Initial commit

.gitignore

@@ -0,0 +1,13 @@
+/.site
+/.store
+/.stack-work
+/.vscode
+
+/node_modules
+
+/uni
+/portfolio.md
+/fonts
+/css/fonts
+
+/.mailmap

blag.cabal

@@ -0,0 +1,25 @@
+name:               blag
+version:            0.1.0.0
+build-type:         Simple
+cabal-version:      >= 1.10
+
+executable site
+  main-is:          site.hs
+  build-depends:    base
+                  , hakyll
+                  , pandoc
+                  , skylighting
+                  , process
+                  , containers
+                  , directory
+                  , pandoc-types
+                  , bytestring
+                  , uri-encode
+                  , deepseq
+                  , text
+                  , hsass
+                  , hakyll-sass
+  ghc-options:      -threaded
+  default-language: Haskell2010
+
+  ghc-options:      -optl-fuse-ld=lld

css/code.css

@@ -0,0 +1,45 @@
+code, div.sourceCode {
+  font-family: Fantasque Sans Mono, Fira Mono, monospace;
+  font-size: 15pt;
+}
+
+code.inline {
+  background-color: rgb(250,250,250);
+  /* border: 1px solid rgb(200,200,200); */
+}
+
+table.sourceCode, tr.sourceCode, td.lineNumbers, td.sourceCode {
+  margin: 0; padding: 0; vertical-align: baseline; border: none;
+}
+
+table.sourceCode {
+  width: 100%; line-height: 100%;
+}
+
+td.lineNumbers { text-align: right; padding-right: 4px; padding-left: 4px; color: #aaaaaa; border-right: 1px solid #aaaaaa; }
+td.sourceCode { padding-left: 5px; }
+code.kw, span.kw { color: #af005f; } /* Keyword */
+code.dt, span.dt { color: #5f5faf; } /* DataType */
+code.dv, span.dv { color: #268bd2; } /* DecVal */
+code.bn, span.bn { color: #268bd2; } /* BaseN */
+code.fl, span.fl { color: #268bd2; } /* Float */
+code.ch, span.ch { color: #cb4b16; } /* Char */
+code.st, span.st { color: #cb4b16; } /* String */
+code.co, span.co { color: #8a8a8a; } /* Comment */
+code.ot, span.ot { color: #007020; } /* Other */
+code.al, span.al { color: #ff0000; } /* Alert */
+code.fu, span.fu { color: #666666; } /* Function */
+code.er, span.er { color: #ff0000; } /* Error */
+code.wa, span.wa { color: #60a0b0; } /* Warning */
+code.cn, span.cn { color: #880000; } /* Constant */
+code.sc, span.sc { color: #4070a0; } /* SpecialChar */
+code.vs, span.vs { color: #4070a0; } /* VerbatimString */
+code.ss, span.ss { color: #2aa198; } /* SpecialString */
+code.va, span.va { color: #073642; } /* Variable */
+code.cf, span.cf { color: #007020; } /* ControlFlow */
+code.op, span.op { color: #d33682; } /* Operator */
+code.pp, span.pp { color: #bc7a00; } /* Preprocessor */
+code.at, span.at { color: #7d9029; } /* Attribute */
+code.do, span.do { color: #ba2121; } /* Documentation */
+code.an, span.an { color: #60a0b0; } /* Annotation */
+code.cv, span.cv { color: #60a0b0; } /* CommentVar */

css/computermodern.css

@@ -0,0 +1,13 @@
+@font-face {
+  font-family: "Computer Modern";
+  src: url('/static/cmunorm.woff');
+}
+
+.math {
+  font-family: Computer Modern, serif;
+}
+
+.math .display {
+  font-size: 18px;
+  text-align: center;
+}

