Remove empty lines from inside equation blocks

Works in VS Code markdown preview, but breaks pandoc conversion.

chapter1/functional-lecture01.md

@@ -117,7 +117,9 @@ $$ \frac{\frac{\begin{array}{ll}
        \small{x}}{\text{go outdoor}}
      \end{array}}{\text{nice view}}
    \end{array}}{\text{happy}}}{\text{sunny} \rightarrow \text{happy}}
-   \small{\text{ using } x} $$Elimination rule for disjunction represents **reasoning by cases**.
+   \small{\text{ using } x} $$
+
+Elimination rule for disjunction represents **reasoning by cases**.
 
 How can we use the fact that it is sunny$\vee$cloudy (but not rainy)?
 
@@ -135,7 +137,6 @@ natural numbers:
 
 $$ \frac{\begin{array}{rr}
      p (0) &
-     
 {{{\frac{\,}{p(x)} \tiny{x}} \atop {\text{\textbar}}} \atop {p(x+1)}}
    \end{array}}{p (n)} \text{ by induction, using } x $$
 
@@ -225,7 +226,6 @@ than these:
 
 $$ \frac{\begin{array}{ll}
      e_{1} : a &
-     
 {{{\frac{\,}{x : a} \tiny{x}} \atop {\text{\textbar}}} \atop {e_2 : b}}
    \end{array}}{\text{{\texttt{let}} } x \text{{\texttt{=}}}
    e_{1} \text{ \text{{\texttt{in}}} } e_{2} : b} $$
@@ -234,9 +234,7 @@ $$ \frac{\begin{array}{ll}
 $\rightarrow$), and:
 
 $$ \frac{\begin{array}{ll}
-     
 {{{\frac{\,}{x : a} \tiny{x}} \atop {\text{\textbar}}} \atop {e_1 : a}} &
-     
 {{{\frac{\,}{x : a} \tiny{x}} \atop {\text{\textbar}}} \atop {e_2 : b}}
    \end{array}}{\text{{\texttt{let rec}} } x
    \text{{\texttt{=}}} e_{1} \text{ \text{{\texttt{in}}} } e_{2}

chapter2/functional-lecture02-deriv1.md

@@ -25,8 +25,7 @@ $$ \frac{\frac{\begin{array}{ll}
 \rightarrow
    [? \alpha]} $$
 
-$$ \text{we know that \text{{\texttt{1}}}} : \text{{\texttt{int}}}
-$$
+$$ \text{we know that \text{{\texttt{1}}}} : \text{{\texttt{int}}} $$
 
 $$ \frac{\frac{\begin{array}{ll}
      \frac{[?]}{\text{{\texttt{(+) x}}} :
@@ -86,8 +85,7 @@ $$ \frac{\frac{\begin{array}{ll}
      \text{{\texttt{int}}}} & \frac{\,}{\text{{\texttt{1}}} :
      \text{{\texttt{int}}}} \tiny{\text{(constant)}}
    \end{array}}{\text{{\texttt{((+) x) 1}}} :
-   \text{{\texttt{int}}}}}{\text{\text{{\texttt{fun x -> ((+) 
-x)
+   \text{{\texttt{int}}}}}{\text{\text{{\texttt{fun x -> ((+) x)
    1}}}} : \text{{\texttt{int}}} \rightarrow
    \text{{\texttt{int}}}} $$
 

chapter2/functional-lecture02.md

@@ -15,16 +15,12 @@ $$ \begin{matrix}
   & \frac{[?]}{\text{{\texttt{fun x -> x}}} : [?]} & \text{use }
   \rightarrow \text{ introduction:}\\\\\\
   & \frac{\frac{\,}{\text{{\texttt{x}}} : a}
-  \tiny{x}}{\text{{\texttt{fun x -> x}}} : [?] \rightarrow 
-[?]}
-  & \frac{\,}{\text{{\texttt{x}}} : a} \tiny{x} \text{ matches
-  with }
-  
+  \tiny{x}}{\text{{\texttt{fun x -> x}}} : [?] \rightarrow [?]}
+  & \frac{\,}{\text{{\texttt{x}}} : a} \tiny{x} \text{ matches with }
 {{{\frac{\,}{x : a} \tiny{x}} \atop {\text{\textbar}}} \atop {e : b}}
  \text{ since } e = \text{{\texttt{x}}}\\\\\\
   & \frac{\frac{\,}{\text{{\texttt{x}}} : a}
-  \tiny{x}}{\text{{\texttt{fun x -> x}}} : a \rightarrow a} 
-&
+  \tiny{x}}{\text{{\texttt{fun x -> x}}} : a \rightarrow a} &
   \text{since } b = a \text{ because } x : a \text{ matched with } e : b
 \end{matrix} $$
 

