Monads/Writer monad: Difference between revisions
< Monads
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(→ES5: updated writer monad to include intermediate values in log) |
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<lang JavaScript>(function () { |
<lang JavaScript>(function () { |
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'use strict'; |
'use strict'; |
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// START WITH THREE SIMPLE FUNCTIONS |
// START WITH THREE SIMPLE FUNCTIONS |
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// Square root of a number more than 0 |
// Square root of a number more than 0 |
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function root(x) { |
function root(x) { |
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return Math.sqrt(x); |
return Math.sqrt(x); |
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} |
} |
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// Add 1 |
// Add 1 |
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function addOne(x) { |
function addOne(x) { |
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return x + 1; |
return x + 1; |
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} |
} |
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// Divide by 2 |
// Divide by 2 |
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function half(x) { |
function half(x) { |
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return x / 2; |
return x / 2; |
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} |
} |
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// DERIVE LOGGING VERSIONS OF EACH FUNCTION |
// DERIVE LOGGING VERSIONS OF EACH FUNCTION |
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function loggingVersion(f, strLog) { |
function loggingVersion(f, strLog) { |
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return function (v) { |
return function (v) { |
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} |
} |
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} |
} |
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var log_root = loggingVersion(root, "obtained square root"), |
var log_root = loggingVersion(root, "obtained square root"), |
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log_addOne = loggingVersion(addOne, "added 1"), |
log_addOne = loggingVersion(addOne, "added 1"), |
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log_half = loggingVersion(half, "divided by 2"); |
log_half = loggingVersion(half, "divided by 2"); |
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// UNIT/RETURN and BIND for the the WRITER MONAD |
// UNIT/RETURN and BIND for the the WRITER MONAD |
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// The Unit / Return function for the Writer monad: |
// The Unit / Return function for the Writer monad: |
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// 'Lifts' a raw value into the wrapped form |
// 'Lifts' a raw value into the wrapped form |
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}; |
}; |
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} |
} |
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// The Bind function for the Writer monad: |
// The Bind function for the Writer monad: |
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// applies a logging version of a function |
// applies a logging version of a function |
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// to the contents of a wrapped value |
// to the contents of a wrapped value |
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// and return a wrapped result (with extended log) |
// and return a wrapped result (with extended log) |
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// Writer a -> (a -> Writer b) -> Writer b |
// Writer a -> (a -> Writer b) -> Writer b |
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function writerBind(w, f) { |
function writerBind(w, f) { |
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var writerB = f(w.value) |
var writerB = f(w.value), |
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v = writerB.value; |
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return { |
return { |
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value: |
value: v, |
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log: w.log + '\n' + writerB.log |
log: w.log + '\n' + writerB.log + ' -> ' + JSON.stringify(v) |
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}; |
}; |
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} |
} |
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// USING UNIT AND BIND TO COMPOSE LOGGING FUNCTIONS |
// USING UNIT AND BIND TO COMPOSE LOGGING FUNCTIONS |
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// We can compose a chain of Writer functions (of any length) with a simple foldr/reduceRight |
// We can compose a chain of Writer functions (of any length) with a simple foldr/reduceRight |
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// which starts by 'lifting' the initial value into a Writer wrapping, |
// which starts by 'lifting' the initial value into a Writer wrapping, |
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}, writerUnit(value)); |
}, writerUnit(value)); |
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} |
} |
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var half_of_addOne_of_root = function (v) { |
var half_of_addOne_of_root = function (v) { |
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return logCompose( |
return logCompose( |
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); |
); |
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}; |
}; |
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return half_of_addOne_of_root(5); |
return half_of_addOne_of_root(5); |
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})();</lang> |
})();</lang> |
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{{Out}} |
{{Out}} |
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<pre>{ |
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<pre>{"value":1.618033988749895, "log":"Initial value: 5\nobtained square root\nadded 1\ndivided by 2"}</pre> |
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"value":1.618033988749895, |
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"log":"Initial value: 5\n |
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obtained square root -> 2.23606797749979\n |
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added 1 -> 3.23606797749979\n |
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divided by 2 -> 1.618033988749895" |
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}</pre> |
Revision as of 19:39, 2 February 2016
The Writer monad is a coding pattern which allows composition of functions which return their results combined with a log string. The final result of a composed function yields both the resulting 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.)
JavaScript
ES5
<lang JavaScript>(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(function (writerA, f) { return writerBind(writerA, f); }, 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);
})();</lang>
- 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" }