Make sure we've got all the docs, etc.
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Simon Forman
parent
cf12b9ce17
commit
230134e6c2
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@ -12215,11 +12215,7 @@ expressions grow each derivation.</p>
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<div class="prompt input_prompt">In [11]:</div>
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<div class="prompt input_prompt">In [11]:</div>
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<div class="inner_cell">
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<div class="inner_cell">
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<div class="input_area">
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<div class="input_area">
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<div class=" highlight hl-ipython2"><pre><span></span><span class="c1"># This is the straightforward version with no "compaction".</span>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">D</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
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<span class="c1"># It works fine, but does waaaay too much work because the</span>
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<span class="c1"># expressions grow each derivation.</span>
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<span class="k">def</span> <span class="nf">D</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
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<span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
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<span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
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@ -232,10 +232,6 @@ expressions grow each derivation.
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```python
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```python
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# This is the straightforward version with no "compaction".
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# It works fine, but does waaaay too much work because the
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# expressions grow each derivation.
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def D(symbol):
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def D(symbol):
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def derv(R):
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def derv(R):
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@ -266,10 +266,6 @@ derivation.
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.. code:: ipython2
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.. code:: ipython2
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# This is the straightforward version with no "compaction".
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# It works fine, but does waaaay too much work because the
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# expressions grow each derivation.
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def D(symbol):
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def D(symbol):
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def derv(R):
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def derv(R):
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@ -0,0 +1,185 @@
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After Width: | Height: | Size: 11 KiB |
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@ -473,6 +473,8 @@
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||||||
<li><a href="pretty.html#joy.utils.pretty_print.TracePrinter">TracePrinter (class in joy.utils.pretty_print)</a>
|
<li><a href="pretty.html#joy.utils.pretty_print.TracePrinter">TracePrinter (class in joy.utils.pretty_print)</a>
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</li>
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</li>
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||||||
<li><a href="library.html#joy.utils.generated_library.tuck">tuck() (in module joy.utils.generated_library)</a>
|
<li><a href="library.html#joy.utils.generated_library.tuck">tuck() (in module joy.utils.generated_library)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="types.html#joy.utils.polytypes.type_check">type_check() (in module joy.utils.polytypes)</a>
|
||||||
</li>
|
</li>
|
||||||
</ul></td>
|
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|
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|
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|
||||||
|
|
@ -147,8 +147,11 @@ interesting aspects. It’s quite a treasure trove.</p>
|
||||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/Newton-Raphson.html">Newton’s method</a></li>
|
<li class="toctree-l2"><a class="reference internal" href="notebooks/Newton-Raphson.html">Newton’s method</a></li>
|
||||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/Zipper.html">Traversing Datastructures with Zippers</a></li>
|
<li class="toctree-l2"><a class="reference internal" href="notebooks/Zipper.html">Traversing Datastructures with Zippers</a></li>
|
||||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/Types.html">The Blissful Elegance of Typing Joy</a></li>
|
<li class="toctree-l2"><a class="reference internal" href="notebooks/Types.html">The Blissful Elegance of Typing Joy</a></li>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="notebooks/TypeChecking.html">Type Checking</a></li>
|
||||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/NoUpdates.html">No Updates</a></li>
|
<li class="toctree-l2"><a class="reference internal" href="notebooks/NoUpdates.html">No Updates</a></li>
|
||||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/Categorical.html">Categorical Programming</a></li>
|
<li class="toctree-l2"><a class="reference internal" href="notebooks/Categorical.html">Categorical Programming</a></li>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="notebooks/The_Four_Operations.html">The Four Fundamental Operations of Definite Action</a></li>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="notebooks/Derivatives_of_Regular_Expressions.html">∂RE</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
</ul>
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<div class="document">
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<div class="bodywrapper">
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<div class="body" role="main">
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||||||
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<div class="section" id="re">
|
||||||
|
<h1>∂RE<a class="headerlink" href="#re" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<div class="section" id="brzozowski-s-derivatives-of-regular-expressions">
|
||||||
|
<h2>Brzozowski’s Derivatives of Regular Expressions<a class="headerlink" href="#brzozowski-s-derivatives-of-regular-expressions" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>Legend:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>∧ intersection
|
||||||
|
∨ union
|
||||||
|
∘ concatenation (see below)
|
||||||
|
¬ complement
|
||||||
|
ϕ empty set (aka ∅)
|
||||||
|
λ singleton set containing just the empty string
|
||||||
|
I set of all letters in alphabet
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Derivative of a set <code class="docutils literal notranslate"><span class="pre">R</span></code> of strings and a string <code class="docutils literal notranslate"><span class="pre">a</span></code>:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>∂a(R)
|
||||||
|
|
||||||
|
∂a(a) → λ
|
||||||
|
∂a(λ) → ϕ
|
||||||
|
∂a(ϕ) → ϕ
|
||||||
|
∂a(¬a) → ϕ
|
||||||
|
∂a(R*) → ∂a(R)∘R*
|
||||||
|
∂a(¬R) → ¬∂a(R)
|
||||||
|
∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)
|
||||||
|
∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)
|
||||||
|
∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
|
||||||
|
|
||||||
|
∂ab(R) = ∂b(∂a(R))
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Auxiliary predicate function <code class="docutils literal notranslate"><span class="pre">δ</span></code> (I call it <code class="docutils literal notranslate"><span class="pre">nully</span></code>) returns either
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">λ</span></code> if <code class="docutils literal notranslate"><span class="pre">λ</span> <span class="pre">⊆</span> <span class="pre">R</span></code> or <code class="docutils literal notranslate"><span class="pre">ϕ</span></code> otherwise:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>δ(a) → ϕ
|
||||||
|
δ(λ) → λ
|
||||||
|
δ(ϕ) → ϕ
|
||||||
|
δ(R*) → λ
|
||||||
|
δ(¬R) δ(R)≟ϕ → λ
|
||||||
|
δ(¬R) δ(R)≟λ → ϕ
|
||||||
|
δ(R∘S) → δ(R) ∧ δ(S)
|
||||||
|
δ(R ∧ S) → δ(R) ∧ δ(S)
|
||||||
|
δ(R ∨ S) → δ(R) ∨ δ(S)
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Some rules we will use later for “compaction”:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>R ∧ ϕ = ϕ ∧ R = ϕ
|
||||||
|
|
||||||
|
R ∧ I = I ∧ R = R
|
||||||
|
|
||||||
|
R ∨ ϕ = ϕ ∨ R = R
|
||||||
|
|
||||||
|
R ∨ I = I ∨ R = I
|
||||||
|
|
||||||
|
R∘ϕ = ϕ∘R = ϕ
|
||||||
|
|
||||||
|
R∘λ = λ∘R = R
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Concatination of sets: for two sets A and B the set A∘B is defined as:</p>
|
||||||
|
<p>{a∘b for a in A for b in B}</p>
|
||||||
|
<p>E.g.:</p>
|
||||||
|
<p>{‘a’, ‘b’}∘{‘c’, ‘d’} → {‘ac’, ‘ad’, ‘bc’, ‘bd’}</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="implementation">
|
||||||
|
<h2>Implementation<a class="headerlink" href="#implementation" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">functools</span> <span class="k">import</span> <span class="n">partial</span> <span class="k">as</span> <span class="n">curry</span>
|
||||||
|
<span class="kn">from</span> <span class="nn">itertools</span> <span class="k">import</span> <span class="n">product</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="and">
|
||||||
|
<h3><code class="docutils literal notranslate"><span class="pre">ϕ</span></code> and <code class="docutils literal notranslate"><span class="pre">λ</span></code><a class="headerlink" href="#and" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>The empty set and the set of just the empty string.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">phi</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">()</span> <span class="c1"># ϕ</span>
|
||||||
|
<span class="n">y</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">''</span><span class="p">})</span> <span class="c1"># λ</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="two-letter-alphabet">
|
||||||
|
<h3>Two-letter Alphabet<a class="headerlink" href="#two-letter-alphabet" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>I’m only going to use two symbols (at first) becaase this is enough to
|
||||||
|
illustrate the algorithm and because you can represent any other
|
||||||
|
alphabet with two symbols (if you had to.)</p>
|
||||||
|
<p>I chose the names <code class="docutils literal notranslate"><span class="pre">O</span></code> and <code class="docutils literal notranslate"><span class="pre">l</span></code> (uppercase “o” and lowercase “L”) to
|
||||||
|
look like <code class="docutils literal notranslate"><span class="pre">0</span></code> and <code class="docutils literal notranslate"><span class="pre">1</span></code> (zero and one) respectively.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">syms</span> <span class="o">=</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">'0'</span><span class="p">}),</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">'1'</span><span class="p">})</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="representing-regular-expressions">
|
||||||
|
<h3>Representing Regular Expressions<a class="headerlink" href="#representing-regular-expressions" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>To represent REs in Python I’m going to use tagged tuples. A <em>regular
|
||||||
|
expression</em> is one of:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">O</span>
|
||||||
|
<span class="n">l</span>
|
||||||
|
<span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="n">R</span><span class="p">)</span>
|
||||||
|
<span class="p">(</span><span class="n">NOT</span><span class="p">,</span> <span class="n">R</span><span class="p">)</span>
|
||||||
|
<span class="p">(</span><span class="n">AND</span><span class="p">,</span> <span class="n">R</span><span class="p">,</span> <span class="n">S</span><span class="p">)</span>
|
||||||
|
<span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">R</span><span class="p">,</span> <span class="n">S</span><span class="p">)</span>
|
||||||
|
<span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">R</span><span class="p">,</span> <span class="n">S</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Where <code class="docutils literal notranslate"><span class="pre">R</span></code> and <code class="docutils literal notranslate"><span class="pre">S</span></code> stand for <em>regular expressions</em>.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">AND</span><span class="p">,</span> <span class="n">CONS</span><span class="p">,</span> <span class="n">KSTAR</span><span class="p">,</span> <span class="n">NOT</span><span class="p">,</span> <span class="n">OR</span> <span class="o">=</span> <span class="s1">'and cons * not or'</span><span class="o">.</span><span class="n">split</span><span class="p">()</span> <span class="c1"># Tags are just strings.</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Because they are formed of <code class="docutils literal notranslate"><span class="pre">frozenset</span></code>, <code class="docutils literal notranslate"><span class="pre">tuple</span></code> and <code class="docutils literal notranslate"><span class="pre">str</span></code> objects
|
||||||
|
only, these datastructures are immutable.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="string-representation-of-re-datastructures">
|
||||||
|
<h3>String Representation of RE Datastructures<a class="headerlink" href="#string-representation-of-re-datastructures" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
|
||||||
|
<span class="sd">'''</span>
|
||||||
|
<span class="sd"> Return a nice string repr for a regular expression datastructure.</span>
|
||||||
|
<span class="sd"> '''</span>
|
||||||
|
<span class="k">if</span> <span class="n">re</span> <span class="o">==</span> <span class="n">I</span><span class="p">:</span> <span class="k">return</span> <span class="s1">'.'</span>
|
||||||
|
<span class="k">if</span> <span class="n">re</span> <span class="ow">in</span> <span class="n">syms</span><span class="p">:</span> <span class="k">return</span> <span class="nb">next</span><span class="p">(</span><span class="nb">iter</span><span class="p">(</span><span class="n">re</span><span class="p">))</span>
|
||||||
|
<span class="k">if</span> <span class="n">re</span> <span class="o">==</span> <span class="n">y</span><span class="p">:</span> <span class="k">return</span> <span class="s1">'^'</span>
|
||||||
|
<span class="k">if</span> <span class="n">re</span> <span class="o">==</span> <span class="n">phi</span><span class="p">:</span> <span class="k">return</span> <span class="s1">'X'</span>
|
||||||
|
|
||||||
|
<span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">re</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">),</span> <span class="nb">repr</span><span class="p">(</span><span class="n">re</span><span class="p">)</span>
|
||||||
|
