skip(20)
res = []
i = 0
repeat while filter.exec(res)
i = i + 1
if i>10 then exit repeat
put res
end repeat```
Output:
```-- 529
-- 576
-- 625
-- 676
-- 784
-- 841
-- 900
-- 961
-- 1024
-- 1089
```

Parent script "generator.power"

```property _exp
property _index

-- @constructor
on new (me, e)
me._exp = e
me._index = 0
return me
end

on exec (me, input)
me._index = me._index+1
input = integer(power(me._index, me._exp))
return TRUE
end

on skip (me, steps)
me._index = me._index + steps
end

on reset (me)
me._index = 0
end```

Parent script "generator.filter"

```property _genv
property _genf

-- @constructor
on new (me, genv, genf)
me._genv = genv
me._genf = genf
return me
end

on exec (me, input)
repeat while TRUE
me._genv.exec(input)
v = input
ok = TRUE
me._genf.reset() -- reset filter generator
repeat while TRUE
me._genf.exec(input)
f = input
if f>v then exit repeat
if f=v then
ok=FALSE
exit repeat
end if
end repeat
if ok then
input = v
exit repeat
end if
end repeat
return TRUE
end

on skip (me, steps)
repeat with i = 1 to steps
me.exec([])
end repeat
end

on reset (me)
me._genv.reset()
me._genf.reset()
end```

## Lua

Generators can be implemented both as closures and as coroutines. The following example demonstrates both.

```--could be done with a coroutine, but a simple closure works just as well.
local function powgen(m)
local count = 0
return function()
count = count + 1
return count^m
end
end

local squares = powgen(2)
local cubes = powgen(3)

local cowrap,coyield = coroutine.wrap, coroutine.yield

local function filter(f,g)
return cowrap(function()
local ff,gg = f(), g()
while true do
if ff == gg then
ff,gg = f(), g()
elseif ff < gg then
coyield(ff)
ff = f()
else
gg = g()
end
end
end)
end

filter = filter(squares,cubes)

for i = 1,30 do
local result = filter()
if i > 20 then
print(result)
end
end
```

## M2000 Interpreter

```Module Generator {
PowGen = Lambda (e)
-> {
= Lambda
i=0, // closure
e // closure
-> {
i++
= i**e
}
}
Squares=Lambda
PowGen=PowGen(2)  // closure
->{
= PowGen()
}
Cubes=Lambda
PowGen=PowGen(3) // closure
-> {
= PowGen()
}
Filter=Lambda
z=Squares(), // closure
Squares, // closure
m, // closure
Cubes // closure
->{
while m<z :m=cubes():end while
if z=m then z=Squares()
= z :  z=Squares()
}
For i=1 to 20 : dropit=Filter() :Next i
Document doc\$="Non-cubic squares (21st to 30th)"
Print doc\$
doc\$={
}       \\ a new line to doc\$
For i=1 to  10
f=Filter()
Print Format\$("I: {0::-2}, F: {1}",i+20, f)
doc\$=Format\$("I: {0::-2}, F: {1}",i+20, f)+{
}
Next
Clipboard doc\$
}
Generator```
Output:
```Non-cubic squares (21st to 30th)
I: 21, F: 529
I: 22, F: 576
I: 23, F: 625
I: 24, F: 676
I: 25, F: 784
I: 26, F: 841
I: 27, F: 900
I: 28, F: 961
I: 29, F: 1024
I: 30, F: 1089
```

## Mathematica / Wolfram Language

Translation of: VBA

Generators are not very natural in Mathemetica, because they avoid the use of lists and instead rely on sequential processing.

```lastsquare = 1;
nextsquare = -1;
lastcube = -1;
midcube = 0;
nextcube = 1;
Gensquares[] := Module[{},
lastsquare += nextsquare;
nextsquare += 2;
squares = lastsquare;
squares
]
Gencubes[] := Module[{},
lastcube += nextcube;
nextcube += midcube;
midcube += 6;
cubes = lastcube
]

c = Gencubes[];
Do[
While[True,
s = Gensquares[];
While[c < s,
c = Gencubes[];
];
If[s =!= c,
Break[]
];
];
If[i > 20,
Print[s]
]
,
{i, 30}
]
```
Output:
```529
576
625
676
784
841
900
961
1024
1089```

## Nim

```type Iterator = iterator(): int

proc `^`*(base: Natural; exp: Natural): int =
var (base, exp) = (base, exp)
result = 1
while exp != 0:
if (exp and 1) != 0:
result *= base
exp = exp shr 1
base *= base

proc next(s: Iterator): int =
for n in s(): return n

proc powers(m: Natural): Iterator =
iterator it(): int {.closure.} =
for n in 0 ..< int.high:
yield n ^ m
result = it

iterator filtered(s1, s2: Iterator): int =
var v = next(s1)
var f = next(s2)
while true:
if v > f:
f = next(s2)
continue
elif v < f:
yield v
v = next(s1)

var
squares = powers(2)
cubes = powers(3)
i = 1
for x in filtered(squares, cubes):
if i > 20: echo x
if i >= 30: break
inc i
```
Output:
```529
576
625
676
784
841
900
961
1024
1089```

## OCaml

Original version by User:Vanyamil

