List comprehensions
You are encouraged to solve this task according to the task description, using any language you may know.
A list comprehension is a special syntax in some programming languages to describe lists. It is similar to the way mathematicians describe sets, with a set comprehension, hence the name.
Some attributes of a list comprehension are:
- They should be distinct from (nested) for loops and the use of map and filter functions within the syntax of the language.
- They should return either a list or an iterator (something that returns successive members of a collection, in order).
- The syntax has parts corresponding to that of set-builder notation.
- Task
Write a list comprehension that builds the list of all Pythagorean triples with elements between 1 and n.
If the language has multiple ways for expressing such a construct (for example, direct list comprehensions and generators), write one example for each.
11l
print(cart_product(1..20, 1..20, 1..20).filter((x, y, z) -> x ^ 2 + y ^ 2 == z ^ 2 & y C x .. z))
- Output:
[(3, 4, 5), (5, 12, 13), (6, 8, 10), (8, 15, 17), (9, 12, 15), (12, 16, 20)]
ABAP
CLASS lcl_pythagorean_triplet DEFINITION CREATE PUBLIC.
PUBLIC SECTION.
TYPES: BEGIN OF ty_triplet,
x TYPE i,
y TYPE i,
z TYPE i,
END OF ty_triplet,
tty_triplets TYPE STANDARD TABLE OF ty_triplet WITH NON-UNIQUE EMPTY KEY.
CLASS-METHODS:
get_triplets
IMPORTING
n TYPE i
RETURNING
VALUE(r_triplets) TYPE tty_triplets.
PRIVATE SECTION.
CLASS-METHODS:
_is_pythagorean
IMPORTING
i_triplet TYPE ty_triplet
RETURNING
VALUE(r_is_pythagorean) TYPE abap_bool.
ENDCLASS.
CLASS lcl_pythagorean_triplet IMPLEMENTATION.
METHOD get_triplets.
DATA(triplets) = VALUE tty_triplets( FOR x = 1 THEN x + 1 WHILE x <= n
FOR y = x THEN y + 1 WHILE y <= n
FOR z = y THEN z + 1 WHILE z <= n
( x = x y = y z = z ) ).
LOOP AT triplets ASSIGNING FIELD-SYMBOL(<triplet>).
IF _is_pythagorean( <triplet> ) = abap_true.
INSERT <triplet> INTO TABLE r_triplets.
ENDIF.
ENDLOOP.
ENDMETHOD.
METHOD _is_pythagorean.
r_is_pythagorean = COND #( WHEN i_triplet-x * i_triplet-x + i_triplet-y * i_triplet-y = i_triplet-z * i_triplet-z THEN abap_true
ELSE abap_false ).
ENDMETHOD.
ENDCLASS.
START-OF-SELECTION.
cl_demo_output=>display( lcl_pythagorean_triplet=>get_triplets( n = 20 ) ).
- Output:
X Y Z 3 4 5 5 12 13 6 8 10 8 15 17 9 12 15 12 16 20
Ada
There is no equivalent construct in Ada. In Ada05, the predefined library Ada.Containers implements 3 types of Doubly_Linked_Lists : Basic; Indefinite; Restricted.
with Ada.Text_IO; use Ada.Text_IO;
with Ada.Containers.Doubly_Linked_Lists;
procedure Pythagore_Set is
type Triangles is array (1 .. 3) of Positive;
package Triangle_Lists is new Ada.Containers.Doubly_Linked_Lists (
Triangles);
use Triangle_Lists;
function Find_List (Upper_Bound : Positive) return List is
L : List := Empty_List;
begin
for A in 1 .. Upper_Bound loop
for B in A + 1 .. Upper_Bound loop
for C in B + 1 .. Upper_Bound loop
if ((A * A + B * B) = C * C) then
Append (L, (A, B, C));
end if;
end loop;
end loop;
end loop;
return L;
end Find_List;
Triangle_List : List;
C : Cursor;
T : Triangles;
begin
Triangle_List := Find_List (Upper_Bound => 20);
C := First (Triangle_List);
while Has_Element (C) loop
T := Element (C);
Put
("(" &
Integer'Image (T (1)) &
Integer'Image (T (2)) &
Integer'Image (T (3)) &
") ");
Next (C);
end loop;
end Pythagore_Set;
program output:
( 3 4 5) ( 5 12 13) ( 6 8 10) ( 8 15 17) ( 9 12 15) ( 12 16 20)
ALGOL 68
ALGOL 68 does not have list comprehension, however it is sometimes reasonably generous about where a flex array is declared. And with the addition of an append operator "+:=" for lists they can be similarly manipulated.
MODE XYZ = STRUCT(INT x,y,z);
OP +:= = (REF FLEX[]XYZ lhs, XYZ rhs)FLEX[]XYZ: (
[UPB lhs+1]XYZ out;
out[:UPB lhs] := lhs;
out[UPB out] := rhs;
lhs := out
);
INT n = 20;
print (([]XYZ(
FLEX[0]XYZ xyz;
FOR x TO n DO FOR y FROM x+1 TO n DO FOR z FROM y+1 TO n DO IF x*x + y*y = z*z THEN xyz +:= XYZ(x,y,z) FI OD OD OD;
xyz), new line
))Output:
+3 +4 +5 +5 +12 +13 +6 +8 +10 +8 +15 +17 +9 +12 +15 +12 +16 +20
AppleScript
AppleScript does not provide built-in notation for list comprehensions. The list monad pattern which underlies list comprehension notation can, however, be used in any language which supports the use of higher order functions and closures. AppleScript can do that, although with limited elegance and clarity, and not entirely without coercion.
-- List comprehension by direct and unsugared use of list monad
-- pythagoreanTriples :: Int -> [(Int, Int, Int)]
on pythagoreanTriples(n)
script x
on |λ|(x)
script y
on |λ|(y)
script z
on |λ|(z)
if x * x + y * y = z * z then
[[x, y, z]]
else
[]
end if
end |λ|
end script
|>>=|(enumFromTo(1 + y, n), z)
end |λ|
end script
|>>=|(enumFromTo(1 + x, n), y)
end |λ|
end script
|>>=|(enumFromTo(1, n), x)
end pythagoreanTriples
-- TEST -----------------------------------------------------------------------
on run
-- Pythagorean triples drawn from integers in the range [1..n]
-- {(x, y, z) | x <- [1..n], y <- [x+1..n], z <- [y+1..n], (x^2 + y^2 = z^2)}
pythagoreanTriples(25)
--> {{3, 4, 5}, {5, 12, 13}, {6, 8, 10}, {7, 24, 25}, {8, 15, 17},
-- {9, 12, 15}, {12, 16, 20}, {15, 20, 25}}
end run
-- GENERIC FUNCTIONS ----------------------------------------------------------
-- Monadic (>>=) (or 'bind') for lists is simply flip concatMap
-- (concatMap with arguments reversed)
-- It applies a function f directly to each value in the list,
-- and returns the set of results as a concat-flattened list
-- The concatenation eliminates any empty lists,
-- combining list-wrapped results into a single results list
-- (>>=) :: Monad m => m a -> (a -> m b) -> m b
on |>>=|(xs, f)
concatMap(f, xs)
end |>>=|
-- concatMap :: (a -> [b]) -> [a] -> [b]
on concatMap(f, xs)
set acc to {}
tell mReturn(f)
repeat with x in xs
set acc to acc & |λ|(contents of x)
end repeat
end tell
return acc
end concatMap
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if n < m then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
- Output:
{{3, 4, 5}, {5, 12, 13}, {6, 8, 10}, {7, 24, 25}, {8, 15, 17}, {9, 12, 15}, {12, 16, 20}, {15, 20, 25}}
Arturo
n: 20
triplets: @[
loop 1..n 'x [
loop x..n 'y [
loop y..n 'z [if (z^2) = (x^2)+(y^2) -> @[x y z]]
]
]
]
print triplets
- Output:
[3 4 5] [5 12 13] [6 8 10] [8 15 17] [9 12 15] [12 16 20]
AutoHotkey
List Comprehension is not built in.
comprehend("show", range(1, 20), "triples")
return
comprehend(doToVariable, inSet, satisfying)
{
set := %satisfying%(inSet.begin, inSet.end)
index := 1
While % set[index, 1]
{
item := set[index, 1] . ", " . set[index, 2] . ", " . set[index, 3]
%doToVariable%(item)
index += 1
}
return
}
show(var)
{
msgbox % var
}
range(begin, end)
{
set := object()
set.begin := begin
set.end := end
return set
}
!r::reload
!q::exitapp
triples(begin, end)
{
set := object()
index := 1
range := end - begin
loop, % range
{
x := begin + A_Index
loop, % range
{
y := A_Index + x
if y > 20
break
loop, % range
{
z := A_Index + y
if z > 20
break
isTriple := ((x ** 2 + y ** 2) == z ** 2)
if isTriple
{
set[index, 1] := x
set[index, 2] := y
set[index, 3] := z
index += 1
; msgbox % "triple: " x . y . z
}
}
}
}
return set
}
Bracmat
Bracmat does not have built-in list comprehension, but nevertheless there is a solution for fixed n that does not employ explicit loop syntax. By their positions in the pattern and the monotonically increasing values in the subject, it is guaranteed that x always is smaller than y and that y always is smaller than z. The combination of flags %@ ensures that x, y and z pick minimally one (%) and at most one (@) element from the subject list.
:?py { Initialize the accumulating result list. }
& ( 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 { This is the subject }
: ? { Here starts the pattern }
%@?x
?
%@?y
?
%@?z
( ?
& -1*!z^2+!x^2+!y^2:0
& (!x,!y,!z) !py:?py
& ~ { This 'failure' expression forces backtracking }
) { Here ends the pattern }
| out$!py { You get here when backtracking has
exhausted all combinations of x, y and z }
);Output:
(12,16,20) (9,12,15) (8,15,17) (6,8,10) (5,12,13) (3,4,5)
C
C doesn't have a built-in syntax for this, but any problem can be solved if you throw enough macros at it:
The program below is C11 compliant. For C99 compilers note the change on line 57 (output remains unchanged).
