Monads/List monad: Difference between revisions
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{{
[[Category:Monads]]
A [[wp:Monad_(functional_programming)|Monad]] is a combination of a data-type with two helper functions written for that type.
The data-type can be of any kind which can contain values of some other type – common examples are lists, records, sum-types, even functions or IO streams. The two special functions, mathematically known as '''eta''' and '''mu''', but usually given more expressive names like 'pure', 'return', or 'yield' and 'bind', abstract away some boilerplate needed for pipe-lining or enchaining sequences of computations on values held in the containing data-type.
The bind operator in the List monad enchains computations which return their values wrapped in lists. One application of this is the representation of indeterminacy, with returned lists representing a set of possible values. An empty list can be returned to express incomputability, or computational failure.
A sequence of two list monad computations (enchained with the use of bind) can be understood as the computation of a cartesian product.
The natural implementation of bind for the List monad is a composition of '''concat''' and '''map''', which, used with a function which returns its value as a (possibly empty) list, provides for filtering in addition to transformation or mapping.
Demonstrate in your programming language the following:
#Construct a List Monad by writing the 'bind' function and the '
#Make two functions, each which take a number and return a monadic number, e.g. Int -> List Int and Int -> List String
#Compose the two functions with bind
=={{header|AppleScript}}==
Line 12 ⟶ 23:
We can use a list monad in AppleScript to express set comprehension for the Pythagorean triples, but the lack of nestable first class (and anonymous) functions means that the closure can only be achieved using script objects, which makes the idiom rather less direct and transparent. AppleScript is creaking at the seams here.
<
-- Monadic bind for lists is simply ConcatMap
Line 127 ⟶ 138:
end script
end if
end mReturn</
{{Out}}
<
=={{header|ATS}}==
<syntaxhighlight lang="ats">
#include "share/atspre_staload.hats"
(* I will use the list type of prelude/SATS/list.sats *)
#define NIL list_nil ()
#define :: list_cons
fn {a : t@ype}
unit_List (x : a) : list (a, 1) =
x :: NIL
fn {a, b : t@ype}
bind_List (m : List a,
f : a -<cloref1> List b) : List0 b =
let
fun
reversed_segments (m : List a,
accum : List0 (List b))
: List0 (List b) =
case+ m of
| NIL => accum
| hd :: tl => reversed_segments (tl, f hd :: accum)
fun
assemble_segments (segments : List (List b),
accum : List0 b)
: List0 b =
case+ segments of
| NIL => accum
| hd :: tl =>
let
prval () = lemma_list_param hd
val accum = list_append (hd, accum)
in
assemble_segments (tl, accum)
end
in
assemble_segments (reversed_segments (m, NIL), NIL)
end
infixl 0 >>=
overload >>= with bind_List
fn
intseq_List {n : nat}
(i0 : int,
n : int n) :<cloref1> list (int, n) =
let
implement
list_tabulate$fopr<int> j = i0 + j
in
list_vt2t (list_tabulate<int> n)
end
implement
main0 () =
let
val n = 25
val pythagorean_triples =
intseq_List (1, n) >>=
(lam i =>
(intseq_List (succ (i : int), n) >>=
(lam j =>
(intseq_List (succ (j : int), n) >>=
(lam k =>
let
val i = i : int
and j = j : int
and k = k : int
in
if (i * i) + (j * j) = (k * k) then
@(i, j, k) :: NIL
else
NIL
end)))))
fun
loop {n : nat}
.<n>.
(m : list (@(int, int, int), n)) : void =
case+ m of
| NIL => ()
| (@(a, b, c) :: tl) =>
begin
println! ("(", a, ",", b, ",", c, ")");
loop tl
end
in
loop pythagorean_triples
end
</syntaxhighlight>
{{out}}
We should get a list of some Pythagorean triples that start with some integer between 1 and 25, inclusive.
<pre>$ patscc -std=gnu2x -g -O2 -DATS_MEMALLOC_GCBDW list_monad_ats.dats -lgc && ./a.out
(3,4,5)
(5,12,13)
(6,8,10)
(7,24,25)
(8,15,17)
(9,12,15)
(10,24,26)
(12,16,20)
(12,35,37)
(15,20,25)
(15,36,39)
(16,30,34)
(18,24,30)
(20,21,29)
(21,28,35)
(24,32,40)
(24,45,51)
</pre>
=={{header|C}}==
The C type which best fits the concept used here for <code>monad</code> would be <code>void*</code>.
There's some limitations -- the list type characteristics in this context, if they had been used, would have required special attention to issues like traversing the list. And, C does not provide syntactic sugar which a user would likely expect from experience in some other languages.