<span class="n">tag</span> <span class="o">=</span> <span class="n">re</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||||||
|
|
||||||
|
<span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">KSTAR</span><span class="p">:</span>
|
||||||
|
<span class="n">body</span> <span class="o">=</span> <span class="n">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||||||
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">body</span><span class="p">:</span> <span class="k">return</span> <span class="n">body</span>
|
||||||
|
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">body</span><span class="p">)</span> <span class="o">></span> <span class="mi">1</span><span class="p">:</span> <span class="k">return</span> <span class="s1">'('</span> <span class="o">+</span> <span class="n">body</span> <span class="o">+</span> <span class="s2">")*"</span>
|
||||||
|
<span class="k">return</span> <span class="n">body</span> <span class="o">+</span> <span class="s1">'*'</span>
|
||||||
|
|
||||||
|
<span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">NOT</span><span class="p">:</span>
|
||||||
|
<span class="n">body</span> <span class="o">=</span> <span class="n">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||||||
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">body</span><span class="p">:</span> <span class="k">return</span> <span class="n">body</span>
|
||||||
|
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">body</span><span class="p">)</span> <span class="o">></span> <span class="mi">1</span><span class="p">:</span> <span class="k">return</span> <span class="s1">'('</span> <span class="o">+</span> <span class="n">body</span> <span class="o">+</span> <span class="s2">")'"</span>
|
||||||
|
<span class="k">return</span> <span class="n">body</span> <span class="o">+</span> <span class="s2">"'"</span>
|
||||||
|
|
||||||
|
<span class="n">r</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
|
||||||
|
<span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">CONS</span><span class="p">:</span> <span class="k">return</span> <span class="n">r</span> <span class="o">+</span> <span class="n">s</span>
|
||||||
|
<span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">OR</span><span class="p">:</span> <span class="k">return</span> <span class="s1">'</span><span class="si">%s</span><span class="s1"> | </span><span class="si">%s</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
|
||||||
|
<span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">AND</span><span class="p">:</span> <span class="k">return</span> <span class="s1">'(</span><span class="si">%s</span><span class="s1">) & (</span><span class="si">%s</span><span class="s1">)'</span> <span class="o">%</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
|
||||||
|
|
||||||
|
<span class="k">raise</span> <span class="ne">ValueError</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="i">
|
||||||
|
<h3><code class="docutils literal notranslate"><span class="pre">I</span></code><a class="headerlink" href="#i" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>Match anything. Often spelled “.”</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">I</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="o">|</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">I</span> <span class="o">=</span> <span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">I</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">.</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="id1">
|
||||||
|
<h3><code class="docutils literal notranslate"><span class="pre">(.111.)</span> <span class="pre">&</span> <span class="pre">(.01</span> <span class="pre">+</span> <span class="pre">11*)'</span></code><a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>The example expression from Brzozowski:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&</span> <span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">+</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">'</span>
|
||||||
|
<span class="n">a</span> <span class="o">&</span> <span class="p">(</span><span class="n">b</span> <span class="o">+</span> <span class="n">c</span><span class="p">)</span><span class="s1">'</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Note that it contains one of everything.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">I</span><span class="p">))))</span>
|
||||||
|
<span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
|
||||||
|
<span class="n">c</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
|
||||||
|
<span class="n">it</span> <span class="o">=</span> <span class="p">(</span><span class="n">AND</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">NOT</span><span class="p">,</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">)))</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">it</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="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="nully">
|
||||||
|
<h3><code class="docutils literal notranslate"><span class="pre">nully()</span></code><a class="headerlink" href="#nully" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>Let’s get that auxiliary predicate function <code class="docutils literal notranslate"><span class="pre">δ</span></code> out of the way.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">nully</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
|
||||||
|
<span class="sd">'''</span>
|
||||||
|
<span class="sd"> δ - Return λ if λ ⊆ R otherwise ϕ.</span>
|
||||||
|
<span class="sd"> '''</span>
|
||||||
|
|
||||||
|
<span class="c1"># δ(a) → ϕ</span>
|
||||||
|
<span class="c1"># δ(ϕ) → ϕ</span>
|
||||||
|
<span class="k">if</span> <span class="n">R</span> <span class="ow">in</span> <span class="n">syms</span> <span class="ow">or</span> <span class="n">R</span> <span class="o">==</span> <span class="n">phi</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="n">phi</span>
|
||||||
|
|
||||||
|
<span class="c1"># δ(λ) → λ</span>
|
||||||
|
<span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="n">y</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="n">y</span>
|
||||||
|
|
||||||
|
<span class="n">tag</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||||||
|
|
||||||
|
<span class="c1"># δ(R*) → λ</span>
|
||||||
|
<span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">KSTAR</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="n">y</span>
|
||||||
|
|
||||||
|
<span class="c1"># δ(¬R) δ(R)≟ϕ → λ</span>
|
||||||
|
<span class="c1"># δ(¬R) δ(R)≟λ → ϕ</span>
|
||||||
|
<span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">NOT</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="n">phi</span> <span class="k">if</span> <span class="n">nully</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="k">else</span> <span class="n">y</span>
|
||||||
|
|
||||||
|
<span class="c1"># δ(R∘S) → δ(R) ∧ δ(S)</span>
|
||||||
|
<span class="c1"># δ(R ∧ S) → δ(R) ∧ δ(S)</span>
|
||||||
|
<span class="c1"># δ(R ∨ S) → δ(R) ∨ δ(S)</span>
|
||||||
|
<span class="n">r</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">nully</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">nully</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
|
||||||
|
<span class="k">return</span> <span class="n">r</span> <span class="o">&</span> <span class="n">s</span> <span class="k">if</span> <span class="n">tag</span> <span class="ow">in</span> <span class="p">{</span><span class="n">AND</span><span class="p">,</span> <span class="n">CONS</span><span class="p">}</span> <span class="k">else</span> <span class="n">r</span> <span class="o">|</span> <span class="n">s</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="no-compaction">
|
||||||
|
<h3>No “Compaction”<a class="headerlink" href="#no-compaction" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>This is the straightforward version with no “compaction”. It works fine,
|
||||||
|
but does waaaay too much work because the expressions grow each
|
||||||
|
derivation.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
|
||||||
|
|
||||||
|
<span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
|
||||||
|
|
||||||
|
<span class="c1"># ∂a(a) → λ</span>
|
||||||
|
<span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="p">{</span><span class="n">symbol</span><span class="p">}:</span>
|
||||||
|
<span class="k">return</span> <span class="n">y</span>
|
||||||
|
|
||||||
|
<span class="c1"># ∂a(λ) → ϕ</span>
|
||||||
|
<span class="c1"># ∂a(ϕ) → ϕ</span>
|
||||||
|
<span class="c1"># ∂a(¬a) → ϕ</span>
|
||||||
|
<span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="n">y</span> <span class="ow">or</span> <span class="n">R</span> <span class="o">==</span> <span class="n">phi</span> <span class="ow">or</span> <span class="n">R</span> <span class="ow">in</span> <span class="n">syms</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="n">phi</span>
|
||||||
|
|
||||||
|
<span class="n">tag</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||||||
|
|
||||||
|
<span class="c1"># ∂a(R*) → ∂a(R)∘R*</span>
|
||||||
|
<span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">KSTAR</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">R</span><span class="p">)</span>
|
||||||
|
|
||||||
|
<span class="c1"># ∂a(¬R) → ¬∂a(R)</span>
|
||||||
|
<span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">NOT</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="p">(</span><span class="n">NOT</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>
|
||||||
|
|
||||||
|
<span class="n">r</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
|
||||||
|
|
||||||
|
<span class="c1"># ∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)</span>
|
||||||
|
<span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">CONS</span><span class="p">:</span>
|
||||||
|
<span class="n">A</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">s</span><span class="p">)</span> <span class="c1"># A = ∂a(R)∘S</span>
|
||||||
|
<span class="c1"># A ∨ δ(R) ∘ ∂a(S)</span>
|
||||||
|
<span class="c1"># A ∨ λ ∘ ∂a(S) → A ∨ ∂a(S)</span>
|
||||||
|
<span class="c1"># A ∨ ϕ ∘ ∂a(S) → A ∨ ϕ → A</span>
|
||||||
|
<span class="k">return</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">A</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">s</span><span class="p">))</span> <span class="k">if</span> <span class="n">nully</span><span class="p">(</span><span class="n">r</span><span class="p">)</span> <span class="k">else</span> <span class="n">A</span>
|
||||||
|
|
||||||
|
<span class="c1"># ∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)</span>
|
||||||
|
<span class="c1"># ∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)</span>
|
||||||
|
<span class="k">return</span> <span class="p">(</span><span class="n">tag</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">derv</span><span class="p">(</span><span class="n">s</span><span class="p">))</span>
|
||||||
|
|
||||||
|
<span class="k">return</span> <span class="n">derv</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="compaction-rules">
|
||||||
|
<h3>Compaction Rules<a class="headerlink" href="#compaction-rules" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_compaction_rule</span><span class="p">(</span><span class="n">relation</span><span class="p">,</span> <span class="n">one</span><span class="p">,</span> <span class="n">zero</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
||||||
|
<span class="k">return</span> <span class="p">(</span>
|
||||||
|
<span class="n">b</span> <span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="n">one</span> <span class="k">else</span> <span class="c1"># R*1 = 1*R = R</span>
|
||||||
|
<span class="n">a</span> <span class="k">if</span> <span class="n">b</span> <span class="o">==</span> <span class="n">one</span> <span class="k">else</span>
|
||||||
|
<span class="n">zero</span> <span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="n">zero</span> <span class="ow">or</span> <span class="n">b</span> <span class="o">==</span> <span class="n">zero</span> <span class="k">else</span> <span class="c1"># R*0 = 0*R = 0</span>
|
||||||
|
<span class="p">(</span><span class="n">relation</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
|
||||||
|
<span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>An elegant symmetry.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># R ∧ I = I ∧ R = R</span>
|
||||||
|
<span class="c1"># R ∧ ϕ = ϕ ∧ R = ϕ</span>
|
||||||
|
<span class="n">_and</span> <span class="o">=</span> <span class="n">curry</span><span class="p">(</span><span class="n">_compaction_rule</span><span class="p">,</span> <span class="n">AND</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
|
||||||
|
|
||||||
|
<span class="c1"># R ∨ ϕ = ϕ ∨ R = R</span>
|
||||||
|
<span class="c1"># R ∨ I = I ∨ R = I</span>
|
||||||
|
<span class="n">_or</span> <span class="o">=</span> <span class="n">curry</span><span class="p">(</span><span class="n">_compaction_rule</span><span class="p">,</span> <span class="n">OR</span><span class="p">,</span> <span class="n">phi</span><span class="p">,</span> <span class="n">I</span><span class="p">)</span>
|
||||||
|
|
||||||
|
<span class="c1"># R∘λ = λ∘R = R</span>
|
||||||
|
<span class="c1"># R∘ϕ = ϕ∘R = ϕ</span>
|
||||||
|
<span class="n">_cons</span> <span class="o">=</span> <span class="n">curry</span><span class="p">(</span><span class="n">_compaction_rule</span><span class="p">,</span> <span class="n">CONS</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="memoizing">
|
||||||
|
<h3>Memoizing<a class="headerlink" href="#memoizing" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>We can save re-processing by remembering results we have already
|
||||||
|
computed. RE datastructures are immutable and the <code class="docutils literal notranslate"><span class="pre">derv()</span></code> functions
|
||||||
|
are <em>pure</em> so this is fine.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">Memo</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
|
||||||
|
|
||||||
|
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
|
||||||
|
<span class="bp">self</span><span class="o">.</span><span class="n">f</span> <span class="o">=</span> <span class="n">f</span>
|
||||||
|
<span class="bp">self</span><span class="o">.</span><span class="n">calls</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hits</span> <span class="o">=</span> <span class="mi">0</span>
|
||||||
|
<span class="bp">self</span><span class="o">.</span><span class="n">mem</span> <span class="o">=</span> <span class="p">{}</span>
|
||||||
|
|
||||||
|
<span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">):</span>
|
||||||
|
<span class="bp">self</span><span class="o">.</span><span class="n">calls</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||||
|
<span class="k">try</span><span class="p">:</span>
|
||||||
|
<span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mem</span><span class="p">[</span><span class="n">key</span><span class="p">]</span>
|
||||||
|
<span class="bp">self</span><span class="o">.</span><span class="n">hits</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||||
|
<span class="k">except</span> <span class="ne">KeyError</span><span class="p">:</span>
|
||||||
|
<span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mem</span><span class="p">[</span><span class="n">key</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">f</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
|
||||||
|
<span class="k">return</span> <span class="n">result</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="with-compaction">
