183 lines
4.4 KiB
HTML
183 lines
4.4 KiB
HTML
<!DOCTYPE html>
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<html xmlns="http://www.w3.org/1999/xhtml" lang="" xml:lang="">
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<head>
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<title>lambda-calculus-1</title>
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<![endif]-->
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</head>
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<body>
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<h1 id="lambda-calculus-1">Lambda calculus 1</h1>
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<p>Let’s get started with some funny things. If we have a function
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<code>f(x) = x + 1</code>, it could be described in lambda calculus as
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<code>λx.x+1</code>.</p>
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<p>Something more interesting could be a function accepting two
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parameters <code>x</code> and <code>y</code>, and returning the sum of
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the squares of each parameter. Semantically, we could express the idea
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like so: <code>f(x, y) = x^2 + y^2</code>. In lambda calculus, we can
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write it like this: <code>λx.λy.x^2+y^2</code>.</p>
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<p>Note that instead of one function call we make two calls to a lambda
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and pass one parameter each, that’s because each lambda function can
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only accept one argument at a time.</p>
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<p>I am going to have a bit of fun, if you allow me, and I am going to
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rewrite some algebraic functions as lambda expressions:</p>
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<ol type="1">
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<li><code>x - y + 2z</code></li>
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<li><code>-x + 5</code></li>
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<li><code>a^2+b^2-c^2</code></li>
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<li><code>t^2 - π</code></li>
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</ol>
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</body>
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</html>
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