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<div class="section" id="joypy">
<h1>Joypy<a class="headerlink" href="#joypy" title="Permalink to this headline"></a></h1>
<div class="section" id="joy-in-python">
<h2>Joy in Python<a class="headerlink" href="#joy-in-python" title="Permalink to this headline"></a></h2>
<p>This implementation is meant as a tool for exploring the programming
model and method of Joy. Python seems like a great implementation
language for Joy for several reasons.</p>
<p>We can lean on the Python immutable types for our basic semantics and
types: ints, floats, strings, and tuples, which enforces functional
purity. We get garbage collection for free. Compilation via Cython. Glue
language with loads of libraries.</p>
<div class="section" id="read-eval-print-loop-repl">
<h3><a class="reference external" href="https://en.wikipedia.org/wiki/Read%E2%80%93eval%E2%80%93print_loop">Read-Eval-Print Loop (REPL)</a><a class="headerlink" href="#read-eval-print-loop-repl" title="Permalink to this headline"></a></h3>
<p>The main way to interact with the Joy interpreter is through a simple
<a class="reference external" href="https://en.wikipedia.org/wiki/Read%E2%80%93eval%E2%80%93print_loop">REPL</a>
that you start by running the package:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>$ python -m joy
Joypy - Copyright © 2017 Simon Forman
This program comes with ABSOLUTELY NO WARRANTY; for details type &quot;warranty&quot;.
This is free software, and you are welcome to redistribute it
under certain conditions; type &quot;sharing&quot; for details.
Type &quot;words&quot; to see a list of all words, and &quot;[&lt;name&gt;] help&quot; to print the
docs for a word.
&lt;-top
joy? _
</pre></div>
</div>
<p>The <code class="docutils literal notranslate"><span class="pre">&lt;-top</span></code> marker points to the top of the (initially empty) stack.
You can enter Joy notation at the prompt and a <a class="reference external" href="#The-TracePrinter.">trace of
evaluation</a> will be printed followed by the stack
and prompt again:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>joy? 23 sqr 18 +
. 23 sqr 18 +
23 . sqr 18 +
23 . dup mul 18 +
23 23 . mul 18 +
529 . 18 +
529 18 . +
547 .
547 &lt;-top
joy?
</pre></div>
</div>
</div>
</div>
</div>
<div class="section" id="stacks-aka-list-quote-sequence-etc">
<h1>Stacks (aka list, quote, sequence, etc.)<a class="headerlink" href="#stacks-aka-list-quote-sequence-etc" title="Permalink to this headline"></a></h1>
<p>In Joy, in addition to the types Boolean, integer, float, and string,
there is a single sequence type represented by enclosing a sequence of
terms in brackets <code class="docutils literal notranslate"><span class="pre">[...]</span></code>. This sequence type is used to represent
both the stack and the expression. It is a <a class="reference external" href="https://en.wikipedia.org/wiki/Cons#Lists">cons
list</a> made from Python
tuples.</p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">inspect</span>
<span class="kn">import</span> <span class="nn">joy.utils.stack</span>
<span class="nb">print</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getdoc</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">stack</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>§ Stack
When talking about Joy we use the terms &quot;stack&quot;, &quot;list&quot;, &quot;sequence&quot; and
&quot;aggregate&quot; to mean the same thing: a simple datatype that permits
certain operations such as iterating and pushing and popping values from
(at least) one end.
We use the venerable two-tuple recursive form of sequences where the
empty tuple () is the empty stack and (head, rest) gives the recursive
form of a stack with one or more items on it.
()
(1, ())
(2, (1, ()))
(3, (2, (1, ())))
...
And so on.
We have two very simple functions to build up a stack from a Python
iterable and also to iterate through a stack and yield its items
one-by-one in order, and two functions to generate string representations
of stacks:
list_to_stack()
iter_stack()
expression_to_string() (prints left-to-right)
stack_to_string() (prints right-to-left)
A word about the stack data structure.
Python has very nice &quot;tuple packing and unpacking&quot; in its syntax which
means we can directly &quot;unpack&quot; the expected arguments to a Joy function.