Still, the task example is constrained enough that we can provide an implementation like:
<syntaxhighlight lang="c">#include <stdio.h>
#include <stdlib.h>
#define MONAD void*
#define INTBIND(f, g, x) (f((int*)g(x)))
#define RETURN(type,x) &((type)*)(x)
MONAD boundInt(int *x) {
return (MONAD)(x);
}
MONAD boundInt2str(int *x) {
char buf[100];
char*str= malloc(1+sprintf(buf, "%d", *x));
sprintf(str, "%d", *x);
return (MONAD)(str);
}
void task(int y) {
char *z= INTBIND(boundInt2str, boundInt, &y);
printf("%s\n", z);
free(z);
}
int main() {
task(13);
}</syntaxhighlight>
Which, from the command line, might look like:
<syntaxhighlight lang="bash">$ ./monad
13</syntaxhighlight>
=={{header|C++}}==
<syntaxhighlight lang="cpp">#include <iostream>
#include <vector>
using namespace std;
// std::vector can be a list monad. Use the >> operator as the bind function
template <typename T>
auto operator>>(const vector<T>& monad, auto f)
{
// Declare a vector of the same type that the function f returns
vector<remove_reference_t<decltype(f(monad.front()).front())>> result;
for(auto& item : monad)
{
// Apply the function f to each item in the monad. f will return a
// new list monad containing 0 or more items.
const auto r = f(item);
// Concatenate the results of f with previous results
result.insert(result.end(), begin(r), end(r));
}
return result;
}
// The Pure function returns a vector containing one item, t
auto Pure(auto t)
{
return vector{t};
}
// A function to double items in the list monad
auto Double(int i)
{
return Pure(2 * i);
}
// A function to increment items
auto Increment(int i)
{
return Pure(i + 1);
}
// A function to convert items to a string
auto NiceNumber(int i)
{
return Pure(to_string(i) + " is a nice number\n");
}
// A function to map an item to a sequence ending at max value
// for example: 497 -> {497, 498, 499, 500}
auto UpperSequence = [](auto startingVal)
{
const int MaxValue = 500;
vector<decltype(startingVal)> sequence;
while(startingVal <= MaxValue)
sequence.push_back(startingVal++);
return sequence;
};
// Print contents of a vector
void PrintVector(const auto& vec)
{
cout << " ";
for(auto value : vec)
{
cout << value << " ";
}
cout << "\n";
}
// Print the Pythagorean triples
void PrintTriples(const auto& vec)
{
cout << "Pythagorean triples:\n";
for(auto it = vec.begin(); it != vec.end();)
{
auto x = *it++;
auto y = *it++;
auto z = *it++;
cout << x << ", " << y << ", " << z << "\n";
}
cout << "\n";
}
int main()
{
// Apply Increment, Double, and NiceNumber to {2, 3, 4} using the monadic bind
auto listMonad =
vector<int> {2, 3, 4} >>
Increment >>
Double >>
NiceNumber;
PrintVector(listMonad);
// Find Pythagorean triples using the list monad. The 'x' monad list goes
// from 1 to the max; the 'y' goes from the current 'x' to the max; and 'z'
// goes from the current 'y' to the max. The last bind returns the triplet
// if it is Pythagorean, otherwise it returns an empty list monad.
auto pythagoreanTriples = UpperSequence(1) >>
[](int x){return UpperSequence(x) >>
[x](int y){return UpperSequence(y) >>
[x, y](int z){return (x*x + y*y == z*z) ? vector{x, y, z} : vector<int>{};};};};
PrintTriples(pythagoreanTriples);
}
</syntaxhighlight>
{{out}}
<pre>
6 is a nice number
8 is a nice number
10 is a nice number
Pythagorean triples:
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
. . .
. . .