css/default.scss

@@ -0,0 +1,469 @@
+$purple: #424969;
+$orange: #ffac5f;
+$blonde: #f5ddbc;
+$light-purple: #faf0fa;
+$yugo: #ea8472;
+
+$header: $orange;
+$header-height: 50px;
+
+$max-width: 95ch;
+
+.mathpar, .math-paragraph {
+  display: flex;
+  flex-direction: row;
+  flex-wrap: wrap;
+  justify-content: space-around;
+  align-items: center;
+}
+
+a#mastodon {
+  display: none;
+}
+
+html, body {
+  min-height: 100%;
+  height: 100%;
+  margin: 0;
+
+  background-color: white;
+
+  font-family: -apple-system,BlinkMacSystemFont,"Segoe UI",Roboto,Oxygen-Sans,Ubuntu,Cantarell,"Helvetica Neue",sans-serif;
+}
+
+body {
+  display: flex;
+  flex-direction: column;
+
+  counter-reset: theorem figure;
+}
+
+div#header {
+  background-color: $header;
+  height: $header-height;
+
+  display: flex;
+  flex-direction: row;
+  align-items: stretch;
+  justify-content: space-between;
+
+  flex-wrap: nowrap;
+  overflow-x: auto;
+
+  div#logo {
+    margin-left: .5em;
+    line-height: $header-height;
+
+    padding-left: .5em;
+    padding-right: .5em;
+    font-size: 18pt;
+
+    a {
+      color: $purple;
+      text-decoration: none;
+    }
+
+    transition: background-color .2s ease-in-out;
+  }
+
+  div#logo:hover {
+    background-color: darken($header, 10%);
+  }
+
+  div#navigation {
+    margin-right: .5em;
+
+    display: flex;
+    flex-direction: row;
+    align-items: stretch;
+    align-self: flex-end;
+    justify-content: flex-end;
+
+    line-height: $header-height;
+
+    a {
+      color: $purple;
+      text-decoration: none;
+
+      margin-left: .5em;
+      margin-right: .5em;
+    }
+
+    div.nav-button {
+      height: 100%;
+      transition: background-color .2s ease-in-out;
+    }
+
+    div.nav-button:hover {
+      background-color: darken($header, 10%);
+    }
+  }
+
+}
+
+div#content {
+  max-width: $max-width;
+  margin: 0px auto 0px auto;
+  flex: 1 0 auto;
+
+  span.katex, span.together {
+    display: inline-block;
+  }
+
+  p {
+    text-align: justify;
+    letter-spacing: 1.75;
+
+    code {
+      display: inline-block;
+    }
+
+    span.qed {
+      float: right;
+    }
+
+    span.theorem ::after {
+      counter-increment: theorem;
+      content: " " counter(theorem);
+    }
+
+    span.theorem, span.paragraph-marker {
+      font-style: italic;
+    }
+  }
+
+  p.image {
+    text-align: center !important;
+  }
+
+  h1 {
+    font-variant: small-caps;
+    max-width: 120ch;
+  }
+
+  blockquote {
+    background-color: $light-purple;
+
+    border-radius: 10px;
+    border: 1px solid $purple;
+
+    padding: 0em 1em;
+  }
+
+  > article > blockquote {
+    width: 80%;
+    margin: auto;
+  }
+
+  > article > div.code-container {
+    width: 80%;
+    margin: auto;
+
+    pre {
+      padding: 0px 1em;
+    }
+
+    > span {
+      display: inline;
+    }
+  }
+
+  div.code-container {
+    background-color: $light-purple;
+
+    border-radius: 10px;
+    border: 1px solid darken($light-purple, 10%);
+
+    overflow-x: auto;
+
+    > span {
+      padding: 0.5em 1em 0.25em 1em;
+      background-color: darken($light-purple, 10%);
+
+      border-top-left-radius: 10px;
+
+      box-shadow: 1px 1px darken($light-purple, 20%);
+      display: none;
+    }
+
+    > span::after {
+      content: " code";
+    }
+
+    div.sourceCode {
+      padding: 0px .5em;
+    }
+  }
+
+  div.code-container.custom-tag {
+    > span::after {
+      display: none;
+    }
+  }
+
+  div.code-container.continues {
+    > span {
+      display: none;
+    }
+  }
+
+  * {
+    max-width: 100%;
+  }
+
+  details {
+    summary {
+      margin-left: 1em;
+      font-size: 14pt;
+      padding: .2em 1em;
+    }
+
+    border-radius: 5px;
+    border: 1px solid $purple;
+
+    padding: .2em 1em;
+
+    background-color: white;
+    font-size: 0pt;
+
+    margin-top: 0.5em;
+    margin-bottom: 0.5em;
+
+    transition: font-size 0.3s ease-in-out, background-color 0.3s ease-in-out;
+    transform: rotate3d(0, 0, 0, 0);
