Monads/Maybe monad

Demonstrate in your programming language the following:

  1. Construct a Maybe Monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
  2. Make two functions, each which take a number and return a monadic number, e.g. Int -> Maybe Int and Int -> Maybe String
  3. Compose the two functions with bind
Task
Monads/Maybe monad
You are encouraged to solve this task according to the task description, using any language you may know.


A Monad is a single type which encapsulates several other types, eliminating boilerplate code. In practice it acts like a dynamically typed computational sequence, though in many cases the type issues can be resolved at compile time.

A Maybe Monad is a monad which specifically encapsulates the type of an undefined value.

ALGOL 68Edit

Translation of: JavaScript
BEGIN

    # This is a translation of the Javascript sample, main differences are because Algol 68    #
    # is strongly typed and "on-the-fly" constructon of functions is not really possible -     #
    # we need to define a STRUCT where Javascript would just construct a new function.         #
    # As Algol 68 does not allow procedure overloading, we use custom operators (which do      #
    # allow overloading) so the techniques used here could be extended to procedures with      #
    # signatures other than PROC(REAL)REAL                                                     #
    # The comments are generally the same as in the javascript original, changed as necessary  #
    # to reflect Algol 68...                                                                   #
 
    # START WITH SOME SIMPLE (UNSAFE) PARTIAL FUNCTIONS:                                       #
 
    # error in n < 0 #
    PROC unsafe reciprocal = (REAL n)REAL: 1 / n;
    # error if n < 0 #
    PROC unsafe root       = (REAL n)REAL: sqrt(n);
    # error if n <= 0 #
    PROC unsafe log        = (REAL n)REAL: ln(n);
 
 
    # NOW DERIVE SAFE VERSIONS OF THESE SIMPLE FUNCTIONS:                                      #
    # These versions use a validity test, and return a wrapped value                           #
    # with a boolean is valid property as well as a value property                             #

    MODE SAFEFUNCTION = STRUCT( PROC(REAL)REAL fn, PROC(REAL)BOOL fn safety check ); 
    MODE MAYBE        = STRUCT( BOOL is valid, REAL value );
 
    SAFEFUNCTION safe reciprocal = ( unsafe reciprocal, ( REAL n )BOOL: n /= 0 );
    SAFEFUNCTION safe root       = ( unsafe root,       ( REAL n )BOOL: n >= 0 );
    SAFEFUNCTION safe log        = ( unsafe log,        ( REAL n )BOOL: n >  0 );
 
COMMENT 
    the original Javascript contains this:

    // THE DERIVATION OF THE SAFE VERSIONS USED THE 'UNIT' OR 'RETURN' 
    // FUNCTION OF THE MAYBE MONAD
 
    // Named maybe() here, the unit function of the Maybe monad wraps a raw value 
    // in a datatype with two elements: .isValid (Bool) and .value (Number)
 
    // a -> Ma
    function maybe(n) {
        return {
            isValid: (typeof n !== 'undefined'),
            value: n
        };
    }

    However Algol 68 is strongly typed, so the type (MODE) of the function parameters
    cannot be anything other than REAL. We therefore use "MAYBE( TRUE, n )" instead.
COMMENT

    # THE PROBLEM FOR FUNCTION NESTING (COMPOSITION) OF THE SAFE FUNCTIONS                     #
    # IS THAT THEIR INPUT AND OUTPUT TYPES ARE DIFFERENT                                       #
 
    # Our safe versions of the functions take simple numeric arguments (i.e. REAL), but return #
    # wrapped results. If we feed a wrapped result as an input to another safe function, the   #
    # compiler will object. The solution is to write a higher order                            #
    # function (sometimes called 'bind' or 'chain') which handles composition, taking a        #
    # a safe function and a wrapped value as arguments,                                        #
 
    # The 'bind' function of the Maybe monad:                                                  #
    # 1. Applies a 'safe' function directly to the raw unwrapped value, and                    #
    # 2. returns the wrapped result.                                                           #
 
    # Ma -> (a -> Mb) -> Mb #
    # defined as an operator to allow overloading to other PROC modes                          #
    PRIO BIND = 1;
    OP   BIND = (MAYBE maybe n, SAFEFUNCTION mf )MAYBE:
        IF is valid OF maybe n THEN mf CALL ( value OF maybe n ) ELSE maybe n FI;
    # we need an operator to call the wrapped function                                         #
    PRIO CALL = 1;
    OP   CALL = ( SAFEFUNCTION f, REAL value )MAYBE:
         BEGIN
             BOOL is valid = ( fn safety check OF f )( value );
             MAYBE( is valid, IF is valid THEN ( fn OF f )( value ) ELSE value FI )
         END; # CALL #

    # Using the bind function, we can nest applications of safe functions,                     #
    # without the compiler choking on unexpectedly wrapped values returned from                #
    # other functions of the same kind.                                                        #
    REAL root one over four = value OF ( MAYBE( TRUE, 4 ) BIND safe reciprocal BIND safe root );

#   print( ( root one over four, newline ) ); #
    # -> 0.5 #
 
    # We can compose a chain of safe functions (of any length) with a simple foldr/reduceRight #
    # which starts by 'lifting' the numeric argument into a Maybe wrapping,                    #
    # and then nests function applications (working from right to left)                        #
    # again, defined as an operator here to allow extension to other PROC modes                #
    # also, as Algol 68 doesn't have builtin foldr/reduceRight, we need a loop...              #
    PRIO SAFECOMPOSE = 1;
    OP   SAFECOMPOSE = ( []SAFEFUNCTION lst functions, REAL value )MAYBE:
         BEGIN
             MAYBE result := MAYBE( TRUE, value );
             FOR fn pos FROM UPB lst functions BY -1 TO LWB lst functions DO
                 result := result BIND lst functions[ fn pos ]
             OD;
             result
         END; # SAFECOMPOSE #
 
    # TEST INPUT VALUES WITH A SAFELY COMPOSED VERSION OF LOG(SQRT(1/X))                       #
 
    PROC safe log root reciprocal = ( REAL n )MAYBE:
         BEGIN
             # this declaration is requied for Algol 68G 2.8                                   #
             []SAFEFUNCTION function list = ( safe log, safe root, safe reciprocal );
             function list SAFECOMPOSE n
         END; # safe log root reciprocal #

    # Algol 68 doesn't have a builtin map operator, we could define one here but we can just   #
    # use a loop for the purposes of this task...                                              #
    REAL e = exp( 1 );
    []REAL test values = ( -2, -1, -0.5, 0, 1 / e, 1, 2, e, 3, 4, 5 );

    STRING prefix := "[";
    FOR test pos FROM LWB test values TO UPB test values DO
        MAYBE result = safe log root reciprocal( test values[ test pos ] );
        print( ( prefix, IF is valid OF result THEN fixed( value OF result, -12, 8 ) ELSE "undefined" FI ) );
        IF test pos MOD 4 = 0 THEN print( ( newline ) ) FI;
        prefix := ", "
    OD;
    print( ( "]", newline ) )
 
END
Output:
[undefined, undefined, undefined, undefined
,   0.50000000,   0.00000000,  -0.34657359,  -0.50000000
,  -0.54930614,  -0.69314718,  -0.80471896]

AppleScriptEdit

Translation of: JavaScript


Algebraically-reasoned defence against invalid arguments for partial functions buried deep in function nests is probably more than a light-weight scripting language will really need on an average weekday, but we can usually do most things in most languages, and stretching a language a little bit is a way of exploring both its limits, and its relationships with other languages.