```(*  Task : Generator/Exponential

Version using the Seq module types, but transparently
*)

(*** Helper functions ***)

(* Generator type *)
type 'a gen = unit -> 'a node
and 'a node = Nil | Cons of 'a * 'a gen

(* Power function on integers *)
let power (base : int) (exp : int) : int =
let rec helper exp acc =
if exp = 0 then acc
else helper (exp - 1) (base * acc)
in
helper exp 1

(* Take (at most) n from generator *)
let rec take (n : int) (gen : 'a gen) : 'a list =
if n = 0 then []
else
match gen () with
| Nil -> []
| Cons (x, tl) -> x :: take (n - 1) tl

(* Stop existing generator at a given condition *)
let rec keep_while (p : 'a -> bool) (gen : 'a gen) : 'a gen = fun () ->
match gen () with
| Nil -> Nil
| Cons (x, tl) ->
if p x then Cons (x, keep_while p tl)
else Nil

(* Drop the first n elements of a generator *)
let rec drop (n : int) (gen : 'a gen) : 'a gen =
if n = 0 then gen
else
match gen () with
| Nil -> (fun () -> Nil)
| Cons (_, tl) -> drop (n - 1) tl

(* Filter based on predicate, lazily *)
let rec filter (p : 'a -> bool) (gen : 'a gen) : 'a gen = fun () ->
match gen () with
| Nil -> Nil
| Cons (x, tl) ->
if p x then Cons (x, filter p tl)
else filter p tl ()

(* Is this value inside this generator? Does not terminate for infinite streams! *)
let rec mem (val_ : 'a) (gen : 'a gen) : bool =
match gen () with
| Nil -> false
| Cons (x, tl) ->
if x = val_ then true
else mem val_ tl

(*  Create a function that returns a generation of the m'th powers of the positive integers
starting from zero, in order, and without obvious or simple upper limit.
(Any upper limit to the generator should not be stated in the source but should be down
to factors such as the languages natural integer size limit or computational time/size).
*)
let power_gen k : int gen =
let rec generator n () =
Cons (power n k, generator (n + 1))
in
generator 0

(* Use it to create generators of squares and cubes *)
let squares = power_gen 2
let cubes = power_gen 3

(* Create a new generator that filters all cubes from the generator of squares. *)
let squares_no_cubes =
let filter_p square =
(* Get all cubes up to square *)
let cubes_up_to_n2 = keep_while ((>=) square) cubes in
not (mem square cubes_up_to_n2)
in
filter filter_p squares

(*** Output ***)

(* Drop the first 20 values from this last generator of filtered results, and then show the next 10 values. *)
let _ =
squares_no_cubes |> drop 20 |> take 10
```
Output:
```- : int list = [529; 576; 625; 676; 784; 841; 900; 961; 1024; 1089]
```

## PARI/GP

Define two generator functions genpow() and genpow2().

```g = List(1);		\\ generator stack

genpow(p) = my(a=g++);listput(g,[0,p]);()->g[a]++^g[a];

genpowf(p,f) = my(a=g++);listput(g,[0,p]);(s=0)->my(q);while(ispower(p=g[a]++^g[a],f)||(s&&q++<=s),);p;```

genpow(power) returns a function that returns a simple power generator.
genpowf(power,filter) returns a function thats returns a filtered power generator. This generator accepts an optional skip-parameter.

Create simple power generators:

```gp > squares = genpow(2);
gp > cubes = genpow(3);
gp > cubes()
1
gp > cubes()
8
gp > squares()
1
gp > squares()
4
gp > cubes()
27
gp > squares()
9```

Create filtered power generator, skip first 20 results and print next 10 values:

```gp > powf2 = genpowf(2,3);
gp > print(powf2(20)); for(i=1,9,print(powf2()))
529
576
625
676
784
841
900
961
1024
1089```

## Perl

These generators are anonymous subroutines, which are closures.

```# gen_pow(\$m) creates and returns an anonymous subroutine that will
# generate and return the powers 0**m, 1**m, 2**m, ...
sub gen_pow {
my \$m = shift;
my \$e = 0;
return sub { return \$e++ ** \$m; };
}

# gen_filter(\$g1, \$g2) generates everything returned from \$g1 that
# is not also returned from \$g2. Both \$g1 and \$g2 must be references
# to subroutines that generate numbers in increasing order. gen_filter
# creates and returns an anonymous subroutine.
sub gen_filter {
my(\$g1, \$g2) = @_;
my \$v1;
my \$v2 = \$g2->();
return sub {
for (;;) {
\$v1 = \$g1->();
\$v2 = \$g2->() while \$v1 > \$v2;
return \$v1 unless \$v1 == \$v2;
}
};
}

# Create generators.
my \$squares = gen_pow(2);
my \$cubes = gen_pow(3);
my \$squares_without_cubes = gen_filter(\$squares, \$cubes);

# Drop 20 values.
\$squares_without_cubes->() for (1..20);

# Print 10 values.
print "[", join(", ", @answer), "]\n";
```
Output:
`[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]`