old_lectures_as_book.md

@@ -133,7 +133,9 @@ $$ \frac{\frac{\begin{array}{ll}
        \small{x}}{\text{go outdoor}}
      \end{array}}{\text{nice view}}
    \end{array}}{\text{happy}}}{\text{sunny} \rightarrow \text{happy}}
-   \small{\text{ using } x} $$Elimination rule for disjunction represents **reasoning by cases**.
+   \small{\text{ using } x} $$
+
+Elimination rule for disjunction represents **reasoning by cases**.
 
 How can we use the fact that it is sunny$\vee$cloudy (but not rainy)?
 
@@ -151,7 +153,6 @@ natural numbers:
 
 $$ \frac{\begin{array}{rr}
      p (0) &
-     
 {{{\frac{\,}{p(x)} \tiny{x}} \atop {\text{\textbar}}} \atop {p(x+1)}}
    \end{array}}{p (n)} \text{ by induction, using } x $$
 
@@ -241,7 +242,6 @@ than these:
 
 $$ \frac{\begin{array}{ll}
      e_{1} : a &
-     
 {{{\frac{\,}{x : a} \tiny{x}} \atop {\text{\textbar}}} \atop {e_2 : b}}
    \end{array}}{\text{{\texttt{let}} } x \text{{\texttt{=}}}
    e_{1} \text{ \text{{\texttt{in}}} } e_{2} : b} $$
@@ -250,9 +250,7 @@ $$ \frac{\begin{array}{ll}
 $\rightarrow$), and:
 
 $$ \frac{\begin{array}{ll}
-     
 {{{\frac{\,}{x : a} \tiny{x}} \atop {\text{\textbar}}} \atop {e_1 : a}} &
-     
 {{{\frac{\,}{x : a} \tiny{x}} \atop {\text{\textbar}}} \atop {e_2 : b}}
    \end{array}}{\text{{\texttt{let rec}} } x
    \text{{\texttt{=}}} e_{1} \text{ \text{{\texttt{in}}} } e_{2}
@@ -361,16 +359,12 @@ $$ \begin{matrix}
   & \frac{[?]}{\text{{\texttt{fun x -> x}}} : [?]} & \text{use }
   \rightarrow \text{ introduction:}\\\\\\
   & \frac{\frac{\,}{\text{{\texttt{x}}} : a}
-  \tiny{x}}{\text{{\texttt{fun x -> x}}} : [?] \rightarrow 
-[?]}
-  & \frac{\,}{\text{{\texttt{x}}} : a} \tiny{x} \text{ matches
-  with }
-  
+  \tiny{x}}{\text{{\texttt{fun x -> x}}} : [?] \rightarrow [?]}
+  & \frac{\,}{\text{{\texttt{x}}} : a} \tiny{x} \text{ matches with }
 {{{\frac{\,}{x : a} \tiny{x}} \atop {\text{\textbar}}} \atop {e : b}}
  \text{ since } e = \text{{\texttt{x}}}\\\\\\
   & \frac{\frac{\,}{\text{{\texttt{x}}} : a}
-  \tiny{x}}{\text{{\texttt{fun x -> x}}} : a \rightarrow a} 
-&
+  \tiny{x}}{\text{{\texttt{fun x -> x}}} : a \rightarrow a} &
   \text{since } b = a \text{ because } x : a \text{ matched with } e : b
 \end{matrix} $$
 
