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<!doctype html>
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<meta
name="description"
content="Functional programming language based on pure de Bruijn indexed lambda calculus."
/>
<link rel="stylesheet" href="style.css" type="text/css" media="all" />
<title>bruijn programming language</title>
</head>
<body>
<div class="header">
<img src="res/logo.png" />
<h1>bruijn</h1>
</div>
<div class="example">
<div class="left">
<pre class="code">
<span class="def">pow</span> <span class="term">[<span class="symbol">index</span> (<span class="symbol">iterate</span> (<span class="symbol">mul</span> 0) <span class="ternary">(+1)</span>)]</span>
<span class="def">…**…</span> <span class="symbol">pow</span>
<span class="com">:test</span> <span class="test">(<span class="term"><span class="ternary">(+2)</span> <span class="mixfix">**</span> <span class="ternary">(+3)</span> <span class="mixfix">=?</span> <span class="ternary">(+8)</span></span>)</span> <span class="test">(<span class="symbol">true</span>)</span></pre>
</div>
<div class="right">
<p>
Functional programming language based on pure de Bruijn indexed lambda
calculus.
</p>
</div>
</div>
<div class="bar small">
<b>Hint</b>: Click on anything you don't understand.
</div>
<div class="example">
<div class="left">
<p>
Lambdas all the way down.<br />
No primitive functions.
</p>
</div>
<div class="right">
<pre class="code">
<span class="repl">></span> <span class="ternary">(+5)</span>
<span class="term">[[[[2 (2 (1 3))]]]]</span>
<span class="repl">></span> <span class="char">'a'</span>
<span class="term">[[[1 (0 (0 (0 (0 (1 (1 (0 2)))))))]]]</span>
<span class="repl">></span> <span class="symbol">add</span>
<span class="term">[[(([([[1 0 [[0]]]] ((((0 [[(((0...</span></pre>
</div>
<div class="left">
<pre class="code">
<span class="repl">></span> <span class="com">:time</span> <span class="symbol">factorial</span> <span class="ternary">(+42)</span>
<span class="time">0.01 seconds</span></pre>
</div>
<div class="right">
<p>
<a href="wiki/technical/performance/">Efficient</a> reduction using
abstract machines and higher-order encodings.
</p>
</div>
<div class="left">
<p>
Substantial standard library.<br />
<a href="std/">Source</a>
</p>
</div>
<div class="right">
<pre class="code">
<span class="repl">></span> <span class="mixfix">∏</span> <span class="ternary">(+1)</span> <span class="mixfix">→</span> <span class="ternary">(+3)</span> <span class="mixfix">|</span> <span class="symbol">++‣</span>
<span class="repl">></span> <span class="symbol">number!</span> <span class="mixfix"><$></span> <span class="left-app">(</span><span class="symbol">lines</span> <span class="string">"42\n25"</span><span class="right-app">)</span>
<span class="repl">></span> <span class="term"><span class="symbol">sum</span> (<span class="symbol">take</span> <span class="ternary">(+3)</span> (<span class="symbol">repeat</span> <span class="ternary">(+4)</span>))</span>
<span class="repl">></span> <span class="binary">(+10b)</span> <span class="mixfix">⋀!</span> <span class="binary">(+12b)</span></pre>
</div>
<div class="left">
<pre class="code">
$ echo "main [0]" > echo.bruijn
$ bruijn -b echo.bruijn > echo
$ wc -c echo
2 echo
$ echo "hello world!" | bruijn -e echo
hello world!</pre
>
</div>
<div class="right">
<p>
<a href="wiki/coding/compilation/">Compilation</a> to Tromp's binary
lambda calculus.<br />
Support for byte and ASCII encoding.
</p>
</div>
<div class="left">
<p>
<a href="wiki/coding/meta-programming/">Meta-programming</a><br />
and self-interpretation.
</p>
</div>
<div class="right">
<pre class="code">
<span class="repl">></span> <span class="symbol">length</span> <span class="meta">`</span><span class="symbol">factorial</span>
<span class="repl">></span> <span class="prefix">!</span><span class="left-app">(</span><span class="symbol">swap</span> <span class="meta">`</span><span class="left-app">(</span><span class="unary">(+2u)</span> <span class="unary">(+3u)</span><span class="right-app">))</span>
<span class="repl">></span> <span class="symbol">lhs</span> <span class="left-app">(</span><span class="symbol">blc→meta</span> <span class="string">"010000100000110"</span><span class="right-app">)</span>
</pre>
</div>
</div>
<div class="bar big">
Learn more: <a href="wiki/">Wiki</a>, <a href="std/">Std</a>,
<a href="samples/">Samples</a>
</div>
<div class="instructions">
<h1>Installation</h1>
<pre class="code">
$ git clone https://github.com/marvinborner/bruijn.git && cd bruijn
$ <span class="stack">stack</span> run # for playing around
$ <span class="stack">stack</span> install
$ bruijn</pre>
</div>
<div class="instructions">
<h1>Broogle</h1>
<pre class="code">
$ ./broogle.sh -f add
<span class="def">add</span> ⧗ Unary → Unary → Unary
also known as <span class="def">…+…</span>
in std/Number/Unary.bruijn:35
# adds two unary numbers
...</pre>
</div>
<div class="instructions">
<h1>Why?</h1>
<ul>
<li>
By having a very small core (the reducer), bruijn is safe, consistent,
and (potentially) proven to be correct!
</li>
<li>
Since it doesn't have builtin functions, bruijn is independent of
hardware internals and could easily be run on almost any architecture.
</li>
<li>
Compiled binary lambda calculus is incredibly expressive and tiny.
Read the articles by
<a href="https://justine.lol/lambda/#why">Jart</a> and
<a href="https://tromp.github.io/cl/cl.html">Tromp</a>.
</li>
<li>
Exploring different encodings of data as function abstractions is
really fascinating.
</li>
<li>
Naming parameters of functions is annoying. De Bruijn indices are a
universal reference independent of the function and can actually help
readability!
</li>
<li>
Really, <a href="https://justforfunnoreally.dev/">just for fun</a>.
</li>
</ul>
</div>
<div class="instructions">
<h1>Articles</h1>
<ul>
<!-- feel free to add your own -->
<li>
<a href="https://text.marvinborner.de/2023-04-06-01.html"
>The bruijn programming language</a
>
</li>
<li>
<a href="https://text.marvinborner.de/2023-04-07-01.html"
>Data structures in pure lambda calculus</a
>
</li>
<li>
<a href="https://text.marvinborner.de/2023-06-18-15.html"
>Variadic fixed-point combinators</a
>
</li>
<li>
<a href="https://text.marvinborner.de/2023-09-03-21.html"
>Metaprogramming and self interpretation</a
>
</li>
</ul>
</div>
<div class="bar big">
Open-source: <a href="https://github.com/marvinborner/bruijn">GitHub</a>
</div>
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</body>
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