## Phix

```--
-- demo\rosetta\Generator_Exponential.exw
-- ======================================
--
bool terminate = false

atom res

procedure powers(integer p)
integer i=0
while not terminate do
res = power(i,p)
i += 1
end while
end procedure

atom square, cube
cube = res
for i=1 to 30 do
while 1 do
square = res
while cube<square do
cube = res
end while
if square!=cube then exit end if
end while
if i>20 then
?square
end if
end for

terminate = 1
{} = wait_key()
```
Output:
```529
576
625
676
784
841
900
961
1024
1089
```

## PHP

Translation of: Python
Works with: PHP version 5.5+
```<?php
function powers(\$m) {
for (\$n = 0; ; \$n++) {
yield pow(\$n, \$m);
}
}

function filtered(\$s1, \$s2) {
while (true) {
list(\$v, \$f) = [\$s1->current(), \$s2->current()];
if (\$v > \$f) {
\$s2->next();
continue;
} else if (\$v < \$f) {
yield \$v;
}
\$s1->next();
}
}

list(\$squares, \$cubes) = [powers(2), powers(3)];
\$f = filtered(\$squares, \$cubes);
foreach (range(0, 19) as \$i) {
\$f->next();
}
foreach (range(20, 29) as \$i) {
echo \$i, "\t", \$f->current(), "\n";
\$f->next();
}
?>
```
Output:
```20	529
21	576
22	625
23	676
24	784
25	841
26	900
27	961
28	1024
29	1089
```

## PicoLisp

Coroutines are available only in the 64-bit version.

```(de powers (M)
(co (intern (pack 'powers M))
(for (I 0 (inc 'I))
(yield (** I M)) ) ) )

(de filtered (N M)
(co 'filtered
(let (V (powers N)  F (powers M))
(loop
(if (> V F)
(setq F (powers M))
(and (> F V) (yield V))
(setq V (powers N)) ) ) ) ) )

(do 20 (filtered 2 3))
(do 10 (println (filtered 2 3)))```
Output:
```529
576
625
676
784
841
900
961
1024
1089```

## PL/I

```Generate: procedure options (main);   /* 27 October 2013 */
declare j fixed binary;
declare r fixed binary;

/* Ignore the first 20 values */
do j = 1 to 20;
/* put edit (filter() ) (f(6)); */
r = filter ();
end;
put skip;
do j = 1 to 10;
put edit (filter() ) (f(6));
end;

/* filters out cubes from the result of the square generator. */
filter: procedure returns (fixed binary);
declare n fixed binary static initial (-0);
declare (i, j, m) fixed binary;

do while ('1'b);
m = squares();
r = 0;
do j = 1 to m;
if m = cubes() then go to ignore;
end;
return (m);
ignore:
end;
end filter;

squares: procedure returns (fixed binary);
declare i fixed binary static initial (-0);

i = i + 1;
return (i**2);
end squares;

cubes: procedure returns (fixed binary);

r = r + 1;
return (r**3);
end cubes;

end Generate;```
```20 dropped values:
4     9    16    25    36    49    81   100   121   144   169   196   225
256   289   324   361   400   441   484

Next 10 values:
529   576   625   676   784   841   900   961  1024  1089
```

## Python

In Python, any function that contains a yield statement becomes a generator. The standard libraries itertools module provides the following functions used in the solution: count, that will count up from zero; and islice, which will take a slice from an iterator/generator.

Works with: Python version 2.6+ and 3.x
(in versions prior to 2.6, replace `next(something)` with `something.next()`)
```from itertools import islice, count

def powers(m):
for n in count():
yield n ** m

def filtered(s1, s2):
v, f = next(s1), next(s2)
while True:
if v > f:
f = next(s2)
continue
elif v < f:
yield v
v = next(s1)

squares, cubes = powers(2), powers(3)
f = filtered(squares, cubes)
print(list(islice(f, 20, 30)))
```
Output:
`[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]`

Or, deriving custom generators compositionally:

Works with: Python version 3.7
```'''Exponentials as generators'''

from itertools import count, islice

# powers :: Gen [Int]
def powers(n):
'''A non-finite succession of integers,
starting at zero,
raised to the nth power.'''

def f(x):
return pow(x, n)

return map(f, count(0))

# main :: IO ()
def main():
'''Taking the difference between two derived generators.'''
print(
take(10)(
drop(20)(
differenceGen(powers(2))(
powers(3)
)
)
)
)

# GENERIC -------------------------------------------------

# differenceGen :: Gen [a] -> Gen [a] -> Gen [a]
def differenceGen(ga):
'''All values of ga except any
def go(a, b):
stream = zip(a, b)
bs = set([])
while True:
xy = next(stream, None)
if None is not xy:
x, y = xy
if x not in bs:
yield x
else:
return
return lambda gb: go(ga, gb)

