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improved indentation and whitespace for markdown code blocks

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All code blocks in markdown have been intended by at least 4 spaces.

We add `--tab-stop=8` to all `pandoc(1)` executions in order to set
a better tab stop indentation, especially for tab intended code blocks.

Changed `bin/pandoc-wrapper.sh` VERSION from "1.5.3 2024-03-26"
to "1.6 2024-03-31".

Fixed `1991/brnstnd/sorta.README.md` so that the sorta code
is code blocks.

Removed unneeded paragraph group in copyright in `inc/footer.default.html`.

Fixed excess whitespace after list Author on entry `index.html` page.

Changed `bin/output-index-author.sh` VERSION from "1.5.2 2024-03-26"
to "1.6 2024-03-31".

Performed `make www` to perform the above and test under macOS.

TODO: Fix the problem of the initial line of code being extra intended.
TODO: Fix excess whitespace around code that is inline.
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Landon Curt Noll committed 2024-04-01 04:48:48 -07:00
1 parent b84c27ce02
commit a996f8d2b8
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2012/tromp/index.html
+124 -125
View File
@@ -132,8 +132,7 @@
<h2 id="author"><a name="author"></a>Author:</h2>
<ul>
<li>Name: <a href="../../authors.html#John_Tromp">John Tromp</a><br>
Location: <a href="../../location.html#US">US</a> - <em>United States of America</em> (<em>United States</em>)
<br><br></li>
Location: <a href="../../location.html#US">US</a> - <em>United States of America</em> (<em>United States</em>)</li>
</ul>
<!-- END: next line ends content generated by: bin/output-index-author.sh -->
@@ -142,21 +141,21 @@ Location: <a href="../../location.html#US">US</a> - <em>United States of America
<!-- START: this line starts content for HTML phase 21 by: bin/pandoc-wrapper.sh via bin/md2html.sh -->
<h2 id="to-build">To build:</h2>
<div class="sourceCode" id="cb1"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">make</span> all <span class="co"># On a 64-bit machine (default)</span></span>
<div class="sourceCode" id="cb1"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a> <span class="fu">make</span> all <span class="co"># On a 64-bit machine (default)</span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">make</span> tromp32 <span class="co"># On a 32-bit machine</span></span></code></pre></div>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">make</span> tromp32 <span class="co"># On a 32-bit machine</span></span></code></pre></div>
<h3 id="bugs-and-misfeatures">Bugs and (Mis)features:</h3>
<p>The current status of this entry is:</p>
<pre><code>STATUS: INABIAF - please **DO NOT** fix</code></pre>
<pre><code> STATUS: INABIAF - please **DO NOT** fix</code></pre>
<p>For more detailed information see <a href="../../bugs.html#2012_tromp">2012 tromp bugs</a>.</p>
<h2 id="to-use">To use:</h2>
<div class="sourceCode" id="cb3"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./tromp</span> <span class="pp">[-</span><span class="ss">b</span><span class="pp">]</span></span></code></pre></div>
<div class="sourceCode" id="cb3"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">./tromp</span> <span class="pp">[-</span><span class="ss">b</span><span class="pp">]</span></span></code></pre></div>
<p>Use <code>./tromp32</code> as you would <code>./tromp</code> if on a 32-bit machine.</p>
<h2 id="to-use-1">To use:</h2>
<div class="sourceCode" id="cb4"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="fu">cat</span> ascii-prog.blc data <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="fu">cat</span> binary-prog.Blc data <span class="kw">|</span> <span class="ex">./tromp</span></span></code></pre></div>
<div class="sourceCode" id="cb4"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a> <span class="fu">cat</span> ascii-prog.blc data <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">cat</span> binary-prog.Blc data <span class="kw">|</span> <span class="ex">./tromp</span></span></code></pre></div>
<h2 id="try">Try:</h2>
<div class="sourceCode" id="cb5"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./try.sh</span></span></code></pre></div>
<div class="sourceCode" id="cb5"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">./try.sh</span></span></code></pre></div>
<h2 id="judges-remarks">Judges’ remarks:</h2>
<p>The judges dare to say that the data files this entry is processing
are more obfuscated than the entry itself.</p>
@@ -196,10 +195,10 @@ under 6K in size.</p>
With one (arbitrary) argument, it runs in bit mode, using only the least significant
bit of input, and using characters <code>0</code> and <code>1</code> for output.</p>
<p>The program uses the following exit codes:</p>
<pre><code>0: OK; result is a finite list
5: Out of term space
6: Out of memory
1,2,3,4,8,9: result not in list form</code></pre>
<pre><code> 0: OK; result is a finite list
5: Out of term space
6: Out of memory
1,2,3,4,8,9: result not in list form</code></pre>
<p>The size of the term space is fixed at compile time with <code>-DA</code>.</p>
<h3 id="a-half-byte-cat">A half byte <code>cat</code></h3>
<p>The shortest (closed) lambda calculus term is <code>\x x (\ 1</code> in <a href="https://en.wikipedia.org/wiki/De_Bruijn_notation">De Bruijn
@@ -207,23 +206,23 @@ notation</a>) which is the