+  }
+
+  details[open] {
+    background-color: $light-purple;
+    font-size: 14pt;
+  }
+
+  .special-thanks {
+    display: flex;
+    flex-direction: column;
+    align-items: center;
+    justify-content: space-around;
+
+    p {
+      font-size: 21pt;
+      margin-top: .5em;
+      margin-bottom: 0px;
+    }
+
+    ul {
+      list-style: none;
+      li {
+        margin: .5em 0px;
+        border-radius: 10px;
+        border: 1px solid $purple;
+        background-color: $light-purple;
+        
+        padding: 1em;
+
+        a {
+          text-decoration: underline;
+        }
+
+        transition: all 0.2s ease-in-out;
+      }
+
+      li:hover {
+        border-radius: 5px;
+        transform: scale(1.01);
+        background-color: lighten($light-purple, 5%);
+      }
+    }
+  }
+
+  .eqn-list {
+    list-style: none;
+    direction: rtl;
+    counter-reset: equation;
+
+    li {
+      counter-increment: equation;
+
+      span.katex-display {
+        margin: 2px; 
+      }
+
+      * {
+        direction: ltr;
+      }
+    }
+
+    li::marker {
+      content: "(" counter(equation) ")";
+      font-family: KaTeX_Main, Times New Roman, serif;
+    }
+  }
+
+  font-size: 14pt;
+  line-height: 1.6;
+}
+
+div.info, span#reading-length {
+  padding-left: 1em;
+  font-style: italic;
+}
+
+span#reading-length::before {
+  content: "Word count: "
+}
+
+div#footer {
+  display: flex;
+  align-items: center;
+  justify-content: space-between;
+
+  padding-left: 1em;
+  padding-right: 1em;
+
+  background-color: $light-purple;
+}
+
+.definition {
+  text-decoration: dotted underline;
+}
+
+.post-list {
+  list-style: none;
+  padding: 0px;
+
+  div.post-list-item {
+    margin-top: .2em;
+    margin-bottom: .2em;
+
+    padding: 1em;
+
+    border-radius: 10px;
+    background-color: $light-purple;
+
+    display: flex;
+    justify-content: space-between;
+    flex-wrap: wrap;
+    align-items: flex-end;
+
+    font-size: 11pt;
+
+    a {
+      font-size: 14pt;
+      padding-right: 2em;
+    }
+  }
+}
+
+table {
+  margin: auto;
+  border-collapse: collapse;
+
+  td, th {
+    border: 1px solid $purple;
+    text-align: center;
+    padding: 0px 1em 0px 1em;
+
+    > * {
+      vertical-align: middle;
+    }
+  }
+
+  td.image {
+    padding: 0px;
+    img {
+      margin-top: auto;
+    }
+  }
+}
+
+figure {
+  width: 100%;
+  margin: auto;
+
+  display: flex;
+  flex-direction: column;
+  align-items: center;
+  justify-content: space-around;
+
+  div {
+    width: 100%;
+    overflow-x: auto;
+  }
+
+  figcaption {
+    font-size: 14pt;
+  }
+
+  figcaption::before {
+    counter-increment: figure;
+    content: "Figure " counter(figure) ". ";
+  }
+}
+
+
+@media only screen and (max-width: $max-width) {
+  div#content {
+    margin-left: 1em;
+    margin-right: 1em;
+  }
+
+  .mathpar {
+    overflow-x: auto;
+    justify-content: space-evenly;
+
+    > * {
+      margin-left: .2em;
+      margin-right: .2em;
+      flex-shrink: 0;
+      flex-grow: 0;
+    }
+  }
+}
+
+// Contact page
+
+.contact-list {
+  display: flex;
+  flex-direction: row;
+  flex-wrap: wrap;
+  justify-content: space-around;
+  align-items: center;
+
+  .contact-card {
+    margin: 0px .5em;
+
+    border: 1px solid $purple;
+    border-radius: 10px;
+    background-color: $blonde;
+
+    padding: 0px 1em;
+
+    .username, .username * {
+      font-size: 21pt;
+      color: $purple;
+    }
+
+    p {
+      display: flex;
+      align-items: center;
+      justify-content: space-evenly;
+
+      max-width: 40ch !important;
+    }
+
+    transition: all 0.2s ease-in-out;
+  }
+
+  .contact-card:hover {
+    margin: 0px .55em;
+    background-color: darken($blonde, 10%);
+    border-radius: 5px;
+    transform: scale(1.01);
+  }
+}
+
+@font-face {
+  font-family: 'Fantasque Sans Mono';
+  src: url('fonts/FantasqueSansMono-Regular.woff2') format('woff2');
+  font-weight: 400;
+  font-style: normal;
+}