# drop :: Int -> [a] -> [a]
# drop :: Int -> String -> String
def drop(n):
'''The sublist of xs beginning at
(zero-based) index n.'''
def go(xs):
if isinstance(xs, list):
return xs[n:]
else:
take(n)(xs)
return xs
return lambda xs: go(xs)

# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
'''The prefix of xs of length n,
or xs itself if n > length xs.'''
return lambda xs: (
xs[0:n]
if isinstance(xs, list)
else list(islice(xs, n))
)

# MAIN ---
if __name__ == '__main__':
main()
```
Output:
`[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]`

## Quackery

```  [ ' [ this -1 peek
this -2 peek **
1 this tally
done ]
swap join
0 join ]                         is expogen (   n --> [ )

[ ' [ this temp put
temp share -3 peek do
dup temp share share = iff
[ drop
temp share -2 peek do
temp take replace ] again
[ dup temp share share > iff
[ temp share -2 peek do
temp share replace ]
again ]
temp release
done ]
unrot
dip nested
dup dip nested
do 3 times join ]                 is taskgen ( [ [ --> [ )

2 expogen

20 times [ dup do drop ]
10 times [ dup do echo sp ]
drop```
Output:
`529 576 625 676 784 841 900 961 1024 1089 `

## R

```powers = function(m)
{n = -1
function()
{n <<- n + 1
n^m}}

noncubic.squares = local(
{squares = powers(2)
cubes = powers(3)
cube = cubes()
function()
{square = squares()
while (1)
{if (square > cube)
{cube <<- cubes()
next}
else if (square < cube)
{return(square)}
else
{square = squares()}}}})

for (i in 1:20)
noncubic.squares()
for (i in 1:10)
message(noncubic.squares())
```

## Racket

```#lang racket

(require racket/generator)

;; this is a function that returns a powers generator, not a generator
(define (powers m)
(generator ()
(for ([n (in-naturals)]) (yield (expt n m)))))

(define squares (powers 2))
(define cubes   (powers 3))

;; same here
(define (filtered g1 g2)
(generator ()
(let loop ([n1 (g1)] [n2 (g2)])
(cond [(< n1 n2) (yield n1) (loop (g1) n2)]
[(> n1 n2) (loop n1 (g2))]
[else (loop (g1) (g2))]))))

(for/list ([x (in-producer (filtered squares cubes) (lambda (_) #f))]
[i 30] #:when (>= i 20))
x)
```
Output:
```'(529 576 625 676 784 841 900 961 1024 1089)
```

## Raku

(formerly Perl 6)

As with Haskell, generators are disguised as lazy lists in Raku.

```sub powers(\$m) { 0..* X** \$m }

my @squares = powers(2);
my @cubes   = powers(3);

sub infix:<with-out> (@orig, @veto) {
gather for @veto -> \$veto {
take @orig.shift while @orig before \$veto;
@orig.shift if @orig eqv \$veto;
}
}

say (@squares with-out @cubes)[20 ..^ 20+10].join(', ');
```
Output:
`529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089`

## REXX

The generators   (below, the   Gxxxxx   functions)   lie dormant until a request is made for a specific generator index.

```/*REXX program demonstrates how to use a  generator  (also known as an  iterator).      */
parse arg N .;   if N=='' |  N==","  then N=20   /*N  not specified?   Then use default.*/
@.=                                              /* [↓]  calculate squares,cubes,pureSq.*/
do i=1  for N;   call Gsquare     i
call Gcube       i
call GpureSquare i     /*these are  cube─free  square numbers.*/
end   /*i*/

do k=1  for N;  @.pureSquare.k=;  end /*k*/ /*this is used to drop  1st  N  values.*/

w=length(N+10);               ps= 'pure square'  /*the width of the numbers;  a literal.*/

do m=N+1  for 10;    say ps   right(m, w)":"     right(GpureSquare(m), 3*w)
end       /*m*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Gpower:      procedure expose @.;       parse arg x,p;   q=@.pow.x.p
if q\==''  then return q;  _=x**p;          @.pow.x.p=_
return _
/*──────────────────────────────────────────────────────────────────────────────────────*/
Gsquare:     procedure expose @.;       parse arg x;     q=@.square.x
if q==''  then @.square.x=Gpower(x, 2)
return @.square.x
/*──────────────────────────────────────────────────────────────────────────────────────*/
Gcube:       procedure expose @.;       parse arg x;     q=@.cube.x
if q==''  then @.cube.x=Gpower(x, 3)        _=@.cube.x;     @.3pow._=1
return @.cube.x
/*──────────────────────────────────────────────────────────────────────────────────────*/
GpureSquare: procedure expose @.;       parse arg x;     q=@.pureSquare.x
if q\==''  then return q
#=0
do j=1  until #==x;  ?=Gpower(j, 2)        /*search for pure square. */
if @.3pow.?==1  then iterate               /*is it a power of three? */
#=#+1;               @.pureSquare.#=?      /*assign next pureSquare. */
end   /*j*/
return @.pureSquare.x
```

output   when using the default value:

```pure square 21:    529
pure square 22:    576
pure square 23:    625
pure square 24:    676
pure square 25:    784
pure square 26:    841
pure square 27:    900
pure square 28:    961
pure square 29:   1024
pure square 30:   1089
```

## Ruby

This first solution cheats and uses only one generator! It has three iterators powers(2), powers(3) and squares_without_cubes, but the only generator runs powers(3).