For example:
def dup(stack):
head, tail = stack
return head, (head, tail)
We replace the argument &quot;stack&quot; by the expected structure of the stack,
in this case &quot;(head, tail)&quot;, and Python takes care of de-structuring the
incoming argument and assigning values to the names. Note that Python
syntax doesn&#39;t require parentheses around tuples used in expressions
where they would be redundant.
</pre></div>
</div>
<p>The 0th item in the list will be on the top of the stack and <em>vise
versa</em>.</p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">stack</span><span class="o">.</span><span class="n">list_to_stack</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">())))</span>
</pre></div>
</div>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">list</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">stack</span><span class="o">.</span><span class="n">iter_stack</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">())))))</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>
</pre></div>
</div>
<p>This requires reversing the sequence (or iterating backwards) otherwise:</p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">stack</span> <span class="o">=</span> <span class="p">()</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]:</span>
<span class="n">stack</span> <span class="o">=</span> <span class="n">n</span><span class="p">,</span> <span class="n">stack</span>
<span class="nb">print</span> <span class="n">stack</span>
<span class="nb">print</span> <span class="nb">list</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">stack</span><span class="o">.</span><span class="n">iter_stack</span><span class="p">(</span><span class="n">stack</span><span class="p">))</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">())))</span>
<span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
</pre></div>
</div>
<p>Because Joy lists are made out of Python tuples they are immutable, so
all Joy datastructures are <em>`purely
functional &lt;https://en.wikipedia.org/wiki/Purely_functional_data_structure&gt;`__</em>.</p>
</div>
<div class="section" id="the-joy-function">
<h1>The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> function.<a class="headerlink" href="#the-joy-function" title="Permalink to this headline"></a></h1>
<div class="section" id="an-interpreter">
<h2>An Interpreter<a class="headerlink" href="#an-interpreter" title="Permalink to this headline"></a></h2>
<p>The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> function is extrememly simple. It accepts a stack, an
expression, and a dictionary, and it iterates through the expression
putting values onto the stack and delegating execution to functions it
looks up in the dictionary.</p>
<p>Each function is passed the stack, expression, and dictionary and
returns them. Whatever the function returns becomes the new stack,
expression, and dictionary. (The dictionary is passed to enable e.g.
writing words that let you enter new words into the dictionary at
runtime, which nothing does yet and may be a bad idea, and the <code class="docutils literal notranslate"><span class="pre">help</span></code>
command.)</p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">joy.joy</span>
<span class="nb">print</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getsource</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">joy</span><span class="o">.</span><span class="n">joy</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">joy</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">,</span> <span class="n">viewer</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">&#39;&#39;&#39;</span>
<span class="sd"> Evaluate the Joy expression on the stack.</span>
<span class="sd"> &#39;&#39;&#39;</span>
<span class="k">while</span> <span class="n">expression</span><span class="p">:</span>
<span class="k">if</span> <span class="n">viewer</span><span class="p">:</span> <span class="n">viewer</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">)</span>
<span class="n">term</span><span class="p">,</span> <span class="n">expression</span> <span class="o">=</span> <span class="n">expression</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="n">Symbol</span><span class="p">):</span>
<span class="n">term</span> <span class="o">=</span> <span class="n">dictionary</span><span class="p">[</span><span class="n">term</span><span class="p">]</span>
<span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span> <span class="o">=</span> <span class="n">term</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">stack</span> <span class="o">=</span> <span class="n">term</span><span class="p">,</span> <span class="n">stack</span>
<span class="k">if</span> <span class="n">viewer</span><span class="p">:</span> <span class="n">viewer</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">)</span>
<span class="k">return</span> <span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span>
</pre></div>
</div>
<div class="section" id="view-function">
<h3>View function<a class="headerlink" href="#view-function" title="Permalink to this headline"></a></h3>
<p>The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> function accepts a “viewer” function which it calls on
each iteration passing the current stack and expression just before
evaluation. This can be used for tracing, breakpoints, retrying after
exceptions, or interrupting an evaluation and saving to disk or sending
over the network to resume later. The stack and expression together
contain all the state of the computation at each step.</p>
</div>
<div class="section" id="the-traceprinter">
<h3>The <code class="docutils literal notranslate"><span class="pre">TracePrinter</span></code>.<a class="headerlink" href="#the-traceprinter" title="Permalink to this headline"></a></h3>
<p>A <code class="docutils literal notranslate"><span class="pre">viewer</span></code> records each step of the evaluation of a Joy program. The
<code class="docutils literal notranslate"><span class="pre">TracePrinter</span></code> has a facility for printing out a trace of the
evaluation, one line per step. Each step is aligned to the current
interpreter position, signified by a period separating the stack on the
left from the pending expression (“continuation”) on the right.</p>
</div>
<div class="section" id="continuation-passing-style">
<h3><a class="reference external" href="https://en.wikipedia.org/wiki/Continuation-passing_style">Continuation-Passing Style</a><a class="headerlink" href="#continuation-passing-style" title="Permalink to this headline"></a></h3>
<p>One day I thought, What happens if you rewrite Joy to use
<a class="reference external" href="https://en.wikipedia.org/wiki/Continuation-passing_style">CSP</a>? I
made all the functions accept and return the expression as well as the
stack and found that all the combinators could be rewritten to work by
modifying the expression rather than making recursive calls to the
<code class="docutils literal notranslate"><span class="pre">joy()</span></code> function.</p>
</div>
</div>
</div>
<div class="section" id="parser">
<h1>Parser<a class="headerlink" href="#parser" title="Permalink to this headline"></a></h1>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">joy.parser</span>
<span class="nb">print</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getdoc</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>§ Converting text to a joy expression.
This module exports a single function:
text_to_expression(text)
As well as a single Symbol class and a single Exception type:
ParseError
When supplied with a string this function returns a Python datastructure
that represents the Joy datastructure described by the text expression.
Any unbalanced square brackets will raise a ParseError.
</pre></div>
</div>
<p>The parser is extremely simple, the undocumented <code class="docutils literal notranslate"><span class="pre">re.Scanner</span></code> class
does most of the tokenizing work and then you just build the tuple
structure out of the tokens. There’s no Abstract Syntax Tree or anything
like that.</p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getsource</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">_parse</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_parse</span><span class="p">(</span><span class="n">tokens</span><span class="p">):</span>
<span class="sd">&#39;&#39;&#39;</span>
<span class="sd"> Return a stack/list expression of the tokens.</span>
<span class="sd"> &#39;&#39;&#39;</span>
<span class="n">frame</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">stack</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">tok</span> <span class="ow">in</span> <span class="n">tokens</span><span class="p">:</span>
<span class="k">if</span> <span class="n">tok</span> <span class="o">==</span> <span class="s1">&#39;[&#39;</span><span class="p">:</span>
<span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">frame</span><span class="p">)</span>
<span class="n">frame</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">stack</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">frame</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">tok</span> <span class="o">==</span> <span class="s1">&#39;]&#39;</span><span class="p">:</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">frame</span> <span class="o">=</span> <span class="n">stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<span class="k">except</span> <span class="ne">IndexError</span><span class="p">:</span>
<span class="k">raise</span> <span class="n">ParseError</span><span class="p">(</span><span class="s1">&#39;One or more extra closing brackets.&#39;</span><span class="p">)</span>
<span class="n">frame</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">list_to_stack</span><span class="p">(</span><span class="n">frame</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">frame</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tok</span><span class="p">)</span>
<span class="k">if</span> <span class="n">stack</span><span class="p">:</span>
<span class="k">raise</span> <span class="n">ParseError</span><span class="p">(</span><span class="s1">&#39;One or more unclosed brackets.&#39;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">list_to_stack</span><span class="p">(</span><span class="n">frame</span><span class="p">)</span>
</pre></div>
</div>
<p>That’s pretty much all there is to it.</p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;1 2 3 4 5&#39;</span><span class="p">)</span> <span class="c1"># A simple sequence.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="p">())))))</span>
</pre></div>
</div>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[1 2 3] 4 5&#39;</span><span class="p">)</span> <span class="c1"># Three items, the first is a list with three items</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">()))),</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="p">())))</span>
</pre></div>
</div>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;1 23 [&quot;four&quot; [-5.0] cons] 8888&#39;</span><span class="p">)</span> <span class="c1"># A mixed bag. cons is</span>
<span class="c1"># a Symbol, no lookup at</span>
<span class="c1"># parse-time. Haiku docs.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">23</span><span class="p">,</span> <span class="p">((</span><span class="s1">&#39;four&#39;</span><span class="p">,</span> <span class="p">((</span><span class="o">-</span><span class="mf">5.0</span><span class="p">,</span> <span class="p">()),</span> <span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="p">()))),</span> <span class="p">(</span><span class="mi">8888</span><span class="p">,</span> <span class="p">()))))</span>
</pre></div>
</div>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[][][][][]&#39;</span><span class="p">)</span> <span class="c1"># Five empty lists.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((),</span> <span class="p">((),</span> <span class="p">((),</span> <span class="p">((),</span> <span class="p">((),</span> <span class="p">())))))</span>
</pre></div>
</div>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[[[[[]]]]]&#39;</span><span class="p">)</span> <span class="c1"># Five nested lists.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((((((),</span> <span class="p">()),</span> <span class="p">()),</span> <span class="p">()),</span> <span class="p">()),</span> <span class="p">())</span>
</pre></div>
</div>
</div>
<div class="section" id="library">
<h1>Library<a class="headerlink" href="#library" title="Permalink to this headline"></a></h1>
<p>The Joy library of functions (aka commands, or “words” after Forth
usage) encapsulates all the actual functionality (no pun intended) of
the Joy system. There are simple functions such as addition <code class="docutils literal notranslate"><span class="pre">add</span></code> (or
<code class="docutils literal notranslate"><span class="pre">+</span></code>, the library module supports aliases), and combinators which
provide control-flow and higher-order operations.</p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">joy.library</span>
<span class="nb">print</span> <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">sorted</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">initialize</span><span class="p">()))</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>!= % &amp; * *fraction *fraction0 + ++ - -- / &lt; &lt;&lt; &lt;= &lt;&gt; = &gt; &gt;= &gt;&gt; ? ^ add anamorphism and app1 app2 app3 average b binary branch choice clear cleave concat cons dinfrirst dip dipd dipdd disenstacken div down_to_zero dudipd dup dupd dupdip enstacken eq first flatten floordiv gcd ge genrec getitem gt help i id ifte infra le least_fraction loop lshift lt map min mod modulus mul ne neg not nullary or over pam parse pm pop popd popdd popop pow pred primrec product quoted range range_to_zero rem remainder remove rest reverse roll&lt; roll&gt; rolldown rollup rshift run second select sharing shunt size sqr sqrt stack step sub succ sum swaack swap swoncat swons ternary third times truediv truthy tuck unary uncons unit unquoted unstack void warranty while words x xor zip •
</pre></div>
</div>
<p>Many of the functions are defined in Python, like <code class="docutils literal notranslate"><span class="pre">dip</span></code>:</p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getsource</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">dip</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">dip</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">):</span>
<span class="p">(</span><span class="n">quote</span><span class="p">,</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span> <span class="o">=</span> <span class="n">stack</span>
<span class="n">expression</span> <span class="o">=</span> <span class="n">x</span><span class="p">,</span> <span class="n">expression</span>
<span class="k">return</span> <span class="n">stack</span><span class="p">,</span> <span class="n">pushback</span><span class="p">(</span><span class="n">quote</span><span class="p">,</span> <span class="n">expression</span><span class="p">),</span> <span class="n">dictionary</span>
</pre></div>
</div>
<p>Some functions are defined in equations in terms of other functions.
