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POMap and Reduce Monad for Clojure... What about a Juxt Monad?
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copied!<p>Whilst learning Clojure, I've spent ages trying to make sense of monads - what they are and how we can use them.... with not too much success. However, I found an excellent 'Monads for Dummies' Video Series - <a href="http://vimeo.com/20717301" rel="nofollow">http://vimeo.com/20717301</a> - by Brian Marik for Clojure</p> <p>So far, my understanding of monads is that it is sort of like a macro in that it allows a set of statements to be written in a form that is easy to read - but monads are much more formalised. My observations are limited to two examples:</p> <p><strong>1. The Identity Monad (or the 'let' monad)</strong> taken from <a href="http://onclojure.com/2009/03/05/a-monad-tutorial-for-clojure-programmers-part-1/" rel="nofollow">http://onclojure.com/2009/03/05/a-monad-tutorial-for-clojure-programmers-part-1/</a></p> <p>The form that we wish to write is:</p> <pre><code>(let [a 1 b (inc a)] (* a b)) </code></pre> <p>and the corresponding monad is</p> <pre><code>(domonad identity-m [a 1 b (inc a)] (* a b)) </code></pre> <p><strong>2. The Sequence Monad (or the 'for' monad)</strong> taken from <a href="http://onclojure.com/2009/03/06/a-monad-tutorial-for-clojure-programmers-part-2/" rel="nofollow">http://onclojure.com/2009/03/06/a-monad-tutorial-for-clojure-programmers-part-2/</a></p> <p>The form we wish to write is:</p> <pre><code>(for [a (range 5) b (range a)] (* a b)) </code></pre> <p>and the corresponding monad is</p> <pre><code>(domonad sequence-m [a (range 5) b (range a)] (* a b)) </code></pre> <p><strong>Monad Definitions in Clojure</strong></p> <p>Looking at the source, using clojure monads library - <a href="https://github.com/clojure/algo.monads" rel="nofollow">https://github.com/clojure/algo.monads</a>:</p> <pre><code>user=>(use 'clojure.algo.monads) nil </code></pre> <p>indentity monad:</p> <pre><code>user=> (source identity-m) (defmonad identity-m [m-result identity m-bind (fn m-result-id [mv f] (f mv)) ]) </code></pre> <p>sequence monad:</p> <pre><code>user=> (source sequence-m) (defmonad sequence-m [m-result (fn m-result-sequence [v] (list v)) m-bind (fn m-bind-sequence [mv f] (flatten* (map f mv))) m-zero (list) m-plus (fn m-plus-sequence [& mvs] (flatten* mvs)) ]) </code></pre> <p>So my conclusion is that a monad is some sort of a generalised higher-order function that takes in an input-function and input-values, adds its own control logic and spits out a 'thing' that can be used in a 'domonad' block.</p> <p><strong>Question 1</strong></p> <p>So finally, to the questions: I want to learn how to write a monad and say I want to write a 'map monad' that imitates the 'map' form in clojure:</p> <pre><code>(domonad map-m [a [1 2 3 4 5] b [5 6 7 8 9]] (+ a b)) </code></pre> <p>Should be equivalent to</p> <pre><code>(map + [1 2 3 4 5] [5 6 7 8 9]) </code></pre> <p>and return the values</p> <pre><code>[6 8 10 12 14] </code></pre> <p>If I look at the source, it should give me something similar to identity-m and sequence-m:</p> <pre><code>user=> (source map-m) (defmonad map-m [m-result ... m-bind ... m-zero ... m-plus ... ]) </code></pre> <p><strong>Question 2</strong></p> <p>I also want to be able to define 'reduce-m' such that I can write:</p> <pre><code>(domonad reduce-m [a [1 2 3 4 5]] (* a)) </code></pre> <p>this could potentially give me 1 x 2 x 3 x 4 x 5 = 120 or</p> <pre><code>(domonad reduce-m [a [1 2 3 4 5] b [1 2 3 4 5]] (+ a b)) </code></pre> <p>will give me (1+2+3+4+5) + (1+2+3+4+5) = 30</p> <p><strong>Finally</strong> Would I also be able to write a 'juxt monad' that imitates the juxt function but instead of passing in values for binding, I pass in a set of functions. :</p> <pre><code>(domonad juxt-m [a #(+ % 1) b #(* % 2)] '([1 2 3 4 5] b a) ) </code></pre> <p>gives</p> <pre><code>[ [2 2] [4 3] [6 4] [8 5] [9 6] ] </code></pre> <p>Potentially, I could do all of those things with macros so I don't really know how useful these 'monads' will be or if they are even considered 'monads'... With all the resources on the internet, It seems to me that if I wanted to learn Monads properly, I have to learn Haskell and right now, learning another syntactic form is just too hard. I think I found some links that maybe relevant but it is too cryptic for me</p> <p>Please can someone shed some light!</p>

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