An iterator is a Ruby method that takes a block parameter, and loops the block for each element. So powers(2) { |i| puts "Got #{i}" } would loop forever and print Got 0, Got 1, Got 4, Got 9 and so on. Starting with Ruby 1.8.7, one can use Object#enum_for to convert an iterator method to an Enumerator object. The Enumerator#next method is a generator that runs the iterator method on a separate coroutine. Here cubes.next generates the next cube number.

```# This solution cheats and uses only one generator!

def powers(m)
return enum_for(__method__, m) unless block_given?
0.step{|n| yield n**m}
end

def squares_without_cubes
return enum_for(__method__) unless block_given?

cubes = powers(3)
c = cubes.next
powers(2) do |s|
c = cubes.next while c < s
yield s unless c == s
end
end

p squares_without_cubes.take(30).drop(20)
# p squares_without_cubes.lazy.drop(20).first(10)   # Ruby 2.0+
```
Output:
```[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
```

Here is the correct solution, which obeys the requirement of three generators.

```# This solution uses three generators.

def powers(m)
return enum_for(__method__, m) unless block_given?
0.step{|n| yield n**m}
end

def squares_without_cubes
return enum_for(__method__) unless block_given?

cubes = powers(3) #no block, so this is the first generator
c = cubes.next
squares = powers(2) # second generator
loop do
s = squares.next
c = cubes.next while c < s
yield s unless c == s
end
end

answer = squares_without_cubes # third generator
```
Output:
```[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
```

If we change both programs to drop the first 1_000_020 values (output: [1000242014641, 1000244014884, 1000246015129, 1000248015376, 1000250015625, 1000252015876, 1000254016129, 1000256016384, 1000258016641, 1000260016900]), then the one-generator solution runs much faster than the three-generator solution on a machine with MRI 1.9.2.

The other way. Powers method is the same as the above.

Translation of: Python
```def filtered(s1, s2)
return enum_for(__method__, s1, s2) unless block_given?
v, f = s1.next, s2.next
loop do
v > f and f = s2.next and next
v < f and yield v
v = s1.next
end
end

squares, cubes = powers(2), powers(3)
f = filtered(squares, cubes)
p f.take(30).last(10)
# p f.lazy.drop(20).first(10)   # Ruby 2.0+
```

Output is the same as the above.

## Rust

```use std::cmp::Ordering;
use std::iter::Peekable;

fn powers(m: u32) -> impl Iterator<Item = u64> {
(0u64..).map(move |x| x.pow(m))
}

fn noncubic_squares() -> impl Iterator<Item = u64> {
NoncubicSquares {
squares: powers(2).peekable(),
cubes: powers(3).peekable(),
}
}

struct NoncubicSquares<T: Iterator<Item = u64>, U: Iterator<Item = u64>> {
squares: Peekable<T>,
cubes: Peekable<U>,
}

impl<T: Iterator<Item = u64>, U: Iterator<Item = u64>> Iterator for NoncubicSquares<T, U> {
type Item = u64;
fn next(&mut self) -> Option<u64> {
loop {
match self.squares.peek()?.cmp(self.cubes.peek()?) {
Ordering::Equal => self.squares.next(),
Ordering::Greater => self.cubes.next(),
Ordering::Less => return self.squares.next(),
};
}
}
}

fn main() {
noncubic_squares()
.skip(20)
.take(10)
.for_each(|x| print!("{} ", x));
println!();
}
```
Output:
`529 576 625 676 784 841 900 961 1024 1089 `

## Scala

```object Generators {
def main(args: Array[String]): Unit = {
def squares(n:Int=0):Stream[Int]=(n*n) #:: squares(n+1)
def cubes(n:Int=0):Stream[Int]=(n*n*n) #:: cubes(n+1)

def filtered(s:Stream[Int], c:Stream[Int]):Stream[Int]={
else filtered(s.tail, c)
}

filtered(squares(), cubes()) drop 20 take 10 print
}
}
```

Here is an alternative filter implementation using pattern matching.

```def filtered2(s:Stream[Int], c:Stream[Int]):Stream[Int]=(s, c) match {
case (sh#::_, ch#::ct) if (sh>ch) => filtered2(s, ct)
case (sh#::st, ch#::_) if (sh<ch) => sh #:: filtered2(st, c)
case (_#::st, _) => filtered2(st, c)
}
```
Output:
`529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089, empty`

## Scheme

### Scheme using conventional closures

```(define (power-seq n)
(let ((i 0))
(lambda ()
(set! i (+ 1 i))
(expt i n))))

(define (filter-seq m n)
(let* ((s1 (power-seq m)) (s2 (power-seq n))
(a 0) (b 0))
(lambda ()
(set! a (s1))
(let loop ()
(if (>= a b) (begin
(cond ((> a b) (set! b (s2)))
((= a b) (set! a (s1))))
(loop))))
a)))

(let loop ((seq (filter-seq 2 3)) (i 0))
(if (< i 30)
(begin
(if (> i 20)
(begin
(display (seq))
(newline))
(seq))
(loop seq (+ 1 i)))))
```
Output:
```576
625
676
784
841
900
961
1024
1089```

### Scheme using call with current continuation

This method can be elaborated upon to, for instance, provide functionality similar to that of Icon co-expressions.