|
||||||
|
<h3>With “Compaction”<a class="headerlink" href="#with-compaction" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>This version uses the rules above to perform compaction. It keeps the
|
||||||
|
expressions from growing too large.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D_compaction</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
|
||||||
|
|
||||||
|
<span class="nd">@Memo</span>
|
||||||
|
<span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
|
||||||
|
|
||||||
|
<span class="c1"># ∂a(a) → λ</span>
|
||||||
|
<span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="p">{</span><span class="n">symbol</span><span class="p">}:</span>
|
||||||
|
<span class="k">return</span> <span class="n">y</span>
|
||||||
|
|
||||||
|
<span class="c1"># ∂a(λ) → ϕ</span>
|
||||||
|
<span class="c1"># ∂a(ϕ) → ϕ</span>
|
||||||
|
<span class="c1"># ∂a(¬a) → ϕ</span>
|
||||||
|
<span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="n">y</span> <span class="ow">or</span> <span class="n">R</span> <span class="o">==</span> <span class="n">phi</span> <span class="ow">or</span> <span class="n">R</span> <span class="ow">in</span> <span class="n">syms</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="n">phi</span>
|
||||||
|
|
||||||
|
<span class="n">tag</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||||||
|
|
||||||
|
<span class="c1"># ∂a(R*) → ∂a(R)∘R*</span>
|
||||||
|
<span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">KSTAR</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="n">_cons</span><span class="p">(</span><span class="n">derv</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">R</span><span class="p">)</span>
|
||||||
|
|
||||||
|
<span class="c1"># ∂a(¬R) → ¬∂a(R)</span>
|
||||||
|
<span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">NOT</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="p">(</span><span class="n">NOT</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>
|
||||||
|
|
||||||
|
<span class="n">r</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
|
||||||
|
|
||||||
|
<span class="c1"># ∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)</span>
|
||||||
|
<span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">CONS</span><span class="p">:</span>
|
||||||
|
<span class="n">A</span> <span class="o">=</span> <span class="n">_cons</span><span class="p">(</span><span class="n">derv</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">s</span><span class="p">)</span> <span class="c1"># A = ∂a(r)∘s</span>
|
||||||
|
<span class="c1"># A ∨ δ(R) ∘ ∂a(S)</span>
|
||||||
|
<span class="c1"># A ∨ λ ∘ ∂a(S) → A ∨ ∂a(S)</span>
|
||||||
|
<span class="c1"># A ∨ ϕ ∘ ∂a(S) → A ∨ ϕ → A</span>
|
||||||
|
<span class="k">return</span> <span class="n">_or</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">s</span><span class="p">))</span> <span class="k">if</span> <span class="n">nully</span><span class="p">(</span><span class="n">r</span><span class="p">)</span> <span class="k">else</span> <span class="n">A</span>
|
||||||
|
|
||||||
|
<span class="c1"># ∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)</span>
|
||||||
|
<span class="c1"># ∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)</span>
|
||||||
|
<span class="n">dr</span><span class="p">,</span> <span class="n">ds</span> <span class="o">=</span> <span class="n">derv</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">derv</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
|
||||||
|
<span class="k">return</span> <span class="n">_and</span><span class="p">(</span><span class="n">dr</span><span class="p">,</span> <span class="n">ds</span><span class="p">)</span> <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">AND</span> <span class="k">else</span> <span class="n">_or</span><span class="p">(</span><span class="n">dr</span><span class="p">,</span> <span class="n">ds</span><span class="p">)</span>
|
||||||
|
|
||||||
|
<span class="k">return</span> <span class="n">derv</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="let-s-try-it-out">
|
||||||
|
<h2>Let’s try it out…<a class="headerlink" href="#let-s-try-it-out" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>(FIXME: redo.)</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">o</span><span class="p">,</span> <span class="n">z</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">'0'</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">'1'</span><span class="p">)</span>
|
||||||
|
<span class="n">REs</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
|
||||||
|
<span class="n">N</span> <span class="o">=</span> <span class="mi">5</span>
|
||||||
|
<span class="n">names</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">product</span><span class="p">(</span><span class="o">*</span><span class="p">(</span><span class="n">N</span> <span class="o">*</span> <span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)])))</span>
|
||||||
|
<span class="n">dervs</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">product</span><span class="p">(</span><span class="o">*</span><span class="p">(</span><span class="n">N</span> <span class="o">*</span> <span class="p">[(</span><span class="n">o</span><span class="p">,</span> <span class="n">z</span><span class="p">)])))</span>
|
||||||
|
<span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">ds</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">names</span><span class="p">,</span> <span class="n">dervs</span><span class="p">):</span>
|
||||||
|
<span class="n">R</span> <span class="o">=</span> <span class="n">it</span>
|
||||||
|
<span class="n">ds</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">ds</span><span class="p">)</span>
|
||||||
|
<span class="k">while</span> <span class="n">ds</span><span class="p">:</span>
|
||||||
|
<span class="n">R</span> <span class="o">=</span> <span class="n">ds</span><span class="o">.</span><span class="n">pop</span><span class="p">()(</span><span class="n">R</span><span class="p">)</span>
|
||||||
|
<span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="n">phi</span> <span class="ow">or</span> <span class="n">R</span> <span class="o">==</span> <span class="n">I</span><span class="p">:</span>
|
||||||
|
<span class="k">break</span>
|
||||||
|
<span class="n">REs</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">R</span><span class="p">)</span>
|
||||||
|
|
||||||
|
<span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">it</span><span class="p">)</span> <span class="p">;</span> <span class="nb">print</span>
|
||||||
|
<span class="nb">print</span> <span class="n">o</span><span class="o">.</span><span class="n">hits</span><span class="p">,</span> <span class="s1">'/'</span><span class="p">,</span> <span class="n">o</span><span class="o">.</span><span class="n">calls</span>
|
||||||
|
<span class="nb">print</span> <span class="n">z</span><span class="o">.</span><span class="n">hits</span><span class="p">,</span> <span class="s1">'/'</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">calls</span>
|
||||||
|
<span class="nb">print</span>
|
||||||
|
<span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">stringy</span><span class="p">,</span> <span class="n">REs</span><span class="p">),</span> <span class="n">key</span><span class="o">=</span><span class="k">lambda</span> <span class="n">n</span><span class="p">:</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">n</span><span class="p">),</span> <span class="n">n</span><span class="p">)):</span>
|
||||||
|
<span class="nb">print</span> <span class="n">s</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
|
||||||
|
<span class="mi">92</span> <span class="o">/</span> <span class="mi">122</span>
|
||||||
|
<span class="mi">92</span> <span class="o">/</span> <span class="mi">122</span>
|
||||||
|
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mi">01</span><span class="p">)</span><span class="s1">'</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="p">)</span><span class="s1">'</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="o">^</span><span class="p">)</span><span class="s1">'</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">'</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="o">^</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Should match:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
|
||||||
|
<span class="mi">92</span> <span class="o">/</span> <span class="mi">122</span>
|
||||||
|
<span class="mi">92</span> <span class="o">/</span> <span class="mi">122</span>
|
||||||
|
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="p">)</span><span class="s1">'</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span> <span class="p">)</span><span class="s1">'</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="o">^</span> <span class="p">)</span><span class="s1">'</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">'</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span> <span class="p">)</span><span class="s1">')</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="o">^</span> <span class="p">)</span><span class="s1">')</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="p">)</span><span class="s1">')</span>
|
||||||
|
<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="larger-alphabets">
|
||||||
|
<h2>Larger Alphabets<a class="headerlink" href="#larger-alphabets" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>We could parse larger alphabets by defining patterns for e.g. each byte
|
||||||
|
of the ASCII code. Or we can generalize this code. If you study the code
|
||||||
|
above you’ll see that we never use the “set-ness” of the symbols <code class="docutils literal notranslate"><span class="pre">O</span></code>
|
||||||
|
and <code class="docutils literal notranslate"><span class="pre">l</span></code>. The only time Python set operators (<code class="docutils literal notranslate"><span class="pre">&</span></code> and <code class="docutils literal notranslate"><span class="pre">|</span></code>) appear
|
||||||
|
is in the <code class="docutils literal notranslate"><span class="pre">nully()</span></code> function, and there they operate on (recursively
|
||||||
|
computed) outputs of that function, never <code class="docutils literal notranslate"><span class="pre">O</span></code> and <code class="docutils literal notranslate"><span class="pre">l</span></code>.</p>
|
||||||
|
<p>What if we try:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>(OR, O, l)
|
||||||
|
|
||||||
|
∂1((OR, O, l))
|
||||||
|
∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
|
||||||
|
∂1(O) ∨ ∂1(l)
|
||||||
|
∂a(¬a) → ϕ
|
||||||
|
ϕ ∨ ∂1(l)
|
||||||
|
∂a(a) → λ
|
||||||
|
ϕ ∨ λ
|
||||||
|
ϕ ∨ R = R
|
||||||
|
λ
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>And compare it to:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>{'0', '1')
|
||||||
|
|
||||||
|
∂1({'0', '1'))
|
||||||
|
∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
|
||||||
|
∂1({'0')) ∨ ∂1({'1'))
|
||||||
|
∂a(¬a) → ϕ
|
||||||
|
ϕ ∨ ∂1({'1'))
|
||||||
|
∂a(a) → λ
|
||||||
|
ϕ ∨ λ
|
||||||
|
ϕ ∨ R = R
|
||||||
|
λ
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>This suggests that we should be able to alter the functions above to
|
||||||
|
detect sets and deal with them appropriately. Exercise for the Reader
|
||||||
|
for now.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="state-machine">
|
||||||
|
<h2>State Machine<a class="headerlink" href="#state-machine" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>We can drive the regular expressions to flesh out the underlying state
|
||||||
|
machine transition table.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">.</span><span class="mf">111.</span> <span class="o">&</span> <span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">+</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">'</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Says, “Three or more 1’s and not ending in 01 nor composed of all 1’s.”</p>
|
||||||
|
<div class="figure">
|
||||||
|
<img alt="State Machine Diagram" src="../_images/omg.svg" /></div>
|
||||||
|
<p>Start at <code class="docutils literal notranslate"><span class="pre">a</span></code> and follow the transition arrows according to their
|
||||||
|
labels. Accepting states have a double outline. (Graphic generated with
|
||||||
|
<a class="reference external" href="http://www.graphviz.org/">Dot from Graphviz</a>.) You’ll see that only
|
||||||
|
paths that lead to one of the accepting states will match the regular
|
||||||
|
expression. All other paths will terminate at one of the non-accepting
|
||||||
|
states.</p>
|
||||||
|
<p>There’s a happy path to <code class="docutils literal notranslate"><span class="pre">g</span></code> along 111:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>a→c→e→g
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>After you reach <code class="docutils literal notranslate"><span class="pre">g</span></code> you’re stuck there eating 1’s until you see a 0,
|
||||||
|
which takes you to the <code class="docutils literal notranslate"><span class="pre">i→j→i|i→j→h→i</span></code> “trap”. You can’t reach any
|
||||||
|
other states from those two loops.</p>
|
||||||
|
<p>If you see a 0 before you see 111 you will reach <code class="docutils literal notranslate"><span class="pre">b</span></code>, which forms
|
||||||
|
another “trap” with <code class="docutils literal notranslate"><span class="pre">d</span></code> and <code class="docutils literal notranslate"><span class="pre">f</span></code>. The only way out is another happy
|
||||||
|
path along 111 to <code class="docutils literal notranslate"><span class="pre">h</span></code>:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>b→d→f→h
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Once you have reached <code class="docutils literal notranslate"><span class="pre">h</span></code> you can see as many 1’s or as many 0’ in a
|
||||||
|
row and still be either still at <code class="docutils literal notranslate"><span class="pre">h</span></code> (for 1’s) or move to <code class="docutils literal notranslate"><span class="pre">i</span></code> (for
|
||||||
|
0’s). If you find yourself at <code class="docutils literal notranslate"><span class="pre">i</span></code> you can see as many 0’s, or
|
||||||
|
repetitions of 10, as there are, but if you see just a 1 you move to
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">j</span></code>.</p>
|
||||||
|
<div class="section" id="re-to-fsm">
|
||||||
|
<h3>RE to FSM<a class="headerlink" href="#re-to-fsm" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>So how do we get the state machine from the regular expression?</p>
|
||||||
|
<p>It turns out that each RE is effectively a state, and each arrow points
|
||||||
|
to the derivative RE in respect to the arrow’s symbol.</p>
|
||||||
|
<p>If we label the initial RE <code class="docutils literal notranslate"><span class="pre">a</span></code>, we can say:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>a --0--> ∂0(a)
|
||||||
|
a --1--> ∂1(a)
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>And so on, each new unique RE is a new state in the FSM table.</p>
|
||||||
|
<p>Here are the derived REs at each state:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
<span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
<span class="n">c</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
<span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="o">^</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