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#ifndef __GNUC__
#include <setjmp.h>
struct LOOP_T; typedef struct LOOP_T LOOP;
struct LOOP_T {
jmp_buf b; LOOP * p;
} LOOP_base, * LOOP_V = &LOOP_base;
#define FOR(I, C, A, ACT) (LOOP_V = &(LOOP){ .p = LOOP_V }, \
(I), setjmp(LOOP_V->b), \
((C) ? ((ACT),(A), longjmp(LOOP_V->b, 1), 0) : 0), \
LOOP_V = LOOP_V->p, 0)
#else
#define FOR(I, C, A, ACT) (({for(I;C;A){ACT;}}), 0) // GNU version
#endif
typedef struct List { struct List * nx; char val[]; } List;
typedef struct { int _1, _2, _3; } Triple;
#define SEQ(OUT, SETS, PRED) (SEQ_var=&(ITERATOR){.l=NULL,.p=SEQ_var}, \
M_FFOLD(((PRED)?APPEND(OUT):0),M_ID SETS), \
SEQ_var->p->old=SEQ_var->l,SEQ_var=SEQ_var->p,SEQ_var->old)
typedef struct ITERATOR { List * l, * old; struct ITERATOR * p; } ITERATOR;
ITERATOR * FE_var, SEQ_base, * SEQ_var = &SEQ_base;
#define FOR_EACH(V, T, L, ACT) (FE_var=&(ITERATOR){.l=(L),.p=FE_var}, \
FOR((V) = *(T*)&FE_var->l->val, FE_var->l?((V)=*(T*)&FE_var->l->val,1):0, \
FE_var->l=FE_var->l->nx, ACT), FE_var=FE_var->p)
#define M_FFOLD(ID, ...) M_ID(M_CONC(M_FFOLD_, M_NARGS(__VA_ARGS__)) (ID, __VA_ARGS__))
#define FORSET(V, T, L) V, T, L
#define APPEND(T, val) (SEQ_var->l?listAppend(SEQ_var->l,sizeof(T),&val):(SEQ_var->l=listNew(sizeof(T),&val)))
#define M_FFOLD_1(ID, E) FOR_EACH M_IDP(FORSET E, ID)
#define M_FFOLD_2(ID, E, ...) FOR_EACH M_IDP(FORSET E, M_FFOLD_1(ID, __VA_ARGS__))
#define M_FFOLD_3(ID, E, ...) FOR_EACH M_IDP(FORSET E, M_FFOLD_2(ID, __VA_ARGS__)) //...
#define M_NARGS(...) M_NARGS_(__VA_ARGS__, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0)
#define M_NARGS_(_10, _9, _8, _7, _6, _5, _4, _3, _2, _1, N, ...) N
#define M_CONC(A, B) M_CONC_(A, B)
#define M_CONC_(A, B) A##B
#define M_ID(...) __VA_ARGS__
#define M_IDP(...) (__VA_ARGS__)
#define R(f, t) int,intRangeList(f, t)
#define T(a, b, c) Triple,((Triple){(a),(b),(c)})
List * listNew(int sz, void * val) {
List * l = malloc(sizeof(List) + sz); l->nx = NULL; memcpy(l->val, val, sz); return l;
}
List * listAppend(List * l, int sz, void * val) {
while (l->nx) { l = l->nx; } l->nx = listNew(sz, val); return l;
}
List * intRangeList(int f, int t) {
List * l = listNew(sizeof f, &f), * e = l;
for (int i = f + 1; i <= t; i ++) { e = e->nx = listNew(sizeof i, &i); } // C11 compliant
//int i;
//for (i = f + 1; i <= t; i ++) { e = e->nx = listNew(sizeof i, &i); } // use this for C99
return l;
}
int main(void) {
volatile int x, y, z; const int n = 20;
List * pTriples = SEQ(
T(x, y, z),
(
(x, R(1, n)),
(y, R(x, n)),
(z, R(y, n))
),
(x*x + y*y == z*z)
);
volatile Triple t;
FOR_EACH(t, Triple, pTriples, printf("%d, %d, %d\n", t._1, t._2, t._3) );
return 0;
}
Output:
3, 4, 5 5, 12, 13 6, 8, 10 8, 15, 17 9, 12, 15 12, 16, 20
Either GCC's "statement expressions" extension, or a minor piece of undefined behaviour, are required for this to work (technically setjmp, which powers the non-GCC version, isn't supposed to be part of a comma expression, but almost all compilers will treat it as intended). Variables used by one of these looping expressions should be declared volatile to prevent them from being modified by setjmp.
The list implementation in this example is a) terrible and b) leaks memory, neither of which are important to the example. In reality you would want to combine any lists being generated in expressions with an automatic memory management system (GC, autorelease pools, something like that).
C#
LINQ
using System.Linq;
static class Program
{
static void Main()
{
var ts =
from a in Enumerable.Range(1, 20)
from b in Enumerable.Range(a, 21 - a)
from c in Enumerable.Range(b, 21 - b)
where a * a + b * b == c * c
select new { a, b, c };
foreach (var t in ts)
System.Console.WriteLine("{0}, {1}, {2}", t.a, t.b, t.c);
}
}
C++
There is no equivalent construct in C++. The code below uses two nested loops and an if statement:
#include <vector>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <iterator>
void list_comprehension( std::vector<int> & , int ) ;
int main( ) {
std::vector<int> triangles ;
list_comprehension( triangles , 20 ) ;
std::copy( triangles.begin( ) , triangles.end( ) ,
std::ostream_iterator<int>( std::cout , " " ) ) ;
std::cout << std::endl ;
return 0 ;
}
void list_comprehension( std::vector<int> & numbers , int upper_border ) {
for ( int a = 1 ; a < upper_border ; a++ ) {
for ( int b = a + 1 ; b < upper_border ; b++ ) {
double c = pow( a * a + b * b , 0.5 ) ; //remembering Mr. Pythagoras
if ( ( c * c ) < pow( upper_border , 2 ) + 1 ) {
if ( c == floor( c ) ) {
numbers.push_back( a ) ;
numbers.push_back( b ) ;
numbers.push_back( static_cast<int>( c ) ) ;
}
}
}
}
}
This produces the following output:
3 4 5 5 12 13 6 8 10 8 15 17 9 12 15 12 16 20
#include <functional>
#include <iostream>
void PythagoreanTriples(int limit, std::function<void(int,int,int)> yield)
{
for (int a = 1; a < limit; ++a) {
for (int b = a+1; b < limit; ++b) {
for (int c = b+1; c <= limit; ++c) {
if (a*a + b*b == c*c) {
yield(a, b, c);
}
}
}
}
}
int main()
{
PythagoreanTriples(20, [](int x, int y, int z)
{
std::cout << x << "," << y << "," << z << "\n";
});
return 0;
}
Output:
3,4,5 5,12,13 6,8,10 8,15,17 9,12,15 12,16,20
Clojure
(defn pythagorean-triples [n]
(for [x (range 1 (inc n))
y (range x (inc n))
z (range y (inc n))
:when (= (+ (* x x) (* y y)) (* z z))]
[x y z]))
CoffeeScript
flatten = (arr) -> arr.reduce ((memo, b) -> memo.concat b), []
pyth = (n) ->
flatten (for x in [1..n]
flatten (for y in [x..n]
for z in [y..n] when x*x + y*y is z*z
[x, y, z]
))
# pyth can also be written more concisely as
# pyth = (n) -> flatten (flatten ([x, y, z] for z in [y..n] when x*x + y*y is z*z for y in [x..n]) for x in [1..n])
console.dir pyth 20
Common Lisp
Common Lisp's loop macro has all of the features of list comprehension, except for nested iteration. (loop for x from 1 to 3 for y from x to 3 collect (list x y)) only returns ((1 1) (2 2) (3 3)). You can nest your macro calls, so (loop for x from 1 to 3 append (loop for y from x to 3 collect (list x y))) returns ((1 1) (1 2) (1 3) (2 2) (2 3) (3 3)).
Here are the Pythagorean triples:
(defun pythagorean-triples (n)
(loop for x from 1 to n
append (loop for y from x to n
append (loop for z from y to n
when (= (+ (* x x) (* y y)) (* z z))
collect (list x y z)))))
We can also define a new macro for list comprehensions. We can implement them easily with the help of the iterate package.
(defun nest (l)
(if (cdr l)
`(,@(car l) ,(nest (cdr l)))
(car l)))
(defun desugar-listc-form (form)
(if (string= (car form) 'for)
`(iter ,form)
form))
(defmacro listc (expr &body (form . forms) &aux (outer (gensym)))
(nest
`((iter ,outer ,form)
,@(mapcar #'desugar-listc-form forms)
(in ,outer (collect ,expr)))))
We can then define a function to compute Pythagorean triples as follows:
(defun pythagorean-triples (n)
(listc (list x y z)
(for x from 1 to n)
(for y from x to n)
(for z from y to n)
(when (= (+ (expt x 2) (expt y 2)) (expt z 2)))))
D
D doesn't have list comprehensions. One implementation:
import std.stdio, std.meta, std.range;
TA[] select(TA, TI1, TC1, TI2, TC2, TI3, TC3, TP)
(lazy TA mapper,
ref TI1 iter1, TC1 items1,
ref TI2 iter2, lazy TC2 items2,
ref TI3 iter3, lazy TC3 items3,
lazy TP where) {
Appender!(TA[]) result;
auto iters = AliasSeq!(iter1, iter2, iter3);
foreach (el1; items1) {
iter1 = el1;
foreach (el2; items2) {
iter2 = el2;
foreach (el3; items3) {
iter3 = el3;
if (where())
result ~= mapper();
}
}
}
AliasSeq!(iter1, iter2, iter3) = iters;
return result.data;
}
void main() {
enum int n = 21;
int x, y, z;
auto r = select(
[x,y,z],
x, iota( 1, n+1),
y, iota(x+1, n+1),
z, iota(y+1, n+1),
x*x + y*y == z*z
);
writeln(r);
}
- Output:
[[3, 4, 5], [5, 12, 13], [6, 8, 10], [8, 15, 17], [9, 12, 15], [12, 16, 20]]
DuckDB
DuckDB supports a table-oriented form of "list comprehension" as well as a list-oriented form. The latter relies on so-called lambda functions (anonymous functions).
