Monads/Writer monad

From Rosetta Code
Monads/Writer monad is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

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:

  1. 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)
  2. Write three simple functions: root, addOne, and half
  3. Derive Writer monad versions of each of these functions
  4. 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.)


AppleScript[edit]

Translation of: 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
Output:
{
    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[edit]

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
sin0
cos1
add-one → 2
half → 1
 

Haskell[edit]

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)
Output:
(1.618033988749895,"obtained square root, added 1, divided by 2, ")

J[edit]

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[edit]

ES5[edit]

(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);
})();
Output:
{
    "value":1.618033988749895,
    "log":"Initial value: 5\n
           obtained square root -> 2.23606797749979\n
           added 1 -> 3.23606797749979\n
           divided by 2 -> 1.618033988749895"
}

Kotlin[edit]

// 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}")
}
Output:
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[edit]

Translation of: 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();
Output:
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)))
Output:
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();
Output:
Result = 1.61803
  init → 5
  root → 2.23607
  + 1 → 3.23607
  / 2 → 1.61803