```;;; Generators using call/cc.

(cond-expand
(r7rs)
(chicken (import r7rs)))

(define-library (suspendable-procedures)
(export suspend)
(export make-generator-procedure)

(import (scheme base))

(begin

(define *suspend* (make-parameter (lambda (x) x)))
(define (suspend v) ((*suspend*) v))

(define (make-generator-procedure thunk)
;; This is for making a suspendable procedure that takes no
;; arguments when resumed. The result is a simple generator of
;; values.
(define (next-run return)
(define (my-suspend v)
(set! return (call/cc (lambda (resumption-point)
(set! next-run resumption-point)
(return v)))))
(parameterize ((*suspend* my-suspend))
(suspend (thunk))))
(lambda () (call/cc next-run)))

)) ;; end library (suspendable-procedures)

(import (scheme base))
(import (scheme case-lambda))
(import (scheme write))
(import (suspendable-procedures))

(define (make-integers-generator i0)
(make-generator-procedure
(lambda ()
(let loop ((i i0))
(suspend i)
(loop (+ i 1))))))

(define make-nth-powers-generator
(case-lambda
((n i0)
(define next-int (make-integers-generator i0))
(make-generator-procedure
(lambda ()
(let loop ()
(suspend (expt (next-int) n))
(loop)))))
((n)
(make-nth-powers-generator n 0))))

(define (make-filter-generator gen1 gen2)
(make-generator-procedure
(lambda ()
(let loop ((x1 (gen1))
(x2 (gen2)))
(cond ((= x1 x2) (loop (gen1) x2)) ; Skip this x1.
((< x1 x2) (begin            ; Return this x1.
(suspend x1)
(loop (gen1) x2)))
(else (loop x1 (gen2))))))))

(define (gen-drop n)
(lambda (generator)
(make-generator-procedure
(lambda ()
(do ((i 0 (+ i 1)))
((= i n))
(generator))
(let loop ()
(suspend (generator))
(loop))))))

(define (gen-take n)
(lambda (generator)
(make-generator-procedure
(lambda ()
(do ((i 0 (+ i 1)))
((= i n))
(suspend (generator)))
(let loop ()
(suspend #f)
(loop))))))

(define my-generator
((gen-take 10)
((gen-drop 20)
(make-filter-generator
(make-nth-powers-generator 2)
(make-nth-powers-generator 3)))))

(let loop ()
(let ((x (my-generator)))
(when x
(display " ")
(display x)
(loop))))
(newline)
```
Output:

Using Gauche Scheme.

```\$ gosh generator-exponential.scm
529 576 625 676 784 841 900 961 1024 1089```

Using CHICKEN Scheme (which has efficient call/cc). You will need the r7rs egg.

```\$ csi -s generator-exponential.scm && ./a.out
529 576 625 676 784 841 900 961 1024 1089```

## SenseTalk

The ExponentialGenerator script is a generator object for exponential values.

```// ExponentialGenerator.script

to initialize
set my base to 0
if my exponent is empty then set my exponent to 1 -- default if not given
end initialize

to handle nextValue
return my base to the power of my exponent
end nextValue```

The FilteredGenerator takes source and filter generators. It gets values from the source generator but excludes those from the filter generator.

```// FilteredGenerator.script

// Takes a source generator, and a filter generator, which must both produce increasing values
// Produces values from the source generator that don't match values from the filter generator

to initialize
set my nextFilteredValue to the nextValue of my filter
end initialize

to handle nextValue
put the nextValue of my source into value -- get a candidate value

-- advance the filter as needed if it is behind
repeat while my nextFilteredValue is less than or equal to value
-- advance value if it's equal to the next filtered value
if my nextFilteredValue = value then set value to my source's nextValue
set my nextFilteredValue to my filter's nextValue
end repeat

return value
end nextValue```

This script shows the use of both of the generators.

