Monads/Maybe monad
< Monads
You are encouraged to solve this task according to the task description, using any language you may know.
Demonstrate in your programming language the following:
- 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)
- Make two functions, each which take a number and return a monadic number, e.g. Int -> Maybe Int and Int -> Maybe String
- Compose the two functions with bind
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 68
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]
AppleScript
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}
ATS
#include "share/atspre_staload.hats"
(* There are "Option" and "Option_vt" in the ATS2 prelude, but I shall
construct something anew. *)
datatype Maybe (a : t@ype+) =
| Nothing of ()
| Just of a
fn {a, b : t@ype}
bind_Maybe {u : bool}
(m : Maybe a,
f : a -<cloref1> Maybe b) : Maybe b =
case+ m of
| Nothing {a} () => Nothing {b} ()
| Just {a} x => f x
infixl 0 >>=
overload >>= with bind_Maybe
implement
main0 () =
let
val f : int -<cloref1> Maybe int =
lam i =<cloref1> if (i : int) < 0 then Nothing () else Just i
val g : int -<cloref1> Maybe string =
lam i =<cloref1> Just (tostring_val<int> i)
in
case+ Just 123 >>= f >>= g of
| Nothing () => println! ("Nothing ()")
| Just s => println! ("Just (\"", s : string, "\")");
case+ Just ~123 >>= f >>= g of
| Nothing () => println! ("Nothing ()")
| Just s => println! ("Just (\"", s : string, "\")")
end- Output:
$ patscc -std=gnu2x -g -O2 -DATS_MEMALLOC_GCBDW maybe_monad_ats.dats -lgc && ./a.out
Just ("123")
Nothing ()
C
#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++
#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#
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.");
}
}
}
}
}
Clojure
(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}
Delphi
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
EchoLisp
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)
FreeBASIC
Type mmaybe
As Integer value
End Type
Function Bindf(m As mmaybe, f As Function(As mmaybe) As mmaybe) As mmaybe
Return f(m)
End Function
Function Unit(i As Integer) As mmaybe
Dim As mmaybe m
m.value = i
Return m
End Function
Function Decrement(mm As mmaybe) As mmaybe
Dim As mmaybe result
result.value = Iif(mm.value = 0, 0, mm.value - 1)
Return Unit(result.value)
End Function
Function Triple(mm As mmaybe) As mmaybe
Dim As mmaybe result
result.value = Iif(mm.value = 0, 0, 3 * mm.value)
Return Unit(result.value)
End Function
Dim As Integer values(3) = {3, 4, 0, 5}
Dim As Function(As mmaybe) As mmaybe Ptr decrementPtr = @Decrement
Dim As Function(As mmaybe) As mmaybe Ptr triplePtr = @Triple
For i As Integer = Lbound(values) To Ubound(values)
Dim As mmaybe m1 = Unit(values(i))
Dim As mmaybe m2 = Bindf(Bindf(m1, decrementPtr), triplePtr)
Dim As String s1 = Iif(m1.value = 0, "none", Str(m1.value))
Dim As String s2 = Iif(m2.value = 0, "none", Str(m2.value))
Print Using "\ \ -> \ \"; s1; s2
Next i
Sleep
- Output:
3 -> 6 4 -> 9 none -> none 5 -> 12
F#
// 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
Factor
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 .
Go
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
Haskell
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)]
Hoon
:- %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 ~ ~
J
Monad implementation:
'J N'=. s:'Just';'Nothing'
unit =. J,&<]
bind =. ]:@(1{::])^:(N-.@-:])
Monad utilities:
fail =. unit@:[.`(N"_)@.]. NB. if v —> fail, else apply u
show =. [: ": (,' '&,)&":&>/
comp =. [: > {{<x`:6 bind>y}}/@(,<@unit) NB. multi-compose
Demonstration:
^.%:_2 NB. ln ∘ sqrt; gives complex numbers for inputs < 0
0.346574j1.5708
sqrt=. %: fail ([: +./ <&0) NB. avoid complex numbers
ln =. ^. fail ([: +./ <:&0) NB. same
show ln bind sqrt bind unit 2 _3 4 NB. short-circuits on input < 0
`Nothing
([: show [: ln bind [: sqrt bind unit)&> 2 _3 4
`Just 0.346574
`Nothing
`Just 0.693147
show ln bind sqrt bind unit 2 3 4
`Just 0.346574 0.549306 0.693147
show unit@:*:`ln`sqrt comp 2 3 4
`Just 0.120113 0.301737 0.480453
Java
Java has a built-in generic "Maybe" monad in form of the Optional<T> class.
The class has static methods, "of" and "ofNullable", which act as the unit function for wrapping nullable and non-nullable values respectively.
