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<title>BLisp: A Statically Typed Lisp Like Language</title>
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<body class="article">
<div id="header">
<h1>BLisp: A Statically Typed Lisp Like Language</h1>
<div class="details">
<span id="author" class="author">Yuuki Takano</span><br>
<span id="email" class="email"><a href="mailto:ytakano@wide.ad.jp">ytakano@wide.ad.jp</a></span><br>
<span id="revnumber">version 0.4.0,</span>
<span id="revdate">2023-02</span>
</div>
<div id="toc" class="toc">
<div id="toctitle">Table of Contents</div>
<ul class="sectlevel1">
<li><a href="#_features">1. Features</a></li>
<li><a href="#_values">2. Values</a></li>
<li><a href="#_basic_types">3. Basic Types</a></li>
<li><a href="#_function_definition">4. Function Definition</a></li>
<li><a href="#_arithmetic_operations">5. Arithmetic Operations</a></li>
<li><a href="#_boolean_operations">6. Boolean Operations</a></li>
<li><a href="#_comparison">7. Comparison</a></li>
<li><a href="#_bitwise_operations">8. Bitwise Operations</a></li>
<li><a href="#_mathematical_operations">9. Mathematical Operations</a></li>
<li><a href="#_algebraic_data_type">10. Algebraic Data Type</a></li>
<li><a href="#_generics">11. Generics</a></li>
<li><a href="#_generic_function">12. Generic Function</a></li>
<li><a href="#_if_expression">13. If Expression</a></li>
<li><a href="#_match_expression">14. Match Expression</a></li>
<li><a href="#_let_expression">15. Let Expression</a></li>
<li><a href="#_lambda_expression">16. Lambda Expression</a></li>
<li><a href="#_macro">17. Macro</a></li>
<li><a href="#_string_and_character">18. String and Character</a></li>
<li><a href="#_foreign_function_interface">19. Foreign Function Interface</a></li>
<li><a href="#_transpilation_to_coq_experimental">20. Transpilation to Coq (Experimental)</a></li>
<li><a href="#_examples">21. Examples</a>
<ul class="sectlevel2">
<li><a href="#_reverse">21.1. Reverse</a></li>
<li><a href="#_filter">21.2. Filter</a></li>
<li><a href="#_factorial">21.3. Factorial</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="content">
<div id="preamble">
<div class="sectionbody">
<div class="paragraph">
<p>BLisp is a statically typed Lisp like programming language which adopts effect system for no_std environments.
BLisp supports higher order RPC like higher order functions of functional programming languages.</p>
</div>
<div class="ulist">
<ul>
<li>
<p><a href="https://github.com/ytakano/blisp">GitHub’s Repository</a></p>
</li>
<li>
<p><a href="https://crates.io/crates/blisp">BLisp’s crates.io</a></p>
</li>
</ul>
</div>
<div class="paragraph">
<p>This repository provides only a library crate.
Please see <a href="https://github.com/ytakano/blisp-repl">blisp-repl</a> to use BLisp,
and <a href="https://github.com/ytakano/baremetalisp">baremetalisp</a> which is a toy OS.</p>
</div>
<div class="paragraph">
<p><a href="https://ytakano.github.io/blisp/index.ja.html">日本語版はこちら</a></p>
</div>
<div class="paragraph">
<div class="title">BLisp on no_std Environment</div>
<p><span class="image"><img src="https://cdn-ak.f.st-hatena.com/images/fotolife/y/ytakano/20210221/20210221155657.gif" alt="BLisp on no_std Environment"></span></p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_features">1. Features</h2>
<div class="sectionbody">
<div class="ulist">
<ul>
<li>
<p>Algebraic data type</p>
</li>
<li>
<p>Generics</p>
</li>
<li>
<p>Hindley–Milner based type inference</p>
</li>
<li>
<p>Effect system to separate side effects from pure functions</p>
</li>
<li>
<p>Big integer</p>
</li>
<li>
<p>Supporting no_std environments</p>
</li>
</ul>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_values">2. Values</h2>
<div class="sectionbody">
<div class="listingblock">
<div class="title">values</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-o">`</span><span class="tok-nv">A</span><span class="tok-o">`</span><span class="tok-w"> </span><span class="tok-c1">; character literal</span>
<span class="tok-s">"Hello"</span><span class="tok-w"> </span><span class="tok-c1">; string literal</span>
<span class="tok-mi">144</span><span class="tok-w"> </span><span class="tok-c1">; integer value</span>
<span class="tok-nv">0xabcDEF</span><span class="tok-w"> </span><span class="tok-c1">; hexadecimal</span>
<span class="tok-nv">0o777</span><span class="tok-w"> </span><span class="tok-c1">; octal</span>
<span class="tok-nv">0b1001</span><span class="tok-w"> </span><span class="tok-c1">; binary</span>
<span class="tok-nv">true</span><span class="tok-w"> </span><span class="tok-c1">; boolean value</span>
<span class="tok-nv">false</span><span class="tok-w"> </span><span class="tok-c1">; boolean value</span>
<span class="tok-nv">[true</span><span class="tok-w"> </span><span class="tok-nv">10]</span><span class="tok-w"> </span><span class="tok-c1">; tuple</span>
<span class="tok-nv">[]</span><span class="tok-w"> </span><span class="tok-c1">; empty tuple</span>
<span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; list</span>
<span class="tok-o">'</span><span class="tok-p">()</span><span class="tok-w"> </span><span class="tok-c1">; empty list, Nil</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_basic_types">3. Basic Types</h2>
<div class="sectionbody">
<div class="listingblock">
<div class="title">types</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-nv">Char</span><span class="tok-w"> </span><span class="tok-c1">; character</span>
<span class="tok-nv">String</span><span class="tok-w"> </span><span class="tok-c1">; string</span>
<span class="tok-nv">Int</span><span class="tok-w"> </span><span class="tok-c1">; signed integer</span>
<span class="tok-nv">Bool</span><span class="tok-w"> </span><span class="tok-c1">; boolean</span>
<span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; list of Int</span>
<span class="tok-nv">[Int</span><span class="tok-w"> </span><span class="tok-nv">Bool]</span><span class="tok-w"> </span><span class="tok-c1">; tuple of Int and Bool</span>
<span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">Bool</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; Pure function, which takes 2 integers and return boolean value</span>
<span class="tok-p">(</span><span class="tok-nv">IO</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">[]</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; IO function, which takes an integer and return []</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Pure and IO are function effects.
In IO functions, both Pure and IO functions can be called.
However, in Pure functions, calling only Pure functions is permitted.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_function_definition">4. Function Definition</h2>
<div class="sectionbody">
<div class="paragraph">
<p>Functions can be defined by defun or export.
