List comprehensions: Difference between revisions
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Revision as of 13:48, 16 December 2016
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.
ABAP
<lang 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 ) ).
</lang>
- 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. <lang Ada>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; </lang>
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.
<lang algol68>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
))</lang> 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.
<lang AppleScript>-- List comprehension by direct and unsugared use of list monad
-- pythagoreanTriples :: Int -> [(Int, Int, Int)] on pythagoreanTriples(maxInteger)
script X
on lambda(X)
script Y
on lambda(Y)
script Z
on lambda(Z)
if X * X + Y * Y = Z * Z then
unit([X, Y, Z])
else
[]
end if
end lambda
end script
bind(Z, range(1 + Y, maxInteger))
end lambda
end script
bind(Y, range(1 + X, maxInteger))
end lambda
end script
bind(X, range(1, maxInteger))
end pythagoreanTriples
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
-- MONADIC FUNCTIONS (for list monad)
-- Monadic bind for lists is simply ConcatMap -- which applies a function f directly to each value in the list, -- and returns the set of results as a concat-flattened list
-- bind :: (a -> [b]) -> [a] -> [b] on bind(f, xs)
-- concat :: a -> a -> [a]
script concat
on lambda(a, b)
a & b
end lambda
end script
foldl(concat, {}, map(f, xs))
end bind
-- Monadic return/unit/inject for lists: just wraps a value in a list -- a -> [a] on unit(a)
[a]
end unit
-- GENERIC LIBRARY FUNCTIONS
-- foldl :: (a -> b -> a) -> a -> [b] -> a on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to lambda(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl
-- map :: (a -> b) -> [a] -> [b] on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to lambda(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- 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 lambda : f
end script
end if
end mReturn
-- range :: Int -> Int -> [Int] on range(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 range</lang>
- Output:
<lang AppleScript>{{3, 4, 5}, {5, 12, 13}, {6, 8, 10}, {7, 24, 25}, {8, 15, 17}, {9, 12, 15}, {12, 16, 20}, {15, 20, 25}}</lang>
AutoHotkey
List Comprehension is not built in. <lang AutoHotkey> 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 } </lang>
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.
<lang bracmat>
:?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 }
);</lang>
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:
<lang c>
- 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); }
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;
} </lang> 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
<lang csharp>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);
}
} </lang>
C++
There is no equivalent construct in C++. The code below uses two nested loops and an if statement:
<lang cpp>#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 ) ) ; } }
} }
} </lang>
This produces the following output:
3 4 5 5 12 13 6 8 10 8 15 17 9 12 15 12 16 20
<lang cpp>#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;
}</lang>
Output:
3,4,5 5,12,13 6,8,10 8,15,17 9,12,15 12,16,20
Clojure
<lang lisp>(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]))</lang>
CoffeeScript
<lang 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]
))
console.dir pyth 20</lang>
pyth can also be written more concisely as
<lang coffeescript>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])</lang>
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:
<lang lisp>(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)))))</lang>
We can also define a new macro for list comprehensions. We can implement them easily with the help of the iterate package.
<lang lisp>(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)))))</lang>
We can then define a function to compute Pythagorean triples as follows:
<lang lisp>(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)))))</lang>
D
D doesn't have list comprehensions. One implementation: <lang d>import std.stdio, std.typetuple, 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 = TypeTuple!(iter1, iter2, iter3);
foreach (el1; items1) {
iter1 = el1;
foreach (el2; items2) {
iter2 = el2;
foreach (el3; items3) {
iter3 = el3;
if (where())
result ~= mapper();
}
}
}
TypeTuple!(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,n+1), z,
iota(y, n + 1), x*x + y*y == z*z);
writeln(r);
}</lang>
- Output:
[[3, 4, 5], [5, 12, 13], [6, 8, 10], [8, 15, 17], [9, 12, 15], [12, 16, 20]]
E
<lang 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]) } } } }</lang>
EchoLisp
<lang lisp>
- 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))