When the interpreter executes a definition function that function just
pushes its body expression onto the pending expression (the
continuation) and returns control to the interpreter.</p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">definitions</span>
</pre></div>
</div>
<pre class="literal-block">
second == rest first
third == rest rest first
product == 1 swap [*] step
swons == swap cons
swoncat == swap concat
flatten == [] swap [concat] step
unit == [] cons
quoted == [unit] dip
unquoted == [i] dip
enstacken == stack [clear] dip
disenstacken == ? [uncons ?] loop pop
? == dup truthy
dinfrirst == dip infra first
nullary == [stack] dinfrirst
unary == [stack [pop] dip] dinfrirst
binary == [stack [popop] dip] dinfrirst
ternary == [stack [popop pop] dip] dinfrirst
pam == [i] map
run == [] swap infra
sqr == dup mul
size == 0 swap [pop ++] step
cleave == [i] app2 [popd] dip
average == [sum 1.0 <em>] [size] cleave /
gcd == 1 [tuck modulus dup 0 &gt;] loop pop
least_fraction == dup [gcd] infra [div] concat map
*fraction == [uncons] dip uncons [swap] dip concat [</em>] infra [*] dip cons
<em>fraction0 == concat [[swap] dip * [</em>] dip] infra
down_to_zero == [0 &gt;] [dup --] while
range_to_zero == unit [down_to_zero] infra
anamorphism == [pop []] swap [dip swons] genrec
range == [0 &lt;=] [1 - dup] anamorphism
while == swap [nullary] cons dup dipd concat loop
dudipd == dup dipd
primrec == [i] genrec
</pre>
<p>Currently, there’s no function to add new definitions to the dictionary
from “within” Joy code itself. Adding new definitions remains a
meta-interpreter action. You have to do it yourself, in Python, and wash
your hands afterward.</p>
<p>It would be simple enough to define one, but it would open the door to
<em>name binding</em> and break the idea that all state is captured in the
stack and expression. There’s an implicit <em>standard dictionary</em> that
defines the actual semantics of the syntactic stack and expression
datastructures (which only contain symbols, not the actual functions.
Pickle some and see for yourself.)</p>
<p>Which brings me to talking about one of my hopes and dreams for this
notation: “There should be only one.” What I mean is that there should
be one universal standard dictionary of commands, and all bespoke work
done in a UI for purposes takes place by direct interaction and macros.
There would be a <em>Grand Refactoring</em> biannually (two years, not six
months, that’s semi-annually) where any new definitions factored out of
the usage and macros of the previous time, along with new algorithms and
such, were entered into the dictionary and posted to e.g. IPFS.</p>
<p>Code should not burgeon wildly, as it does today. The variety of code
should map more-or-less to the well-factored variety of human
computably-solvable problems. There shouldn’t be dozens of chat apps, JS
frameworks, programming languages. It’s a waste of time, a <a class="reference external" href="https://en.wikipedia.org/wiki/Thundering_herd_problem">fractal
“thundering herd”
attack</a> on
human mentality.</p>
<p>If you read over the other notebooks you’ll see that developing code in
Joy is a lot like doing simple mathematics, and the descriptions of the
code resemble math papers. The code also works the first time, no bugs.
If you have any experience programming at all, you are probably
skeptical, as I was, but it seems to work: deriving code mathematically
seems to lead to fewer errors.</p>
<p>But my point now is that this great ratio of textual explanation to wind
up with code that consists of a few equations and could fit on an index
card is highly desirable. Less code has fewer errors. The structure of
Joy engenders a kind of thinking that seems to be very effective for
developing structured processes.</p>
<p>There seems to be an elegance and power to the notation.</p>
</div>
</div>
</div>
</div>
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<h3><a href="../index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Joypy</a><ul>
<li><a class="reference internal" href="#joy-in-python">Joy in Python</a><ul>
<li><a class="reference internal" href="#read-eval-print-loop-repl">Read-Eval-Print Loop (REPL)</a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#stacks-aka-list-quote-sequence-etc">Stacks (aka list, quote, sequence, etc.)</a></li>
<li><a class="reference internal" href="#the-joy-function">The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> function.</a><ul>
<li><a class="reference internal" href="#an-interpreter">An Interpreter</a><ul>
<li><a class="reference internal" href="#view-function">View function</a></li>
<li><a class="reference internal" href="#the-traceprinter">The <code class="docutils literal notranslate"><span class="pre">TracePrinter</span></code>.</a></li>
<li><a class="reference internal" href="#continuation-passing-style">Continuation-Passing Style</a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#parser">Parser</a></li>
<li><a class="reference internal" href="#library">Library</a></li>
</ul>
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<h3>Related Topics</h3>
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<li><a href="../index.html">Documentation overview</a><ul>
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