```// Main.script to use the generators

set squares to new ExponentialGenerator with {exponent:2}

set cubes to new ExponentialGenerator with {exponent:3}

put "First 10 Squares:"
repeat 10 times
put squares.nextValue
end repeat

put "-" repeated 30 times

put "First 10 Cubes:"
repeat 10 times
put cubes.nextValue
end repeat

put "-" repeated 30 times

set filteredSquares to new FilteredGenerator with {
source: new ExponentialGenerator with {exponent:2},
filter: new ExponentialGenerator with {exponent:3}
}

repeat 20 times
get filteredSquares.nextValue
end repeat

put "Filtered Squares 21 to 30:"
repeat with n=21 to 30
put n & ":" && filteredSquares.nextValue
end repeat```
Output:
```First 10 Squares:
1
4
9
16
25
36
49
64
81
100
------------------------------
First 10 Cubes:
1
8
27
64
125
216
343
512
729
1000
------------------------------
Filtered Squares 21 to 30:
21: 529
22: 576
23: 625
24: 676
25: 784
26: 841
27: 900
28: 961
29: 1024
30: 1089
```

## Sidef

Translation of: Perl
```func gen_pow(m) {
var e = 0;
func { e++ ** m };
}

func gen_filter(g1, g2) {
var v2 = g2.run;
func {
loop {
var v1 = g1.run;
while (v1 > v2) { v2 = g2.run };
v1 == v2 || return v1;
}
}
}

# Create generators.
var squares = gen_pow(2);
var cubes = gen_pow(3);
var squares_without_cubes = gen_filter(squares, cubes);

# Drop 20 values.
20.times { squares_without_cubes() };

# Print 10 values.
```
Output:
```[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
```

## SuperCollider

```f = { |m| {:x, x<-(0..) } ** m };
g = f.(2);
g.nextN(10); // answers  [ 0, 1, 4, 9, 16, 25, 36, 49, 64, 81 ]
```

patterns are stream generators:

```(
f = Pseries(0, 1)
g = f ** 2;
g.asStream.nextN(10); // answers  [ 0, 1, 4, 9, 16, 25, 36, 49, 64, 81 ]
)
```

supercollider has no "without" stream function, this builds one:

```(
var filter = { |a, b, func| // both streams are assumed to be ordered
Prout {
var astr, bstr;
var aval, bval;
astr = a.asStream;
bstr = b.asStream;
bval = bstr.next;
while {
aval = astr.next;
aval.notNil
} {
while {
bval.notNil and: { bval < aval }
} {
bval = bstr.next;
};
if(func.value(aval, bval)) { aval.yield };
}
}
};
var without = filter.(_, _, { |a, b|  a != b }); // partially apply function

f = Pseries(0, 1);

g = without.(f ** 2, f ** 3);
h = g.drop(20);
h.asStream.nextN(10);
)

answers: [ 529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089 ]
```

## Swift

```func powGen(m: Int) -> GeneratorOf<Int> {
let power = Double(m)
var cur: Double = 0
return GeneratorOf { Int(pow(cur++, power)) }
}

var squares = powGen(2)
var cubes = powGen(3)

var nCube = cubes.next()

var filteredSqs = GeneratorOf<Int> {
for var nSq = squares.next() ;; nCube = cubes.next() {
if nCube > nSq {
return nSq
} else if nCube == nSq {
nSq = squares.next()
}
}
}

extension GeneratorOf {
func drop(n: Int) -> GeneratorOf<T> {
var g = self
for _ in 0..<n {g.next()}
return GeneratorOf{g.next()}
}
func take(n: Int) -> GeneratorOf<T> {
var (i, g) = (0, self)
return GeneratorOf{++i > n ? nil : g.next()}
}
}

for num in filteredSqs.drop(20).take(10) {
print(num)
}

//529
//576
//625
//676
//784
//841
//900
//961
//1024
//1089
```

## Tcl

Works with: Tcl version 8.6

Tcl implements generators in terms of coroutines. If these generators were terminating, they would finish by doing `return -code break` so as to terminate the calling loop context that is doing the extraction of the values from the generator.

```package require Tcl 8.6

proc powers m {
yield
for {set n 0} true {incr n} {
yield [expr {\$n ** \$m}]
}
}
coroutine squares powers 2
coroutine cubes powers 3
coroutine filtered apply {{s1 s2} {
yield
set f [\$s2]
set v [\$s1]
while true {
if {\$v > \$f} {
set f [\$s2]
continue
} elseif {\$v < \$f} {
yield \$v
}
set v [\$s1]
}
}} squares cubes

# Drop 20
for {set i 0} {\$i<20} {incr i} {filtered}
# Take/print 10
for {} {\$i<30} {incr i} {
puts [filtered]
}
```
Output:
```529
576
625
676
784
841
900
961
1024
1089
```

## VBA

```Public lastsquare As Long
Public nextsquare As Long
Public lastcube As Long
Public midcube As Long
Public nextcube As Long
Private Sub init()
lastsquare = 1
nextsquare = -1
lastcube = -1
midcube = 0
nextcube = 1
End Sub

Private Function squares() As Long
lastsquare = lastsquare + nextsquare
nextsquare = nextsquare + 2
squares = lastsquare
End Function

Private Function cubes() As Long
lastcube = lastcube + nextcube
nextcube = nextcube + midcube
midcube = midcube + 6
cubes = lastcube
End Function

Public Sub main()
init
cube = cubes
For i = 1 To 30
Do While True
square = squares
Do While cube < square
cube = cubes
Loop
If square <> cube Then
Exit Do
End If
Loop
If i > 20 Then
Debug.Print square;
End If
Next i
End Sub
```
Output:
` 529  576  625  676  784  841  900  961  1024  1089 `

