{{task}} {{omit from|Lilypond}} [[Category:Non parametric generators]] [[Category:Stateful transactions]]

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.

;Task:

• 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:

• [[wp:Generator (computer_science)|Generator]]

Ada

{{works with|Ada 2005}}

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.

generator.ads:

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;

generator-filtered.ads:

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;

generator.adb:

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;

generator-filtered.adb:

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 ("I:" & Integer'Image (I));
      Ada.Text_IO.Put (", F:" & Integer'Image (F.Get_Next));
      Ada.Text_IO.New_Line;
   end loop;

end Generator_Test;

{{out}}

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

AppleScript

Composable generators can be constructed from the methods and persistent properties of ''script'' objects: {{Trans|JavaScript}} {{Trans|Python}}

-- 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
    -- already seen in gb.
    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

{{Out}}

{529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089}

ALGOL 68

{{trans|Python}}{{works with|ALGOL 68|Revision 1 - with [[currying]] of functions and PRAGMA READ extensions}} {{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-2.3.5 algol68g-2.3.5].}} {{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d] - due to extensive use of '''format'''[ted] ''transput''.}} '''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 #
# Thread 1 #
      # 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 #)),
# Thread 2 #
      # 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;
PR READ "Template.Generator.a68" PR

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

printf(($g(0)x$, get list(gen slice(fil, 20, 30, )) ))

{{out}}

529 576 625 676 784 841 900 961 1024 1089

C

==={{libheader|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 {
	cothread_t giver;	/* this cothread calls yield64() */
	cothread_t taker;	/* this cothread calls next64() */
	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 */
		fputs("co_create: Cannot create cothread\n", stderr);
		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;
}

One must download [http://byuu.org/programming/ libco] and give libco.c to the compiler.

$ 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;
}

{{out}}

529
576
625
676
784
841
900
961
1024
1089

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;
}

{{out}}

20: 529
21: 576
22: 625
23: 676
24: 784
25: 841
26: 900
27: 961
28: 1024
29: 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++;
    }
}

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;
}

{{out}}

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

===Simple Ranges-Based Implementation=== {{trans|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=== {{trans|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;
}

{{out}}

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;
}

{{out}}

[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)))

(drop task 20)
(take task 10)
    → (529 576 625 676 784 841 900 961 1024 1089)

; inspect
task → #generator:state: 1331

Elixir

{{trans|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})
    receive do
      x -> x
    end
  end

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

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

IO.inspect Generator.task

{{out}}

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

Emacs Lisp

This code requires generator library which was introduced in Emacs 25.2

(require 'generator)
(setq lexical-binding t)

(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()},
    receive X -> X end.

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

task() ->
    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 ) ->
        receive
        {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 ).

{{out}}

31> generator:task().
[529,576,625,676,784,841,900,961,1024,1089]

=={{header|F_Sharp|F#}}== {{trans|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"

{{out}}

[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 .

{{out}}

{ 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)
    }
  }
}

{{out}}

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

{{out}}

$ gforth -e "include genexp-rcode.fs"
529 576 625 676 784 841 900 961 1024 1089
$

FunL

{{trans|Haskell}} (for the powers function) {{trans|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) )

{{out}}

[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()
}

{{out}}

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()
}

Haskell

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

{{Out}}

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

=={{header|Icon}} and {{header|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.

{{out}}

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|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

{{works with|Firefox 3.6 using JavaScript 1.7|}}

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: {{Trans|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[0]);
            sb.add(y);
            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[0]))
            v = take(1, gen)
        }
    }

    // fst :: (a, b) -> a
    const fst = tpl => tpl[0];

    // 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[1];

    // 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[0], xs.slice(1))) // Finite list
            ) : (() => {
                const nxt = take(1, xs);
                return 0 < nxt.length ? (
                    Just(Tuple(nxt[0], 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();
})();

{{Out}}

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

jq

{{works with|jq|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): .[0] + 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)) | .[1]

# Generate all the values in the sequence i^3 less than 100:
[0,0] | recurse(next_power(3) | if .[1] < 100 then . else empty end) | .[1]

'''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
  | (.[0] | next_power(m1)) as $next1
  | (.[1] | while( .[1] <= $next1[1]; next_power(m2))) as $next2
  | if $next1[1] == $next2[1]
    then [$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))
  | .[0][1]

{{out}}

$ 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)

{{out}}

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()
}

{{out}}

Non-cubic squares (21st to 30th) : 529 576 625 676 784 841 900 961 1024 1089

M2000 Interpreter

Module Generator {
      PowGen = Lambda (e)-> {
            =lambda i=0, e -> {
                  i++
                  =i**e
            }
      }

      Squares=lambda PowGen=PowGen(2) ->{
            =PowGen()
      }

      Cubes=Lambda PowGen=PowGen(3) -> {
            =PowGen()
      }

      Filter=Lambda  z=Squares(), Squares, m, Cubes->{
            while m<Z {m=cubes()}
            if z=m then z=Squares()
            =z
            z=Squares()
      }

      For i=1 to 20 : dropit=Filter() :Next i

      Document doc$="Non-cubic squares (21st to 30th)"
      Print doc$
      \\ a new line to doc$
      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)+{
            }
      }
      Clipboard doc$
}
Generator

{{out}}

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