diagrams/cc/delimcc.tex

@@ -0,0 +1,15 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (Stk0) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, 0)     {shift};
+\node (Stk1) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -0.75) {foo};
+\node (Stk2) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -1.5)  {bar};
+\node (Stk3) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -2.25) {reset};
+\node (Stk3) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -3)  {baz};
+\draw [red, very thick, dashed] (-3.6, -2.625) -- (-1.89, -2.625) -- (-1.89, 0.375) -- (-3.6, 0.375) -- cycle;
+\draw [arrows={Latex}-] (-4, 0.375) -- (-4, -3.375);
+\end{scope}

diagrams/eq/0cube.tex

@@ -0,0 +1 @@
+\node[draw,circle,label=right:$A$,fill,outer sep=0.1cm, inner sep=0pt, minimum size=0.1cm] (i0) at (0, 0) {};

diagrams/eq/1cube.tex

@@ -0,0 +1,4 @@
+\node[draw,circle,label=left:{$A[0/i]$},fill,outer sep=0.1cm, inner sep=0pt, minimum size=0.1cm] (i0) at (-1, 0) {};
+\node[draw,circle,label=right:{$A[1/i]$},fill,outer sep=0.1cm, inner sep=0pt, minimum size=0.1cm] (i1) at (1, 0) {};
+
+\draw (i0) -- (i1);

diagrams/eq/2cube.tex

@@ -0,0 +1,6 @@
+\node[draw,circle,label=left:{$A[0/i, 0/j]$},fill,outer sep=0.1cm, inner sep=0pt, minimum size=0.1cm] (i0j0) at (-1, -1) {};
+\node[draw,circle,label=right:{$A[1/i, 0/j]$},fill,outer sep=0.1cm, inner sep=0pt, minimum size=0.1cm] (i1j0) at (1, -1) {};
+\node[draw,circle,label=left:{$A[0/i, 1/j]$},fill,outer sep=0.1cm, inner sep=0pt, minimum size=0.1cm] (i0j1) at (-1, 1) {};
+\node[draw,circle,label=right:{$A[1/i, 1/j]$},fill,outer sep=0.1cm, inner sep=0pt, minimum size=0.1cm] (i1j1) at (1, 1) {};
+
+\draw (i0j0) -- (i1j0) -- (i1j1) -- (i0j1) -- (i0j0);

diagrams/eq/interval.tex

@@ -0,0 +1,5 @@
+\node[draw,circle,label=below:$i_0$,fill,outer sep=0.1cm, inner sep=0pt, minimum size=0.1cm] (i0) at (-1, 0) {};
+\node[draw,circle,label=below:$i_1$,fill,outer sep=0.1cm, inner sep=0pt, minimum size=0.1cm] (i1) at (1, 0) {};
+
+\draw (i0) -- (i1) node [midway, above] (seg) {seg};
+% \draw[-] (i0) -- (i1);

diagrams/gm/app_gx.tex

@@ -0,0 +1,39 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (FGX) [inner xsep=0.01cm, inner ysep=0.03cm]        at (0, 0) {@};
+\node (FG)  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, left of=FGX]  {@};
+\node (X)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, right of=FGX] {x};
+\node (F)   [xshift=0.25cm, inner xsep=0.04cm, inner ysep=0.05cm, below of=FG, left of=FG, xshift=2]   {f};
+\node (G)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FG, right of=FG, xshift=-2] {g};
+
+\node (GX)
+  [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=F, xshift=0.75cm]
+  {@};
+
+\draw[->] (FGX) to (X);
+\draw[->] (FGX) to (FG);
+\draw[->] (FG)  to (F.north east);
+\draw[->] (FG)  to (G.north west);
+
+\draw[->] (GX) to ([shift=({-0.35cm,-0.35cm})]GX)
+               -- ++(0, -0.10cm)
+               -| (G);
+
+\draw[->] (GX) to ([shift=({0.45cm,-0.35cm})]GX)
+               -| (X);
+
+\node (Stk0) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, 0)     {};
+\node (Stk1) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -0.75) {};
+\node (Stk2) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -1.5)  {};
+\node (Stk3) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -2.25) {};
+
+\draw[->] (Stk0.center) to (FGX);
+\draw[->] (Stk1.center) to (FG);
+\draw[->] (Stk2.center) to (F);
+\draw[->] (Stk3.center) to (GX);
+
+\end{scope}