identity function. When its encoding <code>0010</code> is fed into the universal machine,
it will simply copy the input to the output (well, not that simply, since each
byte is smashed to bits and rebuilt from scratch). Voila: a half byte cat:</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> echo <span class="st">&quot; Hello, world&quot;</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a><span class="ex">Hello,</span> world</span></code></pre></div>
<div class="sourceCode" id="cb7"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> echo <span class="st">&quot; Hello, world&quot;</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">Hello,</span> world</span></code></pre></div>
<p>Since the least significant 4 bits of the first byte are just arbitrary padding
that is ignored by the program, any character from ASCII 32 (space) through 47
(<code>/</code>) will do, e.g.:</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> echo <span class="st">&quot;*Hello, world&quot;</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a><span class="ex">Hello,</span> world</span></code></pre></div>
<div class="sourceCode" id="cb8"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> echo <span class="st">&quot;*Hello, world&quot;</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">Hello,</span> world</span></code></pre></div>
<h3 id="bad-programs">Bad programs</h3>
<p>If the input doesn’t start with a valid program, that is,
if the interpreter reaches end-of-file during program parsing,
it will crash in some way. E.g. the following might dump core:</p>
<div class="sourceCode" id="cb9"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="bu">echo</span> <span class="at">-n</span> <span class="st">&quot;U&quot;</span> <span class="kw">|</span> <span class="ex">./tromp</span></span></code></pre></div>
<div class="sourceCode" id="cb9"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">&quot;U&quot;</span> <span class="kw">|</span> <span class="ex">./tromp</span></span></code></pre></div>
<p>Furthermore, the interpreter requires the initial encoded lambda term to be
closed, that is, variable <code>n</code> can only appear within at least <code>n</code> enclosing
lambdas. For instance, here the term <code>\ 5</code> is not closed, causing the
interpreter to crash when looking into a null-pointer environment:</p>
<div class="sourceCode" id="cb10"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="bu">echo</span> <span class="st">&quot;&gt;Hello, world&quot;</span> <span class="kw">|</span> <span class="ex">./tromp</span></span></code></pre></div>
<div class="sourceCode" id="cb10"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a> <span class="bu">echo</span> <span class="st">&quot;&gt;Hello, world&quot;</span> <span class="kw">|</span> <span class="ex">./tromp</span></span></code></pre></div>
<p>will likely dump core.</p>
<p>Since these properties can be checked when creating
<a href="https://tromp.github.io/cl/Binary_lambda_calculus.html">BLC</a> programs,
@@ -266,8 +265,8 @@ as a self interpreter in BLC it is downright minuscule at 232 bits (29 bytes):</
0b7fb 00cf6
7bb03 91a1a
</code></pre>
<div class="sourceCode" id="cb13"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> uni8.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="st">&quot; Ni hao&quot;</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a><span class="ex">Ni</span> hao</span></code></pre></div>
<div class="sourceCode" id="cb13"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> uni8.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="st">&quot; Ni hao&quot;</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">Ni</span> hao</span></code></pre></div>
<h3 id="a-prime-number-sieve">A prime number sieve</h3>
<p>Even shorter than the self-interpreter is this prime number sieve in 167 bits
(under 21 bytes):</p>
@@ -282,14 +281,14 @@ as a self interpreter in BLC it is downright minuscule at 232 bits (29 bytes):</
0000110110
</code></pre>
<p>The <code>n</code>th bit in the output indicates whether n is prime:</p>
<div class="sourceCode" id="cb15"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> cat primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 70</span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a><span class="ex">0011010100010100010100010000010100000100010100010000010000010100000100</span></span></code></pre></div>
<div class="sourceCode" id="cb15"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> cat primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 70</span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">0011010100010100010100010000010100000100010100010000010000010100000100</span></span></code></pre></div>
<p>For those who prefer to digest their primes in decimal, there is <code>oddindices.Blc</code>,
which will print the indices of all odd characters (with
<a href="https://en.wikipedia.org/wiki/Bit_numbering">LSB</a> = 1)
separated by a given character:</p>
<pre><code>$ (cat oddindices.Blc; echo -n &quot; &quot;; cat primes.blc | ./tromp -b) | ./tromp | head -c 70
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97</code></pre>
<pre><code> $ (cat oddindices.Blc; echo -n &quot; &quot;; cat primes.blc | ./tromp -b) | ./tromp | head -c 70
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97</code></pre>
<h3 id="a-space-filling-program">A Space filling program</h3>