To sharpen the spotlight on "comprehensions", we abstract the "for x in 1 to n, y in (x+1) to n, z from (y+1) to n" component of list comprehension into the following function:
# for x in 1 to n, for y in x+1 to n, for z in y+1 to n
create or replace function xyz(n) as table (
from range(1,n+1) x(x)
cross join (from range(x+1,n+1) y(y))
cross join (from range(y+1, n+1) z(z))
);
Table-oriented approach
create or replace function triples(n) as table (
from xyz(n)
where x*x + y*y = z*z
);
from triples(10);
- Output:
┌───────┬───────┬───────┐ │ x │ y │ z │ │ int64 │ int64 │ int64 │ ├───────┼───────┼───────┤ │ 4 │ 3 │ 5 │ │ 3 │ 4 │ 5 │ │ 8 │ 6 │ 10 │ │ 6 │ 8 │ 10 │ └───────┴───────┴───────┘
List-oriented approach
create or replace function list_triples(n) as (
list_filter(
(select array_agg([x,y,z]) from xyz(n)),
x -> x[1]*x[1] + x[2]*x[2] = x[3]*x[3] )
);
select list_triples(10);
- Output:
┌────────────────────────────────────────────────┐ │ list_triples(10) │ │ int64[][] │ ├────────────────────────────────────────────────┤ │ [[3, 4, 5], [4, 3, 5], [6, 8, 10], [8, 6, 10]] │ └────────────────────────────────────────────────┘
E
pragma.enable("accumulator") # considered experimental
accum [] for x in 1..n { for y in x..n { for z in y..n { if (x**2 + y**2 <=> z**2) { _.with([x,y,z]) } } } }EchoLisp
;; copied from Racket
(for*/list ([x (in-range 1 21)]
[y (in-range x 21)]
[z (in-range y 21)])
#:when (= (+ (* x x) (* y y)) (* z z))
(list x y z))
→ ((3 4 5) (5 12 13) (6 8 10) (8 15 17) (9 12 15) (12 16 20))
Efene
pythag = fn (N) {
[(A, B, C) for A in lists.seq(1, N) \
for B in lists.seq(A, N) \
for C in lists.seq(B, N) \
if A + B + C <= N and A * A + B * B == C * C]
}
@public
run = fn () {
io.format("~p~n", [pythag(20)])
}Ela
pyth n = [(x,y,z) \\ x <- [1..n], y <- [x..n], z <- [y..n] | x**2 + y**2 == z**2]Elixir
iex(30)> pytha3 = fn(n) ->
...(30)> for x <- 1..n, y <- x..n, z <- y..n, x*x+y*y == z*z, do: {x,y,z}
...(30)> end
#Function<6.90072148/1 in :erl_eval.expr/5>
iex(31)> pytha3.(20)
[{3, 4, 5}, {5, 12, 13}, {6, 8, 10}, {8, 15, 17}, {9, 12, 15}, {12, 16, 20}]
Erlang
pythag(N) ->
[ {A,B,C} || A <- lists:seq(1,N),
B <- lists:seq(A,N),
C <- lists:seq(B,N),
A+B+C =< N,
A*A+B*B == C*C ].
F#
let pyth n = [ for a in [1..n] do
for b in [a..n] do
for c in [b..n] do
if (a*a+b*b = c*c) then yield (a,b,c)]
Factor
Factor does not support list comprehensions by default. The backtrack vocabulary can make for a faithful imitation, however.
USING: backtrack kernel locals math math.ranges ;
:: pythagorean-triples ( n -- seq )
[
n [1,b] amb-lazy :> a
a n [a,b] amb-lazy :> b
b n [a,b] amb-lazy :> c
a a * b b * + c c * = must-be-true { a b c }
] bag-of ;
Fortran
Complex numbers simplify the task. However, the reshape intrinsic function along with implicit do loops can generate high rank matrices.
!-*- mode: compilation; default-directory: "/tmp/" -*-
!Compilation started at Fri Jun 7 23:39:20
!
!a=./f && make $a && $a
!gfortran -std=f2008 -Wall -fopenmp -ffree-form -fall-intrinsics -fimplicit-none f.f08 -o f
! 3 4 5
! 5 12 13
! 6 8 10
! 8 15 17
! 9 12 15
! 12 16 20
!
!Compilation finished at Fri Jun 7 23:39:20
program list_comprehension
integer, parameter :: n = 20
integer, parameter :: m = n*(n+1)/2
integer :: i, j
complex, dimension(m) :: a
real, dimension(m) :: b
logical, dimension(m) :: c
integer, dimension(3, m) :: d
a = [ ( ( cmplx(i,j), i=j,n), j=1,n) ] ! list comprehension, implicit do loop
b = abs(a)
c = (b .eq. int(b)) .and. (b .le. n)
i = sum(merge(1,0,c))
d(2,:i) = int(real(pack(a, c))) ! list comprehensions: array
d(1,:i) = int(imag(pack(a, c))) ! assignments and operations.
d(3,:i) = int(pack(b,c))
print '(3i4)',d(:,:i)
end program list_comprehension
FreeBASIC
FreeBASIC no tiene listas de comprensión. Una implementación:
Dim As Integer x, y, z, n = 25
For x = 1 To n
For y = x To n
For z = y To n
If x^2 + y^2 = z^2 Then Print Using "{##_, ##_, ##}"; x; y; z
Next z
Next y
Next x
Sleep
- Output:
{ 3, 4, 5}
{ 5, 12, 13}
{ 6, 8, 10}
{ 7, 24, 25}
{ 8, 15, 17}
{ 9, 12, 15}
{12, 16, 20}
{15, 20, 25}
FunL
def triples( n ) = [(a, b, c) | a <- 1..n-2, b <- a+1..n-1, c <- b+1..n if a^2 + b^2 == c^2]
println( triples(20) )- Output:
[(3, 4, 5), (5, 12, 13), (6, 8, 10), (8, 15, 17), (9, 12, 15), (12, 16, 20)]
GAP
# We keep only primitive pythagorean triples
pyth := n ->
Filtered(Cartesian([1 .. n], [1 .. n], [1 .. n]),
u -> u[3]^2 = u[1]^2 + u[2]^2 and u[1] < u[2]
and GcdInt(u[1], u[2]) = 1);
pyth(100);
# [ [ 3, 4, 5 ], [ 5, 12, 13 ], [ 7, 24, 25 ], [ 8, 15, 17 ], [ 9, 40, 41 ], [ 11, 60, 61 ], [ 12, 35, 37 ],
# [ 13, 84, 85 ], [ 16, 63, 65 ], [ 20, 21, 29 ], [ 28, 45, 53 ], [ 33, 56, 65 ], [ 36, 77, 85 ], [ 39, 80, 89 ],
# [ 48, 55, 73 ], [ 65, 72, 97 ] ]
Go
Go doesn't have special syntax for list comprehensions but we can build a function which behaves similarly.
package main
import "fmt"
type (
seq []int
sofs []seq
)
func newSeq(start, end int) seq {
if end < start {
end = start
}
s := make(seq, end-start+1)
for i := 0; i < len(s); i++ {
s[i] = start + i
}
return s
}
func newSofs() sofs {
return sofs{seq{}}
}
func (s sofs) listComp(in seq, expr func(sofs, seq) sofs, pred func(seq) bool) sofs {
var s2 sofs
for _, t := range expr(s, in) {
if pred(t) {
s2 = append(s2, t)
}
}
return s2
}
func (s sofs) build(t seq) sofs {
var u sofs
for _, ss := range s {
for _, tt := range t {
uu := make(seq, len(ss))
copy(uu, ss)
uu = append(uu, tt)
u = append(u, uu)
}
}
return u
}
func main() {
pt := newSofs()
in := newSeq(1, 20)
expr := func(s sofs, t seq) sofs {
return s.build(t).build(t).build(t)
}
pred := func(t seq) bool {
if len(t) != 3 {
return false
}
return t[0]*t[0]+t[1]*t[1] == t[2]*t[2] && t[0] < t[1] && t[1] < t[2]
}
pt = pt.listComp(in, expr, pred)
fmt.Println(pt)
}
- Output:
[[3 4 5] [5 12 13] [6 8 10] [8 15 17] [9 12 15] [12 16 20]]
Haskell
pyth :: Int -> [(Int, Int, Int)]
pyth n =
[ (x, y, z)
| x <- [1 .. n]
, y <- [x .. n]
, z <- [y .. n]
, x ^ 2 + y ^ 2 == z ^ 2 ]
List-comprehensions and do notation are two alternative and equivalent forms of syntactic sugar in Haskell.
The list comprehension above could be re-sugared in Do notation as:
pyth :: Int -> [(Int, Int, Int)]
pyth n = do
x <- [1 .. n]
y <- [x .. n]
z <- [y .. n]
if x ^ 2 + y ^ 2 == z ^ 2
then [(x, y, z)]
else []
and both of the above could be de-sugared to:
pyth :: Int -> [(Int, Int, Int)]
pyth n =
[1 .. n] >>=
\x ->
[x .. n] >>=
\y ->
[y .. n] >>=
\z ->
case x ^ 2 + y ^ 2 == z ^ 2 of
True -> [(x, y, z)]
_ -> []
which can be further specialised (given the particular context of the list monad,
in which (>>=) is flip concatMap, pure is flip (:) [], and empty is []) to:
pyth :: Int -> [(Int, Int, Int)]
pyth n =
concatMap
(\x ->
concatMap
(\y ->
concatMap
(\z ->
if x ^ 2 + y ^ 2 == z ^ 2
then [(x, y, z)]
else [])
[y .. n])
[x .. n])
[1 .. n]
main :: IO ()
main = print $ pyth 25
- Output:
[(3,4,5),(5,12,13),(6,8,10),(7,24,25),(8,15,17),(9,12,15),(12,16,20),(15,20,25)]
Finally an alternative to the list comprehension from the beginning. First introduce all triplets:
triplets n = [(x, y, z) | x <- [1 .. n], y <- [x .. n], z <- [y .. n]]
If we apply this to our list comprehension we get this tidy line of code:
[(x, y, z) | (x, y, z) <- triplets n, x^2 + y^2 == z^2]
Hy
(defn triples [n]
(list-comp (, a b c) [a (range 1 (inc n))
b (range a (inc n))
c (range b (inc n))]
(= (pow c 2)
(+ (pow a 2)
(pow b 2)))))
(print (triples 15))
; [(3, 4, 5), (5, 12, 13), (6, 8, 10), (9, 12, 15)]
Icon and Unicon
Icon's (and Unicon's) natural goal-directly evaluation produces result sequences and can be used to form list comprehensions. For example, the expression:
|(x := seq(), x^2 > 3, x*2)
is capable of producing successive elements from the infinite list described in the Wikipedia article. For example, to produce the first 100 elements:
procedure main()
every write(|(x := seq(), x^2 > 3, x*2) \ 100
end
While result sequences are lexically bound to the code that describes them, that code can be embedded in a co-expression to allow access to the result sequence throughout the code. So Pythagorean triples can be produced with (works in both languages):
procedure main(a)
n := integer(!a) | 20
s := create (x := 1 to n, y := x to n, z := y to n, x^2+y^2 = z^2, [x,y,z])
while a := @s do write(a[1]," ",a[2]," ",a[3])
end
Sample output:
->lc 3 4 5 5 12 13 6 8 10 8 15 17 9 12 15 12 16 20 ->
Insitux
(function pythagorean-triples n
(let n+1 (inc n))
(for x (range 1 n+1)
y (range x n+1)
z (range y n+1)
(unless (= (+ (* x x) (* y y)) (* z z))
(continue))
[x y z]))
(pythagorean-triples 20)- Output:
[[3 4 5] [5 12 13] [6 8 10] [8 15 17] [9 12 15] [12 16 20]]
Ioke
for(
x <- 1..20,
y <- x..20,
z <- y..20,
x * x + y * y == z * z,
[x, y, z]
)
J
require'stats'
buildSet=:conjunction def '(#~ v) u y'
triples=: 1 + 3&comb
isPyth=: 2&{"1 = 1&{"1 +&.:*: 0&{"1
pythTr=: triples buildSet isPyth
The idiom here has two major elements:
First, you need a statement indicating the values of interest. In this case, (1+3&comb) which when used as a function of n specifies a list of triples each in the range 1..n.