## Visual Basic .NET

Compiler: >= Visual Studio 2012

```Module Program
Iterator Function IntegerPowers(exp As Integer) As IEnumerable(Of Integer)
Dim i As Integer = 0
Do
Yield CInt(Math.Pow(i, exp))
i += 1
Loop
End Function

Function Squares() As IEnumerable(Of Integer)
Return IntegerPowers(2)
End Function

Function Cubes() As IEnumerable(Of Integer)
Return IntegerPowers(3)
End Function

Iterator Function SquaresWithoutCubes() As IEnumerable(Of Integer)
Dim cubeSequence = Cubes().GetEnumerator()
Dim nextGreaterOrEqualCube As Integer = 0
For Each curSquare In Squares()
Do While nextGreaterOrEqualCube < curSquare
cubeSequence.MoveNext()
nextGreaterOrEqualCube = cubeSequence.Current
Loop
If nextGreaterOrEqualCube <> curSquare Then Yield curSquare
Next
End Function

Sub Main()
For Each x In From i In SquaresWithoutCubes() Skip 20 Take 10
Console.WriteLine(x)
Next
End Sub
End Module
```

More concise but slower implementation that relies on LINQ-to-objects to achieve generator behavior (runs slower due to re-enumerating Cubes() for every element of Squares()).

```    Function SquaresWithoutCubesLinq() As IEnumerable(Of Integer)
Return Squares().Where(Function(s) s <> Cubes().First(Function(c) c >= s))
End Function
```
Output:
```529
576
625
676
784
841
900
961
1024
1089```

## XPL0

```code ChOut=8, IntOut=11;

func Gen(M);            \Generate Mth powers of positive integers
int  M;
int  N, R, I;
[N:= [0, 0, 0, 0];      \provides own/static variables
R:= 1;
for I:= 1 to M do R:= R*N(M);
N(M):= N(M)+1;
return R;
];

func Filter;            \Generate squares of positive integers that aren't cubes
int  S, C;
[C:= ;               \static variable = smallest cube > current square
repeat  S:= Gen(2);
while S > C(0) do C(0):= Gen(3);
until   S # C(0);
return S;
];

int  I;
[for I:= 1 to 20 do Filter;                             \drop first 20 values
for I:= 1 to 10 do [IntOut(0, Filter);  ChOut(0, ^ )]; \show next 10 values
]```
Output:
```529 576 625 676 784 841 900 961 1024 1089
```

## Wren

Closure based solution. Similar approach to Go (first example).

```var powers = Fn.new { |m|
var i = 0
return Fn.new {
var p = i.pow(m)
i = i + 1
return p
}
}

var squaresNotCubes = Fn.new { |squares, cubes|
var sq = squares.call()
var cu = cubes.call()
return Fn.new {
var p
while (true) {
if (sq < cu) {
p = sq
sq = squares.call()
return p
}
if (sq == cu) sq = squares.call()
cu = cubes.call()
}
}
}

var squares = powers.call(2)
var cubes = powers.call(3)
var sqNotCu = squaresNotCubes.call(squares, cubes)
for (i in 0..29) {
var p = sqNotCu.call()
if (i > 19) System.write("%(p) ")
}
System.print()
```
Output:
```529 576 625 676 784 841 900 961 1024 1089
```

## zkl

Translation of: Python

Generators are implemented with fibers (aka VMs) and return [lazy] iterators.

```fcn powers(m){ n:=0.0; while(1){vm.yield(n.pow(m).toInt()); n+=1} }
var squared=Utils.Generator(powers,2), cubed=Utils.Generator(powers,3);

fcn filtered(sg,cg){s:=sg.next(); c:=cg.next();
while(1){
if(s>c){c=cg.next(); continue;}
else if(s<c) vm.yield(s);
s=sg.next()
}
}
var f=Utils.Generator(filtered,squared,cubed);
f.drop(20);
f.walk(10).println();```
Output:
`L(529,576,625,676,784,841,900,961,1024,1089)`

For this task, generators are overkill and overweight, and lazy infinite squences can be used. There is no real change to the algorithms (since generators are lazy sequences), it just has been rewritten in a more functional style.

Translation of: Clojure
```fcn powers(m){[0.0..].tweak(fcn(n,m){a:=n; do(m-1){a*=n} a}.fp1(m))}
var squared=powers(2), cubed=powers(3);

fcn filtered(sg,cg){s:=sg.peek(); c:=cg.peek();
if(s==c){ cg.next(); sg.next(); return(self.fcn(sg,cg)) }
if(s>c) { cg.next(); return(self.fcn(sg,cg)); }
sg.next(); return(s);
}
var f=[0..].tweak(filtered.fp(squared,cubed))
f.drop(20).walk(10).println();```