<p>The program <code>hilbert.Blc</code>, at 143 bytes, is a very twisty “one-liner” (shown in hexadecimal):</p>
<pre><code> 1818181 8111154 6806041 55ff041
@@ -309,120 +308,120 @@ separated by a given character:</p>
60 8191a00167fb cbcfdf65f7c0 a20</code></pre>
<p>It expects <code>n</code> arbitrary characters of input, and draws a space filling <a href="https://en.wikipedia.org/wiki/Hilbert_curve">Hilbert
curve</a> of order <code>n</code>:</p>
<div class="sourceCode" id="cb18"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">&quot;1&quot;</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span></span>
<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="kw">|</span></span>
<div class="sourceCode" id="cb18"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">&quot;1&quot;</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span></span>
<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="kw">|</span></span>
<span id="cb18-4"><a href="#cb18-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb18-5"><a href="#cb18-5" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">&quot;12&quot;</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb18-6"><a href="#cb18-6" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _</span>
<span id="cb18-7"><a href="#cb18-7" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
<span id="cb18-8"><a href="#cb18-8" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
<span id="cb18-9"><a href="#cb18-9" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
<span id="cb18-5"><a href="#cb18-5" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">&quot;12&quot;</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb18-6"><a href="#cb18-6" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _</span>
<span id="cb18-7"><a href="#cb18-7" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
<span id="cb18-8"><a href="#cb18-8" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
<span id="cb18-9"><a href="#cb18-9" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
<span id="cb18-10"><a href="#cb18-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb18-11"><a href="#cb18-11" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">&quot;123&quot;</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb18-12"><a href="#cb18-12" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _ _ _</span>
<span id="cb18-13"><a href="#cb18-13" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
<span id="cb18-14"><a href="#cb18-14" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
<span id="cb18-15"><a href="#cb18-15" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_____</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
<span id="cb18-16"><a href="#cb18-16" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span></span>
<span id="cb18-17"><a href="#cb18-17" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span></span>
<span id="cb18-18"><a href="#cb18-18" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span></span>
<span id="cb18-19"><a href="#cb18-19" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span></span>
<span id="cb18-11"><a href="#cb18-11" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">&quot;123&quot;</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb18-12"><a href="#cb18-12" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _ _ _</span>
<span id="cb18-13"><a href="#cb18-13" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
<span id="cb18-14"><a href="#cb18-14" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
<span id="cb18-15"><a href="#cb18-15" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_____</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
<span id="cb18-16"><a href="#cb18-16" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span></span>
<span id="cb18-17"><a href="#cb18-17" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span></span>
<span id="cb18-18"><a href="#cb18-18" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span></span>
<span id="cb18-19"><a href="#cb18-19" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span></span>
<span id="cb18-20"><a href="#cb18-20" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb18-21"><a href="#cb18-21" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">&quot;1234&quot;</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb18-22"><a href="#cb18-22" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _ _ _ _ _ _ _</span>
<span id="cb18-23"><a href="#cb18-23" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
<span id="cb18-24"><a href="#cb18-24" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
<span id="cb18-25"><a href="#cb18-25" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_____</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_____</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
<span id="cb18-26"><a href="#cb18-26" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span> <span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span></span>
<span id="cb18-27"><a href="#cb18-27" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span></span>
<span id="cb18-28"><a href="#cb18-28" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> _ <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span></span>
<span id="cb18-29"><a href="#cb18-29" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span></span>