@@ -888,8 +882,7 @@ $$ \frac{\frac{\begin{array}{ll}
 \rightarrow
    [? \alpha]} $$
 
-$$ \text{we know that \text{{\texttt{1}}}} : \text{{\texttt{int}}}
-$$
+$$ \text{we know that \text{{\texttt{1}}}} : \text{{\texttt{int}}} $$
 
 $$ \frac{\frac{\begin{array}{ll}
      \frac{[?]}{\text{{\texttt{(+) x}}} :
@@ -949,8 +942,7 @@ $$ \frac{\frac{\begin{array}{ll}
      \text{{\texttt{int}}}} & \frac{\,}{\text{{\texttt{1}}} :
      \text{{\texttt{int}}}} \tiny{\text{(constant)}}
    \end{array}}{\text{{\texttt{((+) x) 1}}} :
-   \text{{\texttt{int}}}}}{\text{\text{{\texttt{fun x -> ((+) 
-x)
+   \text{{\texttt{int}}}}}{\text{\text{{\texttt{fun x -> ((+) x)
    1}}}} : \text{{\texttt{int}}} \rightarrow
    \text{{\texttt{int}}}} $$
 

site/dune

@@ -41,3 +41,12 @@
  (action
   (system
    "pandoc -s --katex %{deps} -o %{target}")))
+
+; (rule
+;  (alias old_lectures_as_book)
+;  (mode promote)
+;  (target old_lectures_as_book.hs)
+;  (deps old_lectures_as_book.md)
+;  (action
+;   (system
+;    "pandoc -s --katex --to native %{deps} -o %{target}")))