320, 336, 464
325, 360, 485
340, 357, 493
</pre>
=={{header|Clojure}}==
<
(defn bind [coll f] (apply vector (mapcat f coll)))
(defn unit [val] (vector val))
Line 144 ⟶ 446:
(bind doubler)
(bind vecstr)) ; also evaluates to ["6" "8" "10"]
</syntaxhighlight>
=={{header|Delphi}}==
{{libheader| System.SysUtils}}
{{Trans|Go}}
<syntaxhighlight lang="delphi">
program List_monad;
{$APPTYPE CONSOLE}
uses
System.SysUtils;
type
TmList = record
Value: TArray<Integer>;
function ToString: string;
function Bind(f: TFunc<TArray<Integer>, TmList>): TmList;
end;
function Create(aValue: TArray<Integer>): TmList;
begin
Result.Value := copy(aValue, 0, length(aValue));
end;
{ TmList }
function TmList.Bind(f: TFunc<TArray<Integer>, TmList>): TmList;
begin
Result := f(self.Value);
end;
function TmList.ToString: string;
var
i: Integer;
begin
Result := '[ ';
for i := 0 to length(value) - 1 do
begin
if i > 0 then
Result := Result + ', ';
Result := Result + value[i].toString;
end;
Result := Result + ']';
end;
function Increment(aValue: TArray<Integer>): TmList;
var
i: integer;
begin
SetLength(Result.Value, length(aValue));
for i := 0 to High(aValue) do
Result.Value[i] := aValue[i] + 1;
end;
function Double(aValue: TArray<Integer>): TmList;
var
i: integer;
begin
SetLength(Result.Value, length(aValue));
for i := 0 to High(aValue) do
Result.Value[i] := aValue[i] * 2;
end;
var
ml1, ml2: TmList;
begin
ml1 := Create([3, 4, 5]);
ml2 := ml1.Bind(Increment).Bind(double);
Writeln(ml1.ToString, ' -> ', ml2.ToString);
readln;
end.</syntaxhighlight>
{{out}}
<pre>[ 3, 4, 5] -> [ 8, 10, 12]</pre>
=={{header|EchoLisp}}==
Our monadic lists will take the form (List a b c ...), ie raw lists prefixed by the List symbol.
<
;; -> and ->> are the pipeline operators
;; (-> x f g h) = (h (g ( f x)))
Line 168 ⟶ 542:
(-> '(1 -2 3 -5) List.unit (List.bind List.cube) (List.bind List.tostr))
→ (List "1" "-8" "27" "-125")
</syntaxhighlight>
=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">
type ListMonad() =
member o.Bind( (m:'a list), (f: 'a -> 'b list) ) = List.concat( List.map f m )
member o.Return(x) = [x]
member o.Zero() = []
let list = ListMonad()
let pyth_triples n = list { let! x = [1..n]
let! y = [x..n]
let! z = [y..n]
if x*x + y*y = z*z then return (x,y,z) }
printf "%A" (pyth_triples 100)
</syntaxhighlight>
The list monad is equivalent to [[List comprehensions]] which are built into F#:
<syntaxhighlight lang="fsharp">
// Monads/List monad . Nigel Galloway: March 8th., 2021
List.iter ((+) 1>>(*) 2>>printf "%d ") [3;4;5]; printfn "";;
let pT n=[for i in 1..n do for g in i+1..n do for n in g+1..n do if i*i+g*g=n*n then yield(i,g,n)]
Seq.iter(printf "%A ")(pT 25)
let fN g=match g<10 with false->Error "is greater than 9"|_->Ok g
let fG n=match n>5 with false->Error "is less than 6" |_->Ok n
let valid n=n|>Result.bind fN|>Result.bind fG
let test n=match valid(Ok n) with Ok g->printfn "%d is valid" g|Error e->printfn "Error: %d %s" n e
[5..10]|>List.iter test
</syntaxhighlight>
{{out}}
<pre>
8 10 12
(3, 4, 5) (5, 12, 13) (6, 8, 10) (7, 24, 25) (8, 15, 17) (9, 12, 15) (12, 16, 20) (15, 20, 25)
Error: 5 is less than 6
6 is valid
7 is valid
8 is valid
9 is valid
Error: 10 is greater than 9
</pre>
=={{header|Factor}}==
Factor comes with an implementation of Haskell-style monads in the <code>monads</code> vocabulary.
