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    <p>Currying is a transformation that can be applied to functions to allow them to take one less argument than previously.</p> <p>For example, in F# you can define a function thus:-</p> <pre><code>let f x y z = x + y + z </code></pre> <p>Here function f takes parameters x, y and z and sums them together so:-</p> <pre><code>f 1 2 3 </code></pre> <p>Returns 6.</p> <p>From our definition we can can therefore define the curry function for f:-</p> <pre><code>let curry f = fun x -&gt; f x </code></pre> <p>Where 'fun x -> f x' is a lambda function equivilent to x => f(x) in C#. This function inputs the function you wish to curry and returns a function which <em>takes a single argument</em> and returns the specified function with the first argument set to the input argument.</p> <p>Using our previous example we can obtain a curry of f thus:-</p> <pre><code>let curryf = curry f </code></pre> <p>We can then do the following:-</p> <pre><code>let f1 = curryf 1 </code></pre> <p>Which provides us with a function f1 which is equivilent to f1 y z = 1 + y + z. This means we can do the following:-</p> <pre><code>f1 2 3 </code></pre> <p>Which returns 6.</p> <p>This process is often confused with 'partial function application' which can be defined thus:-</p> <pre><code>let papply f x = f x </code></pre> <p>Though we can extend it to more than one parameter, i.e.:-</p> <pre><code>let papply2 f x y = f x y let papply3 f x y z = f x y z etc. </code></pre> <p>A partial application will take the function and parameter(s) and return a function that requires one or more less parameters, and as the previous two examples show is implemented directly in the standard F# function definition so we could achieve the previous result thus:-</p> <pre><code>let f1 = f 1 f1 2 3 </code></pre> <p>Which will return a result of 6.</p> <p>In conclusion:-</p> <p>The difference between currying and partial function application is that:-</p> <p>Currying takes a function and provides a new function accepting a single argument, and returning the specified function with its first argument set to that argument. <em>This allows us to represent functions with multiple parameters as a series of single argument functions</em>. Example:-</p> <pre><code>let f x y z = x + y + z let curryf = curry f let f1 = curryf 1 let f2 = curryf 2 f1 2 3 6 f2 1 3 6 </code></pre> <p>Partial function application is more direct - it takes a function and one or more arguments and returns a function with the first n arguments set to the n arguments specified. Example:-</p> <pre><code>let f x y z = x + y + z let f1 = f 1 let f2 = f 2 f1 2 3 6 f2 1 3 6 </code></pre>
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    1. POWhat is 'Currying'?
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    1. COSo methods in C# would need to be curried before they could be partially applied?
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