Second, you need a statement of the form (#~ B) where B returns true for the desired members, and false for the undesired members.
In the above example, the word isPyth is our predicate (represented as B in the preceding paragraph). This corresponds to the constraint clause in set builder notation.
In the above example the word triples represents the universe of potential solutions (some of which will be valid, some not). This corresponds to the generator part of set builder notation.
The argument to isPyth will be the candidate solutions (the result of triples). The argument to triples will be the largest element desired in a triple.
Example use:
pythTr 20
3 4 5
5 12 13
6 8 10
8 15 17
9 12 15
12 16 20
Java
Java can stream a list, allowing something like a list comprehension. The syntax is (unsurprisingly) verbose, so you might wonder how good the likeness is. I've labeled the parts according to the description in Wikipedia.
Using list-of-arrays made the syntax easier than list-of-lists, but meant that you need the "output expression" part to get to something easily printable.
// Boilerplate
import java.util.Arrays;
import java.util.List;
import static java.util.function.Function.identity;
import static java.util.stream.Collectors.toList;
import static java.util.stream.IntStream.range;
public interface PythagComp{
static void main(String... args){
System.out.println(run(20));
}
static List<List<Integer>> run(int n){
return
// Here comes the list comprehension bit
// input stream - bit clunky
range(1, n).mapToObj(
x -> range(x, n).mapToObj(
y -> range(y, n).mapToObj(
z -> new Integer[]{x, y, z}
)
)
)
.flatMap(identity())
.flatMap(identity())
// predicate
.filter(a -> a[0]*a[0] + a[1]*a[1] == a[2]*a[2])
// output expression
.map(Arrays::asList)
// the result is a list
.collect(toList())
;
}
}
- Output:
[[3, 4, 5], [5, 12, 13], [6, 8, 10], [8, 15, 17], [9, 12, 15]]
JavaScript
ES5
ES5 does not provide built-in notation for list comprehensions. The list monad pattern which underlies list comprehension notation can, however, be used in any language which supports the use of higher order functions. The following shows how we can achieve the same result by directly using a list monad in ES5, without the abbreviating convenience of any specific syntactic sugar.
// USING A LIST MONAD DIRECTLY, WITHOUT SPECIAL SYNTAX FOR LIST COMPREHENSIONS
(function (n) {
return mb(r(1, n), function (x) { // x <- [1..n]
return mb(r(1 + x, n), function (y) { // y <- [1+x..n]
return mb(r(1 + y, n), function (z) { // z <- [1+y..n]
return x * x + y * y === z * z ? [[x, y, z]] : [];
})})});
// LIBRARY FUNCTIONS
// Monadic bind for lists
function mb(xs, f) {
return [].concat.apply([], xs.map(f));
}
// Monadic return for lists is simply lambda x -> [x]
// as in [[x, y, z]] : [] above
// Integer range [m..n]
function r(m, n) {
return Array.apply(null, Array(n - m + 1))
.map(function (n, x) {
return m + x;
});
}
})(100);
Output:
[[3, 4, 5], [5, 12, 13], [6, 8, 10], [7, 24, 25], [8, 15, 17], [9, 12, 15], [9, 40, 41], [10, 24, 26], [11, 60, 61], [12, 16, 20], [12, 35, 37], [13, 84, 85], [14, 48, 50], [15, 20, 25], [15, 36, 39], [16, 30, 34], [16, 63, 65], [18, 24, 30], [18, 80, 82], [20, 21, 29], [20, 48, 52], [21, 28, 35], [21, 72, 75], [24, 32, 40], [24, 45, 51], [24, 70, 74], [25, 60, 65], [27, 36, 45], [28, 45, 53], [28, 96, 100], [30, 40, 50], [30, 72, 78], [32, 60, 68], [33, 44, 55], [33, 56, 65], [35, 84, 91], [36, 48, 60], [36, 77, 85], [39, 52, 65], [39, 80, 89], [40, 42, 58], [40, 75, 85], [42, 56, 70], [45, 60, 75], [48, 55, 73], [48, 64, 80], [51, 68, 85], [54, 72, 90], [57, 76, 95], [60, 63, 87], [60, 80, 100], [65, 72, 97]]
ES6
See here for more details
function range(begin, end) {
for (let i = begin; i < end; ++i)
yield i;
}
function triples(n) {
return [
[x, y, z]
for each(x in range(1, n + 1))
for each(y in range(x, n + 1))
for each(z in range(y, n + 1))
if (x * x + y * y == z * z)
]
}
for each(var triple in triples(20))
print(triple);
outputs:
3,4,5 5,12,13 6,8,10 8,15,17 9,12,15 12,16,20
List comprehension notation was not, in the end, included in the final ES6 standard, and the code above will not run in fully ES6-compliant browsers or interpreters, but we can still go straight to the underlying monadic logic of list comprehensions and obtain:
[ (x, y, z)
| x <- [1 .. n], y <- [x .. n], z <- [y .. n], x ^ 2 + y ^ 2 == z ^ 2 ]
by using concatMap (the monadic bind function for lists), and x => [x] (monadic pure/return for lists):
(n => {
'use strict';
// GENERIC FUNCTIONS ------------------------------------------------------
// concatMap :: (a -> [b]) -> [a] -> [b]
const concatMap = (f, xs) => [].concat.apply([], xs.map(f));
// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = (m, n) =>
Array.from({
length: Math.floor(n - m) + 1
}, (_, i) => m + i);
// EXAMPLE ----------------------------------------------------------------
// [(x, y, z) | x <- [1..n], y <- [x..n], z <- [y..n], x ^ 2 + y ^ 2 == z ^ 2]
return concatMap(x =>
concatMap(y =>
concatMap(z =>
x * x + y * y === z * z ? [
[x, y, z]
] : [],
enumFromTo(y, n)),
enumFromTo(x, n)),
enumFromTo(1, n));
})(20);
Or, expressed in terms of bind (>>=)
(n => {
'use strict';
// GENERIC FUNCTIONS ------------------------------------------------------
// bind (>>=) :: Monad m => m a -> (a -> m b) -> m b
const bind = (m, mf) =>
Array.isArray(m) ? (
bindList(m, mf)
) : bindMay(m, mf);
// bindList (>>=) :: [a] -> (a -> [b]) -> [b]
const bindList = (xs, mf) => [].concat.apply([], xs.map(mf));
// enumFromTo :: Enum a => a -> a -> [a]
const enumFromTo = (m, n) =>
(typeof m !== 'number' ? (
enumFromToChar
) : enumFromToInt)
.apply(null, [m, n]);
// enumFromToInt :: Int -> Int -> [Int]
const enumFromToInt = (m, n) =>
Array.from({
length: Math.floor(n - m) + 1
}, (_, i) => m + i);
// EXAMPLE ----------------------------------------------------------------
// [(x, y, z) | x <- [1..n], y <- [x..n], z <- [y..n], x ^ 2 + y ^ 2 == z ^ 2]
return bind(enumFromTo(1, n),
x => bind(enumFromTo(x, n),
y => bind(enumFromTo(y, n),
z => x * x + y * y === z * z ? [
[x, y, z]
] : []
)));
})(20);
- Output:
[[3, 4, 5], [5, 12, 13], [6, 8, 10], [8, 15, 17], [9, 12, 15], [12, 16, 20]]
JavaScript now has a built-in bind operator for the list monad, in the form of `Array.prototype.flatMap`, allowing us to express list comprehension semantics more directly:
(() => {
"use strict";
// [(x, y, z) | x <- [1..n], y <- [x..n], z <- [y..n], x ^ 2 + y ^ 2 == z ^ 2]
const main = () => {
const n = 20;
return enumFromTo(1)(n).flatMap(
x => enumFromTo(x)(n).flatMap(
y => enumFromTo(y)(n).flatMap(
z => x ** 2 + y ** 2 === z ** 2
? [[x, y, z]]
: []
)
)
);
};
// --------------------- GENERIC ---------------------
// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = m =>
// Enumeration of the integers from m to n.
n => Array.from(
{ length: 1 + n - m },
(_, i) => m + i
);
// MAIN ---
return JSON.stringify(main());
})();
- Output:
[[3,4,5],[5,12,13],[6,8,10],[8,15,17],[9,12,15],[12,16,20]]
jq
Direct approach:
def triples(n):
range(1;n+1) as $x | range($x;n+1) as $y | range($y;n+1) as $z
| select($x*$x + $y*$y == $z*$z)
| [$x, $y, $z] ;Using listof(stream; criterion)
# listof( stream; criterion) constructs an array of those
# elements in the stream that satisfy the criterion
def listof( stream; criterion): [ stream|select(criterion) ];
def listof_triples(n):
listof( range(1;n+1) as $x | range($x;n+1) as $y | range($y;n+1) as $z
| [$x, $y, $z];
.[0] * .[0] + .[1] * .[1] == .[2] * .[2] ) ;
listof_triples(20)- Output:
$ jq -c -n -f list_of_triples.jq [[3,4,5],[5,12,13],[6,8,10],[8,15,17],[9,12,15],[12,16,20]]
Julia
Array comprehension:
julia> n = 20
20
julia> [(x, y, z) for x = 1:n for y = x:n for z = y:n if x^2 + y^2 == z^2]
6-element Array{Tuple{Int64,Int64,Int64},1}:
(3,4,5)
(5,12,13)
(6,8,10)
(8,15,17)
(9,12,15)
(12,16,20)
A Julia generator comprehension (note the outer round brackets), returns an iterator over the same result rather than an explicit array:
julia> ((x, y, z) for x = 1:n for y = x:n for z = y:n if x^2 + y^2 == z^2)
Base.Flatten{Base.Generator{UnitRange{Int64},##33#37}}(Base.Generator{UnitRange{Int64},##33#37}(#33,1:20))
julia> collect(ans)
6-element Array{Tuple{Int64,Int64,Int64},1}:
(3,4,5)
(5,12,13)
(6,8,10)
(8,15,17)
(9,12,15)
(12,16,20)
Array comprehensions may also be N-dimensional, not just vectors:
julia> [i + j for i in 1:5, j in 1:5]
5×5 Array{Int64,2}:
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8
5 6 7 8 9
6 7 8 9 10
julia> [i + j for i in 1:5, j in 1:5, k in 1:2]
5×5×2 Array{Int64,3}:
[:, :, 1] =
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8
5 6 7 8 9
6 7 8 9 10
[:, :, 2] =
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8
5 6 7 8 9
6 7 8 9 10
Kotlin
// version 1.0.6
fun pythagoreanTriples(n: Int) =
(1..n).flatMap {
x -> (x..n).flatMap {
y -> (y..n).filter {
z -> x * x + y * y == z * z
}.map { Triple(x, y, it) }
}
}
fun main(args: Array<String>) {
println(pythagoreanTriples(20))
}
- Output:
[(3, 4, 5), (5, 12, 13), (6, 8, 10), (8, 15, 17), (9, 12, 15), (12, 16, 20)]
Lasso
Lasso uses query expressions for list manipulation.
