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copied!<p>I found some really good monads resources:</p> <ul> <li><a href="http://www.clojure.net/tags.html#monads-ref" rel="nofollow">http://www.clojure.net/tags.html#monads-ref</a> (Jim Duey's Monads Guide, which really goes into the nitty gritty monad definitions)</li> <li><a href="http://homepages.inf.ed.ac.uk/wadler/topics/monads.html#marktoberdorf" rel="nofollow">http://homepages.inf.ed.ac.uk/wadler/topics/monads.html#marktoberdorf</a> (A whole load of papers on monads)</li> <li><a href="http://vimeo.com/17207564" rel="nofollow">http://vimeo.com/17207564</a> (A talk on category theory, which I half followed)</li> </ul> <p>So from Jim's Guide - <a href="http://www.clojure.net/2012/02/06/Legalities/" rel="nofollow">http://www.clojure.net/2012/02/06/Legalities/</a> - he gives three axioms for definition of 'bind-m' and 'reduce-m' functions:</p> <blockquote> <p><strong>Identity</strong> The first Monad Law can be written as</p> <p><em>(m-bind (m-result x) f) is equal to (f x)</em></p> <p>What this means is that whatever m-result does to x to make it into a monadic value, m-bind undoes before applying f to x. So with regards to m-bind, m-result is sort of like an identity function. Or in category theory terminology, its unit. Which is why sometimes you’ll see it named ‘unit’.</p> <p><strong>Reverse Identity</strong> The second Monad Law can be written as</p> <p><em>(m-bind mv m-result) is equal to mv where mv is a monadic value.</em> </p> <p>This law is something like a complement to the first law. It basically ensures that m-result is a monadic function and that whatever m-bind does to a monadic value to extract a value, m-result undoes to create a monadic value.</p> <p><strong>Associativity</strong> The third Monad Law can be written as</p> <p><em>(m-bind (m-bind mv f) g) is equal to (m-bind mv (fn [x] (m-bind (f x) g))) where f and g are monadic functions and mv is a monadic value.</em></p> <p>What this law is saying is that it doesnt matter whether the f is applied to mv and then g is applied to the result, or whether a new monadic function is created out of a composition of f and g which is then applied to mv. In either order, the resulting value is the same monadic value. Stated another way, m-bind is left and right associative.</p> </blockquote> <p>In <a href="http://www.clojure.net/2012/02/04/Sets-not-lists/" rel="nofollow">http://www.clojure.net/2012/02/04/Sets-not-lists/</a> he gives an monad that takes sets as inputs instead of taking lists. Will work through all the examples...</p>

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