"defun" defines a local function which cannot be called from Rust’s eval function.</p>
</div>
<div class="paragraph">
<p>Suppose following 2 functions.</p>
</div>
<div class="listingblock">
<div class="title">defun</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">defun</span><span class="tok-w"> </span><span class="tok-nv">double</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; function name is "double" and "x" is an argument</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; function Type</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; function body</span></code></pre>
</div>
</div>
<div class="listingblock">
<div class="title">export</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nv">quad</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; function name is "quad" and "x" is an argument</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; function Type</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">double</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">double</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">)))</span><span class="tok-w"> </span><span class="tok-c1">; function body</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>double cannot be called from Rust’s eval, but can be called from internally defined functions.
quad can be called from Rust’s eval, and it calls double internally.</p>
</div>
<div class="paragraph">
<p>This is the code what actually do in Rust.</p>
</div>
<div class="listingblock">
<div class="title">Rust’s eval</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="rust"><span></span><span class="tok-k">use</span><span class="tok-w"> </span><span class="tok-n">blisp</span><span class="tok-p">;</span>
<span class="tok-k">fn</span> <span class="tok-nf">eval</span><span class="tok-p">(</span><span class="tok-n">e</span>: <span class="tok-kp">&</span><span class="tok-kt">str</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">ctx</span>: <span class="tok-kp">&</span><span class="tok-nc">blisp</span>::<span class="tok-n">semantics</span>::<span class="tok-n">Context</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w"> </span><span class="tok-c1">// evaluate expressions</span>
<span class="tok-w"> </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">exprs</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-k">match</span><span class="tok-w"> </span><span class="tok-n">blisp</span>::<span class="tok-n">eval</span><span class="tok-p">(</span><span class="tok-n">e</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">ctx</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w"> </span><span class="tok-nb">Ok</span><span class="tok-p">(</span><span class="tok-n">es</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-o">=></span><span class="tok-w"> </span><span class="tok-n">es</span><span class="tok-p">,</span>
<span class="tok-w"> </span><span class="tok-nb">Err</span><span class="tok-p">(</span><span class="tok-n">err</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-o">=></span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w"> </span><span class="tok-fm">println!</span><span class="tok-p">(</span><span class="tok-s">"error:{}:{}: {}"</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">err</span><span class="tok-p">.</span><span class="tok-n">pos</span><span class="tok-p">.</span><span class="tok-n">line</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">err</span><span class="tok-p">.</span><span class="tok-n">pos</span><span class="tok-p">.</span><span class="tok-n">column</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">err</span><span class="tok-p">.</span><span class="tok-n">msg</span><span class="tok-p">);</span>
<span class="tok-w"> </span><span class="tok-k">return</span><span class="tok-p">;</span>
<span class="tok-w"> </span><span class="tok-p">}</span>
<span class="tok-w"> </span><span class="tok-p">};</span>
<span class="tok-w"> </span><span class="tok-k">for</span><span class="tok-w"> </span><span class="tok-n">r</span><span class="tok-w"> </span><span class="tok-k">in</span><span class="tok-w"> </span><span class="tok-n">exprs</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w"> </span><span class="tok-k">match</span><span class="tok-w"> </span><span class="tok-n">r</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w"> </span><span class="tok-nb">Ok</span><span class="tok-p">(</span><span class="tok-n">msg</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-o">=></span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w"> </span><span class="tok-fm">println!</span><span class="tok-p">(</span><span class="tok-s">"{}"</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">msg</span><span class="tok-p">);</span>
<span class="tok-w"> </span><span class="tok-p">}</span>
<span class="tok-w"> </span><span class="tok-nb">Err</span><span class="tok-p">(</span><span class="tok-n">msg</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-o">=></span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w"> </span><span class="tok-fm">println!</span><span class="tok-p">(</span><span class="tok-s">"error: {}"</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">msg</span><span class="tok-p">);</span>
<span class="tok-w"> </span><span class="tok-p">}</span>
<span class="tok-w"> </span><span class="tok-p">}</span>
<span class="tok-w"> </span><span class="tok-p">}</span>
<span class="tok-p">}</span>
<span class="tok-k">fn</span> <span class="tok-nf">main</span><span class="tok-p">()</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w"> </span><span class="tok-c1">// internal code</span>
<span class="tok-w"> </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">code</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-s">"</span>
<span class="tok-s">(defun double (x) ; function name is double and x is an argument</span>
<span class="tok-s"> (Pure (-> (Int) Int)) ; function Type</span>
<span class="tok-s"> (* 2 x)) ; function body</span>
<span class="tok-s">(export quad (x) ; function name is quad and x is an argument</span>
<span class="tok-s"> (Pure (-> (Int) Int)) ; function Type</span>
<span class="tok-s"> (double (double x))) ; function body</span>
<span class="tok-s">"</span><span class="tok-p">;</span>
<span class="tok-w"> </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">exprs</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-n">blisp</span>::<span class="tok-n">init</span><span class="tok-p">(</span><span class="tok-n">code</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-fm">vec!</span><span class="tok-p">[]).</span><span class="tok-n">unwrap</span><span class="tok-p">();</span>
<span class="tok-w"> </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">ctx</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-n">blisp</span>::<span class="tok-n">typing</span><span class="tok-p">(</span><span class="tok-o">&</span><span class="tok-n">exprs</span><span class="tok-p">).</span><span class="tok-n">unwrap</span><span class="tok-p">();</span>
<span class="tok-w"> </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">e</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-s">"(double 10) ; error"</span><span class="tok-p">;</span>
<span class="tok-w"> </span><span class="tok-n">eval</span><span class="tok-p">(</span><span class="tok-n">e</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-o">&</span><span class="tok-n">ctx</span><span class="tok-p">);</span>
<span class="tok-w"> </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">e</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-s">"(quad 10) ; OK"</span><span class="tok-p">;</span>
<span class="tok-w"> </span><span class="tok-n">eval</span><span class="tok-p">(</span><span class="tok-n">e</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-o">&</span><span class="tok-n">ctx</span><span class="tok-p">);</span>
<span class="tok-p">}</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This code output as follows.</p>
</div>
<div class="literalblock">
<div class="content">
<pre>error:0:1: Typing Error: double is not defined
40</pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_arithmetic_operations">5. Arithmetic Operations</h2>
<div class="sectionbody">
<div class="listingblock">
<div class="title">basic</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-> (Int Int) Int))</span>