</lang>
Efene
<lang 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)])
} </lang>
Ela
<lang ela>pyth n = [(x,y,z) \\ x <- [1..n], y <- [x..n], z <- [y..n] | x**2 + y**2 == z**2]</lang>
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
<lang 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 ].</lang>
F#
<lang fsharp>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)]</lang>
Fortran
Complex numbers simplify the task. However, the reshape intrinsic function along with implicit do loops can generate high rank matrices. <lang FORTRAN> !-*- 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 </lang>
FunL
<lang 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) )</lang>
- Output:
[(3, 4, 5), (5, 12, 13), (6, 8, 10), (8, 15, 17), (9, 12, 15), (12, 16, 20)]
GAP
<lang 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 ] ]</lang>
Haskell
<lang haskell>pyth :: (Enum t, Eq t, Num t) => t -> [(t, t, t)] pyth n = [(x,y,z) | x <- [1..n], y <- [x..n], z <- [y..n], x^2 + y^2 == z^2] </lang>
List-comprehensions in Haskell are in fact syntactic sugar for do-notation, so the above is equivalent to the following:
<lang haskell>import Control.Monad (guard)
pyth :: (Enum t, Eq t, Num t) => t -> [(t, t, t)] pyth n = do
x <- [1..n] y <- [x..n] z <- [y..n] guard $ x^2 + y^2 == z^2 return (x,y,z)</lang>
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:
<lang unicon>
|(x := seq(), x^2 > 3, x*2)
</lang>
is capable of producing successive elements from the infinite list described in the Wikipedia article. For example, to produce the first 100 elements:
<lang unicon>
procedure main()
every write(|(x := seq(), x^2 > 3, x*2) \ 100
end
</lang>
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):
<lang unicon>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</lang>
Sample output:
->lc 3 4 5 5 12 13 6 8 10 8 15 17 9 12 15 12 16 20 ->
Ioke
<lang ioke>for(
x <- 1..20, y <- x..20, z <- y..20, x * x + y * y == z * z, [x, y, z]
)</lang>
J
<lang J>require'stats' buildSet=:conjunction def '(#~ v) u y' triples=: 1 + 3&comb isPyth=: 2&{"1 = 1&{"1 +&.:*: 0&{"1 pythTr=: triples buildSet isPyth</lang>
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:
<lang J> pythTr 20
3 4 5 5 12 13 6 8 10 8 15 17 9 12 15
12 16 20</lang>
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.
<lang javascript>// 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);</lang>
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
<lang javascript>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);</lang>
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 / flatMap (the monadic bind function for lists), and x => [x] (monadic return for lists):
<lang JavaScript> (n => {
const
flatMap = (xs, f) => [].concat.apply([], xs.map(f)),
range = (m, n) => Array.from({
length: (n - m) + 1
}, (_, i) => m + i),
xs = range(1, n);
return flatMap(xs, x =>
flatMap(xs.slice(x), y =>
flatMap(xs.slice(y), z =>
x * x + y * y === z * z ? [
[x, y, z]
] : []
)));
})(20);</lang>
- Output:
[[3, 4, 5], [5, 12, 13], [6, 8, 10], [8, 15, 17], [9, 12, 15], [12, 16, 20]]
jq
Direct approach:<lang jq>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] ;
</lang>
Using listof(stream; criterion) <lang jq># 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)</lang>
- 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:
<lang Julia> 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)
</lang>
A Julia generator comprehension (note the outer round brackets), returns an iterator over the same result rather than an explicit array:
<lang Julia> 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)
</lang>
Array comprehensions may also be N-dimensional, not just vectors:
<lang Julia> 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
</lang>
Lasso
Lasso uses query expressions for list manipulation. <lang lasso>#!/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')</lang>
Output: <lang lasso>staticarray(3, 4, 5) staticarray(5, 12, 13) staticarray(6, 8, 10) staticarray(8, 15, 17) staticarray(9, 12, 15) staticarray(12, 16, 20)</lang>
Lua
Lua doesn't have list comprehensions built in, but they can be constructed from chained coroutines:
<lang lua> 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 </lang>
We can then define a function to compute Pythagorean triples as follows:
<lang lua> 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 </lang>
Mathematica
<lang mathematica>Select[Tuples[Range[100], 3], #11^2 + #12^2 == #13^2 &]</lang>
<lang mathematica>Pick[#, (#^2).{1, 1, -1}, 0] &@Tuples[Range[100], 3]</lang>
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 <lang Matlab>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)])</lang>
- 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.
<lang mercury>
- - 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).