<syntaxhighlight lang="factor">USING: kernel math monads prettyprint ;
FROM: monads => do ;
{ 3 4 5 }
>>= [ 1 + array-monad return ] swap call
>>= [ 2 * array-monad return ] swap call .</syntaxhighlight>
Or:
<syntaxhighlight lang="factor">{ 3 4 5 }
[ 1 + array-monad return ] bind
[ 2 * array-monad return ] bind .</syntaxhighlight>
Or:
<syntaxhighlight lang="factor">{
[ { 3 4 5 } ]
[ 1 + array-monad return ]
[ 2 * array-monad return ]
} do .</syntaxhighlight>
{{out}}
<pre>
{ 8 10 12 }
</pre>
=={{header|FreeBASIC}}==
{{trans|Ring}}
<syntaxhighlight lang="freebasic">Dim As Integer m1(1 To 3) = {3,4,5}
Dim As String m2 = "["
Dim As Integer x, y ,z
For x = 1 To Ubound(m1)
y = m1(x) + 1
z = y * 2
m2 &= Str(z) & ", "
Next x
m2 = Left(m2, Len(m2) -2)
m2 &= "]"
Print m2
Sleep</syntaxhighlight>
{{out}}
<pre>[8, 10, 12]</pre>
=={{header|Go}}==
<syntaxhighlight lang="go">package main
import "fmt"
type mlist struct{ value []int }
func (m mlist) bind(f func(lst []int) mlist) mlist {
return f(m.value)
}
func unit(lst []int) mlist {
return mlist{lst}
}
func increment(lst []int) mlist {
lst2 := make([]int, len(lst))
for i, v := range lst {
lst2[i] = v + 1
}
return unit(lst2)
}
func double(lst []int) mlist {
lst2 := make([]int, len(lst))
for i, v := range lst {
lst2[i] = 2 * v
}
return unit(lst2)
}
func main() {
ml1 := unit([]int{3, 4, 5})
ml2 := ml1.bind(increment).bind(double)
fmt.Printf("%v -> %v\n", ml1.value, ml2.value)
}</syntaxhighlight>
{{out}}
<pre>
[3 4 5] -> [8 10 12]
</pre>
=={{header|Haskell}}==
Haskell has the built-in <code>Monad</code> type class, and the built-in list type already conforms to the <code>Monad</code> type class.
<
Or, written using <code>do</code> notation:
<
y <- return (x+1)
z <- return (y*2)
return z</
Or alternately:
<
let y = x+1
let z = y*2
return z</
Using the list monad to express set comprehension for Pythagorean triples:
<
pythagoreanTriples n =
[1 .. n] >>= (\x ->
Line 195 ⟶ 695:
if x^2 + y^2 == z^2 then return (x,y,z) else [])))
main = print $ pythagoreanTriples 25</
{{out}}
<pre>[(3,4,5),(5,12,13),(6,8,10),(7,24,25),(8,15,17),(9,12,15),(12,16,20),(15,20,25)]</pre>
Which can be written using <code>do</code> notation:
<
pythagoreanTriples n = do x <- [1 .. n]
y <- [x+1 .. n]
z <- [y+1 .. n]
if x^2 + y^2 == z^2 then return (x,y,z) else []</
Or directly as a list comprehension:
<
pythagoreanTriples n = [(x,y,z) | x <- [1 .. n], y <- [x+1 .. n], z <- [y+1 .. n], x^2 + y^2 == z^2]</
=={{header|J}}==
Line 216 ⟶ 716:
That said, here is an implementation which might be adequate for the current task description:
<
unit=: boxopen
m_num=: unit
m_str=: unit@":</
Task example:
<
┌─┐
│5│
└─┘</
=={{header|Java}}==
<syntaxhighlight lang="java">
import java.util.ArrayList;
import java.util.List;
import java.util.function.Function;
public final class MonadList {
public static void main(String[] aArgs) {
Monad<Integer> integers = Monad.unit(List.of( 2, 3, 4 ));
Monad<String> strings = integers.bind(MonadList::doubler).bind(MonadList::letters);
System.out.println(strings.getValue());
}
private static Monad<Integer> doubler(List<Integer> aList) {
return Monad.unit(aList.stream().map( i -> 2 * i ).toList());
}
private static Monad<String> letters(List<Integer> aList) {
return Monad.unit(aList.stream().map( i -> Character.toString((char) (64 + i)).repeat(i) ).toList());
}
}
final class Monad<T> {
public static <T> Monad<T> unit(List<T> aList) {
return new Monad<T>(aList);
}
public <U> Monad<U> bind(Function<List<T>, Monad<U>> aFunction) {
return aFunction.apply(list);
}
public List<T> getValue() {
return list;
}
private Monad(List<T> aList) {
list = new ArrayList<T>(aList);
}
private List<T> list;
}
</syntaxhighlight>
{{ out }}
<pre>
[DDDD, FFFFFF, HHHHHHHH]
</pre>
=={{header|Javascript}}==
<
Array.prototype.bind = function (func) {
return this.map(func).reduce(function (acc, a) { return acc.concat(a); });
Line 250 ⟶ 801:
[3,4,5].bind(listy_inc).bind(listy_doub); // [8, 10, 12]
</syntaxhighlight>
ES5 Example: Using the list monad to express set comprehension
<
// ENCODING A SET COMPREHENSION IN TERMS OF A LIST MONAD
Line 305 ⟶ 856:
}
})(25);</
{{Out}}
<pre>[[3, 4, 5], [5, 12, 13], [6, 8, 10], [7, 24, 25], [8, 15, 17], [9, 12, 15], [12, 16, 20], [15, 20, 25]]</pre>
=={{header|jq}}==
{{works with|jq}}
''Also works with gojq and fq'' modulo the proviso about "::"
In this entry, we adopt the approach described in the Wikipedia article on monads
at [https://en.wikipedia.org/wiki/Monad_(functional_programming)], specifically:
<pre>
"A monad can be created by defining a type constructor M and two operations:
return :: a -> M a (often also called unit), which receives a value of type a and wraps it into a monadic value of type M a,
and
bind :: (M a) -> (a -> M b) -> (M b)
which receives a function f over type a and can transform monadic values m a applying f to the unwrapped value a,
returning a monadic value M b"
</pre>
In the following, the monadic type `a` can be specified as any JSON
value, but for the List monad, it is just "List". Choosing a string has the advantage
that we can use jq's support for function names of the form
`Namespace::identifier` to give convenient names to the "return" and
"bind" functions for the List monad, namely `List::return` and
`List::bind`.