diagrams/gm/app_kgx.tex

@@ -0,0 +1,51 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (FGX) [inner xsep=0.01cm, inner ysep=0.03cm]        at (0, 0) {@};
+\node (FG)  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, left of=FGX]  {@};
+\node (X)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, right of=FGX] {x};
+\node (F)   [xshift=0.25cm, inner xsep=0.04cm, inner ysep=0.05cm, below of=FG, left of=FG, xshift=2]   {f};
+\node (G)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FG, right of=FG, xshift=-2] {g};
+
+\node (KGX)
+  [xshift=-0.55cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=F, xshift=0.75cm]
+  {@};
+
+\node (K)
+  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=KGX, left of=KGX]
+  {K};
+
+\node (GX)
+  [xshift=-0.45cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=KGX, right of=KGX]
+  {@};
+
+\draw[->] (FGX) to (X);
+\draw[->] (FGX) to (FG);
+\draw[->] (FG)  to (F.north east);
+\draw[->] (FG)  to (G.north west);
+
+\draw[->] (KGX) to (K);
+\draw[->] (KGX) to (GX);
+
+\draw[->] (GX) to ([shift=({-0.35cm,-0.35cm})]GX)
+               -- ++(0, -0.10cm)
+               -| (G);
+
+\draw[->] (GX) to ([shift=({0.45cm,-0.35cm})]GX)
+               -| (X);
+
+\node (Stk0) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, 0)     {};
+\node (Stk1) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -0.75) {};
+\node (Stk2) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -1.5)  {};
+\node (Stk3) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -2.25) {};
+
+
+\draw[->] (Stk0.center) to (FGX);
+\draw[->] (Stk1.center) to (FG);
+\draw[->] (Stk2.center) to (F);
+\draw[->] (Stk3.center) to (KGX);
+
+\end{scope}

diagrams/gm/entry.tex

@@ -0,0 +1,25 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (FGX) [inner xsep=0.01cm, inner ysep=0.03cm] at (0, 0) {@};
+\node (FG)  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, left of=FGX]  {@};
+\node (X)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, right of=FGX] {x};
+\node (F)   [xshift=0.25cm, inner xsep=0.04cm, inner ysep=0.05cm, below of=FG, left of=FG, xshift=2]   {f};
+\node (G)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FG, right of=FG, xshift=-2] {g};
+
+\draw[->] (FGX) to (X);
+\draw[->] (FGX) to (FG);
+\draw[->] (FG)  to (F.north east);
+\draw[->] (FG)  to (G.north west);
+
+\node (Stk0) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, 0)     {};
+\node (Stk1) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -0.75) {};
+\node (Stk2) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -1.5)  {};
+
+\draw[->] (Stk0.center) to (FGX);
+\draw[->] (Stk1.center) to (FG);
+\draw[->] (Stk2.center) to (F);
+
+\end{scope}

diagrams/gm/push_g.tex

@@ -0,0 +1,31 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (FGX) [inner xsep=0.01cm, inner ysep=0.03cm]        at (0, 0) {@};
+\node (FG)  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, left of=FGX]  {@};
+\node (X)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, right of=FGX] {x};
+\node (F)   [xshift=0.25cm, inner xsep=0.04cm, inner ysep=0.05cm, below of=FG, left of=FG, xshift=2]   {f};
+\node (G)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FG, right of=FG, xshift=-2] {g};
+
+\draw[->] (FGX) to (X);
+\draw[->] (FGX) to (FG);
+\draw[->] (FG)  to (F.north east);
+\draw[->] (FG)  to (G.north west);
+
+\node (Stk0) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, 0)     {};
+\node (Stk1) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -0.75) {};
+\node (Stk2) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -1.5)  {};
+\node (Stk3) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -2.25) {};
+\node (Stk4) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -3) {};
+
+\draw[->] (Stk0.center) to (FGX);
+\draw[->] (Stk1.center) to (FG);
+\draw[->] (Stk2.center) to (F);
+\draw[->] (Stk3.center) to (X |- 0, -2.25cm)  -- (X);
+\draw[->] (Stk4.center) to (G |- 0, -3cm) -- (G);
+
+\end{scope}