</lang>
Nemerle
Demonstrating a list comprehension and an iterator. List comprehension adapted from Haskell example, iterator adapted from C# example. <lang Nemerle>using System; using System.Console; using System.Collections.Generic;
module Program {
PythTriples(n : int) : list[int * int * int]
{
$[ (x, y, z) | x in [1..n], y in [x..n], z in [y..n], ((x**2) + (y**2)) == (z**2) ]
}
GetPythTriples(n : int) : IEnumerable[int * int * int]
{
foreach (x in [1..n])
{
foreach (y in [x..n])
{
foreach (z in [y..n])
{
when (((x**2) + (y**2)) == (z**2))
{
yield (x, y, z)
}
}
}
}
}
Main() : void
{
WriteLine("Pythagorean triples up to x = 20: {0}", PythTriples(20));
foreach (triple in GetPythTriples(20))
{
Write(triple)
}
}
}</lang>
Nim
There are no list comprehensions in Nim, but thanks to the strong metaprogramming capabilities we can implement our own: <lang nim>import macros
type ListComprehension = object var lc*: ListComprehension
macro `[]`*(lc: ListComprehension, x, t): expr =
expectLen(x, 3) expectKind(x, nnkInfix) expectKind(x[0], nnkIdent) assert($x[0].ident == "|")
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].ident == "<-":
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]]</lang>
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
OCaml Batteries Included has uniform comprehension syntax for lists, arrays, enumerations (like streams), lazy lists (like lists but evaluated on-demand), sets, hashtables, etc.
Comprehension are of the form
[? expression | x <- enumeration ; condition; condition ; ...]
For instance, <lang ocaml># [? 2 * x | x <- 0 -- max_int ; x * x > 3];; - : int Enum.t = <abstr></lang> or, to compute a list, <lang ocaml># [? List: 2 * x | x <- 0 -- 100 ; x * x > 3];; - : int list = [2; 4; 6; 8; 10]</lang> or, to compute a set, <lang ocaml># [? PSet: 2 * x | x <- 0 -- 100 ; x * x > 3];; - : int PSet.t = <abstr></lang>
etc..
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:
<lang oz>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}
end</lang>
PARI/GP
GP 2.6.0 added support for a new comprehension syntax:
<lang parigp>f(n)=[v|v<-vector(n^3,i,vector(3,j,i\n^(j-1)%n)),norml2(v)==2*v[3]^2]</lang>
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).
<lang parigp>f(n)=select(v->norml2(v)==2*v[3]^2,vector(n^3,i,vector(3,j,i\n^(j-1)%n)))</lang>
Version 2.4.2 (obsolete, but widespread on Windows systems) requires inversion:
<lang parigp>f(n)=select(vector(n^3,i,vector(3,j,i\n^(j-1)%n)),v->norml2(v)==2*v[3]^2)</lang>
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:
<lang perl>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;
}</lang>
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.
<lang perl>for my $t (triples(10)) {
print "@$t\n";
}</lang>
Perl 6
Perl 6 has single-dimensional list comprehensions that fall out naturally from nested modifiers; multidimensional comprehensions are also supported via the cross operator; however, Perl 6 does not (yet) support multi-dimensional list comprehensions with dependencies between the lists, so the most straightforward way is currently: <lang perl6>my $n = 20; gather for 1..$n -> $x {
for $x..$n -> $y {
for $y..$n -> $z {
take $x,$y,$z if $x*$x + $y*$y == $z*$z;
}
}
}</lang>
Note that gather/take is the primitive in Perl 6 corresponding to generators or coroutines in other languages. It is not, however, tied to function call syntax in Perl 6. 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.
PicoLisp
PicoLisp doesn't have list comprehensions. We might use a generator function, pipe, coroutine or pilog predicate.
Using a generator function
<lang PicoLisp>(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 @) )</lang>
Using a pipe
<lang PicoLisp>(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 @) ) )</lang>
Using a coroutine
Coroutines are available only in the 64-bit version. <lang PicoLisp>(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 @) )</lang>
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
<lang PicoLisp>(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)) ) ) )</lang>
Test: <lang PicoLisp>: (? (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
-> NIL</lang>
Prolog
SWI-Prolog does not have list comprehension, however we can simulate it.
<lang Prolog>% 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).
</lang>
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
List comprehension:
<lang python>[(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]</lang>
A Python generator comprehension (note the outer round brackets), returns an iterator over the same result rather than an explicit list:
<lang python>((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)</lang>
R
R has inherent list comprehension: <lang R> 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 </lang>
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)
<lang R> subset(expand.grid(x=1:n, y=1:n, z=1:n), x^2 + y^2 == z^2) </lang>
Racket
<lang 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))
</lang>
Rascal
<lang 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]; </lang>
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
<lang rexx>/*REXX program lists (vertically) Pythagorean triples up to a specified number*/ parse arg n . /*get the optional argument from the CL*/ if n== then n=100 /*Not specified? Then use the default.*/ $= /*assign a null to the triples list. */
do a=1 for n-2; aa=a*a /*Note: A*A is faster than A**2, but */
do b=a+1 to n-1; aabb=aa+b*b /* ··· not by much.*/
do c=b+1 to n
if aabb==c*c then $=$ '('a"," || b','c")"
end /*c*/
end /*b*/
end /*a*/
if 'f5'x==5 then do; sup2='b2'x; le='8c'x; end /*EBCDIC?*/
else do; sup2='fd'x; le='f3'x; end /* ASCII?*/
say 'Pythagorean triples (a'sup2 "+ b"sup2 '= c'sup2", c "le n'):' w=words($) /*number of members in the list. */ say; do j=1 for w
say word($,j) /*display a member of the list, */
end /*j*/ /* [↑] list the members vertically. */
say; say w 'members listed.' /*stick a fork in it, we're all done. */</lang> 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
<lang rexx>/*REXX program lists (horizontally) Pythagorean triples up to a specified num.*/ parse arg n . /*get the optional argument from the CL*/ if n== then n=100 /*Not specified? Then use the default.*/ $= /*assign a null to the triples list. */
do a=1 for n-2; aa=a*a /*Note: A*A is faster than A**2, but */
do b=a+1 to n-1; aabb=aa+b*b /* ··· not by much.*/
do c=b+1 to n
if aabb==c*c then $=$ '('a"," || b','c")"
end /*c*/
end /*b*/
end /*a*/
if 'f7'x==7 then do; sup2='b2'x; le='8c'x; end /*EBCDIC ? */
else do; sup2='fd'x; le='f3'x; end /* ASCII ? */
say 'Pythagorean triples (a'sup2 "+ b"sup2 '= c'sup2", c "le n'):' say; say strip($) /*show the Pythagorean triples to term.*/ say; say words($) 'members listed.' /*triples are listed in order of 1st #.*/
/*stick a fork in it, we're all done. */</lang>
output when using for the 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
<lang 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
next </lang>
Ruby
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.
There is no elegant way to comprise a list from multiple variables. Pythagorean triplets need three variables, with 1..n giving x, then x..n giving y, then y..n giving z. A less than elegant way is to nest three blocks.
Ruby 1.9.2
<lang ruby>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_</lang>
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.
Ruby 1.8.6
<lang ruby>n = 20
unless Enumerable.method_defined? :flat_map
module Enumerable
def flat_map
inject([]) { |a, x| a.concat yield(x) }
end
end
end
unless Array.method_defined? :keep_if
class Array
def keep_if
delete_if { |x| not yield(x) }
end
end
end
- 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_</lang>
This is the exact same code, except that it now defines Enumerable#flat_map and Array#keep_if when those methods are missing. It now works with older versions of Ruby, like 1.8.6.
Run BASIC
<lang runbasic>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 x</lang>Output:
[3,4,5] [5,12,13] [6,8,10] [8,15,17] [9,12,15] [12,16,20]
Scala
<lang 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)</lang>
which is a syntactic sugar for:
<lang scala> 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))))</lang>
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:
<lang scala>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)</lang>
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:
<lang scheme> (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))
</lang>
((3 4 5) (5 12 13) (6 8 10) (8 15 17) (9 12 15) (12 16 20))
Sidef
<lang ruby>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)
}
}
}
}</lang>
- Output:
[[3, 4, 5], [5, 12, 13], [6, 8, 10], [8, 15, 17], [9, 12, 15], [12, 16, 20]]
Smalltalk
<lang 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)"
</lang>
SuperCollider
<lang 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</lang> returns <lang supercollider>[ [ 3, 4, 5 ], [ 5, 12, 13 ], [ 6, 8, 10 ], [ 8, 15, 17 ], [ 9, 12, 15 ], [ 12, 16, 20 ] ]</lang>
Tcl
Tcl does not have list comprehensions built-in to the language, but they can be constructed. <lang tcl>package require Tcl 8.5
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}]</lang>
{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.
<lang ti89b>{1, 2, 3, 4} → a seq(a[i]^2, i, 1, dim(a))</lang>
produces {1, 4, 9, 16}. When the input is simply a numeric range, an input list is not needed; this produces the same result:
<lang ti89b>seq(x^2, x, 1, 4)</lang>
Visual Basic .NET
<lang vbnet>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</lang>
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.
<lang visualProlog> 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).
</lang>
Wrapl
<lang 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];</lang>
zkl
<lang 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))</lang> Lazy: <lang zkl>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))</lang>
- Programming Tasks
- Basic language learning
- C/Omit
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- BBC BASIC/Omit
- ABAP
- Ada
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