#!/usr/bin/lasso9
local(n = 20)
local(triples =
with x in generateSeries(1, #n),
y in generateSeries(#x, #n),
z in generateSeries(#y, #n)
where #x*#x + #y*#y == #z*#z
select (:#x, #y, #z)
)
#triples->join('\n')
Output:
staticarray(3, 4, 5)
staticarray(5, 12, 13)
staticarray(6, 8, 10)
staticarray(8, 15, 17)
staticarray(9, 12, 15)
staticarray(12, 16, 20)
Lua
Lua doesn't have list comprehensions built in, but they can be constructed from chained coroutines:
LC={}
LC.__index = LC
function LC:new(o)
o = o or {}
setmetatable(o, self)
return o
end
function LC:add_iter(func)
local prev_iter = self.iter
self.iter = coroutine.wrap(
(prev_iter == nil) and (function() func{} end)
or (function() for arg in prev_iter do func(arg) end end))
return self
end
function maybe_call(maybe_func, arg)
if type(maybe_func) == "function" then return maybe_func(arg) end
return maybe_func
end
function LC:range(key, first, last)
return self:add_iter(function(arg)
for value=maybe_call(first, arg), maybe_call(last, arg) do
arg[key] = value
coroutine.yield(arg)
end
end)
end
function LC:where(pred)
return self:add_iter(function(arg) if pred(arg) then coroutine.yield(arg) end end)
end
We can then define a function to compute Pythagorean triples as follows:
function get(key)
return (function(arg) return arg[key] end)
end
function is_pythagorean(arg)
return (arg.x^2 + arg.y^2 == arg.z^2)
end
function list_pythagorean_triples(n)
return LC:new():range("x",1,n):range("y",1,get("x")):range("z", get("y"), n):where(is_pythagorean).iter
end
for arg in list_pythagorean_triples(100) do
print(arg.x, arg.y, arg.z)
end
Mathematica /Wolfram Language
Select[Tuples[Range[100], 3], #1[[1]]^2 + #1[[2]]^2 == #1[[3]]^2 &]
Pick[#, (#^2).{1, 1, -1}, 0] &@Tuples[Range[100], 3]
MATLAB / Octave
In Matlab/Octave, one does not think much about lists rather than vectors and matrices. Probably, the find() operation comes closes to the task
N = 20
[a,b] = meshgrid(1:N, 1:N);
c = sqrt(a.^2 + b.^2);
[x,y] = find(c == fix(c));
disp([x, y, sqrt(x.^2 + y.^2)])
- Output:
4 3 5
3 4 5
12 5 13
8 6 10
6 8 10
15 8 17
12 9 15
5 12 13
9 12 15
16 12 20
8 15 17
20 15 25
12 16 20
15 20 25
Mercury
Solutions behaves like list comprehension since compound goals resemble set-builder notation.
:- module pythtrip.
:- interface.
:- import_module io.
:- import_module int.
:- type triple ---> triple(int, int, int).
:- pred pythTrip(int::in,triple::out) is nondet.
:- pred main(io::di, io::uo) is det.
:- implementation.
:- import_module list.
:- import_module solutions.
:- import_module math.
pythTrip(Limit,triple(X,Y,Z)) :-
nondet_int_in_range(1,Limit,X),
nondet_int_in_range(X,Limit,Y),
nondet_int_in_range(Y,Limit,Z),
pow(Z,2) = pow(X,2) + pow(Y,2).
main(!IO) :-
solutions((pred(Triple::out) is nondet :- pythTrip(20,Triple)),Result),
write(Result,!IO).Nemerle
Demonstrating a list comprehension and an iterator. List comprehension adapted from Haskell example, iterator adapted from C# example.
using System;
using System.Console;
using System.Collections.Generic;
module Program
{
PythTriples(n : int) : list[int * int * int]
{
$[ (x, y, z) | x in [1..n], y in [x..n], z in [y..n], ((x**2) + (y**2)) == (z**2) ]
}
GetPythTriples(n : int) : IEnumerable[int * int * int]
{
foreach (x in [1..n])
{
foreach (y in [x..n])
{
foreach (z in [y..n])
{
when (((x**2) + (y**2)) == (z**2))
{
yield (x, y, z)
}
}
}
}
}
Main() : void
{
WriteLine("Pythagorean triples up to x = 20: {0}", PythTriples(20));
foreach (triple in GetPythTriples(20))
{
Write(triple)
}
}
}
Nim
List comprehension is done in the standard library with the collect() macro (which uses for-loop macros) from the sugar package:
import sugar, math
let n = 20
let triplets = collect(newSeq):
for x in 1..n:
for y in x..n:
for z in y..n:
if x^2 + y^2 == z^2:
(x,y,z)
echo triplets
Output:
@[(3, 4, 5), (5, 12, 13), (6, 8, 10), (8, 15, 17), (9, 12, 15), (12, 16, 20)]
A special syntax for list comprehensions in Nim can be implemented thanks to the strong metaprogramming capabilities:
import macros
type ListComprehension = object
var lc*: ListComprehension
macro `[]`*(lc: ListComprehension, x, t): untyped =
expectLen(x, 3)
expectKind(x, nnkInfix)
expectKind(x[0], nnkIdent)
assert($x[0].strVal == "|")
result = newCall(
newDotExpr(
newIdentNode("result"),
newIdentNode("add")),
x[1])
for i in countdown(x[2].len-1, 0):
let y = x[2][i]
expectKind(y, nnkInfix)
expectMinLen(y, 1)
if y[0].kind == nnkIdent and $y[0].strVal == "<-":
expectLen(y, 3)
result = newNimNode(nnkForStmt).add(y[1], y[2], result)
else:
result = newIfStmt((y, result))
result = newNimNode(nnkCall).add(
newNimNode(nnkPar).add(
newNimNode(nnkLambda).add(
newEmptyNode(),
newEmptyNode(),
newEmptyNode(),
newNimNode(nnkFormalParams).add(
newNimNode(nnkBracketExpr).add(
newIdentNode("seq"),
t)),
newEmptyNode(),
newEmptyNode(),
newStmtList(
newAssignment(
newIdentNode("result"),
newNimNode(nnkPrefix).add(
newIdentNode("@"),
newNimNode(nnkBracket))),
result))))
const n = 20
echo lc[(x,y,z) | (x <- 1..n, y <- x..n, z <- y..n, x*x + y*y == z*z), tuple[a,b,c: int]]
Output:
@[(a: 3, b: 4, c: 5), (a: 5, b: 12, c: 13), (a: 6, b: 8, c: 10), (a: 8, b: 15, c: 17), (a: 9, b: 12, c: 15), (a: 12, b: 16, c: 20)]
OCaml
As of OCaml 4.08 (2019), binding operators were added to the language syntax. A general notion of "comprehension syntax" can be recovered using them.
Assuming a comprehension is of the form
[ expression | x <- enumeration ; condition ; ... ]
We can rewrite it using binding operators like so
let* x = enumeration in
if not condition then empty else
return expression
For instance, we can write the required Pythagorean triples comprehension:
let pyth n =
let* x = 1 -- n in
let* y = x -- n in
let* z = y -- n in
if x * x + y * y <> z * z then [] else
[x, y, z]
where the (let*) and (--) operators are defined for the List module like so:
let (let*) xs f = List.concat_map f xs
let (--) a b = List.init (b-a+1) ((+)a)
Historical note
- OCaml never had a built-in list-comprehension syntax. However, there have been a couple of preprocessing syntax extensions which aimed to add list comprehensions sugar to the language. One of which was shipped directly with camlp4, a tool for syntax extensions that was bundled with the OCaml compiler distribution, up to version 4.02 (2014), and was completely deprecated after version 4.08 (2019).
- Another, OCaml Batteries Included, had uniform comprehension syntax for lists, arrays, enumerations (like streams), lazy lists (like lists but evaluated on-demand), sets, hashtables, etc. This later split into the now legacy package pa_comprehensions, which is similarly deprecated.
Oz
Oz does not have list comprehension.
However, there is a list comprehension package available here. It uses the unofficial and deprecated macro system. Usage example:
functor
import
LazyList
Application
System
define
fun {Pyth N}
<<list [X Y Z] with
X <- {List.number 1 N 1}
Y <- {List.number X N 1}
Z <- {List.number Y N 1}
where X*X + Y*Y == Z*Z
>>
end
{ForAll {Pyth 20} System.show}
{Application.exit 0}
endPARI/GP
GP 2.6.0 added support for a new comprehension syntax:
f(n)=[v|v<-vector(n^3,i,vector(3,j,i\n^(j-1)%n)),norml2(v)==2*v[3]^2]Older versions of GP can emulate this through select:
- This code uses the select() function, which was added in PARI version 2.4.2. The order of the arguments changed between versions; to use in 2.4.2 change
select(function, vector)toselect(vector, function).
f(n)=select(v->norml2(v)==2*v[3]^2,vector(n^3,i,vector(3,j,i\n^(j-1)%n)))Version 2.4.2 (obsolete, but widespread on Windows systems) requires inversion:
f(n)=select(vector(n^3,i,vector(3,j,i\n^(j-1)%n)),v->norml2(v)==2*v[3]^2)PascalABC.NET
##
(1..20).CartesianPower(3).Where(\(x,y,z) -> (x*x + y*y = z*z) and (x < y)).PrintLines
- Output:
[3,4,5] [5,12,13] [6,8,10] [8,15,17] [9,12,15] [12,16,20]
Perl
Perl 5 does not have built-in list comprehension syntax. The closest approach are the list map and grep (elsewhere often known as filter) operators:
sub triples ($) {
my ($n) = @_;
map { my $x = $_; map { my $y = $_; map { [$x, $y, $_] } grep { $x**2 + $y**2 == $_**2 } 1..$n } 1..$n } 1..$n;
}
map binds $_ to each element of the input list and collects the results from the block. grep returns every element of the input list for which the block returns true. The .. operator generates a list of numbers in a specific range.
for my $t (triples(10)) {
print "@$t\n";
}
Phix
Phix does not have builtin support for list comprehensions.