What AppleScript mostly lacks here (apart from a rich core library) is a coherent first-class function type which allows for anonymous functions. Nevertheless there is enough there to emulate first-class functions (using script objects), and we can set up a working Maybe monad without too much trouble.

It would, at least, spare us from having to structure things around try … on error … end try etc


property e : 2.71828182846

on run {}
    
    -- Derive safe versions of three simple functions
    set sfReciprocal to safeVersion(reciprocal, notZero)
    set sfRoot to safeVersion(root, isPositive)
    set sfLog to safeVersion(ln, aboveZero)
    
    
    -- Test a composition of these function with a range of invalid and valid arguments
    
    -- (The safe composition returns missing value (without error) for invalid arguments)
    
    map([-2, -1, -0.5, 0, 1 / e, 1, 2, e, 3, 4, 5], safeLogRootReciprocal)

    -- 'missing value' is returned by a safe function (and threaded up through the monad) when the input argument is out of range
    --> {missing value, missing value, missing value, missing value, 0.5, 0.0, -0.346573590279, -0.499999999999, -0.549306144333, -0.69314718056, -0.804718956217}
end run


-- START WITH SOME SIMPLE (UNSAFE) PARTIAL FUNCTIONS:

-- Returns ERROR 'Script Error: Can’t divide 1.0 by zero.' if n = 0
on reciprocal(n)
    1 / n
end reciprocal

-- Returns ERROR 'error "The result of a numeric operation was too large." number -2702'
-- for all values below 0
on root(n)
    n ^ (1 / 2)
end root

-- Returns -1.0E+20 for all values of zero and below
on ln(n)
    (do shell script ("echo 'l(" & (n as string) & ")' | bc -l")) as real
end ln

-- DERIVE A SAFE VERSION OF EACH FUNCTION 
-- (SEE on Run() handler)

on safeVersion(f, fnSafetyCheck)
    script
        on call(x)
            if sReturn(fnSafetyCheck)'s call(x) then
                sReturn(f)'s call(x)
            else
                missing value
            end if
        end call
    end script
end safeVersion

on notZero(n)
    n is not 0
end notZero

on isPositive(n)
    n  0
end isPositive

on aboveZero(n)
    n > 0
end aboveZero


-- DEFINE A FUNCTION WHICH CALLS A COMPOSITION OF THE SAFE VERSIONS
on safeLogRootReciprocal(x)
    
    value of mbCompose([my sfLog, my sfRoot, my sfReciprocal], x)
    
end safeLogRootReciprocal


-- UNIT/RETURN and BIND functions for the Maybe monad

-- Unit / Return for maybe
on maybe(n)
    {isValid:n is not missing value, value:n}
end maybe

-- BIND maybe
on mbBind(recMaybe, mfSafe)
    if isValid of recMaybe then
        maybe(mfSafe's call(value of recMaybe))
    else
        recMaybe
    end if
end mbBind

-- lift 2nd class function into 1st class wrapper 
-- handler function --> first class script object
on sReturn(f)
    script
        property call : f
    end script
end sReturn

-- return a new script in which function g is composed
-- with the f (call()) of the Mf script
-- Mf -> (f -> Mg) -> Mg
on sBind(mf, g)
    script
        on call(x)
            sReturn(g)'s call(mf's call(x))
        end call
    end script
end sBind

on mbCompose(lstFunctions, value)
    reduceRight(lstFunctions, mbBind, maybe(value))
end mbCompose

-- xs: list, f: function, a: initial accumulator value
-- the arguments available to the function f(a, x, i, l) are
-- v: current accumulator value
-- x: current item in list
-- i: [ 1-based index in list ] optional
-- l: [ a reference to the list itself ] optional
on reduceRight(xs, f, a)
    set mf to sReturn(f)
    
    repeat with i from length of xs to 1 by -1
        set a to mf's call(a, item i of xs, i, xs)
    end repeat
end reduceRight

-- [a] -> (a -> b) -> [b]
on map(xs, f)
    set mf to sReturn(f)
    set lst to {}
    set lng to length of xs
    repeat with i from 1 to lng
        set end of lst to mf's call(item i of xs, i, xs)
    end repeat
    return lst
end map
Output:
-- 'missing value' is returned by a safe function (and threaded up through the monad) when the input argument is out of range

{missing value, missing value, missing value, missing value, 0.5, 0.0, -0.346573590279, -0.499999999999, -0.549306144333, -0.69314718056, -0.804718956217}

CEdit

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>

typedef enum type
{
  INT,
  STRING
} Type;

typedef struct maybe
{
  int i;
  char *s;
  Type t;
  _Bool is_something;
} Maybe;

void print_Maybe(Maybe *m)
{
  if (m->t == INT)
    printf("Just %d : INT\n", m->i);

  else if (m->t == STRING)
    printf("Just \"%s\" : STRING\n", m->s);

  else
    printf("Nothing\n");

}

Maybe *return_maybe(void *data, Type t)
{
  Maybe *m = malloc(sizeof(Maybe));
  if (t == INT)
  {
    m->i = *(int *) data;
    m->s = NULL;
    m->t = INT;
    m->is_something = true;
  }

  else if (t == STRING)
  {
    m->i = 0;
    m->s = data;
    m->t = STRING;
    m->is_something = true;
  }

  else
  {
    m->i = 0;
    m->s = NULL;
    m->t = 0;
    m->is_something = false;
  }

  return m;
}

Maybe *bind_maybe(Maybe *m, Maybe *(*f)(void *))
{
  Maybe *n = malloc(sizeof(Maybe));
  
  if (f(&(m->i))->is_something)
  {
    n->i = f(&(m->i))->i;
    n->s = f(&(m->i))->s;
    n->t = f(&(m->i))->t;
    n->is_something = true;
  }

  else
  {
    n->i = 0;
    n->s = NULL;
    n->t = 0;
    n->is_something = false;
  }
  return n;
}

Maybe *f_1(void *v) // Int -> Maybe Int
{
  Maybe *m = malloc(sizeof(Maybe));
  m->i = (*(int *) v) * (*(int *) v);
  m->s = NULL;
  m->t = INT;
  m->is_something = true;
  return m;
}