<span id="cb18-30"><a href="#cb18-30" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span> ___ ___ ___ ___ _<span class="kw">|</span></span>
<span id="cb18-31"><a href="#cb18-31" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
<span id="cb18-32"><a href="#cb18-32" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span></span>
<span id="cb18-33"><a href="#cb18-33" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span></span>
<span id="cb18-34"><a href="#cb18-34" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _ <span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span> <span class="ex">_</span> _</span>
<span id="cb18-35"><a href="#cb18-35" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
<span id="cb18-36"><a href="#cb18-36" aria-hidden="true" tabindex="-1"></a><span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
<span id="cb18-37"><a href="#cb18-37" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span></code></pre></div>
<span id="cb18-21"><a href="#cb18-21" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> <span class="er">(</span><span class="fu">cat</span> hilbert.Blc<span class="kw">;</span> <span class="bu">echo</span> <span class="at">-n</span> <span class="st">&quot;1234&quot;</span><span class="kw">)</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb18-22"><a href="#cb18-22" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _ _ _ _ _ _ _</span>
<span id="cb18-23"><a href="#cb18-23" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
<span id="cb18-24"><a href="#cb18-24" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
<span id="cb18-25"><a href="#cb18-25" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_____</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="kw">|</span><span class="ex">_____</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
<span id="cb18-26"><a href="#cb18-26" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span> <span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span></span>
<span id="cb18-27"><a href="#cb18-27" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span></span>
<span id="cb18-28"><a href="#cb18-28" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> _ <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span></span>
<span id="cb18-29"><a href="#cb18-29" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span></span>
<span id="cb18-30"><a href="#cb18-30" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span> ___ ___ ___ ___ _<span class="kw">|</span></span>
<span id="cb18-31"><a href="#cb18-31" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span>
<span id="cb18-32"><a href="#cb18-32" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span></span>
<span id="cb18-33"><a href="#cb18-33" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span></span>
<span id="cb18-34"><a href="#cb18-34" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span> _ <span class="kw">|</span> <span class="ex">___</span> ___ <span class="kw">|</span> <span class="ex">_</span> _</span>
<span id="cb18-35"><a href="#cb18-35" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span></span>
<span id="cb18-36"><a href="#cb18-36" aria-hidden="true" tabindex="-1"></a> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span> <span class="ex">_</span> <span class="kw">|</span><span class="ex">_</span> _<span class="kw">|</span></span>
<span id="cb18-37"><a href="#cb18-37" aria-hidden="true" tabindex="-1"></a> <span class="ex">_</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">___</span><span class="kw">|</span> <span class="kw">|</span><span class="ex">_</span></span></code></pre></div>
<h3 id="a-brainfuck-interpreter">A <a href="https://en.wikipedia.org/wiki/Brainfuck">Brainfuck</a> interpreter</h3>
<p>The smallest known BF interpreter is written in… you guessed it,
<a href="https://tromp.github.io/cl/Binary_lambda_calculus.html">BLC</a>,
coming in at 112 bytes (including 3 bits of padding):</p>
<pre><code>$ od -t x4 bf.Blc
0000000 01a15144 02d55584 223070b7 00f032ff
0000020 7f85f9bf 956fe15e c0ee7d7f 006854e5
0000040 fbfd5558 fd5745e0 b6f0fbeb 07d62ff0
0000060 d7736fe1 c0bc14f1 1f2eff0b 17666fa1
0000100 2fef5be8 ff13ffcf 2034cae1 0bd0c80a
0000120 e51fee99 6a5a7fff ff0fff1f d0049d87
0000140 db0500ab 3bb74023 b0c0cc28 10740e6c
0000160</code></pre>
<pre><code> $ od -t x4 bf.Blc
0000000 01a15144 02d55584 223070b7 00f032ff
0000020 7f85f9bf 956fe15e c0ee7d7f 006854e5
0000040 fbfd5558 fd5745e0 b6f0fbeb 07d62ff0
0000060 d7736fe1 c0bc14f1 1f2eff0b 17666fa1
0000100 2fef5be8 ff13ffcf 2034cae1 0bd0c80a
0000120 e51fee99 6a5a7fff ff0fff1f d0049d87
0000140 db0500ab 3bb74023 b0c0cc28 10740e6c
0000160</code></pre>
<p>It expects its input to consist of a
<a href="https://en.wikipedia.org/wiki/Brainfuck">Brainfuck</a> program
(looking only at bits <code>0</code>, <code>1</code> and <code>4</code> to distinguish among <code>,-.+&lt;&gt;][</code>)
followed by a <code>]</code>, followed by the input for the Brainfuck program.</p>
<pre><code>$ more hw.bf
++++++++++[&gt;+++++++&gt;++++++++++&gt;+++&gt;+&lt;&lt;&lt;&lt;-]&gt;++.&gt;+.+++++++..+++.&gt;++.&lt;&lt;+++++++++++++++.&gt;.+++.------.--------.&gt;+.&gt;.]
$ cat bf.Blc hw.bf | ./tromp
Hello World!</code></pre>
<pre><code> $ more hw.bf
++++++++++[&gt;+++++++&gt;++++++++++&gt;+++&gt;+&lt;&lt;&lt;&lt;-]&gt;++.&gt;+.+++++++..+++.&gt;++.&lt;&lt;+++++++++++++++.&gt;.+++.------.--------.&gt;+.&gt;.]