site/old_lectures_as_book.html

@@ -435,8 +435,9 @@ <h1 id="in-the-beginning-there-was-logos">1 In the Beginning there was
        \small{x}}{\text{go outdoor}}
      \end{array}}{\text{nice view}}
    \end{array}}{\text{happy}}}{\text{sunny} \rightarrow \text{happy}}
-   \small{\text{ using } x} </span>Elimination rule for disjunction
-represents <strong>reasoning by cases</strong>.</p>
+   \small{\text{ using } x} </span></p>
+<p>Elimination rule for disjunction represents <strong>reasoning by
+cases</strong>.</p>
 <p>How can we use the fact that it is sunny<span
 class="math inline">\vee</span>cloudy (but not rainy)?</p>
 <p><span class="math display"> \frac{\begin{array}{rrl}
@@ -452,7 +453,10 @@ <h1 id="in-the-beginning-there-was-logos">1 In the Beginning there was
 need one more kind of rules to do serious math: <strong>reasoning by
 induction</strong> (it is somewhat similar to reasoning by cases).
 Example rule for induction on natural numbers:</p>
-<p>$$ x $$</p>
+<p><span class="math display"> \frac{\begin{array}{rr}
+     p (0) &amp;
+{{{\frac{\,}{p(x)} \tiny{x}} \atop {\text{\textbar}}} \atop {p(x+1)}}
+   \end{array}}{p (n)} \text{ by induction, using } x </span></p>
 <p>So we get any <span class="math inline">p</span> for any natural
 number <span class="math inline">n</span>, provided we can get it for
 <span class="math inline">0</span>, and using it for <span
@@ -605,10 +609,20 @@ <h2 id="definitions">3.1 Definitions</h2>
 definition.</p>
 <p><strong>Definitions for expressions</strong> are introduced by rules
 a bit more complex than these:</p>
-<p>$$ $$</p>
+<p><span class="math display"> \frac{\begin{array}{ll}
+     e_{1} : a &amp;
+{{{\frac{\,}{x : a} \tiny{x}} \atop {\text{\textbar}}} \atop {e_2 : b}}
+   \end{array}}{\text{{\texttt{let}} } x \text{{\texttt{=}}}
+   e_{1} \text{ \text{{\texttt{in}}} } e_{2} : b} </span></p>
 <p>(note that this rule is the same as introducing and eliminating <span
 class="math inline">\rightarrow</span>), and:</p>
-<p>$$ $$</p>
+<p><span class="math display"> \frac{\begin{array}{ll}
+{{{\frac{\,}{x : a} \tiny{x}} \atop {\text{\textbar}}} \atop {e_1 : a}}
+&amp;
+{{{\frac{\,}{x : a} \tiny{x}} \atop {\text{\textbar}}} \atop {e_2 : b}}
+   \end{array}}{\text{{\texttt{let rec}} } x
+   \text{{\texttt{=}}} e_{1} \text{ \text{{\texttt{in}}} } e_{2}
+   \: b} </span></p>
 <p>We will cover what is missing in above rules when we will talk about
 <strong>polymorphism.</strong>* Type definitions we have seen above are
 <em>global</em>: they need to be at the top-level, not nested in
@@ -710,25 +724,20 @@ <h1 id="a-glimpse-at-type-inference">1 A Glimpse at Type Inference</h1>
 <p>For a refresher, let’s try to use the rules we introduced last time
 on some simple examples. Starting with <code>fun x -&gt; x</code>. <span
 class="math inline">[?]</span> will mean “dunno yet”.</p>
-$$
-<span class="math display">\begin{matrix}
+<p><span class="math display"> \begin{matrix}
   &amp; \frac{[?]}{\text{{\texttt{fun x -&gt; x}}} : [?]} &amp;
 \text{use }
   \rightarrow \text{ introduction:}\\\\\\
   &amp; \frac{\frac{\,}{\text{{\texttt{x}}} : a}
-  \tiny{x}}{\text{{\texttt{fun x -&gt; x}}} : [?] \rightarrow
-[?]}
-  &amp; \frac{\,}{\text{{\texttt{x}}} : a} \tiny{x} \text{ matches
-  with }
-
+  \tiny{x}}{\text{{\texttt{fun x -&gt; x}}} : [?] \rightarrow [?]}
+  &amp; \frac{\,}{\text{{\texttt{x}}} : a} \tiny{x} \text{ matches with
+}
 {{{\frac{\,}{x : a} \tiny{x}} \atop {\text{\textbar}}} \atop {e : b}}
 \text{ since } e = \text{{\texttt{x}}}\\\\\\
   &amp; \frac{\frac{\,}{\text{{\texttt{x}}} : a}
-  \tiny{x}}{\text{{\texttt{fun x -&gt; x}}} : a \rightarrow a}
-&amp;
+  \tiny{x}}{\text{{\texttt{fun x -&gt; x}}} : a \rightarrow a} &amp;
   \text{since } b = a \text{ because } x : a \text{ matched with } e : b
-\end{matrix}</span>
-<p>$$</p>
+\end{matrix} </span></p>
 <p>Because <span class="math inline">a</span> is arbitrary, OCaml puts a
 <em>type variable</em> <code>'a</code> for it:</p>
 <div class="sourceCode" id="cb3"><pre
@@ -1186,8 +1195,7 @@ <h1 id="homework">6 Homework</h1>
 \rightarrow
    [? \alpha]} </span></p>
 <p><span class="math display"> \text{we know that \text{{\texttt{1}}}} :
-\text{{\texttt{int}}}
-</span></p>
+\text{{\texttt{int}}} </span></p>
 <p><span class="math display"> \frac{\frac{\begin{array}{ll}
      \frac{[?]}{\text{{\texttt{(+) x}}} :
      \text{{\texttt{int}}} \rightarrow [? \alpha]} &amp;
@@ -1242,8 +1250,7 @@ <h1 id="homework">6 Homework</h1>
      \text{{\texttt{int}}}} &amp; \frac{\,}{\text{{\texttt{1}}} :
      \text{{\texttt{int}}}} \tiny{\text{(constant)}}
    \end{array}}{\text{{\texttt{((+) x) 1}}} :
-   \text{{\texttt{int}}}}}{\text{\text{{\texttt{fun x -&gt; ((+)
-x)
+   \text{{\texttt{int}}}}}{\text{\text{{\texttt{fun x -&gt; ((+) x)
    1}}}} : \text{{\texttt{int}}} \rightarrow
    \text{{\texttt{int}}}} </span></p>
 <h1 id="chapter-3">Chapter 3</h1>