diagrams/gm/push_k.tex

@@ -0,0 +1,44 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (FGX) [inner xsep=0.01cm, inner ysep=0.03cm]        at (0, 0) {@};
+\node (FG)  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, left of=FGX]  {@};
+\node (X)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, right of=FGX] {x};
+\node (F)   [xshift=0.25cm, inner xsep=0.04cm, inner ysep=0.05cm, below of=FG, left of=FG, xshift=2]   {f};
+\node (G)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FG, right of=FG, xshift=-2] {g};
+
+\node (GX)
+  [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=F, xshift=0.75cm]
+  {@};
+
+\draw[->] (FGX) to (X);
+\draw[->] (FGX) to (FG);
+\draw[->] (FG)  to (F.north east);
+\draw[->] (FG)  to (G.north west);
+
+\draw[->] (GX) to ([shift=({-0.35cm,-0.35cm})]GX)
+               -- ++(0, -0.10cm)
+               -| (G);
+
+\draw[->] (GX) to ([shift=({0.45cm,-0.35cm})]GX)
+               -| (X);
+
+\node (Stk0) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, 0)     {};
+\node (Stk1) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -0.75) {};
+\node (Stk2) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -1.5)  {};
+\node (Stk3) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -2.25) {};
+\node (Stk4) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -3) {};
+
+\node (K) [right of=Stk4, xshift=1.5cm] {K};
+
+\draw[->] (Stk0.center) to (FGX);
+\draw[->] (Stk1.center) to (FG);
+\draw[->] (Stk2.center) to (F);
+\draw[->] (Stk3.center) to (GX);
+\draw[->] (Stk4.center) to (K);
+
+\end{scope}

diagrams/gm/push_x.tex

@@ -0,0 +1,33 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (FGX) [inner xsep=0.01cm, inner ysep=0.03cm]
+  at (0, 0) {@};
+\node (FG)  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, left of=FGX]
+  {@};
+\node (X)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, right of=FGX]
+  {x};
+\node (F)   [xshift=0.25cm, inner xsep=0.04cm, inner ysep=0.05cm, below of=FG, left of=FG, xshift=2]
+  {f};
+\node (G)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FG, right of=FG, xshift=-2]
+  {g};
+
+\draw[->] (FGX) to (X);
+\draw[->] (FGX) to (FG);
+\draw[->] (FG)  to (F.north east);
+\draw[->] (FG)  to (G.north west);
+
+\node (Stk0) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, 0)     {};
+\node (Stk1) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -0.75) {};
+\node (Stk2) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -1.5)  {};
+\node (Stk3) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -2.25) {};
+
+\draw[->] (Stk0.center) to (FGX);
+\draw[->] (Stk1.center) to (FG);
+\draw[->] (Stk2.center) to (F);
+\draw[->] (Stk3.center) to (0.5cm, -2.25cm) -- (X);
+
+\end{scope}

diagrams/gm/slide_3.tex

@@ -0,0 +1,34 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (KGX)
+  [xshift=-0.55cm, inner xsep=0.01cm, inner ysep=0.03cm]
+  at (0, 0) {@};
+
+\node (K)
+  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=KGX, left of=KGX]
+  {K};
+
+\node (GX)
+  [xshift=-0.45cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=KGX, right of=KGX]
+  {@};
+
+\node (G)
+  [xshift=0.45cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=GX, left of=GX]
+  {g};
+
+\node (X)
+  [xshift=-0.45cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=GX, right of=GX]
+  {x};
+
+\draw[->] (KGX) to (K);
+\draw[->] (KGX) to (GX);
+
+\draw[->] (GX) to (G);
+\draw[->] (GX) to (X);
+
+\node (Stk0) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, 0)     {};
+
+\draw[->] (Stk0.center) to (KGX);
+
+\end{scope}