<span class="n">e</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
<span class="n">f</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span><span class="p">)</span><span class="s1">')</span>
|
||||||
|
<span class="n">g</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">'</span>
|
||||||
|
<span class="n">h</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mi">01</span><span class="p">)</span><span class="s1">'</span>
|
||||||
|
<span class="n">i</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="p">)</span><span class="s1">'</span>
|
||||||
|
<span class="n">j</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="o">^</span><span class="p">)</span><span class="s1">'</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>You can see the one-way nature of the <code class="docutils literal notranslate"><span class="pre">g</span></code> state and the <code class="docutils literal notranslate"><span class="pre">hij</span></code> “trap”
|
||||||
|
in the way that the <code class="docutils literal notranslate"><span class="pre">.111.</span></code> on the left-hand side of the <code class="docutils literal notranslate"><span class="pre">&</span></code>
|
||||||
|
disappears once it has been matched.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="k">import</span> <span class="n">defaultdict</span>
|
||||||
|
<span class="kn">from</span> <span class="nn">pprint</span> <span class="k">import</span> <span class="n">pprint</span>
|
||||||
|
<span class="kn">from</span> <span class="nn">string</span> <span class="k">import</span> <span class="n">ascii_lowercase</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">d0</span><span class="p">,</span> <span class="n">d1</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">'0'</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">'1'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="explore">
|
||||||
|
<h3><code class="docutils literal notranslate"><span class="pre">explore()</span></code><a class="headerlink" href="#explore" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">explore</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
|
||||||
|
|
||||||
|
<span class="c1"># Don't have more than 26 states...</span>
|
||||||
|
<span class="n">names</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">iter</span><span class="p">(</span><span class="n">ascii_lowercase</span><span class="p">)</span><span class="o">.</span><span class="n">next</span><span class="p">)</span>
|
||||||
|
|
||||||
|
<span class="n">table</span><span class="p">,</span> <span class="n">accepting</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(),</span> <span class="nb">set</span><span class="p">()</span>
|
||||||
|
|
||||||
|
<span class="n">to_check</span> <span class="o">=</span> <span class="p">{</span><span class="n">re</span><span class="p">}</span>
|
||||||
|
<span class="k">while</span> <span class="n">to_check</span><span class="p">:</span>
|
||||||
|
|
||||||
|
<span class="n">re</span> <span class="o">=</span> <span class="n">to_check</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
|
||||||
|
<span class="n">state_name</span> <span class="o">=</span> <span class="n">names</span><span class="p">[</span><span class="n">re</span><span class="p">]</span>
|
||||||
|
|
||||||
|
<span class="k">if</span> <span class="p">(</span><span class="n">state_name</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="ow">in</span> <span class="n">table</span><span class="p">:</span>
|
||||||
|
<span class="k">continue</span>
|
||||||
|
|
||||||
|
<span class="k">if</span> <span class="n">nully</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
|
||||||
|
<span class="n">accepting</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">state_name</span><span class="p">)</span>
|
||||||
|
|
||||||
|
<span class="n">o</span><span class="p">,</span> <span class="n">i</span> <span class="o">=</span> <span class="n">d0</span><span class="p">(</span><span class="n">re</span><span class="p">),</span> <span class="n">d1</span><span class="p">(</span><span class="n">re</span><span class="p">)</span>
|
||||||
|
<span class="n">table</span><span class="p">[</span><span class="n">state_name</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">names</span><span class="p">[</span><span class="n">o</span><span class="p">]</span> <span class="p">;</span> <span class="n">to_check</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">o</span><span class="p">)</span>
|
||||||
|
<span class="n">table</span><span class="p">[</span><span class="n">state_name</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">names</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="p">;</span> <span class="n">to_check</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
|
||||||
|
|
||||||
|
<span class="k">return</span> <span class="n">table</span><span class="p">,</span> <span class="n">accepting</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span> <span class="o">=</span> <span class="n">explore</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
|
||||||
|
<span class="n">table</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{(</span><span class="s1">'a'</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span> <span class="s1">'b'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'a'</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">'c'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'b'</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span> <span class="s1">'b'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'b'</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">'d'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'c'</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span> <span class="s1">'b'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'c'</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">'e'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'d'</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span> <span class="s1">'b'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'d'</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">'f'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'e'</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span> <span class="s1">'b'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'e'</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">'g'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'f'</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span> <span class="s1">'b'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'f'</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">'h'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'g'</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span> <span class="s1">'i'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'g'</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">'g'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'h'</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span> <span class="s1">'i'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'h'</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">'h'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'i'</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span> <span class="s1">'i'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'i'</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">'j'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'j'</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span> <span class="s1">'i'</span><span class="p">,</span>
|
||||||
|
<span class="p">(</span><span class="s1">'j'</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">'h'</span><span class="p">}</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">accepting</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="s1">'h'</span><span class="p">,</span> <span class="s1">'i'</span><span class="p">}</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="generate-diagram">
|
||||||
|
<h3>Generate Diagram<a class="headerlink" href="#generate-diagram" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>Once we have the FSM table and the set of accepting states we can
|
||||||
|
generate the diagram above.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">_template</span> <span class="o">=</span> <span class="s1">'''</span><span class="se">\</span>
|
||||||
|
<span class="s1">digraph finite_state_machine {</span>
|
||||||
|
<span class="s1"> rankdir=LR;</span>
|
||||||
|
<span class="s1"> size="8,5"</span>
|
||||||
|
<span class="s1"> node [shape = doublecircle]; </span><span class="si">%s</span><span class="s1">;</span>
|
||||||
|
<span class="s1"> node [shape = circle];</span>
|
||||||
|
<span class="si">%s</span><span class="s1"></span>
|
||||||
|
<span class="s1">}</span>
|
||||||
|
<span class="s1">'''</span>
|
||||||
|
|
||||||
|
<span class="k">def</span> <span class="nf">link</span><span class="p">(</span><span class="n">fr</span><span class="p">,</span> <span class="n">nm</span><span class="p">,</span> <span class="n">label</span><span class="p">):</span>
|
||||||
|
<span class="k">return</span> <span class="s1">' </span><span class="si">%s</span><span class="s1"> -> </span><span class="si">%s</span><span class="s1"> [ label = "</span><span class="si">%s</span><span class="s1">" ];'</span> <span class="o">%</span> <span class="p">(</span><span class="n">fr</span><span class="p">,</span> <span class="n">nm</span><span class="p">,</span> <span class="n">label</span><span class="p">)</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="k">def</span> <span class="nf">make_graph</span><span class="p">(</span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span><span class="p">):</span>
|
||||||
|
<span class="k">return</span> <span class="n">_template</span> <span class="o">%</span> <span class="p">(</span>
|
||||||
|
<span class="s1">' '</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">accepting</span><span class="p">),</span>
|
||||||
|
<span class="s1">'</span><span class="se">\n</span><span class="s1">'</span><span class="o">.</span><span class="n">join</span><span class="p">(</span>
|
||||||
|
<span class="n">link</span><span class="p">(</span><span class="n">from_</span><span class="p">,</span> <span class="n">to</span><span class="p">,</span> <span class="n">char</span><span class="p">)</span>
|
||||||
|
<span class="k">for</span> <span class="p">(</span><span class="n">from_</span><span class="p">,</span> <span class="n">char</span><span class="p">),</span> <span class="p">(</span><span class="n">to</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">table</span><span class="o">.</span><span class="n">iteritems</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="nb">print</span> <span class="n">make_graph</span><span class="p">(</span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">digraph</span> <span class="n">finite_state_machine</span> <span class="p">{</span>
|
||||||
|
<span class="n">rankdir</span><span class="o">=</span><span class="n">LR</span><span class="p">;</span>
|
||||||
|
<span class="n">size</span><span class="o">=</span><span class="s2">"8,5"</span>
|
||||||
|
<span class="n">node</span> <span class="p">[</span><span class="n">shape</span> <span class="o">=</span> <span class="n">doublecircle</span><span class="p">];</span> <span class="n">i</span> <span class="n">h</span><span class="p">;</span>
|
||||||
|
<span class="n">node</span> <span class="p">[</span><span class="n">shape</span> <span class="o">=</span> <span class="n">circle</span><span class="p">];</span>
|
||||||
|
<span class="n">a</span> <span class="o">-></span> <span class="n">b</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"0"</span> <span class="p">];</span>
|
||||||
|
<span class="n">a</span> <span class="o">-></span> <span class="n">c</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"1"</span> <span class="p">];</span>
|
||||||
|
<span class="n">b</span> <span class="o">-></span> <span class="n">b</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"0"</span> <span class="p">];</span>
|
||||||
|
<span class="n">b</span> <span class="o">-></span> <span class="n">d</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"1"</span> <span class="p">];</span>
|
||||||
|
<span class="n">c</span> <span class="o">-></span> <span class="n">b</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"0"</span> <span class="p">];</span>
|
||||||
|
<span class="n">c</span> <span class="o">-></span> <span class="n">e</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"1"</span> <span class="p">];</span>
|
||||||
|
<span class="n">d</span> <span class="o">-></span> <span class="n">b</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"0"</span> <span class="p">];</span>
|
||||||
|
<span class="n">d</span> <span class="o">-></span> <span class="n">f</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"1"</span> <span class="p">];</span>
|
||||||
|
<span class="n">e</span> <span class="o">-></span> <span class="n">b</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"0"</span> <span class="p">];</span>
|
||||||
|
<span class="n">e</span> <span class="o">-></span> <span class="n">g</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"1"</span> <span class="p">];</span>
|
||||||
|
<span class="n">f</span> <span class="o">-></span> <span class="n">b</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"0"</span> <span class="p">];</span>
|
||||||
|
<span class="n">f</span> <span class="o">-></span> <span class="n">h</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"1"</span> <span class="p">];</span>
|
||||||
|
<span class="n">g</span> <span class="o">-></span> <span class="n">i</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"0"</span> <span class="p">];</span>
|
||||||
|
<span class="n">g</span> <span class="o">-></span> <span class="n">g</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"1"</span> <span class="p">];</span>
|
||||||
|
<span class="n">h</span> <span class="o">-></span> <span class="n">i</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"0"</span> <span class="p">];</span>
|
||||||
|
<span class="n">h</span> <span class="o">-></span> <span class="n">h</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"1"</span> <span class="p">];</span>
|
||||||
|
<span class="n">i</span> <span class="o">-></span> <span class="n">i</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"0"</span> <span class="p">];</span>
|
||||||
|
<span class="n">i</span> <span class="o">-></span> <span class="n">j</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"1"</span> <span class="p">];</span>
|
||||||
|
<span class="n">j</span> <span class="o">-></span> <span class="n">i</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"0"</span> <span class="p">];</span>
|
||||||
|
<span class="n">j</span> <span class="o">-></span> <span class="n">h</span> <span class="p">[</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"1"</span> <span class="p">];</span>
|
||||||
|
<span class="p">}</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="drive-a-fsm">
|
||||||
|
<h3>Drive a FSM<a class="headerlink" href="#drive-a-fsm" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>There are <em>lots</em> of FSM libraries already. Once you have the state
|
||||||
|
transition table they should all be straightforward to use. State
|
||||||
|
Machine code is very simple. Just for fun, here is an implementation in
|
||||||
|
Python that imitates what “compiled” FSM code might look like in an
|
||||||
|
“unrolled” form. Most FSM code uses a little driver loop and a table
