deploy: e57defe

_sources/introOneSharp/functions.ipynb

@@ -47,7 +47,7 @@
         "A *word* is just a sequence of  symbols from our alphabet.\n",
         "\n",
         " \n",
-        "(In contrast to most uses in mathematics and computer science,\n",
+        "In contrast to most uses in mathematics and computer science,\n",
         "our words will all be *non-empty*, unless we say otherwise.\n",
         "\n",
         "Examples of words include \n",
@@ -257,6 +257,7 @@
         "\n",
         "\n",
         "```{prf:definition}\n",
+        "\\:class: tip\n",
         "Every word $p$ gives us a function\n",
         "called $\\phifn^n_p$  on $n$-tuples of words. \n",
         "\n",
@@ -375,7 +376,15 @@
       "source": [
         "# Functions of zero inputs\n",
         "\n",
-        "We started by associating to each program $p$ a function $\\phifn_p$ of one argument, and then for each $n \\geq 2$ we associated  a function $\\phifn_p^n$ of $n$ arguments.  This general definition works in case $n = 0$ also.  For the record: \n",
+        "We started by associating to each program $p$ a function $\\phifn_p$ of one argument, and then for each $n \\geq 2$ we associated  a function $\\phifn_p^n$ of $n$ arguments.  This general definition works in case $n = 0$ also. "
+      ]
+    },
+    {
+      "attachments": {},
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "```{admonition}\n",
         "\n",
         "$$\n",
         "\\phifn^0_p (\\ ) \\simeq y\n",
@@ -391,7 +400,7 @@
         "eventually halts with $y$ in R1 and all other \n",
         "registers \n",
         "empty. \n",
-        "\n"
+        "```\n"
       ]
     },
     {

introOneSharp/functions.html

@@ -471,7 +471,7 @@ <h1>Functions defined by programs<a class="headerlink" href="#functions-defined-
 the world are our words?!</p>
 <p>Answer:
 A <em>word</em> is just a sequence of  symbols from our alphabet.</p>
-<p>(In contrast to most uses in mathematics and computer science,
+<p>In contrast to most uses in mathematics and computer science,
 our words will all be <em>non-empty</em>, unless we say otherwise.</p>
 <p>Examples of words include
 <code class="docutils literal notranslate"><span class="pre">11#11####</span></code> and also the empty word <span class="math notranslate nohighlight">\(\varepsilon\)</span>.</p>
@@ -599,7 +599,8 @@ <h1>Functions of two or more arguments<a class="headerlink" href="#functions-of-
 <div class="proof definition admonition" id="definition-4">
 <p class="admonition-title"><span class="caption-number">Definition 3 </span></p>
 <section class="definition-content" id="proof-content">
-<p>Every word <span class="math notranslate nohighlight">\(p\)</span> gives us a function
+<p>:class: tip
+Every word <span class="math notranslate nohighlight">\(p\)</span> gives us a function
 called <span class="math notranslate nohighlight">\(\phifn^n_p\)</span>  on <span class="math notranslate nohighlight">\(n\)</span>-tuples of words.</p>
 <div class="math notranslate nohighlight">
 \[
@@ -675,21 +676,7 @@ <h1>Functions of two or more arguments<a class="headerlink" href="#functions-of-
 </section>
 <section class="tex2jax_ignore mathjax_ignore" id="functions-of-zero-inputs">
 <h1>Functions of zero inputs<a class="headerlink" href="#functions-of-zero-inputs" title="Link to this heading">#</a></h1>
-<p>We started by associating to each program <span class="math notranslate nohighlight">\(p\)</span> a function <span class="math notranslate nohighlight">\(\phifn_p\)</span> of one argument, and then for each <span class="math notranslate nohighlight">\(n \geq 2\)</span> we associated  a function <span class="math notranslate nohighlight">\(\phifn_p^n\)</span> of <span class="math notranslate nohighlight">\(n\)</span> arguments.  This general definition works in case <span class="math notranslate nohighlight">\(n = 0\)</span> also.  For the record:</p>
-<div class="math notranslate nohighlight">
-\[
-\phifn^0_p (\ ) \simeq y
-\]</div>
-<p>means that
-<span class="math notranslate nohighlight">\(p\)</span> is a program,
-and
-when  we
-run it
-<span class="math notranslate nohighlight">\(p\)</span>  with
-all registers empty, the register machine
-eventually halts with <span class="math notranslate nohighlight">\(y\)</span> in R1 and all other
-registers
-empty.</p>
+<p>We started by associating to each program <span class="math notranslate nohighlight">\(p\)</span> a function <span class="math notranslate nohighlight">\(\phifn_p\)</span> of one argument, and then for each <span class="math notranslate nohighlight">\(n \geq 2\)</span> we associated  a function <span class="math notranslate nohighlight">\(\phifn_p^n\)</span> of <span class="math notranslate nohighlight">\(n\)</span> arguments.  This general definition works in case <span class="math notranslate nohighlight">\(n = 0\)</span> also.</p>
 </section>
 <section class="tex2jax_ignore mathjax_ignore" id="characteristic-functions">
 <h1>Characteristic functions<a class="headerlink" href="#characteristic-functions" title="Link to this heading">#</a></h1>