diagrams/gm/spine+stack.tex

@@ -0,0 +1,25 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (FGX) [color=blue,inner xsep=0.01cm, inner ysep=0.03cm] at (0, 0) {@};
+\node (FG)  [color=blue,xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, left of=FGX]  {@};
+\node (X)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, right of=FGX] {y};
+\node (F)   [color=blue,xshift=0.25cm, inner xsep=0.04cm, inner ysep=0.05cm, below of=FG, left of=FG, xshift=2]   {f};
+\node (G)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FG, right of=FG, xshift=-2] {x};
+
+\draw[->] (FGX) to (X);
+\draw[->,color=blue] (FGX) to (FG);
+\draw[->,color=blue] (FG)  to (F.north east);
+\draw[->] (FG)  to (G.north west);
+
+\node (Stk0) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, 0)     {};
+\node (Stk1) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -0.75) {};
+\node (Stk2) [draw, shape=rectangle, minimum width=1.5cm, minimum height=0.75cm, anchor=center]
+  at (-2.75, -1.5)  {};
+
+\draw[->] (Stk0.center) to (FGX);
+\draw[->] (Stk1.center) to (FG);
+\draw[->] (Stk2.center) to (F);
+
+\end{scope}

diagrams/gm/spine.tex

@@ -0,0 +1,14 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (FGX) [color=blue,inner xsep=0.01cm, inner ysep=0.03cm] at (0, 0) {@};
+\node (FG)  [color=blue,xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, left of=FGX]  {@};
+\node (X)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FGX, right of=FGX] {y};
+\node (F)   [color=blue,xshift=0.25cm, inner xsep=0.04cm, inner ysep=0.05cm, below of=FG, left of=FG, xshift=2]   {f};
+\node (G)   [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=FG, right of=FG, xshift=-2] {x};
+
+\draw[->] (FGX) to (X);
+\draw[->,color=blue] (FGX) to (FG);
+\draw[->,color=blue] (FG)  to (F.north east);
+\draw[->] (FG)  to (G.north west);
+
+\end{scope}

diagrams/template/step1.tex

@@ -0,0 +1 @@
+\node at (0, 0) {main};

diagrams/template/step2.tex

@@ -0,0 +1,26 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (DoDo4) [inner xsep=0.01cm, inner ysep=0.03cm] at (0, 0) {@};
+
+\node (Do)
+  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=DoDo4, left of=DoDo4]
+  {double};
+
+\node (Do4) 
+  [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=DoDo4, right of=DoDo4]
+  {@};
+
+\node (Do_2)
+  [xshift=0.25cm, inner xsep=0.04cm, inner ysep=0.05cm, below of=Do4, left of=Do4, xshift=2]
+  {double};
+
+\node (4)
+  [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=Do4, right of=Do4, xshift=-2]
+  {4};
+
+\draw[->] (DoDo4) to (Do);
+\draw[->] (DoDo4) to (Do4);
+\draw[->] (Do4)  to (Do_2);
+\draw[->] (Do4)  to (4);
+
+\end{scope}

diagrams/template/step3.tex

@@ -0,0 +1,33 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (DoDo4) [inner xsep=0.01cm, inner ysep=0.03cm] at (0, 0) {@};
+
+\node (TimesAp)
+  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=DoDo4, left of=DoDo4]
+  {@};
+
+\node (Times)
+  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=TimesAp, left of=TimesAp]
+  {$+$};
+
+\node (Do4) 
+  [xshift=-0.5cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=DoDo4,
+  right of=DoDo4, yshift=-0.5cm]
+  {@};
+
+\node (Do_2)
+  [xshift=0.25cm, inner xsep=0.04cm, inner ysep=0.05cm, below of=Do4, left of=Do4, xshift=2]
+  {double};
+
+\node (4)
+  [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=Do4, right of=Do4, xshift=-2]
+  {4};
+
+\draw[->] (DoDo4) to (TimesAp);
+\draw[->] (TimesAp) to (Times);
+\draw[->] (TimesAp) |- (Do4);
+\draw[->] (DoDo4) to (Do4);
+\draw[->] (Do4)  to (Do_2);
+\draw[->] (Do4)  to (4);
+
+\end{scope}