Maybe *f_2(void *v) // :: Int -> Maybe String
{
  Maybe *m = malloc(sizeof(Maybe));
  m->i = 0;
  m->s = malloc(*(int *) v * sizeof(char) + 1);
  for (int i = 0; i < *(int *) v; i++)
  {
    m->s[i] = 'x';
  }
  m->s[*(int *) v + 1] = '\0';
  m->t = STRING;
  m->is_something = true;
  return m;
}

int main()
{
  int i = 7;
  char *s = "lorem ipsum dolor sit amet";

  Maybe *m_1 = return_maybe(&i, INT);
  Maybe *m_2 = return_maybe(s, STRING);

  print_Maybe(m_1); // print value of m_1: Just 49
  print_Maybe(m_2); // print value of m_2 : Just "lorem ipsum dolor sit amet"

  print_Maybe(bind_maybe(m_1, f_1)); // m_1 `bind` f_1 :: Maybe Int
  print_Maybe(bind_maybe(m_1, f_2)); // m_1 `bind` f_2 :: Maybe String

  print_Maybe(bind_maybe(bind_maybe(m_1, f_1), f_2)); // (m_1 `bind` f_1) `bind` f_2 :: Maybe String -- it prints 49 'x' characters in a row
}
Output:
Just 7 : INT
Just "lorem ipsum dolor sit amet" : STRING
Just 49 : INT
Just "xxxxxxx" : STRING
Just "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx" : STRING

C++Edit

#include <iostream>
#include <cmath>
#include <optional>
#include <vector>

using namespace std;

// std::optional can be a maybe monad.  Use the >> operator as the bind function
template <typename T>
auto operator>>(const optional<T>& monad, auto f)
{
    if(!monad.has_value())
    {
        // Return an empty maybe monad of the same type as if there 
        // was a value
        return optional<remove_reference_t<decltype(*f(*monad))>>();
    }

    return f(*monad);
}

// The Pure function returns a maybe monad containing the value t
auto Pure(auto t)
{
    return optional{t};
}

// A safe function to invert a value 
auto SafeInverse(double v)
{
    if (v == 0)
    {
        return optional<decltype(v)>();
    }
    else
    {
        return optional(1/v);
    }
}

// A safe function to calculate the arc cosine
auto SafeAcos(double v)
{
    if(v < -1 || v > 1)
    {
        // The input is out of range, return an empty monad
        return optional<decltype(acos(v))>();
    }
    else
    {
        return optional(acos(v));
    }
}

// Print the monad
template<typename T>
ostream& operator<<(ostream& s, optional<T> v)
{
    s << (v ? to_string(*v) : "nothing");
    return s;
}

int main()
{
    // Use bind to compose SafeInverse and SafeAcos
    vector<double> tests {-2.5, -1, -0.5, 0, 0.5, 1, 2.5};
    
    cout << "x -> acos(1/x) , 1/(acos(x)\n";
    for(auto v : tests)
    {
        auto maybeMonad = Pure(v);
        auto inverseAcos = maybeMonad >> SafeInverse >> SafeAcos;
        auto acosInverse = maybeMonad >> SafeAcos >> SafeInverse;
        cout << v << " -> " << inverseAcos << ", " << acosInverse << "\n";
    }
}
Output:
x -> acos(1/x) , 1/(acos(x)
-2.5 -> 1.982313, nothing
-1 -> 3.141593, 0.318310
-0.5 -> nothing, 0.477465
0 -> nothing, 0.636620
0.5 -> nothing, 0.954930
1 -> 0.000000, nothing
2.5 -> 1.159279, nothing

C#Edit

using System;

namespace RosettaMaybe
{
    // courtesy of https://www.dotnetcurry.com/patterns-practices/1510/maybe-monad-csharp
    public abstract class Maybe<T>
    {
        public sealed class Some : Maybe<T>
        {
            public Some(T value) => Value = value;
            public T Value { get; }
        }
        public sealed class None : Maybe<T> { }
    }

    class Program
    {
        static Maybe<double> MonadicSquareRoot(double x)
        {
            if (x >= 0)
            {
                return new Maybe<double>.Some(Math.Sqrt(x));
            }
            else
            {
                return new Maybe<double>.None();
            }
        }
        static void Main(string[] args)
        {
            foreach (double x in new double[] { 4.0D, 8.0D, -15.0D, 16.23D, -42 })
            {
                Maybe<double> maybe = MonadicSquareRoot(x);
                if (maybe is Maybe<double>.Some some)
                {
                    Console.WriteLine($"The square root of {x} is " + some.Value);
                }
                else
                {
                    Console.WriteLine($"Square root of {x} is undefined.");
                }
            }
        }
    }
}


ClojureEdit

(defn bind [val f]
  (if-let [v (:value val)] (f v) val))

(defn unit [val] {:value val})

(defn opt_add_3 [n] (unit (+ 3 n))) ; takes a number and returns a Maybe number
(defn opt_str [n] (unit (str n)))   ; takes a number and returns a Maybe string

(bind (unit 4) opt_add_3)                  ; evaluates to {:value 7}
(bind (unit nil) opt_add_3)                ; evaluates to {:value nil}
(bind (bind (unit 8) opt_add_3) opt_str)   ; evaluates to {:value "11"}
(bind (bind (unit nil) opt_add_3) opt_str) ; evaluates to {:value nil}

DelphiEdit

Translation of: Go
program Maybe_monad;

{$APPTYPE CONSOLE}

uses
  System.SysUtils;

type
  TmList = record
    Value: PInteger;
    function ToString: string;
    function Bind(f: TFunc<PInteger, TmList>): TmList;
  end;

function _Unit(aValue: Integer): TmList; overload;
begin
  Result.Value := GetMemory(sizeof(Integer));
  Result.Value^ := aValue;
end;

function _Unit(aValue: PInteger): TmList; overload;
begin
  Result.Value := aValue;
end;

{ TmList }

function TmList.Bind(f: TFunc<PInteger, TmList>): TmList;
begin
  Result := f(self.Value);
end;

function TmList.ToString: string;
begin
  if Value = nil then
    Result := 'none'
  else
    Result := value^.ToString;
end;

function Decrement(p: PInteger): TmList;
begin
  if p = nil then
    exit(_Unit(nil));
  Result := _Unit(p^ - 1);
end;

function Triple(p: PInteger): TmList;
begin
  if p = nil then
    exit(_Unit(nil));
  Result := _Unit(p^ * 3);
end;

var
  m1, m2: TmList;
  i, a, b, c: Integer;
  p: Tarray<PInteger>;

begin
  a := 3;
  b := 4;
  c := 5;
  p := [@a, @b, nil, @c];

  for i := 0 to High(p) do
  begin
    m1 := _Unit(p[i]);
    m2 := m1.Bind(Decrement).Bind(Triple);

    Writeln(m1.ToString: 4, ' -> ', m2.ToString);
  end;
  Readln;
end.
Output:
   3 -> 6
   4 -> 9
none -> none
   5 -> 12

EchoLispEdit

Our monadic Maybe elements will be pairs (boolean . value), where value is in Maybe.domain. Functions which return something not in Maybe.domain are unsafe and return (#f . input-value), If a function is given as input a (#f . value) element, it will return this element.