$ cat bf.Blc hw.bf | ./tromp
Hello World!</code></pre>
<p>Curiously, the interpreter <code>bf.Blc</code> is the exact same size as <code>hw.bf</code>.</p>
<h3 id="a-blc-assembler">A BLC assembler</h3>
<p>Writing BLC programs can be made slightly less painful with this parser that
translates single-letter-variable lambda calculus into BLC:</p>
<div class="sourceCode" id="cb21"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> echo <span class="st">&quot;\f\x f (f (f x))&quot;</span> <span class="op">&gt;</span> three</span>
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> cat parse.Blc three <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a><span class="ex">000001110011100111010</span></span></code></pre></div>
<div class="sourceCode" id="cb21"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> echo <span class="st">&quot;\f\x f (f (f x))&quot;</span> <span class="op">&gt;</span> three</span>
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> cat parse.Blc three <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a> <span class="ex">000001110011100111010</span></span></code></pre></div>
<h3 id="converting-between-bits-and-bytes">Converting between bits and bytes</h3>
<p>The program <code>inflate.Blc</code> and its inverse <code>deflate.Blc</code> allow us to translate between
BLC and BLC8. If you assemble a byte oriented program, you’ll need to compact it
into BLC8:</p>
<p>So we could assemble an input reversing program as</p>
<div class="sourceCode" id="cb22"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a><span class="bu">echo</span> <span class="st">&quot;\a a ((\b b b) (\b \c \d \e d (b b) (\f f c e))) (\b \c c)&quot;</span> <span class="op">&gt;</span> reverse</span>
<span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a><span class="fu">cat</span> parse.Blc reverse <span class="kw">|</span> <span class="ex">./tromp</span> <span class="op">&gt;</span> reverse.blc</span></code></pre></div>
<div class="sourceCode" id="cb22"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a> <span class="bu">echo</span> <span class="st">&quot;\a a ((\b b b) (\b \c \d \e d (b b) (\f f c e))) (\b \c c)&quot;</span> <span class="op">&gt;</span> reverse</span>
<span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">cat</span> parse.Blc reverse <span class="kw">|</span> <span class="ex">./tromp</span> <span class="op">&gt;</span> reverse.blc</span></code></pre></div>
<p>and change it to BLC8 with</p>
<div class="sourceCode" id="cb23"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> cat deflate.Blc reverse.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="op">&gt;</span> rev.Blc</span>
<span id="cb23-2"><a href="#cb23-2" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> wc rev.Blc</span>
<span id="cb23-3"><a href="#cb23-3" aria-hidden="true" tabindex="-1"></a> <span class="ex">0</span> 1 9 rev.Blc</span></code></pre></div>
<div class="sourceCode" id="cb23"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> cat deflate.Blc reverse.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="op">&gt;</span> rev.Blc</span>
<span id="cb23-2"><a href="#cb23-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> wc rev.Blc</span>
<span id="cb23-3"><a href="#cb23-3" aria-hidden="true" tabindex="-1"></a> <span class="ex">0</span> 1 9 rev.Blc</span></code></pre></div>
<p>and then try it out with:</p>
<div class="sourceCode" id="cb24"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> cat rev.Blc <span class="at">-</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb24-2"><a href="#cb24-2" aria-hidden="true" tabindex="-1"></a><span class="ex">Hello,</span> world!</span>
<span id="cb24-3"><a href="#cb24-3" aria-hidden="true" tabindex="-1"></a><span class="ex">^D</span></span>
<span id="cb24-4"><a href="#cb24-4" aria-hidden="true" tabindex="-1"></a><span class="ex">!dlrow</span> ,olleH</span></code></pre></div>
<div class="sourceCode" id="cb24"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> cat rev.Blc <span class="at">-</span> <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb24-2"><a href="#cb24-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">Hello,</span> world!</span>
<span id="cb24-3"><a href="#cb24-3" aria-hidden="true" tabindex="-1"></a> <span class="ex">^D</span></span>
<span id="cb24-4"><a href="#cb24-4" aria-hidden="true" tabindex="-1"></a> <span class="ex">!dlrow</span> ,olleH</span></code></pre></div>
<h3 id="symbolic-lambda-calculus-reduction">Symbolic Lambda Calculus reduction</h3>
<p>BLC8 program <code>symbolic.Blc</code> shows individual reduction steps on symbolic lambda terms.