Since gojq does not currently support the definition of functions
with a Namespace prefix, the following would have to be adapted; one
possibility wold be to replace occurrences of `::` in function names
by `__`.
Notice that the "return" and "bind" wrappers for List (i.e., `List::return` and
`List::bind`) can be tailored to the List monad independently of the
wrapper definitions for other monads.
<syntaxhighlight lang=jq>
# Constructor:
def Monad($type; $value):
{class: "Monad", $type, $value};
# Is the input a monad of type $Type?
def is_monad($Type):
(type == "object")
and (.class == "Monad")
and (.type == $Type) ;
# input: a value consistent with the "List" monadic type (in practice, a JSON array)
# No checking is done here as the monadic type system is outside the scope of this entry.
def List::return:
Monad("List"; .);
def List::bind(f):
if is_monad("List")
then .value |= f
else error("List::bind error: monadic type of input is \(.type)")
end;
# Two illustrative operations on JSON arrays
def increment: map(. + 1);
def double: map(. * 2);
def ml1:
[3, 4, 5] | List::return;
def ml2:
ml1 | List::bind(increment) | List::bind(double);
"\(ml1.value) -> \(ml2.value)"
</syntaxhighlight>
{{output}}
<pre>
[3,4,5] -> [8,10,12]
</pre>
=={{header|Julia}}==
Julia uses the function bind for binding a channel to a task, but this can be imported and overloaded.
The |> syntax in Julia can also be used to chain functions taking one argument.
<syntaxhighlight lang="julia">julia> unit(v) = [v...]
unit (generic function with 1 method)
julia> import Base.bind
julia> bind(v, f) = f.(v)
bind (generic function with 5 methods)
julia> f1(x) = x + 1
f1 (generic function with 1 method)
julia> f2(x) = 2x
f2 (generic function with 1 method)
julia> bind(bind(unit([2, 3, 4]), f1), f2)
3-element Array{Int64,1}:
6
8
10
julia> unit([2, 3, 4]) .|> f1 .|> f2
3-element Array{Int64,1}:
6
8
10
</syntaxhighlight>
=={{header|Kotlin}}==
<
class MList<T : Any> private constructor(val value: List<T>) {
Line 330 ⟶ 981:
val fv = iv.bind(::doubler).bind(::letters)
println(fv.value)
}</
{{out}}
Line 336 ⟶ 987:
[DDDD, FFFFFF, HHHHHHHH]
</pre>
=={{header|Nim}}==
a natural use of a list-wrapped return value is when there can be more than one result from a function, for example square roots have a positive and negative solution, and the inverse sine function has multiple solutions we might be interested in.