(define (Maybe.domain? x) (or (number? x) (string? x)))
(define (Maybe.unit elem (bool #t)) (cons bool elem))

;; f is a safe or unsafe function
;; (Maybe.lift f) returns a safe Maybe function which returns a Maybe element
(define (Maybe.lift f)     
		(lambda(x) 
             (let [(u (f x))]
             (if (Maybe.domain? u) 
                (Maybe.unit u)
                (Maybe.unit x #f))))) ;; return offending x
                                
                            
;; elem = Maybe element
;; f is safe or unsafe  (lisp) function
;; return Maybe element
(define (Maybe.bind f elem)  
		(if (first elem) ((Maybe.lift f)  (rest elem)) elem))
		
;; pretty-print		
(define (Maybe.print elem)
		(if (first elem)  (writeln elem ) (writeln ' elem)))

;; unsafe functions
(define (u-log x) (if (> x 0) (log x) #f))
(define (u-inv x) (if (zero? x) 'zero-div (/ x)))

;; (print (number->string (exp (log 3))))
(->> 3 Maybe.unit (Maybe.bind u-log) (Maybe.bind exp)  (Maybe.bind number->string) Maybe.print)
     (#t . "3.0000000000000004")    

;; (print (number->string (exp (log -666))))
(->> -666  Maybe.unit (Maybe.bind u-log) (Maybe.bind exp)  (Maybe.bind number->string) Maybe.print)
           (#f . -666)   
      
;; ;; (print (number->string (inverse (log 1))))
(->> 1 Maybe.unit (Maybe.bind u-log)  (Maybe.bind u-inv)  (Maybe.bind number->string) Maybe.print)
            (#f . 0)

F#Edit

// We can use Some as return, Option.bind and the pipeline operator in order to have a very concise code


let f1 (v:int) = Some v  // int -> Option<int>
let f2 (v:int) = Some(string v) // int -> Option<sting>

f1 4 |> Option.bind f2 |> printfn "Value is %A"  // bind when option (maybe) has data
None |> Option.bind f2 |> printfn "Value is %A" // bind when option (maybe) does not have data
Output:
4
null

FactorEdit

Factor comes with an implementation of Haskell-style monads in the monads vocabulary.

USING: monads ;
FROM: monads => do ;

! Prints "T{ just { value 7 } }"
3 maybe-monad return >>= [ 2 * maybe-monad return ] swap call
                     >>= [ 1 + maybe-monad return ] swap call .

! Prints "nothing"
nothing >>= [ 2 * maybe-monad return ] swap call
        >>= [ 1 + maybe-monad return ] swap call .

Or:

3 <just> [ 2 * <just> ] bind [ 1 + <just> ] bind .
nothing [ 2 * <just> ] bind [ 1 + <just> ] bind .

Or with do notation:

{
    [ 3 <just> ]
    [ 2 * <just> ]
    [ 1 + <just> ]
} do .
{
    [ nothing ]
    [ 2 * <just> ]
    [ 1 + <just> ]
} do .

GoEdit

package main

import (
    "fmt"
    "strconv"
)

type maybe struct{ value *int }

func (m maybe) bind(f func(p *int) maybe) maybe {
    return f(m.value)
}

func unit(p *int) maybe {
    return maybe{p}
}

func decrement(p *int) maybe {
    if p == nil {
        return unit(nil)
    } else {
        q := *p - 1
        return unit(&q)
    }
}

func triple(p *int) maybe {
    if p == nil {
        return unit(nil)
    } else {
        q := (*p) * 3
        return unit(&q)
    }
}

func main() {
    i, j, k := 3, 4, 5
    for _, p := range []*int{&i, &j, nil, &k} {
        m1 := unit(p)
        m2 := m1.bind(decrement).bind(triple)
        var s1, s2 string = "none", "none"
        if m1.value != nil {
            s1 = strconv.Itoa(*m1.value)
        }
        if m2.value != nil {
            s2 = strconv.Itoa(*m2.value)
        }
        fmt.Printf("%4s -> %s\n", s1, s2)
    }
}
Output:
   3 -> 6
   4 -> 9
none -> none
   5 -> 12

HaskellEdit

Haskell has the built-in Monad type class, and the built-in Maybe type already conforms to the Monad type class.

main = do print $ Just 3 >>= (return . (*2)) >>= (return . (+1))  -- prints "Just 7"
          print $ Nothing >>= (return . (*2)) >>= (return . (+1)) -- prints "Nothing"

Or, written using do notation:

main = do print (do x <- Just 3
                    y <- return (x*2)
                    z <- return (y+1)
		    return z)
          print (do x <- Nothing
                    y <- return (x*2)
                    z <- return (y+1)
                    return z)

Or alternately:

main = do print (do x <- Just 3
                    let y = x*2
                    let z = y+1
		    return z)
          print (do x <- Nothing
                    let y = x*2
                    let z = y+1
                    return z)

Deriving and composing safe versions of reciprocal, square root and log functions. :

import Control.Monad ((>=>))

safeVersion :: (a -> b) -> (a -> Bool) -> a -> Maybe b
safeVersion f fnSafetyCheck x | fnSafetyCheck x = Just (f x)
                              | otherwise       = Nothing

safeReciprocal = safeVersion (1/) (/=0)
safeRoot = safeVersion sqrt (>=0)
safeLog = safeVersion log (>0)

safeLogRootReciprocal = safeReciprocal >=> safeRoot >=> safeLog

main = print $ map safeLogRootReciprocal [-2, -1, -0.5, 0, exp (-1), 1, 2, exp 1, 3, 4, 5]
Output:
[Nothing,Nothing,Nothing,Nothing,Just 0.5,Just 0.0,Just (-0.3465735902799726),Just (-0.5),Just (-0.5493061443340549),Just (-0.6931471805599453),Just (-0.8047189562170503)]

HoonEdit

:-  %say
|=  [^ [[txt=(unit ,@tas) ~] ~]]
:-  %noun
|^
  %+  biff  txt
    ;~  biff
      m-parse
      m-double
    ==
  ++  m-parse
    |=  a=@tas
    ^-  (unit ,@ud)
    (rust (trip a) dem)
  ::
  ++  m-double
    |=  a=@ud
    ^-  (unit ,@ud)
    (some (mul a 2))
  --

Hoon has a built-in rune, %smsg (;~) that binds gates under a monad.