Here it is used to show the calculation of 2^3 in Church numerals:</p>
<div class="sourceCode" id="cb25"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> echo <span class="st">&quot;(\f\x f (f (f x))) (\f\x f (f x))&quot;</span> <span class="op">&gt;</span> threetwo</span>
<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> cat parse.Blc threetwo <span class="kw">|</span> <span class="ex">./tromp</span> <span class="op">&gt;</span> threetwo.blc</span>
<span id="cb25-3"><a href="#cb25-3" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> cat symbolic.Blc threetwo.blc <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb25-4"><a href="#cb25-4" aria-hidden="true" tabindex="-1"></a><span class="kw">(</span><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> b<span class="kw">)))</span> <span class="kw">(</span><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> b<span class="kw">))</span></span>
<span id="cb25-5"><a href="#cb25-5" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="er">(</span><span class="ex">\b</span> <span class="dt">\c</span> b <span class="er">(</span><span class="ex">b</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\b</span> <span class="dt">\c</span> b <span class="er">(</span><span class="ex">b</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\b</span> <span class="dt">\c</span> b <span class="er">(</span><span class="ex">b</span> c<span class="kw">))</span> <span class="ex">a</span><span class="kw">))</span></span>
<span id="cb25-6"><a href="#cb25-6" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)</span></span>
<span id="cb25-7"><a href="#cb25-7" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> <span class="er">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)</span></span>
<span id="cb25-8"><a href="#cb25-8" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">))</span></span>
<span id="cb25-9"><a href="#cb25-9" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">))</span></span>
<span id="cb25-10"><a href="#cb25-10" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)))</span></span>
<span id="cb25-11"><a href="#cb25-11" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)))</span></span>
<span id="cb25-12"><a href="#cb25-12" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">))))</span></span>
<span id="cb25-13"><a href="#cb25-13" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="er">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> c<span class="kw">))</span> <span class="ex">b</span><span class="kw">))))</span></span>
<span id="cb25-14"><a href="#cb25-14" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> b<span class="kw">)))))</span></span>
<span id="cb25-15"><a href="#cb25-15" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> b<span class="kw">)))))</span></span>
<span id="cb25-16"><a href="#cb25-16" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> b<span class="kw">))))))</span></span>
<span id="cb25-17"><a href="#cb25-17" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="ex">b</span><span class="kw">))))))</span></span>
<span id="cb25-18"><a href="#cb25-18" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> b<span class="kw">)))))))</span></span></code></pre></div>
<div class="sourceCode" id="cb25"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> echo <span class="st">&quot;(\f\x f (f (f x))) (\f\x f (f x))&quot;</span> <span class="op">&gt;</span> threetwo</span>
<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> cat parse.Blc threetwo <span class="kw">|</span> <span class="ex">./tromp</span> <span class="op">&gt;</span> threetwo.blc</span>
<span id="cb25-3"><a href="#cb25-3" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> cat symbolic.Blc threetwo.blc <span class="kw">|</span> <span class="ex">./tromp</span></span>
<span id="cb25-4"><a href="#cb25-4" aria-hidden="true" tabindex="-1"></a> <span class="kw">(</span><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> b<span class="kw">)))</span> <span class="kw">(</span><span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> b<span class="kw">))</span></span>
<span id="cb25-5"><a href="#cb25-5" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="er">(</span><span class="ex">\b</span> <span class="dt">\c</span> b <span class="er">(</span><span class="ex">b</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\b</span> <span class="dt">\c</span> b <span class="er">(</span><span class="ex">b</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\b</span> <span class="dt">\c</span> b <span class="er">(</span><span class="ex">b</span> c<span class="kw">))</span> <span class="ex">a</span><span class="kw">))</span></span>
<span id="cb25-6"><a href="#cb25-6" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)</span></span>
<span id="cb25-7"><a href="#cb25-7" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> <span class="er">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)</span></span>
<span id="cb25-8"><a href="#cb25-8" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">))</span></span>
<span id="cb25-9"><a href="#cb25-9" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> <span class="er">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">))</span></span>
<span id="cb25-10"><a href="#cb25-10" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)))</span></span>
<span id="cb25-11"><a href="#cb25-11" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">)))</span></span>
<span id="cb25-12"><a href="#cb25-12" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span><span class="kw">)</span> <span class="ex">b</span><span class="kw">))))</span></span>
<span id="cb25-13"><a href="#cb25-13" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="er">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\d</span> <span class="dt">\e</span> d <span class="er">(</span><span class="ex">d</span> e<span class="kw">))</span> <span class="ex">a</span> c<span class="kw">))</span> <span class="ex">b</span><span class="kw">))))</span></span>