The class instance method, "flatMap", acts as the bind function.
import java.util.Optional;
public final class MonadMaybe {
public static void main(String[] aArgs) {
System.out.println(doubler(5).flatMap(MonadMaybe::stringify).get());
System.out.println(doubler(2).flatMap(MonadMaybe::stringifyNullable).get());
Optional<String> option = doubler(0).flatMap(MonadMaybe::stringifyNullable);
String result = option.isPresent() ? option.get() : "Result is Null";
System.out.println(result);
}
private static Optional<Integer> doubler(int aN) {
return Optional.of(2 * aN);
}
private static Optional<String> stringify(int aN) {
return Optional.of("A".repeat(aN));
}
private static Optional<String> stringifyNullable(int aN) {
return ( aN > 0 ) ? Optional.ofNullable("A".repeat(aN)) : Optional.ofNullable(null);
}
}
- Output:
AAAAAAAAAA AAAA Result is Null
JavaScript
ES5
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]
Julia
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
K
Instead of wrapping all data in Just, we can assume that all non-Nothing data are of the Just constructor. For brevity, I represent Nothing as `N. This makes our implementation of Just, i.e. return, the identity function. This does mean that we can't distinguish between Nothing and Just Nothing, Just (Just Nothing), etc, but of course why would we want that anyway? join (Just Nothing) is Nothing, so though the types may differ, it's all the same when considered purely monadically. Another consequence is that all functions and data are implicitly in the Maybe category without needing to be lifted.
unit:(::)
bind:{[k;a]:[a~`N;a;k a]}
kcomp:{[f;g](bind[g;]@f@)} / (>=>) i.e. kleisli composition
demonstration:
unit 3
3
bind[(unit 20*);`N] / i.e. fmap (20*) Nothing
`N
bind[(unit 20*);unit 3] / i.e. fmap (20*) (pure 3)
60
/ define some kleisli's to compose
maybeLog:{:[x>0;`ln@x;`N]}
codepointAZ:{:[~(|x>90)|x<65;`c$_x;`N]} / convert number to corresponding A-Z character, if it so corresponds; else `N.
composedKs:kcomp[maybeLog;codepointAZ]
/ short-circuiting computations
composedKs -0.6 / maybeLog returns `N
`N
composedKs 20 / codepointAZ returns `N
`N
/ successful computation b/c floor(log 1e30) is 69 (the codepoint for "E"), which is in range [65,90]
composedKs 1e30
"E"
Because k has not lexical scoping, kcomp can't be defined as {[f;g]{bind[g;f x]}}; x is not in the inner lambda's scope. The easiest way to get around these issues in k is to use "projections" (currying) or tacit (pointfree) expressions. Here I've done the latter.
Kotlin
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
Lua
-- 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")
M2000 Interpreter
Revision 1. Now the operator "=" check if we have same status on haveValue for the two objects. If not we get the false in compare. Also the unit() function return "none" object from a an object not "none".
M2000 create objects (of type Group) either from a Class (which is a function), or from a copy of an object. The life of an object depends of the storing site, and the use of a pointer or not. Here all objects are one of two kinds: Objects like none, m1, m2, m3 and m5 are destruct at the exit of the module. Object on the SetA like none and none.unit() (which is a copy of none), destruct when last pointer (here SetA) deleted, and for this example, because SetA is local variable, the delete happen at the exit of current module. The m object which used in Bind() and Unit() function, and the g object are all objects which life end at the exit of those function, although these functions return a pointer to a copy of the m object, and check an internal field which make it "float". A float object is something different from an object holding by a pointer. M2000 always "expand" a float object when we place it to a variable (as a copy, or if the variable hold another object - always as group else we get error 0 - as a merge of these). So when we pick a "float" object from array, we get a copy. M2000 can use pointer to groups. The second list show how we can use pointers to groups. Pointers can be one of two types: A real pointes (here we use real pointers), or a weak pointer. The -> operator in a ->m (or =pointer(m)) where m hold a group (not a pointer) return a weak pointer (invalid if actual variable not exist). Here we use ->(m) which make m a float group and then change it to a pointer to float group (same as =pointer((m))). A pointer(none) return a real pointer if none is a pointer to group, or a weak pointer if it isn't a pointer. A pointer to group is a group, not an address. A pointer() return the Null pointer (which is a group of type Null). The Null group (user object in M2000), has a type that cannot inherit to other classes, also in a group merge with null we don't merge Null type. Merging is another way to produce groups from two or more other types, using objects (not classes).