However, consider the fact that the compiler essentially converts an expression such as s[i] into calls to the low-level back end (machine code) routines :%opRepe and :%opSubse depending on context (although somtimes it will inline things and sometimes for better performance it will use opRepe1/opRepe1ip/opRepe1is and opSubse1/opSubse1i/opSubse1is/opSubse1ip variants, but that's just detail). It also maps ? to hll print().
Thinking laterally, Phix also does not have any special syntax for dictionaries, instead they are supported via an autoinclude with the following standard hll routines:
global function new_dict(integer pool_only=0) global procedure destroy_dict(integer tid, integer justclear=0) global procedure setd(object key, object data, integer tid=1) global function getd(object key, integer tid=1) global procedure destroy_dict(integer tid, integer justclear=0) global function getd_index(object key, integer tid=1) global function getd_by_index(integer node, integer tid=1) global procedure deld(object key, integer tid=1) global procedure traverse_dict(integer rid, object user_data=0, integer tid=1) global function dict_size(integer tid=1)
Clearly it would be relatively trivial for the compiler, just like it does with s[i], to map some other new dictionary syntax to calls to these routines (not that it would ever use the default tid of 1, and admittedly traverse_dict might prove a bit trickier than the rest). Since Phix is open source, needs no other tools, and compiles itself in 10s, that is not as unreasonable for you (yes, you) to attempt as it might first sound.
With all that in mind, the following (which works just fine as it is) might be a first step to formal list comprehension support:
-- demo\rosetta\List_comprehensions.exw with javascript_semantics function list_comprehension(sequence s, integer rid, integer k, integer level=1, sequence args={}) sequence res = {} args &= 0 for i=1 to length(s) do args[$] = s[i] if level<k then res &= list_comprehension(s,rid,k,level+1,deep_copy(args)) else res &= call_func(rid,args) end if end for return res end function function triangle(integer a, b, c) if a<b and a*a+b*b=c*c then return {{a,b,c}} end if return {} end function ?list_comprehension(tagset(20),routine_id("triangle"),3)
- Output:
{{3,4,5},{5,12,13},{6,8,10},{8,15,17},{9,12,15},{12,16,20}}
Picat
List comprehensions
pyth(N) = [[A,B,C] : A in 1..N, B in A..N, C in B..N, A**2 + B**2 == C**2].Array comprehensions
Picat also has array comprehensions. Arrays are generally used for faster access (using {} instead of []).
pyth(N) = {{A,B,C} : A in 1..N, B in A..N, C in B..N, A**2 + B**2 == C**2}.findall/2
A related construct is findall/2 to get all solutions for the specific goal at the second parameter. Here this is shown with member/2 for generating the numbers to test (which for this task is fairly inefficient).
pyth(N) = findall([A,B,C], (member(A,1..N), member(B,1..N), member(C,1..N), A < B, A**2 + B**2 == C**2)).
PicoLisp
PicoLisp doesn't have list comprehensions. We might use a generator function, pipe, coroutine or pilog predicate.
Using a generator function
(de pythag (N)
(job '((X . 1) (Y . 1) (Z . 0))
(loop
(when (> (inc 'Z) N)
(when (> (inc 'Y) N)
(setq Y (inc 'X)) )
(setq Z Y) )
(T (> X N))
(T (= (+ (* X X) (* Y Y)) (* Z Z))
(list X Y Z) ) ) ) )
(while (pythag 20)
(println @) )Using a pipe
(pipe
(for X 20
(for Y (range X 20)
(for Z (range Y 20)
(when (= (+ (* X X) (* Y Y)) (* Z Z))
(pr (list X Y Z)) ) ) ) )
(while (rd)
(println @) ) )Using a coroutine
Coroutines are available only in the 64-bit version.
(de pythag (N)
(co 'pythag
(for X N
(for Y (range X N)
(for Z (range Y N)
(when (= (+ (* X X) (* Y Y)) (* Z Z))
(yield (list X Y Z)) ) ) ) ) ) )
(while (pythag 20)
(println @) )Output in all three cases:
(3 4 5) (5 12 13) (6 8 10) (8 15 17) (9 12 15) (12 16 20)
Using Pilog
(be pythag (@N @X @Y @Z)
(for @X @N)
(for @Y @X @N)
(for @Z @Y @N)
(^ @
(let (X (-> @X) Y (-> @Y) Z (-> @Z))
(= (+ (* X X) (* Y Y)) (* Z Z)) ) ) )Test:
: (? (pythag 20 @X @Y @Z))
@X=3 @Y=4 @Z=5
@X=5 @Y=12 @Z=13
@X=6 @Y=8 @Z=10
@X=8 @Y=15 @Z=17
@X=9 @Y=12 @Z=15
@X=12 @Y=16 @Z=20
-> NILProlog
SWI-Prolog does not have list comprehension, however we can simulate it.
% We need operators
:- op(700, xfx, <-).
:- op(450, xfx, ..).
:- op(1100, yfx, &).
% use for explicit list usage
my_bind(V, [H|_]) :- V = H.
my_bind(V, [_|T]) :- my_bind(V, T).
% we need to define the intervals of numbers
Vs <- M..N :-
integer(M),
integer(N),
M =< N,
between(M, N, Vs).
% for explicit list comprehension like Vs <- [1,2,3]
Vs <- Xs :-
is_list(Xs),
my_bind(Vs, Xs).
% finally we define list comprehension
% prototype is Vs <- {Var, Dec, Pred} where
% Var is the list of variables to output
% Dec is the list of intervals of the variables
% Pred is the list of predicates
Vs <- {Var & Dec & Pred} :-
findall(Var, maplist(call, [Dec, Pred]), Vs).
% for list comprehension without Pred
Vs <- {Var & Dec} :-
findall(Var, maplist(call, [Dec]), Vs).
Examples of use :
List of Pythagorean triples :
?- V <- {X, Y, Z & X <- 1..20, Y <- X..20, Z <- Y..20 & X*X+Y*Y =:= Z*Z}.
V = [ (3,4,5), (5,12,13), (6,8,10), (8,15,17), (9,12,15), (12,16,20)] ;
false.
List of double of x, where x^2 is greater than 50 :
?- V <- {Y & X <- 1..20 & X*X > 50, Y is 2 * X}.
V = [16,18,20,22,24,26,28,30,32,34,36,38,40] ;
false.
?- Vs <- {X, Y & X <- [1,2,3], Y <- [1,2,3, 4] & X = Y}.
Vs = [ (1, 1), (2, 2), (3, 3)].
?- Vs <- {X, Y & X <- [1,2,3], Y <- 1..5 & X = Y}.
Vs = [ (1, 1), (2, 2), (3, 3)].
?- Vs <- {X, Y & X <- [1,2], Y <- [4,5] }.
Vs = [ (1, 4), (1, 5), (2, 4), (2, 5)].
Python
import itertools
n = 20
# List comprehension:
[(x,y,z) for x in xrange(1,n+1) for y in xrange(x,n+1) for z in xrange(y,n+1) if x**2 + y**2 == z**2]
# A Python generator expression (note the outer round brackets),
# returns an iterator over the same result rather than an explicit list:
((x,y,z) for x in xrange(1,n+1) for y in xrange(x,n+1) for z in xrange(y,n+1) if x**2 + y**2 == z**2)
# A slower but more readable version:
[(x, y, z) for (x, y, z) in itertools.product(xrange(1,n+1),repeat=3) if x**2 + y**2 == z**2 and x <= y <= z]
# Or as an iterator:
((x, y, z) for (x, y, z) in itertools.product(xrange(1,n+1),repeat=3) if x**2 + y**2 == z**2 and x <= y <= z)
# Alternatively we shorten the initial list comprehension but this time without compromising on speed.
# First we introduce a generator which generates all triplets:
def triplets(n):
for x in xrange(1, n + 1):
for y in xrange(x, n + 1):
for z in xrange(y, n + 1):
yield x, y, z
# Apply this to our list comprehension gives:
[(x, y, z) for (x, y, z) in triplets(n) if x**2 + y**2 == z**2]
# Or as an iterator:
((x, y, z) for (x, y, z) in triplets(n) if x**2 + y**2 == z**2)
# More generally, the list comprehension syntax can be understood as a concise syntactic sugaring
# of a use of the list monad, in which non-matches are returned as empty lists, matches are wrapped
# as single-item lists, and concatenation flattens the output, eliminating the empty lists.
# The monadic 'bind' operator for lists is concatMap, traditionally used with its first two arguments flipped.
# The following three formulations of a '''pts''' (pythagorean triangles) function are equivalent:
from functools import (reduce)
from operator import (add)
# pts :: Int -> [(Int, Int, Int)]
def pts(n):
m = 1 + n
return [(x, y, z) for x in xrange(1, m)
for y in xrange(x, m)
for z in xrange(y, m) if x**2 + y**2 == z**2]
# pts2 :: Int -> [(Int, Int, Int)]
def pts2(n):
m = 1 + n
return bindList(
xrange(1, m)
)(lambda x: bindList(
xrange(x, m)
)(lambda y: bindList(
xrange(y, m)
)(lambda z: [(x, y, z)] if x**2 + y**2 == z**2 else [])))
# pts3 :: Int -> [(Int, Int, Int)]
def pts3(n):
m = 1 + n
return concatMap(
lambda x: concatMap(
lambda y: concatMap(
lambda z: [(x, y, z)] if x**2 + y**2 == z**2 else []
)(xrange(y, m))
)(xrange(x, m))
)(xrange(1, m))
# GENERIC ---------------------------------------------------------
# concatMap :: (a -> [b]) -> [a] -> [b]
def concatMap(f):
return lambda xs: (
reduce(add, map(f, xs), [])
)
# (flip concatMap)
# bindList :: [a] -> (a -> [b]) -> [b]
def bindList(xs):
return lambda f: (
reduce(add, map(f, xs), [])
)
def main():
for f in [pts, pts2, pts3]:
print (f(20))
main()
- Output:
[(3, 4, 5), (5, 12, 13), (6, 8, 10), (8, 15, 17), (9, 12, 15), (12, 16, 20)] [(3, 4, 5), (5, 12, 13), (6, 8, 10), (8, 15, 17), (9, 12, 15), (12, 16, 20)] [(3, 4, 5), (5, 12, 13), (6, 8, 10), (8, 15, 17), (9, 12, 15), (12, 16, 20)]
R
R has inherent list comprehension:
x = (0:10)
> x^2
[1] 0 1 4 9 16 25 36 49 64 81 100
> Reduce(function(y,z){return (y+z)},x)
[1] 55
> x[x[(0:length(x))] %% 2==0]
[1] 0 2 4 6 8 10
R's "data frame" functions can be used to achieve the same code clarity (at the cost of expanding the entire grid into memory before the filtering step)
subset(expand.grid(x=1:n, y=1:n, z=1:n), x^2 + y^2 == z^2)
Racket
#lang racket
(for*/list ([x (in-range 1 21)]
[y (in-range x 21)]
[z (in-range y 21)]
#:when (= (+ (* x x) (* y y)) (* z z)))
(list x y z))
Raku
(formerly Perl 6) Raku has single-dimensional list comprehensions that fall out naturally from nested modifiers; multidimensional comprehensions are also supported via the cross operator; however, Raku does not (yet) support multi-dimensional list comprehensions with dependencies between the lists, so the most straightforward way is currently:
my $n = 20;
say gather for 1..$n -> $x {
for $x..$n -> $y {
for $y..$n -> $z {
take $x,$y,$z if $x*$x + $y*$y == $z*$z;
}
}
}
- Output:
((3 4 5) (5 12 13) (6 8 10) (8 15 17) (9 12 15) (12 16 20))
Note that gather/take is the primitive in Raku corresponding to generators or coroutines in other languages. It is not, however, tied to function call syntax in Raku. We can get away with that because lists are lazy, and the demand for more of the list is implicit; it does not need to be driven by function calls.