++unit is Hoon's Maybe: it is either ~ (None) or [~ u=val] (Some)

++biff is the monadic bind, which %smsg uses to wire the gates together. It's defined in the standard library here. m-parse is @tas -> (unit ,@ud), so I use biff a second time in order for the program to be called with (unit ,@tas).

++rust is one of the parser combinator runners: it parses the string `a` with the rule `dem`, returning a unit with the returned value if it success or ~ if it fails. Note that Hoon's type system is complex enough to get a strongly typed result of the parsing rule, in this case an unsigned decimal (@ud)

> +monad (some '2')
[~ 4]
> +monad (some 'a')
~
> +monad ~
~

JEdit

It's difficult to find a useful and illustrative (but simple) example of this task in J. So we shall not try to be useful.

NB. monad implementation:
unit=: <
bind=: (@>)( :: ])

NB. monad utility
safeVersion=: (<@) ( ::((<_.)"_))
safeCompose=:dyad define
  dyad def 'x`:6 bind y'/x,unit y
)

NB. unsafe functions (fail with infinite arguments)
subtractFromSelf=: -~
divideBySelf=: %~

NB. wrapped functions:
safeSubtractFromSelf=: subtractFromSelf safeVersion
safeDivideBySelf=: divideBySelf safeVersion

NB. task example:
     safeSubtractFromSelf bind safeDivideBySelf 1
┌─┐
0
└─┘
     safeSubtractFromSelf bind safeDivideBySelf _
┌──┐
_.
└──┘

JavaScriptEdit

ES5Edit

Example: deriving and composing safe versions of reciprocal, square root and log functions.

(function () {
    'use strict';

    // START WITH SOME SIMPLE (UNSAFE) PARTIAL FUNCTIONS:

    // Returns Infinity if n === 0
    function reciprocal(n) {
        return 1 / n;
    }

    // Returns NaN if n < 0
    function root(n) {
        return Math.sqrt(n);
    }

    // Returns -Infinity if n === 0
    // Returns NaN if n < 0
    function log(n) {
        return Math.log(n);
    }


    // NOW DERIVE SAFE VERSIONS OF THESE SIMPLE FUNCTIONS:
    // These versions use a validity test, and return a wrapped value
    // with a boolean .isValid property as well as a .value property

    function safeVersion(f, fnSafetyCheck) {
        return function (v) {
            return maybe(fnSafetyCheck(v) ? f(v) : undefined);
        }
    }

    var safe_reciprocal = safeVersion(reciprocal, function (n) {
        return n !== 0;
    });

    var safe_root = safeVersion(root, function (n) {
        return n >= 0;
    });


    var safe_log = safeVersion(log, function (n) {
        return n > 0;
    });


    // THE DERIVATION OF THE SAFE VERSIONS USED THE 'UNIT' OR 'RETURN' 
    // FUNCTION OF THE MAYBE MONAD

    // Named maybe() here, the unit function of the Maybe monad wraps a raw value 
    // in a datatype with two elements: .isValid (Bool) and .value (Number)

    // a -> Ma
    function maybe(n) {
        return {
            isValid: (typeof n !== 'undefined'),
            value: n
        };
    }

    // THE PROBLEM FOR FUNCTION NESTING (COMPOSITION) OF THE SAFE FUNCTIONS
    // IS THAT THEIR INPUT AND OUTPUT TYPES ARE DIFFERENT

    // Our safe versions of the functions take simple numeric arguments, but return
    // wrapped results. If we feed a wrapped result as an input to another safe function,
    // it will choke on the unexpected type. The solution is to write a higher order
    // function (sometimes called 'bind' or 'chain') which handles composition, taking a 
    // a safe function and a wrapped value as arguments,

    // The 'bind' function of the Maybe monad:
    // 1. Applies a 'safe' function directly to the raw unwrapped value, and
    // 2. returns the wrapped result.

    // Ma -> (a -> Mb) -> Mb
    function bind(maybeN, mf) {
        return (maybeN.isValid ? mf(maybeN.value) : maybeN);
    }

    // Using the bind function, we can nest applications of safe_ functions,
    // without their choking on unexpectedly wrapped values returned from
    // other functions of the same kind.
    var rootOneOverFour = bind(
        bind(maybe(4), safe_reciprocal), safe_root
    ).value;

    // -> 0.5


    // We can compose a chain of safe functions (of any length) with a simple foldr/reduceRight
    // which starts by 'lifting' the numeric argument into a Maybe wrapping,
    // and then nests function applications (working from right to left)
    function safeCompose(lstFunctions, value) {
        return lstFunctions
            .reduceRight(function (a, f) {
                return bind(a, f);
            }, maybe(value));
    }

    // TEST INPUT VALUES WITH A SAFELY COMPOSED VERSION OF LOG(SQRT(1/X))

    var safe_log_root_reciprocal = function (n) {
        return safeCompose([safe_log, safe_root, safe_reciprocal], n).value;
    }

    return [-2, -1, -0.5, 0, 1 / Math.E, 1, 2, Math.E, 3, 4, 5].map(
        safe_log_root_reciprocal
    );

})();
Output:
[undefined, undefined, undefined, undefined, 0.5, 0,
-0.3465735902799726, -0.5, -0.5493061443340549,
-0.6931471805599453, -0.8047189562170503]

JuliaEdit

struct maybe x::Union{Real, Missing}; end

Base.show(io::IO, m::maybe) = print(io, m.x)

unit(x) = maybe(x)
bind(f, x) = unit(f(x.x))

f1(x) = 5x
f2(x) = x + 4

a = unit(3)
b = unit(missing)

println(a, " -> ", bind(f2, bind(f1, a)))

println(b, " -> ", bind(f2, bind(f1, b)))
Output:
3 -> 19
missing -> missing

KotlinEdit

The JVM already contains a 'Maybe' monad in the form of the java.util.Optional<T> generic class.

Its static methods, 'of' and 'ofNullable', serve as its 'unit' function for wrapping nullable and non-nullable values respectively and its instance method, 'flatMap', serves as its 'bind' function.

Rather than write something from scratch, we use this class to complete this task.

// version 1.2.10

import java.util.Optional

/* doubles 'i' before wrapping it */
fun getOptionalInt(i: Int) = Optional.of(2 * i)

/* returns an 'A' repeated 'i' times wrapped in an Optional<String> */
fun getOptionalString(i: Int) = Optional.of("A".repeat(i))

/* does same as above if i > 0, otherwise returns an empty Optional<String> */
fun getOptionalString2(i: Int) =
   Optional.ofNullable(if (i > 0) "A".repeat(i) else null)

fun main(args: Array<String>) {
    /* prints 10 'A's */
    println(getOptionalInt(5).flatMap(::getOptionalString).get())

    /* prints  4 'A's */
    println(getOptionalInt(2).flatMap(::getOptionalString2).get())

    /* prints 'false' as there is no value present in the Optional<String> instance */
    println(getOptionalInt(0).flatMap(::getOptionalString2).isPresent)
}
Output:
AAAAAAAAAA
AAAA
false

LuaEdit

Works with: lua version 5.3
-- None is represented by an empty table.  Some is represented by any
-- array with one element.  You SHOULD NOT compare maybe values with the
-- Lua operator == because it will give incorrect results.  Use the
-- functions isMaybe(), isNone(), and isSome().