Without using pointers
Class maybe {
private:
variant [val]="none"
boolean haveValue
public:
property val {
value // val return the [val] value
}
function bind(f) {
m=This // we can read private because bind is function of same class as m
if m.haveValue Then m.[val]=f(m.[val])
=m // copy (not pointer)
}
Operator "=" (z as maybe) {
if z.havevalue xor .havevalue then
push false
else
Push z.[val]=.[val]
end if
}
Function unit() {
variant k
if match("G") then // so we can read maybe class
read g as maybe // fail if not maybe class
if g.havevalue then push g.val
end if
Read ? k
m=This
if not type$(k)="Empty" then
integer v=k ' fail if k can't convert to integer
m.[val]=v
m.haveValue=true
else // so now we can produce "none" from an object which isn't "none"
m.[val]="none"
m.haveValue=false
end if
=m // copy (not pointer)
}
class:
// after class: all are temporary for the constuction phase
// module with class name is the contructor
// the object constracted before enter this module
// but we can change it. So we return a new one.
module maybe {
// so the constructor is the same as the .unit
// ![] pick argument list and place to unit()
// optionally we can skip the call if we have empty argument list
if not empty then
this=.unit(![])
end if
}
}
none=maybe()
decrement =lambda (x as integer)->x-1%
triple =lambda (x as integer)->x*3%
variant emptyvariant
// 3 and 4 are double, 5 is integer type
SetA=(3,4,none,5%, emptyvariant, none.unit())
k=each(SetA)
While K
m1=none.unit(array(k)) // pick element k^
m2=m1.bind(decrement).bind(triple)
m3=maybe(m2)
Print m1.val+" -> "+m2.val, m3=m2, m3.val
End While
Try ok {
m5=maybe("Hello")
}
Print not ok // true , "Hello" not accepted
Using pointers
Class maybe {
private:
variant [val]="none"
boolean haveValue
public:
property val {
value // val return the [val] value
}
function bind(f) {
m=This // we can read private because bind is function of same class as m
if m.haveValue Then m.[val]=f(m.[val])
->(m) // pointer
}
Operator "=" (z as maybe) {
if z.havevalue xor .havevalue then
push false
else
Push z.[val]=.[val]
end if
}
Function unit() {
variant k
if match("G") then // so we can read maybe class
read g as maybe // fail if not maybe class
if g.havevalue then push g.val
end if
Read ? k
m=This
if not type$(k)="Empty" then
integer v=k ' fail if k can't convert to integer
m.[val]=v
m.haveValue=true
else // so now we can produce "none" from an object which isn't "none"
m.[val]="none"
m.haveValue=false
end if
->(m) // pointer
}
class:
module maybe {
if not empty then
this=.unit(![])
end if
}
}
none->maybe()
decrement =lambda (x as integer)->x-1%
triple =lambda (x as integer)->x*3%
variant emptyvariant
SetA=(3,4,none,5%, emptyvariant, none=>unit())
k=each(SetA)
document doc$
While k
m1=none=>unit(array(k)) // pick element k^
m2=m1=>bind(decrement)=>bind(triple)
m3=maybe(m2)
doc$=m1=>val+" -> "+m2=>val+" m2=m3 -> "+if$(m2=m3->"True", "False")+{
}
End While
Try ok {
m5=maybe("Hello")
}
Doc$= (not ok)+{
} // true , "Hello" not accepted
report doc$
clipboard doc$- Output:
3 -> 6 True 6 4 -> 9 True 9 none -> none True none 5 -> 12 True 12 none -> none True none none -> none True none True
Nim
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")
OCaml
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
Perl
# 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" : $safeLogRootReciprocal->value;
} (-2, -1, -0.5, 0, exp (-1), 1, 2, exp(1), 3, 4, 5) ), "\n";
- Output:
NaN NaN NaN NaN 0.5 0 -0.346573590279973 -0.5 -0.549306144334055 -0.693147180559945 -0.80471895621705
Phix
Phix has an "object" type which can be an integer or a string, so not entirely un-like Perl.
Here we simply treat all strings or rather non-integers as the "unknown" type.
function bindf(object m, integer f) return f(m) end function function unit(object m) return m end function function times_five(object l) return iff(integer(l)?l*5:l) end function function plus_four(object l) return iff(integer(l)?l+4:l) end function procedure test(object l) printf(1,"%v -> %v\n", {l, bindf(bindf(l,times_five),plus_four)}) end procedure test(3) test("none")
- Output:
3 -> 19 "none" -> "none"
Python
The Maybe class constructor is effectively the unit function. Note that I've used >> as the bind operator. Trying to chain __irshift__ (>>=) would be a syntax error.
"""A Maybe monad. Requires Python >= 3.7 for type hints."""
from __future__ import annotations
from typing import Callable
from typing import Generic
from typing import Optional
from typing import TypeVar
from typing import Union
T = TypeVar("T")
U = TypeVar("U")
class Maybe(Generic[T]):
def __init__(self, value: Union[Optional[T], Maybe[T]] = None):
if isinstance(value, Maybe):
self.value: Optional[T] = value.value
else:
self.value = value
def __rshift__(self, func: Callable[[Optional[T]], Maybe[U]]) -> Maybe[U]:
return self.bind(func)
def bind(self, func: Callable[[Optional[T]], Maybe[U]]) -> Maybe[U]:
return func(self.value)
def __str__(self):
return f"{self.__class__.__name__}({self.value!r})"
def plus_one(value: Optional[int]) -> Maybe[int]:
if value is not None:
return Maybe(value + 1)
return Maybe(None)
def currency(value: Optional[int]) -> Maybe[str]:
if value is not None:
return Maybe(f"${value}.00")
return Maybe(None)
if __name__ == "__main__":
test_cases = [1, 99, None, 4]
for case in test_cases:
result = Maybe(case) >> plus_one >> currency
# or..
# result = Maybe(case).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')
Racket
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)
Raku
(formerly Perl 6)
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')».¢er;
# 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) )».¢er
for -2, -1, -0.5, 0, exp(-1), 1, 2, exp(1), 3, 4, 5, 'WAT', ፴ × ⅐;
- 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
REXX
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
Ruby
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>
Rust
The Maybe monad is called Option<T> in Rust, it's widely used in the standard library and user code for functions that might not have sensible return values in certain cases but it's not an error/failure, such as a key doesn't exist for a hash map.
In addition, pure/just/return is Some(T) and bind is Option::<T>::and_then(self, F).
use std::collections::HashMap;
/// Returns the arithmetic square root of x, if it exists
fn arithmetic_square_root(x: u8) -> Option<u8> {
// the number of perfect squares for u8 is so low you can just fit the entire list in memory
let perfect_squares: HashMap<u8, u8> = HashMap::from([
(0, 0),
(1, 1),
(4, 2),
(9, 3),
(16, 4),
(25, 5),
(36, 6),
(49, 7),
(64, 8),
(81, 9),
(100, 10),
(121, 11),
(144, 12),
(169, 13),
(196, 14),
(225, 15),
]);
// `HashMap::<K, V>::get(&self, &Q)` also returns a `Option<&V>`, we then turn it to `Option<V>`
perfect_squares.get(&x).copied()
}
/// If x in base 10 is also a valid number when looking upside down, return a string slice for that
/// number upside down
fn upside_down_num(x: u8) -> Option<&'static str> {
match x {
0 => Some("0"),
1 => Some("1"),
6 => Some("9"),
8 => Some("8"),
9 => Some("6"),
10 => Some("01"),
11 => Some("11"),
16 => Some("91"),
_ => None
}
}
fn main() {
// if the number from 0 to 36 inclusive, is a perfect square and its square root is also a
// valid number when looking upside down, then we will get a Some containing the string slice,
// otherwise we get a None, indicating it's not a perfect square or the square root is not a
// valid number while looking upside down
(0..=36)
.map(|x| arithmetic_square_root(x).and_then(upside_down_num))
.enumerate()
.for_each(|(i, upside_down_square_root)|
println!("i = {i:02}, upside down square root = {upside_down_square_root:?}"));
}
- Output:
i = 00, upside down square root = Some("0")
i = 01, upside down square root = Some("1")
i = 02, upside down square root = None
i = 03, upside down square root = None
i = 04, upside down square root = None
i = 05, upside down square root = None
i = 06, upside down square root = None
i = 07, upside down square root = None
i = 08, upside down square root = None
i = 09, upside down square root = None
i = 10, upside down square root = None
i = 11, upside down square root = None
i = 12, upside down square root = None
i = 13, upside down square root = None
i = 14, upside down square root = None
i = 15, upside down square root = None
i = 16, upside down square root = None
i = 17, upside down square root = None
i = 18, upside down square root = None
i = 19, upside down square root = None
i = 20, upside down square root = None
i = 21, upside down square root = None
i = 22, upside down square root = None
i = 23, upside down square root = None
i = 24, upside down square root = None
i = 25, upside down square root = None
i = 26, upside down square root = None
i = 27, upside down square root = None
i = 28, upside down square root = None
i = 29, upside down square root = None
i = 30, upside down square root = None
i = 31, upside down square root = None
i = 32, upside down square root = None
i = 33, upside down square root = None
i = 34, upside down square root = None
i = 35, upside down square root = None
i = 36, upside down square root = Some("9")
Swift
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
Wren
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"
Fmt.print("$4s -> $s", s1, s2)
}
- Output:
3 -> 6 4 -> 9 none -> none 5 -> 12
zkl
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