|
||||||
|
datastructure, the code below instead acts like JMP instructions
|
||||||
|
(“jump”, or GOTO in higher-level-but-still-low-level languages) to
|
||||||
|
hard-code the information in the table into a little patch of branches.</p>
|
||||||
|
<div class="section" id="trampoline-function">
|
||||||
|
<h4>Trampoline Function<a class="headerlink" href="#trampoline-function" title="Permalink to this headline">¶</a></h4>
|
||||||
|
<p>Python has no GOTO statement but we can fake it with a “trampoline”
|
||||||
|
function.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">trampoline</span><span class="p">(</span><span class="n">input_</span><span class="p">,</span> <span class="n">jump_from</span><span class="p">,</span> <span class="n">accepting</span><span class="p">):</span>
|
||||||
|
<span class="n">I</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">input_</span><span class="p">)</span>
|
||||||
|
<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
|
||||||
|
<span class="k">try</span><span class="p">:</span>
|
||||||
|
<span class="n">bounce_to</span> <span class="o">=</span> <span class="n">jump_from</span><span class="p">(</span><span class="n">I</span><span class="p">)</span>
|
||||||
|
<span class="k">except</span> <span class="ne">StopIteration</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="n">jump_from</span> <span class="ow">in</span> <span class="n">accepting</span>
|
||||||
|
<span class="n">jump_from</span> <span class="o">=</span> <span class="n">bounce_to</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="stream-functions">
|
||||||
|
<h4>Stream Functions<a class="headerlink" href="#stream-functions" title="Permalink to this headline">¶</a></h4>
|
||||||
|
<p>Little helpers to process the iterator of our data (a “stream” of “1”
|
||||||
|
and “0” characters, not bits.)</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">getch</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="nb">int</span><span class="p">(</span><span class="nb">next</span><span class="p">(</span><span class="n">I</span><span class="p">))</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="k">def</span> <span class="nf">_1</span><span class="p">(</span><span class="n">I</span><span class="p">):</span>
|
||||||
|
<span class="sd">'''Loop on ones.'''</span>
|
||||||
|
<span class="k">while</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">):</span> <span class="k">pass</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="k">def</span> <span class="nf">_0</span><span class="p">(</span><span class="n">I</span><span class="p">):</span>
|
||||||
|
<span class="sd">'''Loop on zeros.'''</span>
|
||||||
|
<span class="k">while</span> <span class="ow">not</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">):</span> <span class="k">pass</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="a-finite-state-machine">
|
||||||
|
<h4>A Finite State Machine<a class="headerlink" href="#a-finite-state-machine" title="Permalink to this headline">¶</a></h4>
|
||||||
|
<p>With those preliminaries out of the way, from the state table of
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">.111.</span> <span class="pre">&</span> <span class="pre">(.01</span> <span class="pre">+</span> <span class="pre">11*)'</span></code> we can immediately write down state machine
|
||||||
|
code. (You have to imagine that these are GOTO statements in C or
|
||||||
|
branches in assembly and that the state names are branch destination
|
||||||
|
labels.)</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">c</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
|
||||||
|
<span class="n">b</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">_0</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="ow">or</span> <span class="n">d</span>
|
||||||
|
<span class="n">c</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">e</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
|
||||||
|
<span class="n">d</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">f</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
|
||||||
|
<span class="n">e</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">g</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
|
||||||
|
<span class="n">f</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">h</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
|
||||||
|
<span class="n">g</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">_1</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="ow">or</span> <span class="n">i</span>
|
||||||
|
<span class="n">h</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">_1</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="ow">or</span> <span class="n">i</span>
|
||||||
|
<span class="n">i</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">_0</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="ow">or</span> <span class="n">j</span>
|
||||||
|
<span class="n">j</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">h</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">i</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Note that the implementations of <code class="docutils literal notranslate"><span class="pre">h</span></code> and <code class="docutils literal notranslate"><span class="pre">g</span></code> are identical ergo
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">h</span> <span class="pre">=</span> <span class="pre">g</span></code> and we could eliminate one in the code but <code class="docutils literal notranslate"><span class="pre">h</span></code> is an
|
||||||
|
accepting state and <code class="docutils literal notranslate"><span class="pre">g</span></code> isn’t.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">acceptable</span><span class="p">(</span><span class="n">input_</span><span class="p">):</span>
|
||||||
|
<span class="k">return</span> <span class="n">trampoline</span><span class="p">(</span><span class="n">input_</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="p">{</span><span class="n">h</span><span class="p">,</span> <span class="n">i</span><span class="p">})</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="o">**</span><span class="mi">5</span><span class="p">):</span>
|
||||||
|
<span class="n">s</span> <span class="o">=</span> <span class="nb">bin</span><span class="p">(</span><span class="n">n</span><span class="p">)[</span><span class="mi">2</span><span class="p">:]</span>
|
||||||
|
<span class="nb">print</span> <span class="s1">'</span><span class="si">%05s</span><span class="s1">'</span> <span class="o">%</span> <span class="n">s</span><span class="p">,</span> <span class="n">acceptable</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="mi">0</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">1</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">10</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">11</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">100</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">101</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">110</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">111</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">1000</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">1001</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">1010</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">1011</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">1100</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">1101</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">1110</span> <span class="kc">True</span>
|
||||||
|
<span class="mi">1111</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">10000</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">10001</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">10010</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">10011</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">10100</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">10101</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">10110</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">10111</span> <span class="kc">True</span>
|
||||||
|
<span class="mi">11000</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">11001</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">11010</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">11011</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">11100</span> <span class="kc">True</span>
|
||||||
|
<span class="mi">11101</span> <span class="kc">False</span>
|
||||||
|
<span class="mi">11110</span> <span class="kc">True</span>
|
||||||
|
<span class="mi">11111</span> <span class="kc">False</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="reversing-the-derivatives-to-generate-matching-strings">
|
||||||
|
<h2>Reversing the Derivatives to Generate Matching Strings<a class="headerlink" href="#reversing-the-derivatives-to-generate-matching-strings" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>(UNFINISHED) Brzozowski also shewed how to go from the state machine to
|
||||||
|
strings and expressions…</p>
|
||||||
|
<p>Each of these states is just a name for a Brzozowskian RE, and so, other
|
||||||
|
than the initial state <code class="docutils literal notranslate"><span class="pre">a</span></code>, they can can be described in terms of the
|
||||||
|
derivative-with-respect-to-N of some other state/RE:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">c</span> <span class="o">=</span> <span class="n">d1</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
|
||||||
|
<span class="n">b</span> <span class="o">=</span> <span class="n">d0</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
|
||||||
|
<span class="n">b</span> <span class="o">=</span> <span class="n">d0</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
|
||||||
|
<span class="o">...</span>
|
||||||
|
<span class="n">i</span> <span class="o">=</span> <span class="n">d0</span><span class="p">(</span><span class="n">j</span><span class="p">)</span>
|
||||||
|
<span class="n">j</span> <span class="o">=</span> <span class="n">d1</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Consider:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">c</span> <span class="o">=</span> <span class="n">d1</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
|
||||||
|
<span class="n">b</span> <span class="o">=</span> <span class="n">d0</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Substituting:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">=</span> <span class="n">d0</span><span class="p">(</span><span class="n">d1</span><span class="p">(</span><span class="n">a</span><span class="p">))</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Unwrapping:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">=</span> <span class="n">d10</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>‘’‘</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">j</span> <span class="o">=</span> <span class="n">d1</span><span class="p">(</span><span class="n">d0</span><span class="p">(</span><span class="n">j</span><span class="p">))</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Unwrapping:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">j</span> <span class="o">=</span> <span class="n">d1</span><span class="p">(</span><span class="n">d0</span><span class="p">(</span><span class="n">j</span><span class="p">))</span> <span class="o">=</span> <span class="n">d01</span><span class="p">(</span><span class="n">j</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>We have a loop or “fixed point”.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">j</span> <span class="o">=</span> <span class="n">d01</span><span class="p">(</span><span class="n">j</span><span class="p">)</span> <span class="o">=</span> <span class="n">d0101</span><span class="p">(</span><span class="n">j</span><span class="p">)</span> <span class="o">=</span> <span class="n">d010101</span><span class="p">(</span><span class="n">j</span><span class="p">)</span> <span class="o">=</span> <span class="o">...</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>hmm…</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">j</span> <span class="o">=</span> <span class="p">(</span><span class="mi">01</span><span class="p">)</span><span class="o">*</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||||
|
<div class="sphinxsidebarwrapper">
|
||||||
|
<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||||
|
<ul>
|
||||||
|
<li><a class="reference internal" href="#">∂RE</a><ul>
|
||||||
|
<li><a class="reference internal" href="#brzozowski-s-derivatives-of-regular-expressions">Brzozowski’s Derivatives of Regular Expressions</a></li>
|
||||||
|
<li><a class="reference internal" href="#implementation">Implementation</a><ul>
|
||||||
|
<li><a class="reference internal" href="#and"><code class="docutils literal notranslate"><span class="pre">ϕ</span></code> and <code class="docutils literal notranslate"><span class="pre">λ</span></code></a></li>
|
||||||
|
<li><a class="reference internal" href="#two-letter-alphabet">Two-letter Alphabet</a></li>
|
||||||
|
<li><a class="reference internal" href="#representing-regular-expressions">Representing Regular Expressions</a></li>
|
||||||
|
<li><a class="reference internal" href="#string-representation-of-re-datastructures">String Representation of RE Datastructures</a></li>
|
||||||
|
<li><a class="reference internal" href="#i"><code class="docutils literal notranslate"><span class="pre">I</span></code></a></li>
|
||||||
|
<li><a class="reference internal" href="#id1"><code class="docutils literal notranslate"><span class="pre">(.111.)</span> <span class="pre">&</span> <span class="pre">(.01</span> <span class="pre">+</span> <span class="pre">11*)'</span></code></a></li>
|
||||||
|
<li><a class="reference internal" href="#nully"><code class="docutils literal notranslate"><span class="pre">nully()</span></code></a></li>
|
||||||
|
<li><a class="reference internal" href="#no-compaction">No “Compaction”</a></li>
|
||||||
|
<li><a class="reference internal" href="#compaction-rules">Compaction Rules</a></li>
|
||||||
|
<li><a class="reference internal" href="#memoizing">Memoizing</a></li>
|
||||||
|
<li><a class="reference internal" href="#with-compaction">With “Compaction”</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a class="reference internal" href="#let-s-try-it-out">Let’s try it out…</a></li>
|
||||||
|
<li><a class="reference internal" href="#larger-alphabets">Larger Alphabets</a></li>
|
||||||
|
<li><a class="reference internal" href="#state-machine">State Machine</a><ul>
|
||||||
|
<li><a class="reference internal" href="#re-to-fsm">RE to FSM</a></li>
|
||||||
|
<li><a class="reference internal" href="#explore"><code class="docutils literal notranslate"><span class="pre">explore()</span></code></a></li>
|
||||||
|
<li><a class="reference internal" href="#generate-diagram">Generate Diagram</a></li>
|
||||||
|
<li><a class="reference internal" href="#drive-a-fsm">Drive a FSM</a><ul>
|
||||||
|
<li><a class="reference internal" href="#trampoline-function">Trampoline Function</a></li>
|
||||||
|
<li><a class="reference internal" href="#stream-functions">Stream Functions</a></li>
|
||||||
|
<li><a class="reference internal" href="#a-finite-state-machine">A Finite State Machine</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a class="reference internal" href="#reversing-the-derivatives-to-generate-matching-strings">Reversing the Derivatives to Generate Matching Strings</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