Rascal
public list[tuple[int, int, int]] PythTriples(int n) = [<a, b, c> | a <- [1..n], b <- [1..n], c <- [1 .. n], a*a + b*b == c*c];REXX
There is no native comprehensive support for lists per se, except that
normal lists can be processed quite easily and without much effort.
vertical list
/*REXX program displays a vertical list of Pythagorean triples up to a specified number.*/
parse arg n . /*obtain optional argument from the CL.*/
if n=='' | n=="," then n= 100 /*Not specified? Then use the default.*/
say 'Pythagorean triples (a² + b² = c², c ≤' n"):" /*display the list's title. */
$= /*assign a null to the triples list. */
do a=1 for n-2; aa=a*a
do b=a+1 to n-1; ab=aa + b*b
do c=b+1 to n ; cc= c*c
if ab<cc then leave /*Too small? Then try the next B. */
if ab==cc then do; $=$ '{'a"," || b','c"}"; leave; end
end /*c*/
end /*b*/
end /*a*/
#= words($); sat
do j=1 for #
say left('', 20) word($, j) /*display a member of the list, */
end /*j*/ /* [↑] list the members vertically. */
say
say # ' members listed.' /*stick a fork in it, we're all done. */
- output when using the default input:
Pythagorean triples (a² + b² = c², c ≤ 100):
{3,4,5}
{5,12,13}
{6,8,10}
{7,24,25}
{8,15,17}
{9,12,15}
{9,40,41}
{10,24,26}
{11,60,61}
{12,16,20}
{12,35,37}
{13,84,85}
{14,48,50}
{15,20,25}
{15,36,39}
{16,30,34}
{16,63,65}
{18,24,30}
{18,80,82}
{20,21,29}
{20,48,52}
{21,28,35}
{21,72,75}
{24,32,40}
{24,45,51}
{24,70,74}
{25,60,65}
{27,36,45}
{28,45,53}
{28,96,100}
{30,40,50}
{30,72,78}
{32,60,68}
{33,44,55}
{33,56,65}
{35,84,91}
{36,48,60}
{36,77,85}
{39,52,65}
{39,80,89}
{40,42,58}
{40,75,85}
{42,56,70}
{45,60,75}
{48,55,73}
{48,64,80}
{51,68,85}
{54,72,90}
{57,76,95}
{60,63,87}
{60,80,100}
{65,72,97}
52 members listed.
horizontal list
/*REXX program shows a horizontal list of Pythagorean triples up to a specified number. */
parse arg n . /*obtain optional argument from the CL.*/
if n=='' | n=="," then n= 100 /*Not specified? Then use the default.*/
do k=1 for n; @.k= k*k /*precompute the squares of usable #'s.*/
end /*k*/
sw= linesize() - 1 /*obtain the terminal width (less one).*/
say 'Pythagorean triples (a² + b² = c², c ≤' n"):" /*display the list's title. */
$= /*assign a null to the triples list. */
do a=1 for n-2; bump= a//2 /*Note: A*A is faster than A**2. */
do b=a+1 to n-1 by 1+bump
ab= @.a + @.b /*AB: a shortcut for the sum of A² & B²*/
if bump==0 & b//2==0 then cump= 2
else cump= 1
do c=b+cump to n by cump
if ab<@.c then leave /*Too small? Then try the next B. */
if ab==@.c then do; $=$ '{'a"," || b','c"}"; leave; end
end /*c*/
end /*b*/
end /*a*/
#= words($); say
do j=1 until p==0; p= lastPos('}', $, sw) /*find the last } */
if p\==0 then do; _= left($, p)
say strip(_)
$= substr($, p+1)
end
end /*j*/
say strip($); say
say # ' members listed.' /*stick a fork in it, we're all done. */
- output when using the following input: 35
Pythagorean triples (a² + b² = c², c ≤ 35):
{3,4,5} {5,12,13} {6,8,10} {7,24,25} {8,15,17} {9,12,15} {10,24,26} {12,16,20} {15,20,25} {16,30,34} {18,24,30} {20,21,29} {21,28,35}
13 members listed.
Ring
for x = 1 to 20
for y = x to 20
for z = y to 20
if pow(x,2) + pow(y,2) = pow(z,2)
see "[" + x + "," + y + "," + z + "]" + nl ok
next
next
nextRuby
Ruby has no special syntax for list comprehensions.
Enumerable#select comprises a list from one variable, like Perl grep() or Python filter(). Some lists need Array#map! to transform the variable.
- (1..100).select { |x| x % 3 == 0 } is the list of all x from 1 to 100 such that x is a multiple of 3.
- methods.select { |name| name.length <= 5 } is the list of all methods from self with names not longer than 5 characters.
- Dir["/bin/*"].select { |p| File.setuid? p }.map! { |p| File.basename p } is the list of all files in /bin with a setuid bit.
Ruby's object-oriented style enforces writing 1..100 before x. Think not of x in 1..100. Think of 1..100 giving x.
Ruby 1.9.2
n = 20
# select Pythagorean triplets
r = ((1..n).flat_map { |x|
(x..n).flat_map { |y|
(y..n).flat_map { |z|
[[x, y, z]].keep_if { x * x + y * y == z * z }}}})
p r # print the array _r_
Output: [[3, 4, 5], [5, 12, 13], [6, 8, 10], [8, 15, 17], [9, 12, 15], [12, 16, 20]]
Ruby 1.9.2 introduces two new methods: Enumerable#flat_map joins all the arrays from the block. Array#keep_if is an alternative to Enumerable#select that modifies the original array. (We avoid Array#select! because it might not return the array.)
- The [[x, y, z]].keep_if { ... } returns either an array of one Pythagorean triplet, or an empty array.
- The inner (y..n).flat_map { ... } concatenates those arrays for all z given some x, y.
- The middle (x..n).flat_map { ... } concatenates the inner arrays for all y given some x.
- The outer (1..n).flat_map { ... } concatenates the middle arrays for all x.
Illustrating a way to avoid all loops (but no list comprehensions) :
n = 20
p (1..n).to_a.combination(3).select{|a,b,c| a*a + b*b == c*c}
Run BASIC
for x = 1 to 20
for y = x to 20
for z = y to 20
if x^2 + y^2 = z^2 then print "[";x;",";y;",";z;"]"
next z
next y
next xOutput:
[3,4,5] [5,12,13] [6,8,10] [8,15,17] [9,12,15] [12,16,20]
Rust
Rust doesn't have comprehension-syntax, but it has powerful lazy-iteration mechanisms topped with a powerful macro system, as such you can implement comprehensions on top of the language fairly easily.
Iterator
First using the built-in iterator trait, we can simply flat-map and then filter-map:
fn pyth(n: u32) -> impl Iterator<Item = [u32; 3]> {
(1..=n).flat_map(move |x| {
(x..=n).flat_map(move |y| {
(y..=n).filter_map(move |z| {
if x.pow(2) + y.pow(2) == z.pow(2) {
Some([x, y, z])
} else {
None
}
})
})
})
}
- Using
flat_mapwe can map and flatten an iterator.
- Use
filter_mapwe can return anOptionwhereSome(value)is returned orNoneisn't. Technically we could also useflat_mapinstead, becauseOptionimplementsIntoIterator.
- Using the
impl Traitsyntax, we return theIteratorgenerically, because it's statically known.
- Using the
movesyntax on the closure, means the closure will take ownership of the values (copying them) which is what we wan't because the captured variables will be returned multiple times.
Comprehension Macro
Using the above and macro_rules! we can implement comprehension with a reasonably sized macro:
macro_rules! comp {
($e:expr, for $x:pat in $xs:expr $(, if $c:expr)?) => {{
$xs.filter_map(move |$x| if $($c &&)? true { Some($e) } else { None })
}};
($e:expr, for $x:pat in $xs:expr $(, for $y:pat in $ys:expr)+ $(, if $c:expr)?) => {{
$xs.flat_map(move |$x| comp!($e, $(for $y in $ys),+ $(, if $c)?))
}};
}
The way to understand a Rust macro is it's a bit like regular expressions. The input matches a type of token, and expands it into the block, for example take the follow pattern:
($e:expr, for $x:pat in $xs:expr $(, if $c:expr)?)
- matches an
exprexpression, defines it to$e - matches the tokens
, for - matches a
patpattern, defines it to$x - matches the tokens
in - matches an
exprexpression, defines it to$xs - matches
$(..)?optional group- patches tokens
, if - matches an
exprexpression, defines it to$c
- patches tokens
This makes the two following blocks equivalent:
comp!(x, for x in 0..10, if x != 5)
(0..10).filter_map(move |x| {
if x != 5 && true {
Some(x)
} else {
None
}
})
The most interesting part of comp! is that it's a recursive macro (it expands within itself), and that means it can handle any number of iterators as inputs.