-- define once for efficiency, to avoid many different empty tables
local NONE = {}

local function unit(x) return { x } end
local Some = unit
local function isNone(mb) return #mb == 0 end
local function isSome(mb) return #mb == 1 end
local function isMaybe(mb) return isNone(mb) or isSome(mb) end

-- inverse of Some(), extract the value from the maybe; get(Some(x)) === x
local function get(mb) return mb[1] end

function maybeToStr(mb)
	return isNone(mb) and "None" or ("Some " .. tostring(get(mb)))
end

local function bind(mb, ...)  -- monadic bind for multiple functions
	local acc = mb
	for _, fun in ipairs({...}) do  -- fun should be a monadic function
		assert(type(fun) == "function")
		if isNone(acc) then return NONE
		else acc = fun(get(acc)) end
	end
	return acc
end

local function fmap(mb, ...)  -- monadic fmap for multiple functions
	local acc = mb
	for _, fun in ipairs({...}) do  -- fun should be a regular function
		assert(type(fun) == "function")
		if isNone(acc) then return NONE
		else acc = Some(fun(get(acc))) end
	end
	return acc
end
-- ^^^ End of generic maybe monad functionality ^^^

--- vvv Start of example code vvv

local function time2(x) return x * 2 end
local function plus1(x) return x + 1 end

local answer
answer = fmap(Some(3), time2, plus1, time2)
assert(get(answer)==14)

answer = fmap(NONE, time2, plus1, time2)
assert(isNone(answer))

local function safeReciprocal(x)
	if x ~= 0 then return Some(1/x) else return NONE end
end
local function safeRoot(x)
	if x >= 0 then return Some(math.sqrt(x)) else return NONE end
end
local function safeLog(x)
	if x > 0 then return Some(math.log(x)) else return NONE end
end
local function safeComputation(x)
	return bind(safeReciprocal(x), safeRoot, safeLog)
end

local function map(func, table)
	local result = {}
	for key, val in pairs(table) do
		result[key] = func(val)
	end
	return result
end

local inList = {-2, -1, -0.5, 0, math.exp (-1), 1, 2, math.exp (1), 3, 4, 5}
print("input:", table.concat(map(tostring, inList), ",  "), "\n")

local outList = map(safeComputation, inList)
print("output:", table.concat(map(maybeToStr, outList), ",  "), "\n")

NimEdit

import options,math,sugar,strformat
template checkAndWrap(x:float,body:typed): untyped =
  if x.classify in {fcNormal,fcZero,fcNegZero}:
    some(body)
  else:
    none(typeof(body))
func reciprocal(x:float):Option[float] =
  let res = 1 / x
  res.checkAndWrap(res)
func log(x:float):Option[float] =
  let res = ln(x)
  res.checkAndWrap(res)
func format(x:float):Option[string] =
  x.checkAndWrap(&"{x:.2f}")

#our bind function:
func `-->`[T,U](input:Option[T], f: T->Option[U]):Option[U] =
  if input.isSome:
    f(input.get)
  else:
    none(U)

when isMainModule:
  for i in [0.9,0.0,-0.9,3.0]:
    echo some(i) --> reciprocal --> log --> format
Output:
some("0.11")

none(string) none(string)

some("-1.10")

OCamlEdit

The Option module already has our bind and return operations. If we wanted to redefine them :

let bind opt func = match opt with
  | Some x -> func x
  | None -> None

let return x = Some x

To easily manipulate bind, we can use infix operators and let pruning :

let (-->) = bind
let (let*) = bind

let print_str_opt x = 
  Format.printf "%s" (Option.value ~default:"None" x)

Example:

let safe_div x y = if y = 0.0 then None else return (x /. y)
let safe_root x = if x < 0.0 then None else return (sqrt x)
let safe_str x = return (Format.sprintf "%#f" x)

(* Version 1 : explicit calls *)
let () =
  let v = bind (bind (safe_div 5. 3.) safe_root) safe_str in
  print_str_opt v

(* Version 2 : with an operator *)
let () =
  let v = safe_div 5. 3. --> safe_root --> safe_str in
  print_str_opt v

(* Version 3 : let pruning really shine when inlining functions *)
let () =
  let v = 
    let* x = safe_div 5. 3. in
    let* y = if x < 0.0 then None else return (sqrt x) in
    return (Format.sprintf "%#f" y)
  in print_str_opt v

PerlEdit

Translation of: Haskell
# 20201101 added Perl programming solution

use strict;
use warnings;

use Data::Monad::Maybe;

sub safeReciprocal { ( $_[0] == 0 ) ? nothing : just(  1 /  $_[0] )   }

sub safeRoot       { ( $_[0] <  0 ) ? nothing : just( sqrt( $_[0] ) ) }

sub safeLog        { ( $_[0] <= 0 ) ? nothing : just( log ( $_[0] ) ) }

print join(' ', map {
   my $safeLogRootReciprocal = just($_)->flat_map( \&safeReciprocal )
                                       ->flat_map( \&safeRoot       )
                                       ->flat_map( \&safeLog        );
   $safeLogRootReciprocal->is_nothing ? "NaN" : $safeLogRootReciprocal->value;
} (-2, -1, -0.5, 0, exp (-1), 1, 2, exp(1), 3, 4, 5) ), "\n";
Output:
NaN NaN NaN NaN 0.5 0 -0.346573590279973 -0.5 -0.549306144334055 -0.693147180559945 -0.80471895621705

PhixEdit

Translation of: Julia

Phix has an "object" type which can be an integer or a string, so not entirely un-like Perl.
Here we simply treat all strings or rather non-integers as the "unknown" type.

function bindf(object m, integer f)
    return f(m)
end function
 
function unit(object m)
    return m
end function
 
function times_five(object l)
    return iff(integer(l)?l*5:l)
end function
 
function plus_four(object l)
    return iff(integer(l)?l+4:l)
end function
 
procedure test(object l)
    printf(1,"%v -> %v\n", {l, bindf(bindf(l,times_five),plus_four)})
end procedure
test(3)
test("none")
Output:
3 -> 19
"none" -> "none"

PythonEdit

In this implementation, a Maybe type's constructor is effectively the unit function. Note that I've used >> as the bind operator. Trying to chain __irshift__ (>>=) would be a syntax error.