<div class="relations">
|
||||||
|
<h3>Related Topics</h3>
|
||||||
|
<ul>
|
||||||
|
<li><a href="../index.html">Documentation overview</a><ul>
|
||||||
|
</ul></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div role="note" aria-label="source link">
|
||||||
|
<h3>This Page</h3>
|
||||||
|
<ul class="this-page-menu">
|
||||||
|
<li><a href="../_sources/notebooks/Derivatives_of_Regular_Expressions.rst.txt"
|
||||||
|
rel="nofollow">Show Source</a></li>
|
||||||
|
</ul>
|
||||||
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||||||
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|
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<br />
|
||||||
|
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
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<div class="body" role="main">
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||||||
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<div class="section" id="the-four-fundamental-operations-of-definite-action">
|
||||||
|
<h1>The Four Fundamental Operations of Definite Action<a class="headerlink" href="#the-four-fundamental-operations-of-definite-action" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<p>All definite actions (computer program) can be defined by four
|
||||||
|
fundamental patterns of combination:</p>
|
||||||
|
<ol class="arabic simple">
|
||||||
|
<li>Sequence</li>
|
||||||
|
<li>Branch</li>
|
||||||
|
<li>Loop</li>
|
||||||
|
<li>Parallel</li>
|
||||||
|
</ol>
|
||||||
|
<div class="section" id="sequence">
|
||||||
|
<h2>Sequence<a class="headerlink" href="#sequence" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>Do one thing after another. In joy this is represented by putting two
|
||||||
|
symbols together, juxtaposition:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">foo</span> <span class="n">bar</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Operations have inputs and outputs. The outputs of <code class="docutils literal notranslate"><span class="pre">foo</span></code> must be
|
||||||
|
compatible in “arity”, type, and shape with the inputs of <code class="docutils literal notranslate"><span class="pre">bar</span></code>.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="branch">
|
||||||
|
<h2>Branch<a class="headerlink" href="#branch" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>Do one thing or another.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">boolean</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="n">branch</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="n">t</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="n">branch</span>
|
||||||
|
<span class="o">----------------------</span>
|
||||||
|
<span class="n">T</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="n">f</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="n">branch</span>
|
||||||
|
<span class="o">----------------------</span>
|
||||||
|
<span class="n">F</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="n">branch</span> <span class="o">==</span> <span class="n">unit</span> <span class="n">cons</span> <span class="n">swap</span> <span class="n">pick</span> <span class="n">i</span>
|
||||||
|
|
||||||
|
<span class="n">boolean</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="n">branch</span>
|
||||||
|
<span class="n">boolean</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="n">unit</span> <span class="n">cons</span> <span class="n">swap</span> <span class="n">pick</span> <span class="n">i</span>
|
||||||
|
<span class="n">boolean</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[[</span><span class="n">T</span><span class="p">]]</span> <span class="n">cons</span> <span class="n">swap</span> <span class="n">pick</span> <span class="n">i</span>
|
||||||
|
<span class="n">boolean</span> <span class="p">[[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]]</span> <span class="n">swap</span> <span class="n">pick</span> <span class="n">i</span>
|
||||||
|
<span class="p">[[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]]</span> <span class="n">boolean</span> <span class="n">pick</span> <span class="n">i</span>
|
||||||
|
<span class="p">[</span><span class="n">F</span><span class="o">-</span><span class="ow">or</span><span class="o">-</span><span class="n">T</span><span class="p">]</span> <span class="n">i</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Given some branch function <code class="docutils literal notranslate"><span class="pre">G</span></code>:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">G</span> <span class="o">==</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="n">branch</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Used in a sequence like so:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">foo</span> <span class="n">G</span> <span class="n">bar</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>The inputs and outputs of <code class="docutils literal notranslate"><span class="pre">F</span></code> and <code class="docutils literal notranslate"><span class="pre">T</span></code> must be compatible with the
|
||||||
|
outputs for <code class="docutils literal notranslate"><span class="pre">foo</span></code> and the inputs of <code class="docutils literal notranslate"><span class="pre">bar</span></code>, respectively.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">foo</span> <span class="n">F</span> <span class="n">bar</span>
|
||||||
|
|
||||||
|
<span class="n">foo</span> <span class="n">T</span> <span class="n">bar</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="ifte">
|
||||||
|
<h3><code class="docutils literal notranslate"><span class="pre">ifte</span></code><a class="headerlink" href="#ifte" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>Often it will be easier on the programmer to write branching code with
|
||||||
|
the predicate specified in a quote. The <code class="docutils literal notranslate"><span class="pre">ifte</span></code> combinator provides
|
||||||
|
this (<code class="docutils literal notranslate"><span class="pre">T</span></code> for “then” and <code class="docutils literal notranslate"><span class="pre">E</span></code> for “else”):</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="n">ifte</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Defined in terms of <code class="docutils literal notranslate"><span class="pre">branch</span></code>:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">ifte</span> <span class="o">==</span> <span class="p">[</span><span class="n">nullary</span> <span class="ow">not</span><span class="p">]</span> <span class="n">dip</span> <span class="n">branch</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>In this case, <code class="docutils literal notranslate"><span class="pre">P</span></code> must be compatible with the stack and return a
|
||||||
|
Boolean value, and <code class="docutils literal notranslate"><span class="pre">T</span></code> and <code class="docutils literal notranslate"><span class="pre">E</span></code> both must be compatible with the
|
||||||
|
preceeding and following functions, as described above for <code class="docutils literal notranslate"><span class="pre">F</span></code> and
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">T</span></code>. (Note that in the current implementation we are depending on
|
||||||
|
Python for the underlying semantics, so the Boolean value doesn’t <em>have</em>
|
||||||
|
to be Boolean because Python’s rules for “truthiness” will be used to
|
||||||
|
evaluate it. I reflect this in the structure of the stack effect comment
|
||||||
|
of <code class="docutils literal notranslate"><span class="pre">branch</span></code>, it will only accept Boolean values, and in the definition
|
||||||
|
of <code class="docutils literal notranslate"><span class="pre">ifte</span></code> above by including <code class="docutils literal notranslate"><span class="pre">not</span></code> in the quote, which also has the
|
||||||
|
effect that the subject quotes are in the proper order for <code class="docutils literal notranslate"><span class="pre">branch</span></code>.)</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="loop">
|
||||||
|
<h2>Loop<a class="headerlink" href="#loop" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>Do one thing zero or more times.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">boolean</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="n">t</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
<span class="o">----------------</span>
|
||||||
|
<span class="n">Q</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="o">...</span> <span class="n">f</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
<span class="o">--------------------</span>
|
||||||
|
<span class="o">...</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>The <code class="docutils literal notranslate"><span class="pre">loop</span></code> combinator generates a copy of itself in the true branch.
|
||||||
|
This is the hallmark of recursive defintions. In Thun there is no
|
||||||
|
equivalent to conventional loops. (There is, however, the <code class="docutils literal notranslate"><span class="pre">x</span></code>
|
||||||
|
combinator, defined as <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">==</span> <span class="pre">dup</span> <span class="pre">i</span></code>, which permits recursive
|
||||||
|
constructs that do not need to be directly self-referential, unlike
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">loop</span></code> and <code class="docutils literal notranslate"><span class="pre">genrec</span></code>.)</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">loop</span> <span class="o">==</span> <span class="p">[]</span> <span class="n">swap</span> <span class="p">[</span><span class="n">dup</span> <span class="n">dip</span> <span class="n">loop</span><span class="p">]</span> <span class="n">cons</span> <span class="n">branch</span>
|
||||||
|
|
||||||
|
<span class="n">boolean</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
<span class="n">boolean</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="p">[]</span> <span class="n">swap</span> <span class="p">[</span><span class="n">dup</span> <span class="n">dip</span> <span class="n">loop</span><span class="p">]</span> <span class="n">cons</span> <span class="n">branch</span>
|
||||||
|
<span class="n">boolean</span> <span class="p">[]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="p">[</span><span class="n">dup</span> <span class="n">dip</span> <span class="n">loop</span><span class="p">]</span> <span class="n">cons</span> <span class="n">branch</span>
|
||||||
|
<span class="n">boolean</span> <span class="p">[]</span> <span class="p">[[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dup</span> <span class="n">dip</span> <span class="n">loop</span><span class="p">]</span> <span class="n">branch</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>In action the false branch does nothing while the true branch does:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">t</span> <span class="p">[]</span> <span class="p">[[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dup</span> <span class="n">dip</span> <span class="n">loop</span><span class="p">]</span> <span class="n">branch</span>
|
||||||
|
<span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dup</span> <span class="n">dip</span> <span class="n">loop</span>
|
||||||
|
<span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dip</span> <span class="n">loop</span>
|
||||||
|
<span class="n">Q</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Because <code class="docutils literal notranslate"><span class="pre">loop</span></code> expects and consumes a Boolean value, the <code class="docutils literal notranslate"><span class="pre">Q</span></code>
|
||||||
|
function must be compatible with the previous stack <em>and itself</em> with a
|
||||||
|
boolean flag for the next iteration:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Q</span> <span class="o">==</span> <span class="n">G</span> <span class="n">b</span>
|
||||||
|
|
||||||
|
<span class="n">Q</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
<span class="n">G</span> <span class="n">b</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
<span class="n">G</span> <span class="n">Q</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
<span class="n">G</span> <span class="n">G</span> <span class="n">b</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
<span class="n">G</span> <span class="n">G</span> <span class="n">Q</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
<span class="n">G</span> <span class="n">G</span> <span class="n">G</span> <span class="n">b</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
<span class="n">G</span> <span class="n">G</span> <span class="n">G</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="while">
|
||||||
|
<h3><code class="docutils literal notranslate"><span class="pre">while</span></code><a class="headerlink" href="#while" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>Keep doing <code class="docutils literal notranslate"><span class="pre">B</span></code> <em>while</em> some predicate <code class="docutils literal notranslate"><span class="pre">P</span></code> is true. This is
|
||||||
|
convenient as the predicate function is made nullary automatically and
|
||||||
|
the body function can be designed without regard to leaving a Boolean
|
||||||
|
flag for the next iteration:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="k">while</span>
|
||||||
|
<span class="o">--------------------------------------</span>
|
||||||
|
<span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="n">nullary</span> <span class="p">[</span><span class="n">B</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="n">nullary</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="k">while</span> <span class="o">==</span> <span class="n">swap</span> <span class="p">[</span><span class="n">nullary</span><span class="p">]</span> <span class="n">cons</span> <span class="n">dup</span> <span class="n">dipd</span> <span class="n">concat</span> <span class="n">loop</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="k">while</span>
|
||||||
|
<span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="n">swap</span> <span class="p">[</span><span class="n">nullary</span><span class="p">]</span> <span class="n">cons</span> <span class="n">dup</span> <span class="n">dipd</span> <span class="n">concat</span> <span class="n">loop</span>
|
||||||
|
<span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">nullary</span><span class="p">]</span> <span class="n">cons</span> <span class="n">dup</span> <span class="n">dipd</span> <span class="n">concat</span> <span class="n">loop</span>
|
||||||
|
<span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[[</span><span class="n">P</span><span class="p">]</span> <span class="n">nullary</span><span class="p">]</span> <span class="n">dup</span> <span class="n">dipd</span> <span class="n">concat</span> <span class="n">loop</span>
|
||||||
|
<span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[[</span><span class="n">P</span><span class="p">]</span> <span class="n">nullary</span><span class="p">]</span> <span class="p">[[</span><span class="n">P</span><span class="p">]</span> <span class="n">nullary</span><span class="p">]</span> <span class="n">dipd</span> <span class="n">concat</span> <span class="n">loop</span>
|
||||||
|