<span id="cb25-14"><a href="#cb25-14" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> b<span class="kw">)))))</span></span>
<span id="cb25-15"><a href="#cb25-15" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="kw">((</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> b<span class="kw">)))))</span></span>
<span id="cb25-16"><a href="#cb25-16" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> c <span class="er">(</span><span class="ex">c</span> d<span class="kw">))</span> <span class="ex">a</span> b<span class="kw">))))))</span></span>
<span id="cb25-17"><a href="#cb25-17" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> a <span class="er">(</span><span class="ex">a</span> c<span class="kw">))</span> <span class="ex">b</span><span class="kw">))))))</span></span>
<span id="cb25-18"><a href="#cb25-18" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="dt">\b</span> a <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> <span class="er">(</span><span class="ex">a</span> b<span class="kw">)))))))</span></span></code></pre></div>
<p>As expected, the resulting normal form is <a href="https://en.wikipedia.org/wiki/Church_encoding">Church
numeral</a> 8.</p>
<p>Taking only the first line of output gives us a sort of BLC disassembler, an
exact inverse of the above assembler. The prime number sieve disassembles as
follows:</p>
<div class="sourceCode" id="cb26"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> cat symbolic.Blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-1</span></span>
<span id="cb26-2"><a href="#cb26-2" aria-hidden="true" tabindex="-1"></a><span class="ex">\a</span> <span class="er">(</span><span class="ex">\b</span> b <span class="er">(</span><span class="ex">b</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> c c<span class="kw">)</span> <span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> <span class="dt">\e</span> e <span class="er">(</span><span class="ex">\f</span> <span class="dt">\g</span> g<span class="kw">)</span> <span class="kw">((</span><span class="ex">\f</span> c c f <span class="er">(</span><span class="kw">(</span><span class="ex">\g</span> g g<span class="kw">)</span> <span class="kw">(</span><span class="ex">\g</span> f <span class="er">(</span><span class="ex">g</span> g<span class="kw">))))</span> <span class="kw">(</span><span class="ex">\f</span> <span class="dt">\g</span> <span class="dt">\h</span> <span class="dt">\i</span> i g <span class="er">(</span><span class="ex">h</span> <span class="er">(</span><span class="ex">d</span> f<span class="kw">)))))</span> <span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> <span class="dt">\e</span> b <span class="er">(</span><span class="ex">e</span> c<span class="kw">)))))</span> <span class="kw">(</span><span class="ex">\b</span> <span class="dt">\c</span> c <span class="er">(</span><span class="ex">\d</span> <span class="dt">\e</span> d<span class="kw">)</span> <span class="ex">b</span><span class="kw">)</span></span></code></pre></div>
<div class="sourceCode" id="cb26"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> cat symbolic.Blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-1</span></span>
<span id="cb26-2"><a href="#cb26-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">\a</span> <span class="er">(</span><span class="ex">\b</span> b <span class="er">(</span><span class="ex">b</span> <span class="er">(</span><span class="kw">(</span><span class="ex">\c</span> c c<span class="kw">)</span> <span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> <span class="dt">\e</span> e <span class="er">(</span><span class="ex">\f</span> <span class="dt">\g</span> g<span class="kw">)</span> <span class="kw">((</span><span class="ex">\f</span> c c f <span class="er">(</span><span class="kw">(</span><span class="ex">\g</span> g g<span class="kw">)</span> <span class="kw">(</span><span class="ex">\g</span> f <span class="er">(</span><span class="ex">g</span> g<span class="kw">))))</span> <span class="kw">(</span><span class="ex">\f</span> <span class="dt">\g</span> <span class="dt">\h</span> <span class="dt">\i</span> i g <span class="er">(</span><span class="ex">h</span> <span class="er">(</span><span class="ex">d</span> f<span class="kw">)))))</span> <span class="kw">(</span><span class="ex">\c</span> <span class="dt">\d</span> <span class="dt">\e</span> b <span class="er">(</span><span class="ex">e</span> c<span class="kw">)))))</span> <span class="kw">(</span><span class="ex">\b</span> <span class="dt">\c</span> c <span class="er">(</span><span class="ex">\d</span> <span class="dt">\e</span> d<span class="kw">)</span> <span class="ex">b</span><span class="kw">)</span></span></code></pre></div>
<p>Hardly any less obfuscated…</p>
<p>The last line of</p>
<div class="sourceCode" id="cb27"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a><span class="fu">cat</span> symbolic.Blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-16</span></span></code></pre></div>
<div class="sourceCode" id="cb27"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a> <span class="fu">cat</span> symbolic.Blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-16</span></span></code></pre></div>
<p>starts out as</p>
<pre><code>\a \b b (\c \d c) (\c c (\d \e d) (\d d (\e \f f) (\e e (\f \g g) ((\f (\g \h \i</code></pre>
<pre><code> \a \b b (\c \d c) (\c c (\d \e d) (\d d (\e \f f) (\e e (\f \g g) ((\f (\g \h \i</code></pre>
<p>The <code>\a</code> is for ignoring the rest of the input (to which the universal machine
applies the decoded lambda term). The <code>\b b (..) (...)</code> is the list constructor,
usually called <code>cons</code>, applied to a head (a list element) and a tail (another list).