<syntaxhighlight lang="nim">import math,sequtils,sugar,strformat
func root(x:float):seq[float] = @[sqrt(x),-sqrt(x)]
func asin(x:float):seq[float] = @[arcsin(x),arcsin(x)+TAU,arcsin(x)-TAU]
func format(x:float):seq[string] = @[&"{x:.2f}"]
#'bind' is a nim keyword, how about an infix operator instead
#our bind is the standard map+cat
func `-->`[T,U](input: openArray[T],f: T->seq[U]):seq[U] =
input.map(f).concat
echo [0.5] --> root --> asin --> format </syntaxhighlight>
{{out}}<pre>@["0.79", "7.07", "-5.50", "-0.79", "5.50", "-7.07"]</pre>
=={{header|OCaml}}==
Defining the list monad is fairly straightforward:
<syntaxhighlight lang="ocaml">let bind : 'a list -> ('a -> 'b list) -> 'b list =
fun l f -> List.flatten (List.map f l)
let return x = [x]</syntaxhighlight>
For convenience, the example will also use the following definitions:
<syntaxhighlight lang="ocaml">let (>>) = bind (* operator for inline binding *)
let (let*) = bind (* let pruning for easy bind *)
let print_str_list l =
Format.printf "[%a]" (fun fmt -> Format.pp_print_list Format.pp_print_string fmt) l</syntaxhighlight>
First example: increment and print
<syntaxhighlight lang="ocaml">let incr x = return (x+1)
let hex x = return (Format.sprintf "%#x" x)
(* Version 1 : With explicit calls *)
let () =
let l = bind (bind (List.init 5 (fun x -> x)) incr) hex in
print_str_list l
(* Version 2 : With >> operator *)
let () =
let l = List.init 5 (fun x -> x) >> incr >> hex in
print_str_list l
(* Version 3 : With let pruning *)
let () =
let l =
let* x = List.init 5 (fun x -> x) in
let* y = incr x in hex y
in print_str_list l</syntaxhighlight>
Second example: pythegorean triplets
<syntaxhighlight lang="ocaml">(* Version 1 : with explicit calls *)
let pythegorean_triple n =
let x = List.init n (fun x -> x) in
let y = List.init n (fun x -> x) in
let z = List.init n (fun x -> x) in
bind x (fun x ->
bind y (fun y ->
bind z (fun z ->
if x*x + y*y = z*z then return (x,y,z) else []
)))
(* Version 2 : with >> operator *)
let pythegorean_triple n =
List.init n (fun x -> x) >> fun x ->
List.init n (fun x -> x) >> fun y ->
List.init n (fun x -> x) >> fun z ->
if x*x + y*y = z*z then return (x,y,z) else []
(* Version 3 : with let pruning *)
let pythegorean_triple n =
let* x = List.init n (fun x -> x) in
let* y = List.init n (fun x -> x) in
let* z = List.init n (fun x -> x) in
if x*x + y*y = z*z then return (x,y,z) else []</syntaxhighlight>
=={{header|Perl}}==
With the help of the CPAN module <code>Data::Monad</code>, we can work with list monads.
<syntaxhighlight lang="perl">use strict;
use feature 'say';
use Data::Monad::List;
# Cartesian product to 'count' in binary
my @cartesian = [(
list_flat_map_multi { scalar_list(join '', @_) }
scalar_list(0..1),
scalar_list(0..1),
scalar_list(0..1)
)->scalars];
say join "\n", @{shift @cartesian};
say '';
# Pythagorean triples
my @triples = [(
list_flat_map_multi { scalar_list(
{ $_[0] < $_[1] && $_[0]**2+$_[1]**2 == $_[2]**2 ? join(',',@_) : () }
) }
scalar_list(1..10),
scalar_list(1..10),
scalar_list(1..10)
)->scalars];
for (@{shift @triples}) {
say keys %$_ if keys %$_;
}</syntaxhighlight>
{{out}}
<pre>000
001
010
011
100
101
110
111
3,4,5
6,8,10</pre>
=={{header|Phix}}==
{{trans|Go}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">function</span> <span style="color: #000000;">bindf</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">unit</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">m</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">increment</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">unit</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">double</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">unit</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">m1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">unit</span><span style="color: #0000FF;">({</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">}),</span>
<span style="color: #000000;">m2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bindf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bindf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">increment</span><span style="color: #0000FF;">),</span><span style="color: #000000;">double</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%v -> %v\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">m1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m2</span><span style="color: #0000FF;">})</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
{3,4,5} -> {8,10,12}
</pre>
=={{header|Python}}==
<syntaxhighlight lang="python">
"""A List Monad. Requires Python >= 3.7 for type hints."""
from __future__ import annotations
from itertools import chain
from typing import Callable
from typing import Iterable
from typing import List
from typing import TypeVar
T = TypeVar("T")
U = TypeVar("U")
class MList(List[T]):
@classmethod
def unit(cls, value: Iterable[T]) -> MList[T]:
return cls(value)
def bind(self, func: Callable[[T], MList[U]]) -> MList[U]:
return MList(chain.from_iterable(map(func, self)))
def __rshift__(self, func: Callable[[T], MList[U]]) -> MList[U]:
return self.bind(func)
if __name__ == "__main__":
# Chained int and string functions.
print(
MList([1, 99, 4])
.bind(lambda val: MList([val + 1]))
.bind(lambda val: MList([f"${val}.00"]))
)
# Same, but using `>>` as the bind operator.
print(
MList([1, 99, 4])
>> (lambda val: MList([val + 1]))
>> (lambda val: MList([f"${val}.00"]))
)
# Cartesian product of [1..5] and [6..10].
print(
MList(range(1, 6)).bind(
lambda x: MList(range(6, 11)).bind(lambda y: MList([(x, y)]))
)
)
# Pythagorean triples with elements between 1 and 25.
print(
MList(range(1, 26)).bind(
lambda x: MList(range(x + 1, 26)).bind(
lambda y: MList(range(y + 1, 26)).bind(
lambda z: MList([(x, y, z)])
if x * x + y * y == z * z
else MList([])
)
)
)
)
</syntaxhighlight>
{{out}}
<pre>
['$2.00', '$100.00', '$5.00']
['$2.00', '$100.00', '$5.00']
[(1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (2, 6), (2, 7), (2, 8), (2, 9), (2, 10), (3, 6), (3, 7), (3, 8), (3, 9), (3, 10), (4, 6), (4, 7), (4, 8), (4, 9), (4, 10), (5, 6), (5, 7), (5, 8), (5, 9), (5, 10)]
[(3, 4, 5), (5, 12, 13), (6, 8, 10), (7, 24, 25), (8, 15, 17), (9, 12, 15), (12, 16, 20), (15, 20, 25)]
</pre>
=={{header|Racket}}==
{{trans|JavaScript}}
=== Vanilla Racket ===
Note that this also demonstrates how to use Racket's macro system to implement the do syntax.
<syntaxhighlight lang="racket">#lang racket
(define (bind x f) (append-map f x))
(define return list)
(define ((lift f) x) (list (f x)))
(define listy-inc (lift add1))
(define listy-double (lift (λ (x) (* 2 x))))
(bind (bind '(3 4 5) listy-inc) listy-double)
;; => '(8 10 12)
(define (pythagorean-triples n)
(bind (range 1 n)
(λ (x)
(bind (range (add1 x) n)
(λ (y)
(bind (range (add1 y) n)
(λ (z)
(if (= (+ (* x x) (* y y)) (* z z))
(return (list x y z))
'()))))))))
(pythagorean-triples 25)
;; => '((3 4 5) (5 12 13) (6 8 10) (8 15 17) (9 12 15) (12 16 20))
(require syntax/parse/define)
(define-syntax-parser do-macro
[(_ [x {~datum <-} y] . the-rest) #'(bind y (λ (x) (do-macro . the-rest)))]
[(_ e) #'e])
(define (pythagorean-triples* n)
(do-macro
[x <- (range 1 n)]
[y <- (range (add1 x) n)]
[z <- (range (add1 y) n)]
(if (= (+ (* x x) (* y y)) (* z z))
(return (list x y z))
'())))
(pythagorean-triples* 25)
;; => '((3 4 5) (5 12 13) (6 8 10) (8 15 17) (9 12 15) (12 16 20))</syntaxhighlight>
=== With functional package ===
The [https://docs.racket-lang.org/functional/interfaces.html functional] package has already implemented the list monad.
<syntaxhighlight lang="racket">#lang racket
(require data/monad
data/applicative)
(define (pythagorean-triples n)
(sequence->list
(do [x <- (range 1 n)]
[y <- (range (add1 x) n)]
[z <- (range (add1 y) n)]
(if (= (+ (* x x) (* y y)) (* z z))
(pure (list x y z))
'()))))
(pythagorean-triples 25)
;; => '((3 4 5) (5 12 13) (6 8 10) (8 15 17) (9 12 15) (12 16 20))</syntaxhighlight>
=={{header|Raku}}==
(formerly Perl 6)
Raku does not have Monad types built in but they can be emulated/implemented without a great deal of difficulty. List Monads especially are of questionable utility in Raku. Most item types and Listy types have a Cool role in Raku. (Cool being a play on the slang term "cool" as in: "That's cool with me." (That's ok with me). So Ints are pretty much treated like one item lists for operators that work with lists. ("I work on a list." "Here's an Int." "Ok, that's cool.") Explicitly wrapping an Int into a List is worse than useless. It won't do anything Raku can't do natively, and will likely '''remove''' some functionality that it would normally have. That being said, just because it is a bad idea (in Raku) doesn't mean it can't be done.
In Raku, bind is essentially map. I'll shadow map here but again, it '''removes''' capability, not adds it. Raku also provided "hyper" operators which will descend into data structures and apply an operator / function to each member of that data structure.
Here's a simple, if contrived example. take the numbers from 0 to 9, add 3 to each, find the divisors of those sums and print the list of divisors for each sum... in base 2. Again, a bind function was implemented but it is more limited than if we just used map directly. The built in map method will work with either items or lists, here we need to implement a multi sub to handle either.
The * in the bind blocks are typically referred to as "whatever"; whatever + 3 etc. The guillemot (») is the hyper operator; descend into the data structure and apply the following operator/function to each member.