<span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="n">nullary</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[[</span><span class="n">P</span><span class="p">]</span> <span class="n">nullary</span><span class="p">]</span> <span class="n">concat</span> <span class="n">loop</span>
|
||||||
|
<span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="n">nullary</span> <span class="p">[</span><span class="n">B</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="n">nullary</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="parallel">
|
||||||
|
<h2>Parallel<a class="headerlink" href="#parallel" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>The <em>parallel</em> operation indicates that two (or more) functions <em>do not
|
||||||
|
interfere</em> with each other and so can run in parallel. The main
|
||||||
|
difficulty in this sort of thing is orchestrating the recombining
|
||||||
|
(“join” or “wait”) of the results of the functions after they finish.</p>
|
||||||
|
<p>The current implementaions and the following definitions <em>are not
|
||||||
|
actually parallel</em> (yet), but there is no reason they couldn’t be
|
||||||
|
reimplemented in terms of e.g. Python threads. I am not concerned with
|
||||||
|
performance of the system just yet, only the elegance of the code it
|
||||||
|
allows us to write.</p>
|
||||||
|
<div class="section" id="cleave">
|
||||||
|
<h3><code class="docutils literal notranslate"><span class="pre">cleave</span></code><a class="headerlink" href="#cleave" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>Joy has a few parallel combinators, the main one being <code class="docutils literal notranslate"><span class="pre">cleave</span></code>:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">x</span> <span class="p">[</span><span class="n">A</span><span class="p">]</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="n">cleave</span>
|
||||||
|
<span class="o">---------------------------------------------------------</span>
|
||||||
|
<span class="o">...</span> <span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">A</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||||
|
<span class="o">---------------------------------------------------------</span>
|
||||||
|
<span class="o">...</span> <span class="n">a</span> <span class="n">b</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>The <code class="docutils literal notranslate"><span class="pre">cleave</span></code> combinator expects a value and two quotes and it executes
|
||||||
|
each quote in “separate universes” such that neither can affect the
|
||||||
|
other, then it takes the first item from the stack in each universe and
|
||||||
|
replaces the value and quotes with their respective results.</p>
|
||||||
|
<p>(I think this corresponds to the “fork” operator, the little
|
||||||
|
upward-pointed triangle, that takes two functions <code class="docutils literal notranslate"><span class="pre">A</span> <span class="pre">::</span> <span class="pre">x</span> <span class="pre">-></span> <span class="pre">a</span></code> and
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">B</span> <span class="pre">::</span> <span class="pre">x</span> <span class="pre">-></span> <span class="pre">b</span></code> and returns a function <code class="docutils literal notranslate"><span class="pre">F</span> <span class="pre">::</span> <span class="pre">x</span> <span class="pre">-></span> <span class="pre">(a,</span> <span class="pre">b)</span></code>, in Conal
|
||||||
|
Elliott’s “Compiling to Categories” paper, et. al.)</p>
|
||||||
|
<p>Just a thought, if you <code class="docutils literal notranslate"><span class="pre">cleave</span></code> two jobs and one requires more time to
|
||||||
|
finish than the other you’d like to be able to assign resources
|
||||||
|
accordingly so that they both finish at the same time.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="apply-functions">
|
||||||
|
<h3>“Apply” Functions<a class="headerlink" href="#apply-functions" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>There are also <code class="docutils literal notranslate"><span class="pre">app2</span></code> and <code class="docutils literal notranslate"><span class="pre">app3</span></code> which run a single quote on more
|
||||||
|
than one value:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">y</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">app2</span>
|
||||||
|
<span class="o">---------------------------------------------------------</span>
|
||||||
|
<span class="o">...</span> <span class="p">[</span><span class="n">y</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="o">...</span> <span class="n">z</span> <span class="n">y</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">app3</span>
|
||||||
|
<span class="o">---------------------------------</span>
|
||||||
|
<span class="o">...</span> <span class="p">[</span><span class="n">z</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||||
|
<span class="p">[</span><span class="n">y</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||||
|
<span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Because the quoted program can be <code class="docutils literal notranslate"><span class="pre">i</span></code> we can define <code class="docutils literal notranslate"><span class="pre">cleave</span></code> in
|
||||||
|
terms of <code class="docutils literal notranslate"><span class="pre">app2</span></code>:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">cleave</span> <span class="o">==</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">app2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>(I’m not sure why <code class="docutils literal notranslate"><span class="pre">cleave</span></code> was specified to take that value, I may
|
||||||
|
make a combinator that does the same thing but without expecting a
|
||||||
|
value.)</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">clv</span> <span class="o">==</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">app2</span>
|
||||||
|
|
||||||
|
<span class="p">[</span><span class="n">A</span><span class="p">]</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="n">clv</span>
|
||||||
|
<span class="o">------------------</span>
|
||||||
|
<span class="n">a</span> <span class="n">b</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="map">
|
||||||
|
<h3><code class="docutils literal notranslate"><span class="pre">map</span></code><a class="headerlink" href="#map" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>The common <code class="docutils literal notranslate"><span class="pre">map</span></code> function in Joy should also be though of as a
|
||||||
|
<em>parallel</em> operator:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="nb">map</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>There is no reason why the implementation of <code class="docutils literal notranslate"><span class="pre">map</span></code> couldn’t distribute
|
||||||
|
the <code class="docutils literal notranslate"><span class="pre">Q</span></code> function over e.g. a pool of worker CPUs.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="pam">
|
||||||
|
<h3><code class="docutils literal notranslate"><span class="pre">pam</span></code><a class="headerlink" href="#pam" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>One of my favorite combinators, the <code class="docutils literal notranslate"><span class="pre">pam</span></code> combinator is just:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">pam</span> <span class="o">==</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="nb">map</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>This can be used to run any number of programs separately on the current
|
||||||
|
stack and combine their (first) outputs in a result list.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[[</span><span class="n">A</span><span class="p">]</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[</span><span class="n">C</span><span class="p">]</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="nb">map</span>
|
||||||
|
<span class="o">-------------------------------</span>
|
||||||
|
<span class="p">[</span> <span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="o">...</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="handling-other-kinds-of-join">
|
||||||
|
<h3>Handling Other Kinds of Join<a class="headerlink" href="#handling-other-kinds-of-join" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>The <code class="docutils literal notranslate"><span class="pre">cleave</span></code> operators and others all have pretty brutal join
|
||||||
|
semantics: everything works and we always wait for every
|
||||||
|
sub-computation. We can imagine a few different potentially useful
|
||||||
|
patterns of “joining” results from parallel combinators.</p>
|
||||||
|
<div class="section" id="first-to-finish">
|
||||||
|
<h4>first-to-finish<a class="headerlink" href="#first-to-finish" title="Permalink to this headline">¶</a></h4>
|
||||||
|
<p>Thinking about variations of <code class="docutils literal notranslate"><span class="pre">pam</span></code> there could be one that only
|
||||||
|
returns the first result of the first-to-finish sub-program, or the
|
||||||
|
stack could be replaced by its output stack.</p>
|
||||||
|
<p>The other sub-programs would be cancelled.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="fulminators">
|
||||||
|
<h4>“Fulminators”<a class="headerlink" href="#fulminators" title="Permalink to this headline">¶</a></h4>
|
||||||
|
<p>Also known as “Futures” or “Promises” (by <em>everybody</em> else. “Fulinators”
|
||||||
|
is what I was going to call them when I was thinking about implementing
|
||||||
|
them in Thun.)</p>
|
||||||
|
<p>The runtime could be amended to permit “thunks” representing the results
|
||||||
|
of in-progress computations to be left on the stack and picked up by
|
||||||
|
subsequent functions. These would themselves be able to leave behind
|
||||||
|
more “thunks”, the values of which depend on the eventual resolution of
|
||||||
|
the values of the previous thunks.</p>
|
||||||
|
<p>In this way you can create “chains” (and more complex shapes) out of
|
||||||
|
normal-looking code that consist of a kind of call-graph interspersed
|
||||||
|
with “asyncronous” … events?</p>
|
||||||
|
<p>In any case, until I can find a rigorous theory that shows that this
|
||||||
|
sort of thing works perfectly in Joy code I’m not going to worry about
|
||||||
|
it. (And I think the Categories can deal with it anyhow? Incremental
|
||||||
|
evaluation, yeah?)</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||||
|
<div class="sphinxsidebarwrapper">
|
||||||
|
<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||||
|
<ul>
|
||||||
|
<li><a class="reference internal" href="#">The Four Fundamental Operations of Definite Action</a><ul>
|
||||||
|
<li><a class="reference internal" href="#sequence">Sequence</a></li>
|
||||||
|
<li><a class="reference internal" href="#branch">Branch</a><ul>
|
||||||
|
<li><a class="reference internal" href="#ifte"><code class="docutils literal notranslate"><span class="pre">ifte</span></code></a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a class="reference internal" href="#loop">Loop</a><ul>
|
||||||
|
<li><a class="reference internal" href="#while"><code class="docutils literal notranslate"><span class="pre">while</span></code></a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a class="reference internal" href="#parallel">Parallel</a><ul>
|
||||||
|
<li><a class="reference internal" href="#cleave"><code class="docutils literal notranslate"><span class="pre">cleave</span></code></a></li>
|
||||||
|
<li><a class="reference internal" href="#apply-functions">“Apply” Functions</a></li>
|
||||||
|
<li><a class="reference internal" href="#map"><code class="docutils literal notranslate"><span class="pre">map</span></code></a></li>
|
||||||
|
<li><a class="reference internal" href="#pam"><code class="docutils literal notranslate"><span class="pre">pam</span></code></a></li>
|
||||||
|
<li><a class="reference internal" href="#handling-other-kinds-of-join">Handling Other Kinds of Join</a><ul>
|
||||||
|
<li><a class="reference internal" href="#first-to-finish">first-to-finish</a></li>
|
||||||
|
<li><a class="reference internal" href="#fulminators">“Fulminators”</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
<div class="relations">
|
||||||
|
<h3>Related Topics</h3>
|
||||||
|
<ul>
|
||||||
|
<li><a href="../index.html">Documentation overview</a><ul>
|
||||||
|
</ul></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div role="note" aria-label="source link">
|
||||||
|
<h3>This Page</h3>
|
||||||
|
<ul class="this-page-menu">
|
||||||
|
<li><a href="../_sources/notebooks/The_Four_Operations.rst.txt"
|
||||||
|
rel="nofollow">Show Source</a></li>
|
||||||
|
</ul>
|
||||||
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</div>
|
||||||
|
<div id="searchbox" style="display: none" role="search">
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<h3>Quick search</h3>
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</div>
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<div class="footer" role="contentinfo">
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<a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">
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</a>
|
||||||
|
<br />
|
||||||
|
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
|
||||||
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Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
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</html>
|
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@ -0,0 +1,209 @@
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||||||
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|
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
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<html xmlns="http://www.w3.org/1999/xhtml">
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
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<title>Type Checking — Thun 0.2.0 documentation</title>
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<div class="document">
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<div class="bodywrapper">
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<div class="body" role="main">
|
||||||
|
|
||||||
|
<div class="section" id="type-checking">
|
||||||
|
<h1>Type Checking<a class="headerlink" href="#type-checking" 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">logging</span><span class="o">,</span> <span class="nn">sys</span>
|
||||||
|
|
||||||
|
<span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span><span class="p">(</span>
|
||||||
|
<span class="nb">format</span><span class="o">=</span><span class="s1">'</span><span class="si">%(message)s</span><span class="s1">'</span><span class="p">,</span>
|
||||||
|
<span class="n">stream</span><span class="o">=</span><span class="n">sys</span><span class="o">.</span><span class="n">stdout</span><span class="p">,</span>
|
||||||
|
<span class="n">level</span><span class="o">=</span><span class="n">logging</span><span class="o">.</span><span class="n">INFO</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="kn">from</span> <span class="nn">joy.utils.polytypes</span> <span class="k">import</span> <span class="p">(</span>
|
||||||
|
<span class="n">doc_from_stack_effect</span><span class="p">,</span>
|
||||||
|
<span class="n">infer</span><span class="p">,</span>
|
||||||