"""A Maybe Monad. Requires Python >= 3.7 for type hints."""
from __future__ import annotations

from typing import Any
from typing import Callable
from typing import Generic
from typing import Optional
from typing import TypeVar
from typing import Union


T = TypeVar("T")


class Maybe(Generic[T]):
    def __init__(self, value: Union[Optional[T], Maybe[T]] = None):
        if isinstance(value, Maybe):
            self.value: Optional[T] = value.value
        else:
            self.value = value

    def __rshift__(self, func: Callable[[Optional[T]], Maybe[Any]]):
        return self.bind(func)

    def bind(self, func: Callable[[Optional[T]], Maybe[Any]]) -> Maybe[Any]:
        return func(self.value)

    def __str__(self):
        return f"{self.__class__.__name__}({self.value!r})"


def plus_one(value: Optional[int]) -> Maybe[int]:
    if value is not None:
        return Maybe[int](value + 1)
    return Maybe[int](None)


def currency(value: Optional[int]) -> Maybe[str]:
    if value is not None:
        return Maybe[str](f"${value}.00")
    return Maybe[str](None)


if __name__ == "__main__":
    test_cases = [1, 99, None, 4]

    for case in test_cases:
        m_int = Maybe[int](case)
        result = m_int >> plus_one >> currency
        # or..
        # result = m_int.bind(plus_one).bind(currency)
        print(f"{str(case):<4} -> {result}")
Output:
1    -> Maybe('$2.00')
99   -> Maybe('$100.00')
None -> Maybe(None)
4    -> Maybe('$5.00')

RacketEdit

It is idiomatic in Racket to use #f for Nothing, and every other value is considered implicitly tagged with Just.

#lang racket

(require syntax/parse/define)

(define (bind x f) (and x (f x)))
(define return identity)

;; error when arg = 0
(define reciprocal (curry / 1))
;; error when arg < 0
(define (root x) (if (< x 0) (error 'bad) (sqrt x)))
;; error whe  arg <= 0
(define (ln x) (if (<= x 0) (error 'bad) (log x)))

(define (lift f check) (λ (x) (and (check x) (f x))))

(define safe-reciprocal (lift reciprocal (negate (curry equal? 0))))
(define safe-root (lift root (curry <= 0)))
(define safe-ln (lift ln (curry < 0)))

(define (safe-log-root-reciprocal x)
  (bind (bind (bind x safe-reciprocal) safe-root) safe-ln))

(define tests `(-2 -1 -0.5 0 1 ,(exp -1) 1 2 ,(exp 1) 3 4 5))

(map safe-log-root-reciprocal tests)

(define-syntax-parser do-macro
  [(_ [x {~datum <-} y] . the-rest) #'(bind y (λ (x) (do-macro . the-rest)))]
  [(_ e) #'e])

(define (safe-log-root-reciprocal* x)
  (do-macro [x <- (safe-reciprocal x)]
            [x <- (safe-root x)]
            [x <- (safe-ln x)]
            (return x)))

(map safe-log-root-reciprocal* tests)
Output:
'(#f #f #f #f 0 0.5 0 -0.3465735902799726 -0.5 -0.5493061443340549 -0.6931471805599453 -0.8047189562170503)
'(#f #f #f #f 0 0.5 0 -0.3465735902799726 -0.5 -0.5493061443340549 -0.6931471805599453 -0.8047189562170503)

RakuEdit

(formerly Perl 6)

Works with: Rakudo version 2019.11

It is exceptionally difficult to come up with a compelling valuable use for a Maybe monad in Raku. Monads are most useful in languages that don't have exceptions and/or only allow a single point of entry/exit from a subroutine.

There are very good reasons to have those restrictions. It makes it much less complex to reason about a programs correctness and actually prove that a program is correct, but those restrictions also lead to oddities like Monads, just as a way to work around those restrictions.

The task description asks for two functions that take an Int and return a Maybe Int or Maybe Str, but those distinctions are nearly meaningless in Raku. See below.

my $monad = <42>;
say 'Is $monad an Int?: ', $monad ~~ Int;
say 'Is $monad a  Str?: ', $monad ~~ Str;
say 'Wait, what? What exactly is $monad?: ', $monad.^name;
Output:
Is $monad an Int?: True
Is $monad a  Str?: True
Wait, what? What exactly is $monad?: IntStr

$monad is both an Int and a Str. It exists in a sort-of quantum state where what-it-is depends on how-it-is-used. Bolting on some 'Monad' type to do this will only remove functionality that Raku already has.

Ok, say you have a situation where you absolutely do not want an incalculable value to halt processing. (In a web process perhaps.) In that case, it might be useful to subvert the normal exception handler and just return a "Nothing" type. Any routine that needs to be able to handle a Nothing type will need to be informed of it, but for the most part, that just means adding a multi-dispatch candidate.

# Build a Nothing type. When treated as a string it returns the string 'Nothing'.
# When treated as a Numeric, returns the value 'Nil'.
class NOTHING {
    method Str { 'Nothing' }
    method Numeric { Nil }
}

# A generic instance of a Nothing type.
my \Nothing = NOTHING.new;

# A reimplementation of the square-root function. Could just use the CORE one
# but this more fully shows how multi-dispatch candidates are added.

# Handle positive numbers & 0
multi root (Numeric $n where * >= 0) { $n.sqrt }
# Handle Negative numbers (Complex number handling is built in.)
multi root (Numeric $n where * <  0) { $n.Complex.sqrt }
# Else return Nothing
multi root ($n) { Nothing }

# Handle numbers > 0
multi ln (Real $n where * > 0) { log $n, e }
# Else return Nothing
multi ln ($n) { Nothing }

# Handle fraction where the denominator != 0
multi recip (Numeric $n where * != 0) { 1/$n }
# Else return Nothing
multi recip ($n) { Nothing }

# Helper formatting routine
sub center ($s) {
    my $pad = 21 - $s.Str.chars;
    ' ' x ($pad / 2).floor ~ $s ~ ' ' x ($pad / 2).ceiling;
}

# Display the "number" the reciprocal, the root, natural log and the 3 functions
# composed together.
put ('"Number"', 'Reciprocal', 'Square root', 'Natural log', 'Composed')».&center;

# Note how it handles the last two "values". The string 'WAT' is not numeric at
# all; but Ethiopic number 30, times vulgar fraction 1/7, is.
put ($_, .&recip, .&root, .&ln, .&(&ln o &root o &recip) )».&center
  for -2, -1, -0.5, 0, exp(-1), 1, 2, exp(1), 3, 4, 5, 'WAT',  × ;
Output:
      "Number"             Reciprocal            Square root           Natural log            Composed       
         -2                   -0.5          0+1.4142135623730951i        Nothing               Nothing       
         -1                    -1                   0+1i                 Nothing               Nothing       
        -0.5                   -2           0+0.7071067811865476i        Nothing               Nothing       
          0                  Nothing                  0                  Nothing               Nothing       
 0.36787944117144233    2.718281828459045    0.6065306597126334            -1                    0.5         
          1                     1                     1                     0                     0          
          2                    0.5           1.4142135623730951    0.6931471805599453    -0.3465735902799726 
  2.718281828459045    0.36787944117144233   1.6487212707001282             1                   -0.5         
          3                 0.333333         1.7320508075688772    1.0986122886681098    -0.5493061443340549 
          4                   0.25                    2            1.3862943611198906    -0.6931471805599453 
          5                    0.2            2.23606797749979     1.6094379124341003    -0.8047189562170503 
         WAT                 Nothing               Nothing               Nothing               Nothing       
      4.285714              0.233333         2.0701966780270626     1.455287232606842    -0.727643616303421

REXXEdit

This REXX version is modeled after the Zkl version.

