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Fixup docs a bit more...

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Simon Forman 2021-11-19 14:03:47 -08:00
parent a69b7e2a56
commit f36b6dc7ca
5 changed files with 29 additions and 29 deletions
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@ -7,7 +7,7 @@ to write a function that can compute the square root of a number.
Cf. `"Why Functional Programming Matters" by John Cf. `"Why Functional Programming Matters" by John
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__ Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__
.. code:: ipython3 .. code:: python
from notebook_preamble import J, V, define from notebook_preamble import J, V, define
@ -75,11 +75,11 @@ The generator can be written as:
1 [23 over / + 2 /] [dup] swoncat make_generator 1 [23 over / + 2 /] [dup] swoncat make_generator
1 [dup 23 over / + 2 /] make_generator 1 [dup 23 over / + 2 /] make_generator
.. code:: ipython3 .. code:: python
define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator') define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
.. code:: ipython3 .. code:: python
J('23 gsra') J('23 gsra')
@ -92,7 +92,7 @@ The generator can be written as:
Let's drive the generator a few time (with the ``x`` combinator) and Let's drive the generator a few time (with the ``x`` combinator) and
square the approximation to see how well it works... square the approximation to see how well it works...
.. code:: ipython3 .. code:: python
J('23 gsra 6 [x popd] times first sqr') J('23 gsra 6 [x popd] times first sqr')
@ -142,7 +142,7 @@ Predicate
abs(a-b) ε <= abs(a-b) ε <=
(abs(a-b)<=ε) (abs(a-b)<=ε)
.. code:: ipython3 .. code:: python
define('_within_P [first - abs] dip <=') define('_within_P [first - abs] dip <=')
@ -156,7 +156,7 @@ Base-Case
[b G] first [b G] first
b b
.. code:: ipython3 .. code:: python
define('_within_B roll< popop first') define('_within_B roll< popop first')
@ -184,7 +184,7 @@ Pretty straightforward:
b [c G] ε within b [c G] ε within
.. code:: ipython3 .. code:: python
define('_within_R [popd x] dip') define('_within_R [popd x] dip')
@ -199,14 +199,14 @@ The recursive function we have defined so far needs a slight preamble:
[a G] x ε ... [a G] x ε ...
a [b G] ε ... a [b G] ε ...
.. code:: ipython3 .. code:: python
define('within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec') define('within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec')
define('sqrt gsra within') define('sqrt gsra within')
Try it out... Try it out...
.. code:: ipython3 .. code:: python
J('36 sqrt') J('36 sqrt')
@ -216,7 +216,7 @@ Try it out...
6.0 6.0
.. code:: ipython3 .. code:: python
J('23 sqrt') J('23 sqrt')
@ -228,7 +228,7 @@ Try it out...
Check it. Check it.
.. code:: ipython3 .. code:: python
4.795831523312719**2 4.795831523312719**2
@ -241,7 +241,7 @@ Check it.
.. code:: ipython3 .. code:: python
from math import sqrt from math import sqrt

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@ -40,7 +40,7 @@
to write a function that can compute the square root of a number.</p> to write a function that can compute the square root of a number.</p>
<p>Cf. <a class="reference external" href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">“Why Functional Programming Matters” by John <p>Cf. <a class="reference external" href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">“Why Functional Programming Matters” by John
Hughes</a></p> Hughes</a></p>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import J, V, define <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
</pre></div> </pre></div>
</div> </div>
<section id="a-generator-for-approximations"> <section id="a-generator-for-approximations">
@ -92,10 +92,10 @@ function we’re writing. If we let 1 be the initial approximation:</p>
<span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">make_generator</span> <span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">make_generator</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define(&#39;gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 gsra&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 gsra&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
@ -103,7 +103,7 @@ function we’re writing. If we let 1 be the initial approximation:</p>
</div> </div>
<p>Let’s drive the generator a few time (with the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator) and <p>Let’s drive the generator a few time (with the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator) and
square the approximation to see how well it works…</p> square the approximation to see how well it works…</p>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 gsra 6 [x popd] times first sqr&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 gsra 6 [x popd] times first sqr&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">23.0000000001585</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">23.0000000001585</span>
@ -145,7 +145,7 @@ generated already and epsilon ε is handy on the stack…</p>
<span class="p">(</span><span class="nb">abs</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="o">&lt;=</span><span class="n">ε</span><span class="p">)</span> <span class="p">(</span><span class="nb">abs</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="o">&lt;=</span><span class="n">ε</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define(&#39;_within_P [first - abs] dip &lt;=&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_P [first - abs] dip &lt;=&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
@ -157,7 +157,7 @@ generated already and epsilon ε is handy on the stack…</p>
<span class="n">b</span> <span class="n">b</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define(&#39;_within_B roll&lt; popop first&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_B roll&lt; popop first&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
@ -182,7 +182,7 @@ generated already and epsilon ε is handy on the stack…</p>
<span class="n">b</span> <span class="p">[</span><span class="n">c</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span> <span class="n">b</span> <span class="p">[</span><span class="n">c</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define(&#39;_within_R [popd x] dip&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_R [popd x] dip&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
@ -194,33 +194,33 @@ generated already and epsilon ε is handy on the stack…</p>
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="o">...</span> <span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="o">...</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define(&#39;within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec&#39;</span><span class="p">)</span>
define(&#39;sqrt gsra within&#39;) <span class="n">define</span><span class="p">(</span><span class="s1">&#39;sqrt gsra within&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<p>Try it out…</p> <p>Try it out…</p>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J(&#39;36 sqrt&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;36 sqrt&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">6.0</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">6.0</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 sqrt&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 sqrt&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span>
</pre></div> </pre></div>
</div> </div>
<p>Check it.</p> <p>Check it.</p>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>4.795831523312719**2 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span><span class="o">**</span><span class="mi">2</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">22.999999999999996</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">22.999999999999996</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>from math import sqrt <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span>
sqrt(23) <span class="n">sqrt</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span>

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@ -533,10 +533,10 @@ 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:: attachment:omg.svg .. figure:: omg.svg
:alt: omg.svg :alt: State Machine Graph
omg.svg State Machine Graph
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