@@ -445,16 +444,16 @@ Syntax</a> which relies on the highly optimized
Haskell runtime system for evaluation. Of course individual BLC programs running
under the interpreter perform much worse than that same program written in Haskell.</p>
<p>Our interpreter copes well with extra levels of interpretation:</p>
<div class="sourceCode" id="cb29"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> time cat primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">&gt;</span> /dev/null</span>
<span id="cb29-2"><a href="#cb29-2" aria-hidden="true" tabindex="-1"></a><span class="ex">real</span> 0m0.043s</span>
<span id="cb29-3"><a href="#cb29-3" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> time cat uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">&gt;</span> /dev/null</span>
<span id="cb29-4"><a href="#cb29-4" aria-hidden="true" tabindex="-1"></a><span class="ex">real</span> 0m0.191s</span>
<span id="cb29-5"><a href="#cb29-5" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> time cat uni.blc uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">&gt;</span> /dev/null</span>
<span id="cb29-6"><a href="#cb29-6" aria-hidden="true" tabindex="-1"></a><span class="ex">real</span> 0m1.919s</span>
<span id="cb29-7"><a href="#cb29-7" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> time cat uni.blc uni.blc uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">&gt;</span> /dev/null</span>
<span id="cb29-8"><a href="#cb29-8" aria-hidden="true" tabindex="-1"></a><span class="ex">real</span> 0m23.514s</span>
<span id="cb29-9"><a href="#cb29-9" aria-hidden="true" tabindex="-1"></a><span class="ex">$</span> time cat uni.blc uni.blc uni.blc uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">&gt;</span> /dev/null</span>
<span id="cb29-10"><a href="#cb29-10" aria-hidden="true" tabindex="-1"></a><span class="ex">real</span> 4m52.700s</span></code></pre></div>
<div class="sourceCode" id="cb29"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> time cat primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">&gt;</span> /dev/null</span>
<span id="cb29-2"><a href="#cb29-2" aria-hidden="true" tabindex="-1"></a> <span class="ex">real</span> 0m0.043s</span>
<span id="cb29-3"><a href="#cb29-3" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> time cat uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">&gt;</span> /dev/null</span>
<span id="cb29-4"><a href="#cb29-4" aria-hidden="true" tabindex="-1"></a> <span class="ex">real</span> 0m0.191s</span>
<span id="cb29-5"><a href="#cb29-5" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> time cat uni.blc uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">&gt;</span> /dev/null</span>
<span id="cb29-6"><a href="#cb29-6" aria-hidden="true" tabindex="-1"></a> <span class="ex">real</span> 0m1.919s</span>
<span id="cb29-7"><a href="#cb29-7" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> time cat uni.blc uni.blc uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">&gt;</span> /dev/null</span>
<span id="cb29-8"><a href="#cb29-8" aria-hidden="true" tabindex="-1"></a> <span class="ex">real</span> 0m23.514s</span>
<span id="cb29-9"><a href="#cb29-9" aria-hidden="true" tabindex="-1"></a> <span class="ex">$</span> time cat uni.blc uni.blc uni.blc uni.blc primes.blc <span class="kw">|</span> <span class="ex">./tromp</span> <span class="at">-b</span> <span class="kw">|</span> <span class="fu">head</span> <span class="at">-c</span> 210 <span class="op">&gt;</span> /dev/null</span>
<span id="cb29-10"><a href="#cb29-10" aria-hidden="true" tabindex="-1"></a> <span class="ex">real</span> 4m52.700s</span></code></pre></div>
<h3 id="obfuscation">Obfuscation</h3>
<p>Obfuscation is due entirely to conciseness. Some questions to ponder:</p>
<p>Which of the term space codes <code>0</code>, <code>1</code>, <code>2</code>, <code>3</code> serve multiple purposes?</p>
@@ -465,15 +464,15 @@ under the interpreter perform much worse than that same program written in Haske
<h3 id="portability">Portability</h3>
<p>The program freely (without casting) converts between <code>int</code> and <code>int *</code>, causing
many warnings;</p>
<pre><code> note: expected &#39;int *&#39; but argument is of type &#39;int&#39;
warning: assignment from incompatible pointer type
warning: assignment makes integer from pointer without a cast
warning: assignment makes pointer from integer without a cast
warning: incompatible implicit declaration of built-in function &#39;calloc&#39;
warning: incompatible implicit declaration of built-in function &#39;exit&#39;
warning: passing argument 1 of &#39;d&#39; makes pointer from integer without a cast
warning: passing argument 1 of &#39;p&#39; makes pointer from integer without a cast
warning: pointer/integer type mismatch in conditional expression</code></pre>
<pre><code> note: expected &#39;int *&#39; but argument is of type &#39;int&#39;
warning: assignment from incompatible pointer type
warning: assignment makes integer from pointer without a cast
warning: assignment makes pointer from integer without a cast
warning: incompatible implicit declaration of built-in function &#39;calloc&#39;
warning: incompatible implicit declaration of built-in function &#39;exit&#39;
warning: passing argument 1 of &#39;d&#39; makes pointer from integer without a cast
warning: passing argument 1 of &#39;p&#39; makes pointer from integer without a cast
warning: pointer/integer type mismatch in conditional expression</code></pre>
<p>Avoiding these would make the program substantially longer,
and detract from its single minded focus on conciseness.</p>
<p>It implicitly declares functions <code>read(2)</code>, <code>write(2)</code>, <code>exit(3)</code> and