<syntaxhighlight lang="raku"
multi bind ($item, &code) { $item.&code };
Line 351 ⟶ 1,295:
sub divisors (Int $int) { gather for 1 .. $int { .take if $int %% $_ } }
put
{{out}}
Line 366 ⟶ 1,310:
=={{header|Ring}}==
<
# Project : Monads/List monad
func main()
Line 382 ⟶ 1,323:
str = str + "]"
see str + nl
</syntaxhighlight>
Output:
<pre>
Line 390 ⟶ 1,331:
=={{header|Ruby}}==
<
class Array
def bind(f)
Line 434 ⟶ 1,375:
[3,4,5].bind_comp(listy_doub, listy_inc) #=> [8, 10, 12]
</syntaxhighlight>
=={{header|Swift}}==
The unit/return function is provided by the constructor for a Swift array. I define a unit function simply to keep the terminology straight. Similarly, the flatmap function provides what we need for bind, but I define a bind function explicitly.
I also define an operator that is the same as bind but which makes chaining easier.
My two functions to use are one that retiurns the two number adjacent to the supplied Int and another that returns the square roots (as Double) of an Int if it is positive or an empty list, if it is negative.
<syntaxhighlight lang="Swift">
precedencegroup MonadPrecedence {
higherThan: BitwiseShiftPrecedence
associativity: left
}
infix operator >>-: MonadPrecedence // Monadic bind
extension Array
{
static func unit(_ x: Element) -> [Element]
{
return [x]
}
func bind<T>(_ f: (Element) -> [T]) -> [T]
{
return flatMap(f)
}
static func >>- <U>(_ m: [Element], _ f: (Element) -> [U]) -> [U]
{
return m.flatMap(f)
}
}
func adjacent(_ x: Int) -> [Int]
{
[x - 1, x + 1]
}
func squareRoots(_ x: Int) -> [Double]
{
guard x >= 0 else { return [] }
return [Double(x).squareRoot(), -(Double(x).squareRoot())]
}
print("\([Int].unit(8).bind(adjacent).bind(squareRoots))")
print("\([Int].unit(8) >>- adjacent >>- squareRoots)")
print("\([Int].unit(0) >>- adjacent >>- squareRoots)")
</syntaxhighlight>
{{out}}
<pre>
[2.6457513110645907, -2.6457513110645907, 3.0, -3.0]
[2.6457513110645907, -2.6457513110645907, 3.0, -3.0]
[1.0, -1.0]
</pre>
=={{header|uBasic/4tH}}==
{{trans|Ring}}
<syntaxhighlight lang="text">s := "[" : Push 5, 4, 3
Do While Used ()
y = Set (x, Pop ()) + 1
s = Join (s, Str (Set (z, y * 2)), ", " )
Loop
Print Show (Set (s, Join (Clip (s, 2), "]")))
</syntaxhighlight>
{{out}}
<pre>
[8, 10, 12]
0 OK, 0:138
</pre>
=={{header|Wren}}==
{{trans|Go}}
<syntaxhighlight lang="wren">class Mlist {
construct new(value) { _value = value }
value { _value }
bind(f) { f.call(_value) }
static unit(lst) { Mlist.new(lst) }
}
var increment = Fn.new { |lst|
var lst2 = lst.map { |v| v + 1 }.toList
return Mlist.unit(lst2)
}
var double = Fn.new { |lst|
var lst2 = lst.map { |v| v * 2 }.toList
return Mlist.unit(lst2)
}
var ml1 = Mlist.unit([3, 4, 5])
var ml2 = ml1.bind(increment).bind(double)
System.print("%(ml1.value) -> %(ml2.value)")</syntaxhighlight>
{{out}}
<pre>
[3, 4, 5] -> [8, 10, 12]
</pre>
=={{header|zkl}}==
Line 441 ⟶ 1,486:
{{trans|Ruby}}
Here we create a class to do Monad like things. Unlike Ruby, we can't augment the baked in List/Array object so this more verbose. Also unlike Ruby, we can directly compose as we are applying the composition to each element (vs the list-as-object).
<
fcn init(xs){ var list=vm.arglist }
fcn bind(f) { list=list.apply(f); self }
fcn toString{ list.toString() }
}</
<
str:="toString";
MList(3,4,5).bind(inc).bind(str).println(" == (4,5,6)");
Line 454 ⟶ 1,499:
comp:=Utils.Helpers.fcomp; // comp(f,g) == f.g == f(g(x))
MList(3,4,5).bind(comp(doub,inc)).println(" == (8,10,12)");</
{{out}}
<pre>
| |||