/*REXX program mimics a bind operation when trying to perform addition upon arguments.  */
call add 1, 2
call add 1, 2.0
call add 1, 2.0, -6
call add self, 2
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
add:   void= 'VOID';                       f=    /*define in terms of a function&binding*/
                     do j=1  for arg()           /*process, classify, bind each argument*/
                     call bind( arg(j) );  f= f arg(j)
                     end   /*j*/
       say
       say 'adding'  f;    call sum f            /*telegraph what's being performed next*/
       return                                    /*Note: REXX treats INT & FLOAT as num.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
bind:  arg a;  type.a= datatype(a);  return      /*bind argument's kind with its "type".*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
sum:   parse arg a;  $= 0                        /*sum all arguments that were specified*/
                             do k=1  for words(a);  ?= word(a, k)
                             if type.?==num & $\==void  then $= ($ + word(a, k)) / 1
                                                        else $= void
                             end   /*k*/
       say 'sum='  $
       return $
output   when using the default inputs:
adding  1 2
sum= 3

adding  1 2.0
sum= 3

adding  1 2.0 -6
sum= -3

adding  SELF 2
sum= VOID

RubyEdit

OOP version using Ruby's block syntax

class Maybe
  def initialize(value)
    @value = value
  end

  def map
    if @value.nil?
      self
    else
      Maybe.new(yield @value)
    end
  end
end

Maybe.new(3).map { |n| 2*n }.map { |n| n+1 }
#=> #<Maybe @value=7>

Maybe.new(nil).map { |n| 2*n }.map { |n| n+1 }
#=> #<Maybe @value=nil>

Maybe.new(3).map { |n| nil }.map { |n| n+1 }
#=> #<Maybe @value=nil>

# alias Maybe#new and write bind to be in line with task

class Maybe
  class << self
    alias :unit :new
  end
  
  def initialize(value)
    @value = value
  end

  def bind
    if @value.nil?
      self
    else
      yield @value
    end
  end
end

Maybe.unit(3).bind { |n| Maybe.unit(2*n) }.bind { |n| Maybe.unit(n+1) }
#=> #<Maybe @value=7>

Maybe.unit(nil).bind { |n| Maybe.unit(2*n) }.bind { |n| Maybe.unit(n+1) }
#=> #<Maybe @value=nil>

SwiftEdit

Works with: Swift version 5

Swift has a "Maybe" type built in, called "Optional". I created a typealias so I could adhere to the naming convention. The unit function is also strictly unnecessary because Optional's constructor serves the same purpose. bind is also strictly unnecessary because Swift's Optional.flatmap function does the same thing.

I also created an infix operator analogous to Haskell's >>=. I can't use >>= itself because it already exists (left shift assignment) and I can't control the precedence.

precedencegroup MonadPrecedence {
	higherThan: BitwiseShiftPrecedence
	associativity: left
}

infix operator >>-: MonadPrecedence	// Monadic bind

typealias Maybe = Optional

extension Maybe
{
	static func unit(_ x: Wrapped) -> Maybe<Wrapped>
	{
		return Maybe(x)
	}

	func bind<T>(_ f: (Wrapped) -> Maybe<T>) -> Maybe<T>
	{
		return self.flatMap(f)
	}

	static func >>- <U>(_ m: Optional<Wrapped>, _ f: (Wrapped) -> Maybe<U>) -> Maybe<U>
	{
		return m.flatMap(f)
	}
}

func dividedBy2IfEven(_ x: Int) -> Maybe<Int>
{
	x.isMultiple(of: 2) ? x / 2 : nil
}

func lineOfAs(_ x: Int) -> Maybe<String>
{
	guard x >= 0 else { return nil }
	let chars = Array<Character>(repeating: "A", count: x)
	return String(chars)
}

print("\(Maybe.unit(6).bind(dividedBy2IfEven).bind(lineOfAs) ?? "nil")")
print("\(Maybe.unit(4) >>- dividedBy2IfEven >>- lineOfAs ?? "nil")")
print("\(Maybe.unit(3) >>- dividedBy2IfEven >>- lineOfAs ?? "nil")")
print("\(Maybe.unit(-4) >>- dividedBy2IfEven >>- lineOfAs ?? "nil")")
Output:
AAA
AA
nil
nil

WrenEdit

Translation of: Go
Library: Wren-fmt
import "/fmt" for Fmt

class Maybe {
    construct new(value) {
        _value = value
    }

    value { _value }

    bind(f) { f.call(_value) }

    static unit(i) { Maybe.new(i) }
}

var decrement = Fn.new { |i|
    if (!i) return Maybe.unit(null)
    return Maybe.unit(i - 1)
}

var triple = Fn.new { |i|
    if (!i) return Maybe.unit(null)
    return Maybe.unit(3 * i)
}

for (i in [3, 4, null, 5]) {
    var m1 = Maybe.unit(i)
    var m2 = m1.bind(decrement).bind(triple)
    var s1 = (m1.value) ? "%(m1.value)" : "none"
    var s2 = (m2.value) ? "%(m2.value)" : "none"
    System.print("%(Fmt.s(4, s1)) -> %(s2)")
}
Output:
   3 -> 6
   4 -> 9
none -> none
   5 -> 12

zklEdit

While I'm unsure of the utility of Monads in a dynamic type-less language, it can be done.

From the Wikipedia

Here we use the Void object as Nothing and define some functions. Since zkl is type-less, we can consider Maybe as a native type and don't need to define it.

fcn bind(a,type,b){ if(type.isType(a)) b else Void }
fcn just(x){ if(Deferred.isType(x)) x() else x }  // force lazy evaluation
fcn rtn(x) { just(x) }

Since zkl is eager, add needs to gyrate a bit by creating a lazy result and evaluating that after the binds have done their bizness.

fcn add(mx,my){
   bind(mx,Int,
      bind(my,Int,
        '+.fp(mx,my))) : rtn(_)  // create a lazy mx+my to avoid eager eval
}
add(1,2).println();    // two ints
add(1,2.0).println();  // int and float
add(self,2).println(); // class and int
Output:
3
Void
Void