|
<span class="n">reify</span><span class="p">,</span>
|
||||||
|
<span class="n">unify</span><span class="p">,</span>
|
||||||
|
<span class="n">FUNCTIONS</span><span class="p">,</span>
|
||||||
|
<span class="n">JoyTypeError</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">D</span> <span class="o">=</span> <span class="n">FUNCTIONS</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
|
||||||
|
<span class="k">del</span> <span class="n">D</span><span class="p">[</span><span class="s1">'product'</span><span class="p">]</span>
|
||||||
|
<span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">D</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="an-example">
|
||||||
|
<h2>An Example<a class="headerlink" href="#an-example" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rrest</span><span class="p">,</span> <span class="n">ccons</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>25 (--) ∘ pop swap rolldown rrest ccons
|
||||||
|
28 (a1 --) ∘ swap rolldown rrest ccons
|
||||||
|
31 (a3 a2 a1 -- a2 a3) ∘ rolldown rrest ccons
|
||||||
|
34 (a4 a3 a2 a1 -- a2 a3 a4) ∘ rrest ccons
|
||||||
|
37 ([a4 a5 ...1] a3 a2 a1 -- a2 a3 [...1]) ∘ ccons
|
||||||
|
40 ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ∘
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</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="n">a4</span> <span class="n">a5</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a3</span> <span class="o">...</span><span class="mi">1</span><span class="p">])</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.parser</span> <span class="k">import</span> <span class="n">text_to_expression</span>
|
||||||
|
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="k">import</span> <span class="n">stack_to_string</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'0 1 2 [3 4]'</span><span class="p">)</span> <span class="c1"># reverse order</span>
|
||||||
|
<span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">e</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="mi">4</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||||
|
<span class="n">u</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">a2</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">a3</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="n">a4</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">a5</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(),</span> <span class="n">s1</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">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
|
||||||
|
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">g</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="o">...</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="p">]</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="p">])</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="unification-works-in-reverse">
|
||||||
|
<h2>Unification Works “in Reverse”<a class="headerlink" href="#unification-works-in-reverse" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'[2 3]'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fo</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># output side, not input side</span>
|
||||||
|
<span class="n">u</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a2</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="n">a3</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(),</span> <span class="n">s1</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">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
|
||||||
|
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">g</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="o">...</span> <span class="p">[</span><span class="n">a4</span> <span class="n">a5</span> <span class="p">]</span> <span class="mi">3</span> <span class="mi">2</span> <span class="n">a1</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="p">])</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="failing-a-check">
|
||||||
|
<h2>Failing a Check<a class="headerlink" href="#failing-a-check" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>25 (--) ∘ dup mul
|
||||||
|
28 (a1 -- a1 a1) ∘ mul
|
||||||
|
31 (f1 -- f2) ∘
|
||||||
|
31 (i1 -- i2) ∘
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'"two"'</span><span class="p">)</span>
|
||||||
|
<span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">'two'</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span>
|
||||||
|
<span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)</span>
|
||||||
|
<span class="k">except</span> <span class="n">JoyTypeError</span><span class="p">,</span> <span class="n">err</span><span class="p">:</span>
|
||||||
|
<span class="nb">print</span> <span class="n">err</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Cannot</span> <span class="n">unify</span> <span class="s1">'two'</span> <span class="ow">and</span> <span class="n">f1</span><span class="o">.</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||||
|
<div class="sphinxsidebarwrapper">
|
||||||
|
<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||||
|
<ul>
|
||||||
|
<li><a class="reference internal" href="#">Type Checking</a><ul>
|
||||||
|
<li><a class="reference internal" href="#an-example">An Example</a></li>
|
||||||
|
<li><a class="reference internal" href="#unification-works-in-reverse">Unification Works “in Reverse”</a></li>
|
||||||
|
<li><a class="reference internal" href="#failing-a-check">Failing a Check</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
<div class="relations">
|
||||||
|
<h3>Related Topics</h3>
|
||||||
|
<ul>
|
||||||
|
<li><a href="../index.html">Documentation overview</a><ul>
|
||||||
|
</ul></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div role="note" aria-label="source link">
|
||||||
|
<h3>This Page</h3>
|
||||||
|
<ul class="this-page-menu">
|
||||||
|
<li><a href="../_sources/notebooks/TypeChecking.rst.txt"
|
||||||
|
rel="nofollow">Show Source</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div id="searchbox" style="display: none" role="search">
|
||||||
|
<h3>Quick search</h3>
|
||||||
|
<div class="searchformwrapper">
|
||||||
|
<form class="search" action="../search.html" method="get">
|
||||||
|
<input type="text" name="q" />
|
||||||
|
<input type="submit" value="Go" />
|
||||||
|
<input type="hidden" name="check_keywords" value="yes" />
|
||||||
|
<input type="hidden" name="area" value="default" />
|
||||||
|
</form>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<script type="text/javascript">$('#searchbox').show(0);</script>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="clearer"></div>
|
||||||
|
</div>
|
||||||
|
<div class="footer" role="contentinfo">
|
||||||
|
<a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">
|
||||||
|
<img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" />
|
||||||
|
</a>
|
||||||
|
<br />
|
||||||
|
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
|
||||||
|
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</body>
|
||||||
|
</html>
|
||||||
|
|
@ -130,8 +130,30 @@
|
||||||
<li class="toctree-l2"><a class="reference internal" href="Types.html#appendix-joy-in-the-logical-paradigm">Appendix: Joy in the Logical Paradigm</a></li>
|
<li class="toctree-l2"><a class="reference internal" href="Types.html#appendix-joy-in-the-logical-paradigm">Appendix: Joy in the Logical Paradigm</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="TypeChecking.html">Type Checking</a><ul>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="TypeChecking.html#an-example">An Example</a></li>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="TypeChecking.html#unification-works-in-reverse">Unification Works “in Reverse”</a></li>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="TypeChecking.html#failing-a-check">Failing a Check</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
<li class="toctree-l1"><a class="reference internal" href="NoUpdates.html">No Updates</a></li>
|
<li class="toctree-l1"><a class="reference internal" href="NoUpdates.html">No Updates</a></li>
|
||||||
<li class="toctree-l1"><a class="reference internal" href="Categorical.html">Categorical Programming</a></li>
|
<li class="toctree-l1"><a class="reference internal" href="Categorical.html">Categorical Programming</a></li>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="The_Four_Operations.html">The Four Fundamental Operations of Definite Action</a><ul>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html#sequence">Sequence</a></li>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html#branch">Branch</a></li>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html#loop">Loop</a></li>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html#parallel">Parallel</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html">∂RE</a><ul>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#brzozowski-s-derivatives-of-regular-expressions">Brzozowski’s Derivatives of Regular Expressions</a></li>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#implementation">Implementation</a></li>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#let-s-try-it-out">Let’s try it out…</a></li>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#larger-alphabets">Larger Alphabets</a></li>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#state-machine">State Machine</a></li>
|
||||||
|
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#reversing-the-derivatives-to-generate-matching-strings">Reversing the Derivatives to Generate Matching Strings</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
|
||||||
Binary file not shown.
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|
|
@ -291,7 +291,7 @@ guard against being used on invalid types.</p>
|
||||||
|
|
||||||
<dl class="data">
|
<dl class="data">
|
||||||
<dt id="joy.utils.polytypes.FUNCTIONS">
|
<dt id="joy.utils.polytypes.FUNCTIONS">
|
||||||
<code class="descclassname">joy.utils.polytypes.</code><code class="descname">FUNCTIONS</code><em class="property"> = {'_Tree_add_Ee': _Tree_add_Ee, '_Tree_delete_R0': _Tree_delete_R0, '_Tree_delete_clear_stuff': _Tree_delete_clear_stuff, '_Tree_get_E': _Tree_get_E, 'add': add, 'and': and, 'b': b, 'bool': bool, 'branch': branch, 'ccons': ccons, 'clear': clear, 'concat_': concat_, 'cons': cons, 'dip': dip, 'dipd': dipd, 'dipdd': dipdd, 'div': div, 'divmod': divmod, 'dup': dup, 'dupd': dupd, 'dupdd': dupdd, 'dupdip': dupdip, 'eq': eq, 'first': first, 'first_two': first_two, 'floordiv': floordiv, 'fourth': fourth, 'ge': ge, 'gt': gt, 'i': i, 'infra': infra, 'le': le, 'loop': loop, 'lshift': lshift, 'lt': lt, 'modulus': modulus, 'mul': mul, 'ne': ne, 'neg': neg, 'not': not, 'nullary': nullary, 'over': over, 'pm': pm, 'pop': pop, 'popd': popd, 'popdd': popdd, 'popop': popop, 'popopd': popopd, 'popopdd': popopdd, 'pow': pow, 'pred': pred, 'product': product, 'rest': rest, 'rolldown': rolldown, 'rollup': rollup, 'rrest': rrest, 'rshift': rshift, 'second': second, 'sqrt': sqrt, 'stack': stack, 'stuncons': stuncons, 'stununcons': stununcons, 'sub': sub, 'succ': succ, 'sum': sum, 'swaack': swaack, 'swap': swap, 'swons': swons, 'third': third, 'truediv': truediv, 'tuck': tuck, 'uncons': uncons, 'unit': unit, 'unswons': unswons, 'x': x}</em><a class="headerlink" href="#joy.utils.polytypes.FUNCTIONS" title="Permalink to this definition">¶</a></dt>
|
<code class="descclassname">joy.utils.polytypes.</code><code class="descname">FUNCTIONS</code><em class="property"> = {'!=': ne, '&': and, '*': mul, '+': add, '++': succ, '-': sub, '--': pred, '/': truediv, '<': lt, '<<': lshift, '<=': le, '<>': ne, '=': eq, '>': gt, '>=': ge, '>>': rshift, '_Tree_add_Ee': _Tree_add_Ee, '_Tree_delete_R0': _Tree_delete_R0, '_Tree_delete_clear_stuff': _Tree_delete_clear_stuff, '_Tree_get_E': _Tree_get_E, 'add': add, 'and': and, 'b': b, 'bool': bool, 'branch': branch, 'ccons': ccons, 'clear': clear, 'concat_': concat_, 'cons': cons, 'dip': dip, 'dipd': dipd, 'dipdd': dipdd, 'div': div, 'divmod': divmod, 'dup': dup, 'dupd': dupd, 'dupdd': dupdd, 'dupdip': dupdip, 'eq': eq, 'first': first, 'first_two': first_two, 'floordiv': floordiv, 'fourth': fourth, 'ge': ge, 'gt': gt, 'i': i, 'infra': infra, 'le': le, 'loop': loop, 'lshift': lshift, 'lt': lt, 'modulus': modulus, 'mul': mul, 'ne': ne, 'neg': neg, 'not': not, 'nullary': nullary, 'over': over, 'pop': pop, 'popd': popd, 'popdd': popdd, 'popop': popop, 'popopd': popopd, 'popopdd': popopdd, 'pow': pow, 'pred': pred, 'product': product, 'rest': rest, 'roll<': rolldown, 'roll>': rollup, 'rolldown': rolldown, 'rollup': rollup, 'rrest': rrest, 'rshift': rshift, 'second': second, 'sqrt': sqrt, 'stack': stack, 'stuncons': stuncons, 'stununcons': stununcons, 'sub': sub, 'succ': succ, 'sum': sum, 'swaack': swaack, 'swap': swap, 'swons': swons, 'third': third, 'truediv': truediv, 'truthy': bool, 'tuck': tuck, 'uncons': uncons, 'unit': unit, 'unswons': unswons, 'x': x}</em><a class="headerlink" href="#joy.utils.polytypes.FUNCTIONS" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Docstring for functions in Sphinx?</p>
|
<dd><p>Docstring for functions in Sphinx?</p>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
|
|
@ -372,6 +372,14 @@ expression is carried along and updated and yielded.</p>
|
||||||
effects. An expression is carried along and updated and yielded.</p>
|
effects. An expression is carried along and updated and yielded.</p>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="function">
|
||||||
|
<dt id="joy.utils.polytypes.type_check">
|
||||||
|
<code class="descclassname">joy.utils.polytypes.</code><code class="descname">type_check</code><span class="sig-paren">(</span><em>name</em>, <em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/polytypes.html#type_check"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.polytypes.type_check" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Trinary predicate. True if named function type-checks, False if it
|
||||||
|
fails, None if it’s indeterminate (because I haven’t entered it into
|
||||||
|
the FUNCTIONS dict yet.)</p>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -266,10 +266,6 @@ derivation.
|
||||||
|
|
||||||
.. code:: ipython2
|
.. code:: ipython2
|
||||||
|
|
||||||
# This is the straightforward version with no "compaction".
|
|
||||||
# It works fine, but does waaaay too much work because the
|
|
||||||
# expressions grow each derivation.
|
|
||||||
|
|
||||||
def D(symbol):
|
def D(symbol):
|
||||||
|
|
||||||
def derv(R):
|
def derv(R):
|
||||||
|
|
@ -539,9 +535,8 @@ machine transition table.
|
||||||
Says, "Three or more 1's and not ending in 01 nor composed of all 1's."
|
Says, "Three or more 1's and not ending in 01 nor composed of all 1's."
|
||||||
|
|
||||||
.. figure:: omg.svg
|
.. figure:: omg.svg
|
||||||
:alt: omg.svg
|
:alt: State Machine Diagram
|
||||||
|
|
||||||
omg.svg
|
|
||||||
|
|
||||||
Start at ``a`` and follow the transition arrows according to their
|
Start at ``a`` and follow the transition arrows according to their
|
||||||
labels. Accepting states have a double outline. (Graphic generated with
|
labels. Accepting states have a double outline. (Graphic generated with
|
||||||
|
|
|
||||||
|
|
@ -18,6 +18,9 @@ These essays are adapted from Jupyter notebooks. I hope to have those hosted so
|
||||||
Newton-Raphson
|
Newton-Raphson
|
||||||
Zipper
|
Zipper
|
||||||
Types
|
Types
|
||||||
|
TypeChecking
|
||||||
NoUpdates
|
NoUpdates
|
||||||
Categorical
|
Categorical
|
||||||
|
The_Four_Operations
|
||||||
|
Derivatives_of_Regular_Expressions
|
||||||
|
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue