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{{draft task}} [[Category:Monads]]
The Writer monad is a programming design pattern which makes it possible to compose functions which return their result values paired with a log string. The final result of a composed function yields both a value, and a concatenation of the logs from each component function application.
Demonstrate in your programming language the following:
Construct a Writer monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that monad (or just use what the language already provides)
Write three simple functions: root, addOne, and half
Derive Writer monad versions of each of these functions
Apply a composition of the Writer versions of root, addOne, and half to the integer 5, deriving both a value for the Golden Ratio φ, and a concatenated log of the function applications (starting with the initial value, and followed by the application of root, etc.)
ALGOL 68
{{Trans|Go}}
BEGIN
MODE MWRITER = STRUCT( LONG REAL value
, STRING log
);
PRIO BIND = 9;
OP BIND = ( MWRITER m, PROC( LONG REAL )MWRITER f )MWRITER:
( MWRITER n := f( value OF m );
log OF n := log OF m + log OF n;
n
);
OP LEN = ( STRING s )INT: ( UPB s + 1 ) - LWB s;
PRIO PAD = 9;
OP PAD = ( STRING s, INT width )STRING: IF LEN s >= width THEN s ELSE s + ( width - LEN s ) * " " FI;
PROC unit = ( LONG REAL v, STRING s )MWRITER: ( v, " " + s PAD 17 + ":" + fixed( v, -19, 15 ) + REPR 10 );
PROC root = ( LONG REAL v )MWRITER: unit( long sqrt( v ), "Took square root" );
PROC add one = ( LONG REAL v )MWRITER: unit( v+1, "Added one" );
PROC half = ( LONG REAL v )MWRITER: unit( v/2, "Divided by two" );
MWRITER mw2 := unit( 5, "Initial value" ) BIND root BIND add one BIND half;
print( ( "The Golden Ratio is", fixed( value OF mw2, -19, 15 ), newline ) );
print( ( newline, "This was derived as follows:-", newline ) );
print( ( log OF mw2 ) )
END
{{out}}
The Golden Ratio is 1.618033988749895
This was derived as follows:-
Initial value : 5.000000000000000
Took square root : 2.236067977499790
Added one : 3.236067977499790
Divided by two : 1.618033988749895
AppleScript
{{trans|JavaScript}}
More than a light-weight scripting language is really likely to need, but a way of stretching it a bit, and understanding its relationship to other languages. What AppleScript mainly lacks (apart from a well-developed library, and introspective records/dictionaries which know what keys/fields they have), is a coherent type of first class (and potentially anonymous) function. To get first class objects, we have to wrap 2nd class handlers in 1st class scripts.
-- WRITER MONAD FOR APPLESCRIPT
-- How can we compose functions which take simple values as arguments
-- but return an output value which is paired with a log string ?
-- We can prevent functions which expect simple values from choking
-- on log-wrapped output (from nested functions)
-- by writing Unit/Return() and Bind() for the Writer monad in AppleScript
on run {}
-- Derive logging versions of three simple functions, pairing
-- each function with a particular comment string
-- (a -> b) -> (a -> (b, String))
set wRoot to writerVersion(root, "obtained square root")
set wSucc to writerVersion(succ, "added one")
set wHalf to writerVersion(half, "divided by two")
loggingHalfOfRootPlusOne(5)
--> value + log string
end run
-- THREE SIMPLE FUNCTIONS
on root(x)
x ^ (1 / 2)
end root
on succ(x)
x + 1
end succ
on half(x)
x / 2
end half
-- DERIVE A LOGGING VERSION OF A FUNCTION BY COMBINING IT WITH A
-- LOG STRING FOR THAT FUNCTION
-- (SEE 'on run()' handler at top of script)
-- (a -> b) -> String -> (a -> (b, String))
on writerVersion(f, strComment)
script
on call(x)
{value:sReturn(f)'s call(x), comment:strComment}
end call
end script
end writerVersion
-- DEFINE A COMPOSITION OF THE SAFE VERSIONS
on loggingHalfOfRootPlusOne(x)
logCompose([my wHalf, my wSucc, my wRoot], x)
end loggingHalfOfRootPlusOne
-- Monadic UNIT/RETURN and BIND functions for the writer monad
on writerUnit(a)
try
set strValue to ": " & a as string
on error
set strValue to ""
end try
{value:a, comment:"Initial value" & strValue}
end writerUnit
on writerBind(recWriter, wf)
set recB to wf's call(value of recWriter)
set v to value of recB
try
set strV to " -> " & (v as string)
on error
set strV to ""
end try
{value:v, comment:(comment of recWriter) & linefeed & (comment of recB) & strV}
end writerBind
-- THE TWO HIGHER ORDER FUNCTIONS ABOVE ENABLE COMPOSITION OF
-- THE LOGGING VERSIONS OF EACH FUNCTION
on logCompose(lstFunctions, varValue)
reduceRight(lstFunctions, writerBind, writerUnit(varValue))
end logCompose
-- 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 sf to sReturn(f)
repeat with i from length of xs to 1 by -1
set a to sf's call(a, item i of xs, i, xs)
end repeat
end reduceRight
-- Unit/Return and bind for composing handlers in script wrappers
-- 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
{{Out}}
{
value:1.61803398875,
comment:"Initial value: 5\n
obtained square root -> 2.2360679775\n
added one -> 3.2360679775\n
divided by two -> 1.61803398875"
}
EchoLisp
Our monadic Writer elements will be pairs (string . value), where string is the log string.
(define (Writer.unit x (log #f))
(if log (cons log x)
(cons (format "init → %d" x) x)))
;; f is a lisp function
;; (Writer.lift f) returns a Writer function which returns a Writer element
(define (Writer.lift f name)
(lambda(elem)
(Writer.unit
(f (rest elem))
(format "%a \n %a → %a" (first elem) name (f (rest elem))))))
;; lifts and applies
(define (Writer.bind f elem) ((Writer.lift f (string f)) elem))
(define (Writer.print elem) (writeln 'result (rest elem)) (writeln (first elem)))
;; Writer monad versions
(define w-root (Writer.lift sqrt "root"))
(define w-half (Writer.lift (lambda(x) (// x 2)) "half"))
(define w-inc ( Writer.lift add1 "add-one"))
;; no binding required, as we use Writer lifted functions
(-> 5 Writer.unit w-root w-inc w-half Writer.print)
result 1.618033988749895
init → 5
root → 2.23606797749979
add-one → 3.23606797749979
half → 1.618033988749895
;; binding
(->> 0 Writer.unit (Writer.bind sin) (Writer.bind cos) w-inc w-half Writer.print)
result 1
init → 0
sin → 0
cos → 1
add-one → 2
half → 1
Factor
Factor comes with an implementation of Haskell-style monads in the monads vocabulary.
{{works with|Factor|0.99 2019-10-06}}
USING: kernel math math.functions monads prettyprint ;
FROM: monads => do ;
{
[ 5 "Started with five, " <writer> ]
[ sqrt "took square root, " <writer> ]
[ 1 + "added one, " <writer> ]
[ 2 / "divided by two." <writer> ]
} do .
{{out}}
T{ writer
{ value 1.618033988749895 }
{ log
"Started with five, took square root, added one, divided by two."
}
}
Go
{{trans|Kotlin}}
package main
import (
"fmt"
"math"
)
type mwriter struct {
value float64
log string
}
func (m mwriter) bind(f func(v float64) mwriter) mwriter {
n := f(m.value)
n.log = m.log + n.log
return n
}
func unit(v float64, s string) mwriter {
return mwriter{v, fmt.Sprintf(" %-17s: %g\n", s, v)}
}
func root(v float64) mwriter {
return unit(math.Sqrt(v), "Took square root")
}
func addOne(v float64) mwriter {
return unit(v+1, "Added one")
}
func half(v float64) mwriter {
return unit(v/2, "Divided by two")
}
func main() {
mw1 := unit(5, "Initial value")
mw2 := mw1.bind(root).bind(addOne).bind(half)
fmt.Println("The Golden Ratio is", mw2.value)
fmt.Println("\nThis was derived as follows:-")
fmt.Println(mw2.log)
}
{{out}}
The Golden Ratio is 1.618033988749895
This was derived as follows:-
Initial value : 5
Took square root : 2.23606797749979
Added one : 3.23606797749979
Divided by two : 1.618033988749895
Haskell
Haskell has the built-in Monad type class, and a built-in Writer monad (as well as the more general WriterT monad transformer that can make a writer monad with an underlying computation that is also a monad) already conforms to the Monad type class.
Making a logging version of functions (unfortunately, if we use the built-in writer monad we cannot get the values into the logs when binding):
import Control.Monad.Trans.Writer
import Control.Monad ((>=>))
loggingVersion :: (a -> b) -> c -> a -> Writer c b
loggingVersion f log x = writer (f x, log)
logRoot = loggingVersion sqrt "obtained square root, "
logAddOne = loggingVersion (+1) "added 1, "
logHalf = loggingVersion (/2) "divided by 2, "
halfOfAddOneOfRoot = logRoot >=> logAddOne >=> logHalf
main = print $ runWriter (halfOfAddOneOfRoot 5)
{{Out}}
(1.618033988749895,"obtained square root, added 1, divided by 2, ")
J
Based on javascript implementation:
root=: %:
incr=: >:
half=: -:
tostr=: ,@":
loggingVersion=: conjunction define
n;~u
)
Lroot=: root loggingVersion 'obtained square root'
Lincr=: incr loggingVersion 'added 1'
Lhalf=: half loggingVersion 'divided by 2'
loggingUnit=: verb define
y;'Initial value: ',tostr y
)
loggingBind=: adverb define
r=. u 0{::y
v=. 0{:: r
v;(1{::y),LF,(1{::r),' -> ',tostr v
)
loggingCompose=: dyad define
;(dyad def '<x`:6 loggingBind;y')/x,<loggingUnit y
)
Task example:
0{::Lhalf`Lincr`Lroot loggingCompose 5
1.61803
1{::Lhalf`Lincr`Lroot loggingCompose 5
Initial value: 5
obtained square root -> 2.23607
added 1 -> 3.23607
divided by 2 -> 1.61803
JavaScript
ES5
(function () {
'use strict';
// START WITH THREE SIMPLE FUNCTIONS
// Square root of a number more than 0
function root(x) {
return Math.sqrt(x);
}
// Add 1
function addOne(x) {
return x + 1;
}
// Divide by 2
function half(x) {
return x / 2;
}
// DERIVE LOGGING VERSIONS OF EACH FUNCTION
function loggingVersion(f, strLog) {
return function (v) {
return {
value: f(v),
log: strLog
};
}
}
var log_root = loggingVersion(root, "obtained square root"),
log_addOne = loggingVersion(addOne, "added 1"),
log_half = loggingVersion(half, "divided by 2");
// UNIT/RETURN and BIND for the the WRITER MONAD
// The Unit / Return function for the Writer monad:
// 'Lifts' a raw value into the wrapped form
// a -> Writer a
function writerUnit(a) {
return {
value: a,
log: "Initial value: " + JSON.stringify(a)
};
}
// The Bind function for the Writer monad:
// applies a logging version of a function
// to the contents of a wrapped value
// and return a wrapped result (with extended log)
// Writer a -> (a -> Writer b) -> Writer b
function writerBind(w, f) {
var writerB = f(w.value),
v = writerB.value;
return {
value: v,
log: w.log + '\n' + writerB.log + ' -> ' + JSON.stringify(v)
};
}
// USING UNIT AND BIND TO COMPOSE LOGGING FUNCTIONS
// We can compose a chain of Writer functions (of any length) with a simple foldr/reduceRight
// which starts by 'lifting' the initial value into a Writer wrapping,
// and then nests function applications (working from right to left)
function logCompose(lstFunctions, value) {
return lstFunctions.reduceRight(
writerBind,
writerUnit(value)
);
}
var half_of_addOne_of_root = function (v) {
return logCompose(
[log_half, log_addOne, log_root], v
);
};
return half_of_addOne_of_root(5);
})();
{{Out}}
{
"value":1.618033988749895,
"log":"Initial value: 5\n
obtained square root -> 2.23606797749979\n
added 1 -> 3.23606797749979\n
divided by 2 -> 1.618033988749895"
}
Jsish
From Javascript ES5 entry.
'use strict';
/* writer monad, in Jsish */
function writerMonad() {
// START WITH THREE SIMPLE FUNCTIONS
// Square root of a number more than 0
function root(x) {
return Math.sqrt(x);
}
// Add 1
function addOne(x) {
return x + 1;
}
// Divide by 2
function half(x) {
return x / 2;
}
// DERIVE LOGGING VERSIONS OF EACH FUNCTION
function loggingVersion(f, strLog) {
return function (v) {
return {
value: f(v),
log: strLog
};
};
}
var log_root = loggingVersion(root, "obtained square root"),
log_addOne = loggingVersion(addOne, "added 1"),
log_half = loggingVersion(half, "divided by 2");
// UNIT/RETURN and BIND for the the WRITER MONAD
// The Unit / Return function for the Writer monad:
// 'Lifts' a raw value into the wrapped form
// a -> Writer a
function writerUnit(a) {
return {
value: a,
log: "Initial value: " + JSON.stringify(a)
};
}
// The Bind function for the Writer monad:
// applies a logging version of a function
// to the contents of a wrapped value
// and return a wrapped result (with extended log)
// Writer a -> (a -> Writer b) -> Writer b
function writerBind(w, f) {
var writerB = f(w.value),
v = writerB.value;
return {
value: v,
log: w.log + '\n' + writerB.log + ' -> ' + JSON.stringify(v)
};
}
// USING UNIT AND BIND TO COMPOSE LOGGING FUNCTIONS
// We can compose a chain of Writer functions (of any length) with a simple foldr/reduceRight
// which starts by 'lifting' the initial value into a Writer wrapping,
// and then nests function applications (working from right to left)
function logCompose(lstFunctions, value) {
return lstFunctions.reduceRight(
writerBind,
writerUnit(value)
);
}
var half_of_addOne_of_root = function (v) {
return logCompose(
[log_half, log_addOne, log_root], v
);
};
return half_of_addOne_of_root(5);
}
var writer = writerMonad();
;writer.value;
;writer.log;
/*
=!EXPECTSTART!=
writer.value ==> 1.61803398874989
writer.log ==> Initial value: 5
obtained square root -> 2.23606797749979
added 1 -> 3.23606797749979
divided by 2 -> 1.61803398874989
=!EXPECTEND!=
*/
{{out}}
prompt$ jsish -u writerMonad.jsi
[PASS] writerMonad.jsi
Julia
struct Writer x::Real; msg::String; end
Base.show(io::IO, w::Writer) = print(io, w.msg, ": ", w.x)
unit(x, logmsg) = Writer(x, logmsg)
bind(f, fmsg, w) = unit(f(w.x), w.msg * ", " * fmsg)
f1(x) = 7x
f2(x) = x + 8
a = unit(3, "after intialization")
b = bind(f1, "after times 7 ", a)
c = bind(f2, "after plus 8", b)
println("$a => $b => $c")
println(bind(f2, "after plus 8", bind(f1, "after times 7", unit(3, "after intialization"))))
{{out}}
after intialization: 3 => after intialization, after times 7: 21 => after intialization, after times 7, after plus 8: 29
after intialization, after times 7, after plus 8: 29
Kotlin
// version 1.2.10
import kotlin.math.sqrt
class Writer<T : Any> private constructor(val value: T, s: String) {
var log = " ${s.padEnd(17)}: $value\n"
private set
fun bind(f: (T) -> Writer<T>): Writer<T> {
val new = f(this.value)
new.log = this.log + new.log
return new
}
companion object {
fun <T : Any> unit(t: T, s: String) = Writer<T>(t, s)
}
}
fun root(d: Double) = Writer.unit(sqrt(d), "Took square root")
fun addOne(d: Double) = Writer.unit(d + 1.0, "Added one")
fun half(d: Double) = Writer.unit(d / 2.0, "Divided by two")
fun main(args: Array<String>) {
val iv = Writer.unit(5.0, "Initial value")
val fv = iv.bind(::root).bind(::addOne).bind(::half)
println("The Golden Ratio is ${fv.value}")
println("\nThis was derived as follows:-\n${fv.log}")
}
{{out}}
The Golden Ratio is 1.618033988749895
This was derived as follows:-
Initial value : 5.0
Took square root : 2.23606797749979
Added one : 3.23606797749979
Divided by two : 1.618033988749895
zkl
{{trans|EchoLisp}}
class Writer{
fcn init(x){ var X=x, logText=Data(Void," init \U2192; ",x.toString()) }
fcn unit(text) { logText.append(text); self }
fcn lift(f,name){ unit("\n %s \U2192; %s".fmt(name,X=f(X))) }
fcn bind(f,name){ lift.fp(f,name) }
fcn toString{ "Result = %s\n%s".fmt(X,logText.text) }
fcn root{ lift(fcn(x){ x.sqrt() },"root") }
fcn half{ lift('/(2),"half") }
fcn inc { lift('+(1),"inc") }
}
Writer(5.0).root().inc().half().println();
{{out}}
Result = 1.61803
init → 5
root → 2.23607
inc → 3.23607
half → 1.61803
w:=Writer(5.0);
Utils.Helpers.fcomp(w.half,w.inc,w.root)(w).println(); // half(inc(root(w)))
{{out}}
Result = 1.61803
init → 5
root → 2.23607
inc → 3.23607
half → 1.61803
Use bind to add functions to an existing Writer:
w:=Writer(5.0);
root,inc,half := w.bind(fcn(x){ x.sqrt() },"root"), w.bind('+(1),"+ 1"), w.bind('/(2),"/ 2");
root(); inc(); half(); w.println();
{{out}}
Result = 1.61803
init → 5
root → 2.23607
+ 1 → 3.23607
/ 2 → 1.61803