<span class="tok-p">(</span><span class="tok-nb">+</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-w"> </span><span class="tok-mi">20</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">-</span><span class="tok-w"> </span><span class="tok-mi">30</span><span class="tok-w"> </span><span class="tok-mi">40</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-mi">6</span><span class="tok-w"> </span><span class="tok-mi">100</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">/</span><span class="tok-w"> </span><span class="tok-mi">100</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nv">%</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-p">)</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_boolean_operations">6. Boolean Operations</h2>
<div class="sectionbody">
<div class="listingblock">
<div class="title">logical</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-> (Bool Bool) Bool))</span>
<span class="tok-p">(</span><span class="tok-nb">and</span><span class="tok-w"> </span><span class="tok-nv">true</span><span class="tok-w"> </span><span class="tok-nv">false</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">or</span><span class="tok-w"> </span><span class="tok-nv">true</span><span class="tok-w"> </span><span class="tok-nv">false</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nv">xor</span><span class="tok-w"> </span><span class="tok-nv">true</span><span class="tok-w"> </span><span class="tok-nv">false</span><span class="tok-p">)</span></code></pre>
</div>
</div>
<div class="listingblock">
<div class="title">negation</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-> (Bool) Bool))</span>
<span class="tok-p">(</span><span class="tok-nb">not</span><span class="tok-w"> </span><span class="tok-nv">true</span><span class="tok-p">)</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_comparison">7. Comparison</h2>
<div class="sectionbody">
<div class="paragraph">
<p>=, !=, <, >, <=, >= can be used for 2 values whose types are same.</p>
</div>
<div class="listingblock">
<div class="title">comparison between 2 values whose types are same</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-> (t t) Bool))</span>
<span class="tok-p">(</span><span class="tok-nb">=</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; true</span>
<span class="tok-p">(</span><span class="tok-nv">!=</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; false</span>
<span class="tok-p">(</span><span class="tok-nb">=</span><span class="tok-w"> </span><span class="tok-s">"Hello"</span><span class="tok-w"> </span><span class="tok-s">"Hello"</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; true</span>
<span class="tok-p">(</span><span class="tok-nb">=</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; false</span>
<span class="tok-p">(</span><span class="tok-nb"><</span><span class="tok-w"> </span><span class="tok-mi">6</span><span class="tok-w"> </span><span class="tok-mi">7</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">></span><span class="tok-w"> </span><span class="tok-mi">6</span><span class="tok-w"> </span><span class="tok-mi">7</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb"><=</span><span class="tok-w"> </span><span class="tok-mi">30</span><span class="tok-w"> </span><span class="tok-mi">40</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">>=</span><span class="tok-w"> </span><span class="tok-mi">30</span><span class="tok-w"> </span><span class="tok-mi">40</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb"><</span><span class="tok-w"> </span><span class="tok-s">"Hello"</span><span class="tok-w"> </span><span class="tok-s">"World"</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb"><=</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p><em>eq</em>, <em>neq</em>, <em>lt</em>, <em>gt</em>, <em>leq</em>, <em>geq</em> can be used for any 2 values</p>
</div>
<div class="listingblock">
<div class="title">comparison between any 2 values</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-> (t1 t1) Bool))</span>
<span class="tok-p">(</span><span class="tok-nv">geq</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-s">"Hello"</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; (Some 1) is greater than or qeual to "Hello"</span>
<span class="tok-p">(</span><span class="tok-nb">eq</span><span class="tok-w"> </span><span class="tok-s">"Hello"</span><span class="tok-w"> </span><span class="tok-mi">100</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; Is "Hello" qeual to 100?</span>
<span class="tok-p">(</span><span class="tok-nv">neq</span><span class="tok-w"> </span><span class="tok-s">"Hello"</span><span class="tok-w"> </span><span class="tok-mi">100</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; Is "Hello" not equal to 100?</span>
<span class="tok-p">(</span><span class="tok-nv">lt</span><span class="tok-w"> </span><span class="tok-mi">100</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">20</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; Is 100 less than (Some 20)?</span>
<span class="tok-p">(</span><span class="tok-nv">gt</span><span class="tok-w"> </span><span class="tok-mi">200</span><span class="tok-w"> </span><span class="tok-s">"Hello"</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; Is 200 greater than "Hello"</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_bitwise_operations">8. Bitwise Operations</h2>
<div class="sectionbody">
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">band</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; bitwise and</span>
<span class="tok-p">(</span><span class="tok-nv">band</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; bitwise and</span>
<span class="tok-p">(</span><span class="tok-nv">bor</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; bitwise or</span>
<span class="tok-p">(</span><span class="tok-nv">bor</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; bitwise or</span>
<span class="tok-p">(</span><span class="tok-nv">bxor</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; bitwise xor</span></code></pre>
</div>
</div>
<div class="listingblock">
<div class="title">bit shift</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-> (Int Int) (Option Int)))</span>
<span class="tok-p">(</span><span class="tok-nv"><<</span><span class="tok-w"> </span><span class="tok-mi">8</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; (Some 128)</span>
<span class="tok-p">(</span><span class="tok-nv">>></span><span class="tok-w"> </span><span class="tok-mi">128</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; (Some 8)</span>
<span class="tok-p">(</span><span class="tok-nv">>></span><span class="tok-w"> </span><span class="tok-mi">-128</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; (Some -8)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>If 2nd argument is greater or equal to 2<sup>64</sup>, then these function return None.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_mathematical_operations">9. Mathematical Operations</h2>
<div class="sectionbody">
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-> (Int Int) (Option Int)))</span>
<span class="tok-p">(</span><span class="tok-nv">pow</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-w"> </span><span class="tok-mi">20</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; (Some 100000000000000000000)</span>
<span class="tok-c1">; (Pure (-> (Int) (Option Int)))</span>
<span class="tok-p">(</span><span class="tok-nb">sqrt</span><span class="tok-w"> </span><span class="tok-mi">16</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; (Some 4)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>If <em>pow</em>'s exponent portion is greater or equal to 2<sup>32</sup>, then <em>pow</em> returns None.</p>
</div>
<div class="paragraph">
<p>If <em>sqrt</em>'s argument is less than 0. then <em>sqrt</em> returns None.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_algebraic_data_type">10. Algebraic Data Type</h2>
<div class="sectionbody">
<div class="paragraph">
<p>Algebraic data type can be defined as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; in BLisp</span>
<span class="tok-p">(</span><span class="tok-nv">data</span><span class="tok-w"> </span><span class="tok-nv">Gender</span><span class="tok-w"> </span><span class="tok-c1">; type name</span>
<span class="tok-w"> </span><span class="tok-nv">Male</span><span class="tok-w"> </span><span class="tok-c1">; value</span>
<span class="tok-w"> </span><span class="tok-nv">Female</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; value</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Type name’s and its value’s first character must be uppercase.
This is equivalent to Rust’s following code.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="rust"><span></span><span class="tok-c1">// in Rust</span>
<span class="tok-k">enum</span> <span class="tok-nc">Gender</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w"> </span><span class="tok-n">Male</span><span class="tok-p">,</span>
<span class="tok-w"> </span><span class="tok-n">Female</span>
<span class="tok-p">}</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Each element can have values as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; in BLisp</span>
<span class="tok-p">(</span><span class="tok-nv">data</span><span class="tok-w"> </span><span class="tok-nv">Dim2</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Dim2</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; Dim2 has integers</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Dim2 can be instantiated as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">Dim2</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-w"> </span><span class="tok-mi">20</span><span class="tok-p">)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This type is equivalent to Rust’s following type.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="rust"><span></span><span class="tok-c1">// in Rust</span>
<span class="tok-k">use</span><span class="tok-w"> </span><span class="tok-n">num_bigint</span>::<span class="tok-n">BigInt</span><span class="tok-p">;</span>
<span class="tok-k">enum</span> <span class="tok-nc">Dim2</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w"> </span><span class="tok-n">Dim2</span><span class="tok-p">(</span><span class="tok-n">BigInt</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">BigInt</span><span class="tok-p">)</span>
<span class="tok-p">}</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_generics">11. Generics</h2>
<div class="sectionbody">
<div class="paragraph">
<p>Option and Result types are defined internally.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">data</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Option</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-nv">None</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nv">data</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Result</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-w"> </span><span class="tok-nv">e</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Ok</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Err</span><span class="tok-w"> </span><span class="tok-nv">e</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p><em>t</em> and <em>e</em> are type variables.
This code is equivalent to Rust’s following code.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="rust"><span></span><span class="tok-c1">// in Rust</span>
<span class="tok-k">enum</span> <span class="tok-nb">Option</span><span class="tok-o"><</span><span class="tok-n">T</span><span class="tok-o">></span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w"> </span><span class="tok-nb">Some</span><span class="tok-p">(</span><span class="tok-n">T</span><span class="tok-p">),</span>
<span class="tok-w"> </span><span class="tok-nb">None</span><span class="tok-p">,</span>
<span class="tok-p">}</span>
<span class="tok-k">enum</span> <span class="tok-nb">Result</span><span class="tok-o"><</span><span class="tok-n">T</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">E</span><span class="tok-o">></span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w"> </span><span class="tok-nb">Ok</span><span class="tok-p">(</span><span class="tok-n">T</span><span class="tok-p">),</span>
<span class="tok-w"> </span><span class="tok-nb">Err</span><span class="tok-p">(</span><span class="tok-n">E</span><span class="tok-p">),</span>
<span class="tok-p">}</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>List type is a built-in type as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">data</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">List</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">List</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-p">))</span>
<span class="tok-w"> </span><span class="tok-no">Nil</span><span class="tok-p">)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>So, following 2 lists are equivalent.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-w"> </span><span class="tok-no">Nil</span><span class="tok-p">)))</span>
<span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-p">)</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_generic_function">12. Generic Function</h2>
<div class="sectionbody">
<div class="paragraph">
<p><em>car</em> and <em>cdr</em> are internally defined generic functions.
These definitions are as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nb">car</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-no">t</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Option</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-p">)))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-nv">x</span>
<span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-w"> </span><span class="tok-nv">_</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-p">))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-nv">None</span><span class="tok-p">)))</span>
<span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nb">cdr</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-no">t</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-no">t</span><span class="tok-p">)))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-nv">x</span>
<span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">())))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p><em>t</em> is a type variable. These functions can be used as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">car</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-mi">3</span><span class="tok-w"> </span><span class="tok-mi">8</span><span class="tok-w"> </span><span class="tok-mi">9</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; returns (Some 3)</span>
<span class="tok-p">(</span><span class="tok-nb">cdr</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-mi">8</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; returns '(10 4)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Normal and type variables' first character must be lowercase.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_if_expression">13. If Expression</h2>
<div class="sectionbody">
<div class="paragraph">
<p>Straightforward.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-k">if</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb"><</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-w"> </span><span class="tok-mi">20</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">())</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_match_expression">14. Match Expression</h2>
<div class="sectionbody">
<div class="paragraph">
<p>A list can be matched as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-w"> </span><span class="tok-nv">_</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-o">'</span><span class="tok-p">()</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>The expression</p>
</div>
<div class="literalblock">
<div class="content">
<pre>(Cons n _)</pre>
</div>
</div>
<div class="paragraph">
<p>is a pattern.
If the pattern is matched to '(1 2 3), 1 is assigned to a variable <em>n</em>. Then, <em>n</em>, namely 1, is returned.</p>
</div>
<div class="paragraph">
<p>This is an example of pattern matching of tuple.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-nv">[1</span><span class="tok-w"> </span><span class="tok-nv">3]</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">[x</span><span class="tok-w"> </span><span class="tok-nv">y]</span><span class="tok-w"> </span><span class="tok-nv">[y</span><span class="tok-w"> </span><span class="tok-nv">x]</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This code swap 1st and 2nd elements of the tuple.</p>
</div>
<div class="paragraph">
<p>Integer values can be also used for pattern matching.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-mi">20</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-mi">20</span><span class="tok-w"> </span><span class="tok-nv">true</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-nv">false</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>More complex example is a as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-nv">[</span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">true]</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">[</span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">false]</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">[</span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">true]</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>BLisp checks exhaustively of pattern.
So, following code will be rejected.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-o">'</span><span class="tok-p">()</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">))</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_let_expression">15. Let Expression</h2>
<div class="sectionbody">
<div class="paragraph">
<p>Let expression is used to bind variables as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-k">let</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">y</span><span class="tok-w"> </span><span class="tok-mi">20</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; x is 10, y is 20</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">))</span>
<span class="tok-p">(</span><span class="tok-k">let</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">)))</span><span class="tok-w"> </span><span class="tok-c1">; x = 10, x = x * x, x = x * x</span>
<span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Destructuring can be also performed as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-k">let</span><span class="tok-w"> </span><span class="tok-p">(((</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-p">)))</span><span class="tok-w"> </span><span class="tok-c1">; x is 10</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">))</span>
<span class="tok-p">(</span><span class="tok-k">let</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">[x</span><span class="tok-w"> </span><span class="tok-nv">y]</span><span class="tok-w"> </span><span class="tok-nv">[10</span><span class="tok-w"> </span><span class="tok-nv">20]</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; x is 10, y is 20</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">))</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_lambda_expression">16. Lambda Expression</h2>
<div class="sectionbody">
<div class="paragraph">
<p>Lambda expression is defined as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-k">lambda</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This lambda takes 2 integers and return the multiplication.
Applying arguments to this is simple as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">((</span><span class="tok-k">lambda</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-w"> </span><span class="tok-mi">20</span><span class="tok-p">)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Every lambda expression is Pure.
IO functions cannot be called in any lambda expressions.</p>
</div>
<div class="paragraph">
<p><em>map</em> and <em>fold</em> functions are internally defined as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nb">map</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">a</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">b</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-nv">a</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-nv">b</span><span class="tok-p">)))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-nv">x</span>
<span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-nv">h</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-nv">h</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">map</span><span class="tok-w"> </span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">)))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">())))</span>
<span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nv">fold</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-nv">init</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">a</span><span class="tok-w"> </span><span class="tok-nv">b</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">b</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-nv">b</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-nv">a</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-nv">b</span><span class="tok-p">))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-nv">x</span>
<span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-nv">h</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">fold</span><span class="tok-w"> </span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-nv">h</span><span class="tok-w"> </span><span class="tok-nv">init</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-nv">init</span><span class="tok-p">)))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p><em>map</em> can be used to apply functions to elements of a list as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; square each element</span>
<span class="tok-p">(</span><span class="tok-k">let</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">l</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-p">))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-k">lambda</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">))))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">map</span><span class="tok-w"> </span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p><em>fold</em> can be used to calculate over elements of a list.
For example, summation can be computed as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; summation</span>
<span class="tok-p">(</span><span class="tok-k">let</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">l</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-mi">20</span><span class="tok-w"> </span><span class="tok-mi">50</span><span class="tok-w"> </span><span class="tok-mi">60</span><span class="tok-p">))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-k">lambda</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">+</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">))))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">fold</span><span class="tok-w"> </span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; 0 is an initial value</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Of course, this can be written as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; summation</span>
<span class="tok-p">(</span><span class="tok-nv">fold</span><span class="tok-w"> </span><span class="tok-nb">+</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-mi">20</span><span class="tok-w"> </span><span class="tok-mi">50</span><span class="tok-w"> </span><span class="tok-mi">60</span><span class="tok-p">))</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_macro">17. Macro</h2>
<div class="sectionbody">
<div class="paragraph">
<p>Macros can be defined by <code>macro</code>.
Each rule consists of a pattern and a template, and the first matching rule is expanded.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">macro</span><span class="tok-w"> </span><span class="tok-nv">add</span>
<span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">add</span><span class="tok-w"> </span><span class="tok-nv">$e1</span><span class="tok-w"> </span><span class="tok-nv">$e2</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">+</span><span class="tok-w"> </span><span class="tok-nv">$e1</span><span class="tok-w"> </span><span class="tok-nv">$e2</span><span class="tok-p">))</span>
<span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">add</span><span class="tok-w"> </span><span class="tok-nv">$e1</span><span class="tok-w"> </span><span class="tok-nv">$e2</span><span class="tok-w"> </span><span class="tok-nv">$e3</span><span class="tok-w"> </span><span class="tok-o">...</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">+</span><span class="tok-w"> </span><span class="tok-nv">$e1</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">add</span><span class="tok-w"> </span><span class="tok-nv">$e2</span><span class="tok-w"> </span><span class="tok-nv">$e3</span><span class="tok-w"> </span><span class="tok-o">...</span><span class="tok-p">))))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Identifiers beginning with <code>$</code> are pattern variables.
They are substituted with the expressions matched at the call site.
<code>…​</code> can be used after a pattern variable or a template fragment to match and expand the remaining arguments.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">add</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; 3</span>
<span class="tok-p">(</span><span class="tok-nv">add</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-w"> </span><span class="tok-mi">5</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; 15</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Macros can also generate expressions that introduce local bindings.
For example, a temporary variable can be introduced in a lambda expression.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">macro</span><span class="tok-w"> </span><span class="tok-nv">with_tmp</span>
<span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-nv">$x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-k">lambda</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">tmp</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">+</span><span class="tok-w"> </span><span class="tok-nv">tmp</span><span class="tok-w"> </span><span class="tok-nv">$x</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)))</span>
<span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nv">test</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">tmp</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">with_tmp</span><span class="tok-w"> </span><span class="tok-nv">tmp</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>BLisp macros are hygienic for local binders introduced by macro templates.
Variables introduced by <code>lambda</code> arguments, <code>let</code> bindings, and <code>match</code> pattern variables are renamed to fresh internal names during expansion, so they do not capture variables from the call site.
Top-level names such as <code>defun</code>, <code>export</code>, and <code>data</code> definitions are not renamed automatically.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_string_and_character">18. String and Character</h2>
<div class="sectionbody">
<div class="paragraph">
<p><em>chars</em> converts String to (List Char).</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-> (String) (List Char)))</span>
<span class="tok-p">(</span><span class="tok-nv">chars</span><span class="tok-w"> </span><span class="tok-s">"Hello"</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; '(`H` `e` `l` `l` `o`)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p><em>str</em> converts (List Char) to String.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-> ((List Char)) String))</span>
<span class="tok-p">(</span><span class="tok-nv">str</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-o">`</span><span class="tok-nv">H</span><span class="tok-o">`</span><span class="tok-w"> </span><span class="tok-o">`</span><span class="tok-nv">e</span><span class="tok-o">`</span><span class="tok-w"> </span><span class="tok-o">`</span><span class="tok-nv">l</span><span class="tok-o">`</span><span class="tok-w"> </span><span class="tok-o">`</span><span class="tok-nv">l</span><span class="tok-o">`</span><span class="tok-w"> </span><span class="tok-o">`</span><span class="tok-nv">o</span><span class="tok-o">`</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; "Hello"</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_foreign_function_interface">19. Foreign Function Interface</h2>
<div class="sectionbody">
<div class="paragraph">
<p><em>blisp::embedded</em> is a macro for foreign function interface.
By using this, Rust’s functions can be called from BLisp easily.</p>
</div>
<div class="paragraph">
<p>For example, first of all, define a Rust function as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="rust"><span></span><span class="tok-k">use</span><span class="tok-w"> </span><span class="tok-n">blisp</span>::<span class="tok-n">embedded</span><span class="tok-p">;</span>
<span class="tok-k">use</span><span class="tok-w"> </span><span class="tok-n">num_bigint</span>::<span class="tok-p">{</span><span class="tok-n">BigInt</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">ToBigInt</span><span class="tok-p">};</span>
<span class="tok-cp">#[embedded]</span>
<span class="tok-k">fn</span> <span class="tok-nf">add_four_ints</span><span class="tok-p">(</span><span class="tok-n">a</span>: <span class="tok-nc">BigInt</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">b</span>: <span class="tok-p">(</span><span class="tok-n">BigInt</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">BigInt</span><span class="tok-p">),</span><span class="tok-w"> </span><span class="tok-n">c</span>: <span class="tok-nb">Option</span><span class="tok-o"><</span><span class="tok-n">BigInt</span><span class="tok-o">></span><span class="tok-p">)</span><span class="tok-w"> </span>-> <span class="tok-nb">Result</span><span class="tok-o"><</span><span class="tok-n">BigInt</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-nb">String</span><span class="tok-o">></span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w"> </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-k">mut</span><span class="tok-w"> </span><span class="tok-n">result</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-n">a</span><span class="tok-w"> </span><span class="tok-o">+</span><span class="tok-w"> </span><span class="tok-n">b</span><span class="tok-p">.</span><span class="tok-mi">0</span><span class="tok-w"> </span><span class="tok-o">+</span><span class="tok-w"> </span><span class="tok-n">b</span><span class="tok-p">.</span><span class="tok-mi">1</span><span class="tok-p">;</span>
<span class="tok-w"> </span><span class="tok-k">if</span><span class="tok-w"> </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-nb">Some</span><span class="tok-p">(</span><span class="tok-n">n</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-n">c</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w"> </span><span class="tok-n">result</span><span class="tok-w"> </span><span class="tok-o">+=</span><span class="tok-w"> </span><span class="tok-n">n</span><span class="tok-p">;</span>
<span class="tok-w"> </span><span class="tok-p">}</span>
<span class="tok-w"> </span><span class="tok-nb">Ok</span><span class="tok-p">(</span><span class="tok-n">result</span><span class="tok-p">)</span>
<span class="tok-p">}</span></code></pre>
</div>
</div>
<div class="paragraph">
<p><em>blisp::embedded</em> macro generates a type definition for FFI.
This function can be called from BLisp as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nv">call_add_four_ints</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">n</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">IO</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">Option</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Result</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-w"> </span><span class="tok-nv">String</span><span class="tok-p">)))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">add_four_ints</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-nv">[2</span><span class="tok-w"> </span><span class="tok-nv">3]</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>To register FFIs, a vector of the definition generated by <em>embedded</em> macro
must be passed to <em>blisp::init</em> as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="rust"><span></span><span class="tok-c1">// add_for_ints</span>
<span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">code</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-s">"(export call_add_four_ints (n)</span>
<span class="tok-s"> (IO (-> ((Option Int)) (Result Int String)))</span>
<span class="tok-s"> (add_four_ints 1 [2 3] n)</span>
<span class="tok-s">)"</span><span class="tok-p">;</span>
<span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">exprs</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-n">blisp</span>::<span class="tok-n">init</span><span class="tok-p">(</span><span class="tok-n">code</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-fm">vec!</span><span class="tok-p">[</span><span class="tok-nb">Box</span>::<span class="tok-n">new</span><span class="tok-p">(</span><span class="tok-n">AddFourInts</span><span class="tok-p">)]).</span><span class="tok-n">unwrap</span><span class="tok-p">();</span>
<span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">ctx</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-n">blisp</span>::<span class="tok-n">typing</span><span class="tok-p">(</span><span class="tok-n">exprs</span><span class="tok-p">).</span><span class="tok-n">unwrap</span><span class="tok-p">();</span>
<span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">result</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-n">blisp</span>::<span class="tok-n">eval</span><span class="tok-p">(</span><span class="tok-s">"(call_add_four_ints (Some 4))"</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-o">&</span><span class="tok-n">ctx</span><span class="tok-p">).</span><span class="tok-n">unwrap</span><span class="tok-p">();</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>The function name is <em>add_four_ints</em>, then <em>AddFourInts</em>, which is camel case,
must be passed to <em>blisp::init</em> capsulated by <em>Box</em> and <em>Vec</em>.</p>
</div>
<div class="paragraph">
<p>FFIs in Rust take and return only types described as follows.
Other types, like <em>Vec<u64></em>, are not supported,
but <em>Vec<Option<bool>></em> is accepted.
Types between BLisp and Rust are automatically converted by
the function generated by <em>embedded</em> macro.</p>
</div>
<table class="tableblock frame-all grid-all stretch">
<caption class="title">Table 1. Type Conversion between BLisp and Rust</caption>
<colgroup>
<col style="width: 50%;">
<col style="width: 50%;">
</colgroup>
<thead>
<tr>
<th class="tableblock halign-left valign-top">BLisp</th>
<th class="tableblock halign-left valign-top">Rust</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>Int</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>BigInt</em></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>Bool</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>bool</em></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>Char</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>char</em></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>String</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>String</em></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>'(T)</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>Vec<T></em></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>[T0, T1]</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>(T0, T1)</em></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>(Option T)</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>Option<T></em></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>(Result T E)</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>Result<T, E></em></p></td>
</tr>
</tbody>
</table>
<div class="paragraph">
<p>Note that every FFI is treated as IO functions.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_transpilation_to_coq_experimental">20. Transpilation to Coq (Experimental)</h2>
<div class="sectionbody">
<div class="paragraph">
<p>BLisp experimentally implements a transpiler to Coq.
It can be invoked by calling <em>blisp::transpile</em> as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="coq"><span></span><span class="tok-k">let</span> <span class="tok-n">expr</span> <span class="tok-o">=</span> <span class="tok-s2">"</span>
<span class="tok-s2">(defun snoc (l y)</span>
<span class="tok-s2">(Pure (-> (</span>
<span class="tok-s2"> '(t) t)</span>
<span class="tok-s2">'(t)))</span>
<span class="tok-s2">(match l</span>
<span class="tok-s2"> (nil (Cons y nil))</span>
<span class="tok-s2"> ((Cons h b) (Cons h (snoc b y)))))</span>
<span class="tok-s2">(defun rev (l)</span>
<span class="tok-s2">(Pure (-> (</span>
<span class="tok-s2"> '(t))</span>
<span class="tok-s2">'(t)))</span>
<span class="tok-s2">(match l</span>
<span class="tok-s2"> (nil nil)</span>
<span class="tok-s2"> ((Cons h t) (snoc (rev t) h))))</span>
<span class="tok-s2"> "</span><span class="tok-o">;</span>
<span class="tok-k">let</span> <span class="tok-n">exprs</span> <span class="tok-o">=</span> <span class="tok-n">blisp</span><span class="tok-o">::</span><span class="tok-n">init</span><span class="tok-o">(</span><span class="tok-n">expr</span><span class="tok-o">,</span> <span class="tok-n">vec</span><span class="tok-o">!</span><span class="tok-bp">[]</span><span class="tok-o">).</span><span class="tok-n">unwrap</span><span class="tok-bp">()</span><span class="tok-o">;</span>
<span class="tok-k">let</span> <span class="tok-n">ctx</span> <span class="tok-o">=</span> <span class="tok-n">blisp</span><span class="tok-o">::</span><span class="tok-n">typing</span><span class="tok-o">(</span><span class="tok-n">exprs</span><span class="tok-o">).</span><span class="tok-n">unwrap</span><span class="tok-bp">()</span><span class="tok-o">;</span>
<span class="tok-n">println</span><span class="tok-o">!(</span><span class="tok-s2">"{}"</span><span class="tok-o">,</span> <span class="tok-n">blisp</span><span class="tok-o">::</span><span class="tok-n">transpile</span><span class="tok-o">(&</span><span class="tok-n">ctx</span><span class="tok-o">));</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This outputs Coq code as follows.
It includes as well as the prelude of BLisp.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="coq"><span></span><span class="tok-kn">Require</span> <span class="tok-kn">Import</span> <span class="tok-n">ZArith</span><span class="tok-o">.</span>
<span class="tok-kn">Require</span> <span class="tok-kn">Import</span> <span class="tok-n">Coq.Lists.List</span><span class="tok-o">.</span>
<span class="tok-kn">Inductive</span> <span class="tok-n">Option</span> <span class="tok-o">(</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">):</span> <span class="tok-kt">Type</span> <span class="tok-o">:=</span>
<span class="tok-o">|</span> <span class="tok-n">Some</span> <span class="tok-o">(</span><span class="tok-n">x0</span><span class="tok-o">:</span> <span class="tok-n">t</span><span class="tok-o">)</span>
<span class="tok-o">|</span> <span class="tok-n">None</span><span class="tok-o">.</span>
<span class="tok-kn">Arguments</span> <span class="tok-n">Some</span><span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">}.</span>
<span class="tok-kn">Arguments</span> <span class="tok-n">None</span><span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">}.</span>
<span class="tok-kn">Inductive</span> <span class="tok-n">Result</span> <span class="tok-o">(</span><span class="tok-n">t</span> <span class="tok-n">e</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">):</span> <span class="tok-kt">Type</span> <span class="tok-o">:=</span>
<span class="tok-o">|</span> <span class="tok-n">Ok</span> <span class="tok-o">(</span><span class="tok-n">x0</span><span class="tok-o">:</span> <span class="tok-n">t</span><span class="tok-o">)</span>
<span class="tok-o">|</span> <span class="tok-n">Err</span> <span class="tok-o">(</span><span class="tok-n">x0</span><span class="tok-o">:</span> <span class="tok-n">e</span><span class="tok-o">).</span>
<span class="tok-kn">Arguments</span> <span class="tok-n">Ok</span><span class="tok-o">{</span><span class="tok-n">t</span> <span class="tok-n">e</span><span class="tok-o">}.</span>
<span class="tok-kn">Arguments</span> <span class="tok-n">Err</span><span class="tok-o">{</span><span class="tok-n">t</span> <span class="tok-n">e</span><span class="tok-o">}.</span>
<span class="tok-kn">Definition</span> <span class="tok-n">car</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">x</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">Option</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">x</span> <span class="tok-k">with</span>
<span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">n</span> <span class="tok-o">_)</span> <span class="tok-o">=></span> <span class="tok-o">(</span><span class="tok-n">Some</span> <span class="tok-n">n</span><span class="tok-o">)</span>
<span class="tok-o">|</span> <span class="tok-o">_</span> <span class="tok-o">=></span> <span class="tok-o">(</span><span class="tok-n">None</span><span class="tok-o">)</span>
<span class="tok-k">end</span><span class="tok-o">.</span>
<span class="tok-kn">Definition</span> <span class="tok-n">cdr</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">x</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">x</span> <span class="tok-k">with</span>
<span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-o">_</span> <span class="tok-n">l</span><span class="tok-o">)</span> <span class="tok-o">=></span> <span class="tok-n">l</span>
<span class="tok-o">|</span> <span class="tok-o">_</span> <span class="tok-o">=></span> <span class="tok-n">nil</span>
<span class="tok-k">end</span><span class="tok-o">.</span>
<span class="tok-kn">Definition</span> <span class="tok-n">filter</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">f</span><span class="tok-o">:</span> <span class="tok-n">t</span> <span class="tok-o">-></span> <span class="tok-n">bool</span><span class="tok-o">)</span> <span class="tok-o">(</span><span class="tok-n">x</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-o">(</span><span class="tok-n">reverse</span> <span class="tok-o">(</span><span class="tok-n">filter'</span> <span class="tok-n">f</span> <span class="tok-n">x</span> <span class="tok-n">nil</span> <span class="tok-o">)</span> <span class="tok-o">).</span>
<span class="tok-kn">Fixpoint</span> <span class="tok-n">filter'</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">f</span><span class="tok-o">:</span> <span class="tok-n">t</span> <span class="tok-o">-></span> <span class="tok-n">bool</span><span class="tok-o">)</span> <span class="tok-o">(</span><span class="tok-n">x</span> <span class="tok-n">l</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">x</span> <span class="tok-k">with</span>
<span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">a</span><span class="tok-o">)</span> <span class="tok-o">=></span> <span class="tok-k">match</span> <span class="tok-o">(</span><span class="tok-n">f</span> <span class="tok-n">h</span> <span class="tok-o">)</span> <span class="tok-k">with</span>
<span class="tok-o">|</span> <span class="tok-bp">true</span> <span class="tok-o">=></span> <span class="tok-o">(</span><span class="tok-n">filter'</span> <span class="tok-n">f</span> <span class="tok-n">a</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">l</span><span class="tok-o">)</span> <span class="tok-o">)</span>
<span class="tok-o">|</span> <span class="tok-bp">false</span> <span class="tok-o">=></span> <span class="tok-o">(</span><span class="tok-n">filter'</span> <span class="tok-n">f</span> <span class="tok-n">a</span> <span class="tok-n">l</span> <span class="tok-o">)</span>
<span class="tok-k">end</span>
<span class="tok-o">|</span> <span class="tok-o">_</span> <span class="tok-o">=></span> <span class="tok-n">l</span>
<span class="tok-k">end</span><span class="tok-o">.</span>
<span class="tok-kn">Fixpoint</span> <span class="tok-k">fold</span> <span class="tok-o">{</span><span class="tok-n">a</span> <span class="tok-n">b</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">f</span><span class="tok-o">:</span> <span class="tok-n">a</span> <span class="tok-o">-></span> <span class="tok-n">b</span> <span class="tok-o">-></span> <span class="tok-n">b</span><span class="tok-o">)</span> <span class="tok-o">(</span><span class="tok-n">init</span><span class="tok-o">:</span> <span class="tok-n">b</span><span class="tok-o">)</span> <span class="tok-o">(</span><span class="tok-n">x</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">a</span><span class="tok-o">):</span> <span class="tok-n">b</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">x</span> <span class="tok-k">with</span>
<span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">l</span><span class="tok-o">)</span> <span class="tok-o">=></span> <span class="tok-o">(</span><span class="tok-k">fold</span> <span class="tok-n">f</span> <span class="tok-o">(</span><span class="tok-n">f</span> <span class="tok-n">h</span> <span class="tok-n">init</span> <span class="tok-o">)</span> <span class="tok-n">l</span> <span class="tok-o">)</span>
<span class="tok-o">|</span> <span class="tok-o">_</span> <span class="tok-o">=></span> <span class="tok-n">init</span>
<span class="tok-k">end</span><span class="tok-o">.</span>
<span class="tok-kn">Fixpoint</span> <span class="tok-n">map</span> <span class="tok-o">{</span><span class="tok-n">a</span> <span class="tok-n">b</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">f</span><span class="tok-o">:</span> <span class="tok-n">a</span> <span class="tok-o">-></span> <span class="tok-n">b</span><span class="tok-o">)</span> <span class="tok-o">(</span><span class="tok-n">x</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">a</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">b</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">x</span> <span class="tok-k">with</span>
<span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">l</span><span class="tok-o">)</span> <span class="tok-o">=></span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-o">(</span><span class="tok-n">f</span> <span class="tok-n">h</span> <span class="tok-o">)</span> <span class="tok-o">(</span><span class="tok-n">map</span> <span class="tok-n">f</span> <span class="tok-n">l</span> <span class="tok-o">))</span>
<span class="tok-o">|</span> <span class="tok-o">_</span> <span class="tok-o">=></span> <span class="tok-n">nil</span>
<span class="tok-k">end</span><span class="tok-o">.</span>
<span class="tok-kn">Fixpoint</span> <span class="tok-n">rev</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">l</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">l</span> <span class="tok-k">with</span>
<span class="tok-o">|</span> <span class="tok-n">nil</span> <span class="tok-o">=></span> <span class="tok-n">nil</span>
<span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">t</span><span class="tok-o">)</span> <span class="tok-o">=></span> <span class="tok-o">(</span><span class="tok-n">snoc</span> <span class="tok-o">(</span><span class="tok-n">rev</span> <span class="tok-n">t</span> <span class="tok-o">)</span> <span class="tok-n">h</span> <span class="tok-o">)</span>
<span class="tok-k">end</span><span class="tok-o">.</span>
<span class="tok-kn">Definition</span> <span class="tok-n">reverse</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">x</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-o">(</span><span class="tok-n">reverse'</span> <span class="tok-n">x</span> <span class="tok-n">nil</span> <span class="tok-o">).</span>
<span class="tok-kn">Fixpoint</span> <span class="tok-n">reverse'</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">x</span> <span class="tok-n">l</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">x</span> <span class="tok-k">with</span>
<span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">a</span><span class="tok-o">)</span> <span class="tok-o">=></span> <span class="tok-o">(</span><span class="tok-n">reverse'</span> <span class="tok-n">a</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">l</span><span class="tok-o">)</span> <span class="tok-o">)</span>
<span class="tok-o">|</span> <span class="tok-o">_</span> <span class="tok-o">=></span> <span class="tok-n">l</span>
<span class="tok-k">end</span><span class="tok-o">.</span>
<span class="tok-kn">Fixpoint</span> <span class="tok-n">snoc</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">l</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">)</span> <span class="tok-o">(</span><span class="tok-n">y</span><span class="tok-o">:</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">l</span> <span class="tok-k">with</span>
<span class="tok-o">|</span> <span class="tok-n">nil</span> <span class="tok-o">=></span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">y</span> <span class="tok-n">nil</span><span class="tok-o">)</span>
<span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">b</span><span class="tok-o">)</span> <span class="tok-o">=></span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-o">(</span><span class="tok-n">snoc</span> <span class="tok-n">b</span> <span class="tok-n">y</span> <span class="tok-o">))</span>
<span class="tok-k">end</span><span class="tok-o">.</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Not that this transpiler is experimental.
So, Coq cannot interpret some outputs.
Please fix it manually when you encounter that situation.
It is probably easy.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_examples">21. Examples</h2>
<div class="sectionbody">
<div class="sect2">
<h3 id="_reverse">21.1. Reverse</h3>
<div class="paragraph">
<p><em>reverse</em> is a internally defined function. It reverses order of a list.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">reverse</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-w"> </span><span class="tok-mi">5</span><span class="tok-w"> </span><span class="tok-mi">6</span><span class="tok-w"> </span><span class="tok-mi">7</span><span class="tok-w"> </span><span class="tok-mi">8</span><span class="tok-w"> </span><span class="tok-mi">9</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This outputs as follows.</p>
</div>
<div class="literalblock">
<div class="content">
<pre>'(9 8 7 6 5 4 3 2 1)</pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_filter">21.2. Filter</h3>
<div class="paragraph">
<p><em>filter</em> is a internally defined function. It filters the elements in a list.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">filter</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-k">lambda</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">=</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">%</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-w"> </span><span class="tok-mi">5</span><span class="tok-w"> </span><span class="tok-mi">6</span><span class="tok-w"> </span><span class="tok-mi">7</span><span class="tok-w"> </span><span class="tok-mi">8</span><span class="tok-w"> </span><span class="tok-mi">9</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This outputs as follows.</p>
</div>
<div class="literalblock">
<div class="content">
<pre>'(2 4 6 8)</pre>
</div>
</div>
<div class="paragraph">
<p><em>filter</em>'s type is as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span>
<span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-no">t</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">Bool</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; take a function</span>
<span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-no">t</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; take a list</span>
<span class="tok-w"> </span><span class="tok-o">'</span><span class="tok-p">(</span><span class="tok-no">t</span><span class="tok-p">)))</span><span class="tok-w"> </span><span class="tok-c1">; return a list</span></code></pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_factorial">21.3. Factorial</h3>
<div class="paragraph">
<p>Tail call factorial can be coded as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nv">factorial</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">n</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">fact</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">))</span>
<span class="tok-p">(</span><span class="tok-nb">defun</span><span class="tok-w"> </span><span class="tok-nv">fact</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">n</span><span class="tok-w"> </span><span class="tok-nv">total</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-></span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">))</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-k">if</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb"><=</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">)</span>
<span class="tok-w"> </span><span class="tok-nv">total</span>
<span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">fact</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">-</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-w"> </span><span class="tok-nv">total</span><span class="tok-p">))))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This function can be called as follows.</p>
</div>
<div class="literalblock">
<div class="content">
<pre>>> (factorial 10)
3628800
>>
>> (factorial 1000)
402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
>>
>> (factorial 100)
93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
>>
>> (factorial 500)
1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000</pre>
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