Iterator Comprehension
The pythagorean function could as such be defined as the following:
fn pyth(n: u32) -> impl Iterator<Item = [u32; 3]> {
comp!(
[x, y, z],
for x in 1..=n,
for y in x..=n,
for z in y..=n,
if x.pow(2) + y.pow(2) == z.pow(2)
)
}
Scala
def pythagoranTriangles(n: Int) = for {
x <- 1 to 21
y <- x to 21
z <- y to 21
if x * x + y * y == z * z
} yield (x, y, z)
which is a syntactic sugar for:
def pythagoranTriangles(n: Int) = (1 to n) flatMap (x =>
(x to n) flatMap (y =>
(y to n) filter (z => x * x + y * y == z * z) map (z =>
(x, y, z))))
Alas, the type of collection returned depends on the type of the collection
being comprehended. In the example above, we are comprehending a Range.
Since a Range of triangles doesn't make sense, it returns the
closest (supertype) collection for which it does, an IndexedSeq.
To get a List out of it, just pass a List to it:
def pythagoranTriangles(n: Int) = for {
x <- List.range(1, n + 1)
y <- x to 21
z <- y to 21
if x * x + y * y == z * z
} yield (x, y, z)
Sample:
scala> pythagoranTriangles(21) res36: List[(Int, Int, Int)] = List((3,4,5), (5,12,13), (6,8,10), (8,15,17), (9,12,15), (12,16,20))
Scheme
Scheme has no native list comprehensions, but SRFI-42 [1] provides them:
(list-ec (:range x 1 21)
(:range y x 21)
(:range z y 21)
(if (= (* z z) (+ (* x x) (* y y))))
(list x y z))
((3 4 5) (5 12 13) (6 8 10) (8 15 17) (9 12 15) (12 16 20))
Solution 2.
The previous solution was excellent, but let's do a little golfing. (By the way, in the SRFI-42 library "ec" stands for "eager comprehensions". The package contains very useful looping macros.)
(use srfi-42) ;; for Gauche or Chicken
or
(require srfi/42) ;; for Racket
(list-ec (: x 1 21)
(: y x 21)
(: z y 21)
(if (= (* z z) (+ (* x x) (* y y))))
(list x y z))
Sidef
var n = 20
say gather {
for x in (1 .. n) {
for y in (x .. n) {
for z in (y .. n) {
take([x,y,z]) if (x*x + y*y == z*z)
}
}
}
}
- Output:
[[3, 4, 5], [5, 12, 13], [6, 8, 10], [8, 15, 17], [9, 12, 15], [12, 16, 20]]
Smalltalk
| test |
test := [ :a :b :c | a*a+(b*b)=(c*c) ].
(1 to: 20)
combinations: 3 atATimeDo: [ :x |
(test valueWithArguments: x)
ifTrue: [ ':-)' logCr: x ] ].
"output on Transcript:
#(3 4 5)
#(5 12 13)
#(6 8 10)
#(8 15 17)
#(9 12 15)
#(12 16 20)"
Stata
Stata does no have list comprehensions, but the Mata matrix language helps simplify this task.
function grid(n,p) {
return(colshape(J(1,p,1::n),1),J(n,1,1::p))
}
n = 20
a = grid(n,n)
a = a,sqrt(a[.,1]:^2+a[.,2]:^2)
a[selectindex(floor(a[.,3]):==a[.,3] :& a[.,3]:<=n),]
Output
1 2 3
+----------------+
1 | 3 4 5 |
2 | 4 3 5 |
3 | 5 12 13 |
4 | 6 8 10 |
5 | 8 6 10 |
6 | 8 15 17 |
7 | 9 12 15 |
8 | 12 5 13 |
9 | 12 9 15 |
10 | 12 16 20 |
11 | 15 8 17 |
12 | 16 12 20 |
+----------------+
SuperCollider
var pyth = { |n|
all {: [x,y,z],
x <- (1..n),
y <- (x..n),
z <- (y..n),
(x**2) + (y**2) == (z**2)
}
};
pyth.(20) // example call
returns
[ [ 3, 4, 5 ], [ 5, 12, 13 ], [ 6, 8, 10 ], [ 8, 15, 17 ], [ 9, 12, 15 ], [ 12, 16, 20 ] ]
Swift
typealias F1 = (Int) -> [(Int, Int, Int)]
typealias F2 = (Int) -> Bool
func pythagoreanTriples(n: Int) -> [(Int, Int, Int)] {
(1...n).flatMap({x in
(x...n).flatMap({y in
(y...n).filter({z in
x * x + y * y == z * z
} as F2).map({ (x, y, $0) })
} as F1)
} as F1)
}
print(pythagoreanTriples(n: 20))
- Output:
[(3, 4, 5), (5, 12, 13), (6, 8, 10), (8, 15, 17), (9, 12, 15), (12, 16, 20)]
Tcl
Tcl does not have list comprehensions built-in to the language, but they can be constructed.
package require Tcl 8.5
# from http://wiki.tcl.tk/12574
proc lcomp {expression args} {
# Check the number of arguments.
if {[llength $args] < 2} {
error "wrong # args: should be \"lcomp expression var1 list1\
?... varN listN? ?condition?\""
}
# Extract condition from $args, or use default.
if {[llength $args] % 2 == 1} {
set condition [lindex $args end]
set args [lrange $args 0 end-1]
} else {
set condition 1
}
# Collect all var/list pairs and store in reverse order.
set varlst [list]
foreach {var lst} $args {
set varlst [concat [list $var] [list $lst] $varlst]
}
# Actual command to be executed, repeatedly.
set script {lappend result [subst $expression]}
# If necessary, make $script conditional.
if {$condition ne "1"} {
set script [list if $condition $script]
}
# Apply layers of foreach constructs around $script.
foreach {var lst} $varlst {
set script [list foreach $var $lst $script]
}
# Do it!
set result [list]
{*}$script ;# Change to "eval $script" if using Tcl 8.4 or older.
return $result
}
set range {1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20}
puts [lcomp {$x $y $z} x $range y $range z $range {$x < $y && $x**2 + $y**2 == $z**2}]
{3 4 5} {5 12 13} {6 8 10} {8 15 17} {9 12 15} {12 16 20}
TI-89 BASIC
TI-89 BASIC does not have a true list comprehension, but it has the seq() operator which can be used for some similar purposes.
{1, 2, 3, 4} → a
seq(a[i]^2, i, 1, dim(a))produces {1, 4, 9, 16}. When the input is simply a numeric range, an input list is not needed; this produces the same result:
seq(x^2, x, 1, 4)Transd
The language's construct for list comprehension closely follows the established set-builder notation:
FOR x IN <SET> WHERE predicate(x) PROJECT f(x)
The special form of 'for' construct performs list comprehension and returns a collection with selected elements.
In basic form, the returned vector is created and filled automatically:
(with v (for x in Range(10)
project (* x x))
(textout v))
- Output:
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
Basic form with 'WHERE' clause:
(with v (for x in Range(10)
where (mod x 2)
project Vector<ULong>([x,(* x x)]))
(textout v))
- Output:
[[1, 1], [3, 9], [5, 25], [7, 49], [9, 81]]
In cases when more customized behaviour is required, there is an option to define and fill the returned collection directly:
(with v (for x in Range(1 n) project<Vector<ULong>>
(for y in Range(x n) do
(for z in Range(y n)
where (== (* z z) (+ (* y y) (* x x)))
do (append @projRes Vector<ULong>([x,y,z])))))
(textout "Pythagorean triples:\n" v))
}
- Output:
Pythagorean triples: [[3, 4, 5], [5, 12, 13], [6, 8, 10], [9, 12, 15]]
Uiua
☇1⊞≡⊂⊞⊂..+1⇡20 # Cartesian product, flattened.
▽⊸≡(=1/↧/≥◫2) # Keep triplets which are in ascending order.
▽⊸≡(=⊃(/+⊏0_1|⊡2)×.) # Keep pythagorean triplets.- Output:
╭─
╷ 3 4 5
5 12 13
6 8 10
8 15 17
9 12 15
12 16 20
╯
Visual Basic .NET
Module ListComp
Sub Main()
Dim ts = From a In Enumerable.Range(1, 20) _
From b In Enumerable.Range(a, 21 - a) _
From c In Enumerable.Range(b, 21 - b) _
Where a * a + b * b = c * c _
Select New With { a, b, c }
For Each t In ts
System.Console.WriteLine("{0}, {1}, {2}", t.a, t.b, t.c)
Next
End Sub
End Module
Output:
3, 4, 5 5, 12, 13 6, 8, 10 8, 15, 17 9, 12, 15 12, 16, 20
Visual Prolog
VP7 has explicit list comprehension syntax.
implement main
open core, std
domains
pythtrip = pt(integer, integer, integer).
class predicates
pythTrips : (integer) -> pythtrip nondeterm (i).
clauses
pythTrips(Limit) = pt(X,Y,Z) :-
X = fromTo(1,Limit),
Y = fromTo(X,Limit),
Z = fromTo(Y,Limit),
Z^2 = X^2 + Y^2.
run():-
console::init(),
Triples = [ X || X = pythTrips(20) ],
console::write(Triples),
Junk = console::readLine(),
succeed().
end implement main
goal
mainExe::run(main::run).Wrapl
ALL WITH x <- 1:to(n), y <- x:to(n), z <- y:to(n) DO (x^2 + y^2 = z^2) & [x, y, z];Wren
Using a generator.
var pythTriples = Fiber.new { |n|
(1..n-2).each { |x|
(x+1..n-1).each { |y|
(y+1..n).each { |z| (x*x + y*y == z*z) && Fiber.yield([x, y, z]) }
}
}
}
var n = 20
while (!pythTriples.isDone) {
var res = pythTriples.call(n)
res && System.print(res)
}- Output:
[3, 4, 5] [5, 12, 13] [6, 8, 10] [8, 15, 17] [9, 12, 15] [12, 16, 20]
zkl
var n=20;
[[(x,y,z); [1..n]; {[x..n]}; {[y..n]},{ x*x + y*y == z*z }; _]]
//-->L(L(3,4,5),L(5,12,13),L(6,8,10),L(8,15,17),L(9,12,15),L(12,16,20))Lazy:
var n=20;
lp:=[& (x,y,z); // three variables, [& means lazy/iterator
[1..n]; // x: a range
{[x..n]}; // y: another range, fcn(x) is implicit (via "{")
{[y..n]}, // z with a filter/guard, expands to fcn(x,y){[y..n]}
{ x*x + y*y == z*z }; // the filter, fcn(x,y,z)
{ T(x,y,z) } // the result, could also be written as fcn(x,y,z){ T(x,y,z) }
// or just T (read only list) as T(x,y,z) creates a new list
// with values x,y,z, or just _ (which means return arglist)
]];
lp.walk(2) //-->L(L(3,4,5),L(5,12,13))- Programming Tasks
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