diagrams/template/step4.tex

@@ -0,0 +1,38 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (DoDo4) [inner xsep=0.01cm, inner ysep=0.03cm] at (0, 0) {@};
+
+\node (TimesAp)
+  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=DoDo4, left of=DoDo4]
+  {@};
+
+\node (Times)
+  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=TimesAp, left of=TimesAp]
+  {$+$};
+
+\node (Times44) 
+  [xshift=-0.5cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=DoDo4, right of=DoDo4, yshift=-0.5cm]
+  {@};
+
+\node (4)
+  [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=Times44, right of=Times44, yshift=-0.75cm]
+  {4};
+
+\node (Times4)
+  [xshift=0.25cm, inner xsep=0.04cm, inner ysep=0.05cm, below of=Times44, left of=Times44, xshift=2]
+  {@};
+
+\node (Times2)
+  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=Times4, left of=Times4]
+  {$+$};
+
+\draw[->] (DoDo4)   to (TimesAp);
+\draw[->] (TimesAp) to (Times);
+\draw[->] (TimesAp) to (Times44);
+\draw[->] (DoDo4)   to (Times44);
+\draw[->] (Times44) to (Times4);
+\draw[->] (Times4)  to (Times2);
+\draw[->] (Times4)  |- (4);
+\draw[->] (Times44) to (4);
+
+\end{scope}

diagrams/template/step4red.tex

@@ -0,0 +1,38 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (DoDo4) [inner xsep=0.01cm, inner ysep=0.03cm] at (0, 0) {@};
+
+\node (TimesAp)
+  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=DoDo4, left of=DoDo4]
+  {@};
+
+\node (Times)
+  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=TimesAp, left of=TimesAp]
+  {$+$};
+
+\node (Times44) 
+  [xshift=-0.5cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=DoDo4, right of=DoDo4, yshift=-0.5cm, color=blue]
+  {@};
+
+\node (4)
+  [xshift=-0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=Times44, right of=Times44, yshift=-0.75cm, color=blue]
+  {4};
+
+\node (Times4)
+  [xshift=0.25cm, inner xsep=0.04cm, inner ysep=0.05cm, below of=Times44, left of=Times44, xshift=2, color=blue]
+  {@};
+
+\node (Times2)
+  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=Times4, left of=Times4, color=blue]
+  {$+$};
+
+\draw[->] (DoDo4)   to (TimesAp);
+\draw[->] (TimesAp) to (Times);
+\draw[->] (TimesAp) to (Times44);
+\draw[->] (DoDo4)   to (Times44);
+\draw[->,color=blue,dashed] (Times44) to (Times4);
+\draw[->,color=blue,dashed] (Times4)  to (Times2);
+\draw[->,color=blue,dashed] (Times4)  |- (4);
+\draw[->,color=blue,dashed] (Times44) to (4);
+
+\end{scope}

diagrams/template/step5.tex

@@ -0,0 +1,22 @@
+\begin{scope}[node distance=0.75cm]
+
+\node (DoDo4) [inner xsep=0.01cm, inner ysep=0.03cm] at (0, 0) {@};
+
+\node (TimesAp)
+  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=DoDo4, left of=DoDo4]
+  {@};
+
+\node (Times)
+  [xshift=0.25cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=TimesAp, left of=TimesAp]
+  {$+$};
+
+\node (8) 
+  [xshift=-0.5cm, inner xsep=0.01cm, inner ysep=0.03cm, below of=DoDo4, right of=DoDo4, yshift=-0.75cm]
+  {8};
+
+\draw[->] (DoDo4)   to (TimesAp);
+\draw[->] (TimesAp) to (Times);
+\draw[->] (TimesAp) |- (8);
+\draw[->] (DoDo4)   to (8);
+
+\end{scope}

hie.yaml

@@ -0,0 +1,2 @@
+cradle:
+  stack:

package-lock.json

@@ -0,0 +1,140 @@
+{
+  "name": "blag",
+  "version": "1.0.0",
+  "lockfileVersion": 1,
+  "requires": true,
+  "dependencies": {
+    "anymatch": {
+      "version": "3.1.1",
+      "resolved": "https://registry.npmjs.org/anymatch/-/anymatch-3.1.1.tgz",
+      "integrity": "sha512-mM8522psRCqzV+6LhomX5wgp25YVibjh8Wj23I5RPkPppSVSjyKD2A2mBJmWGa+KN7f2D6LNh9jkBCeyLktzjg==",
+      "requires": {
+        "normalize-path": "^3.0.0",
+        "picomatch": "^2.0.4"
+      }
+    },
+    "binary-extensions": {
+      "version": "2.1.0",
+      "resolved": "https://registry.npmjs.org/binary-extensions/-/binary-extensions-2.1.0.tgz",
+      "integrity": "sha512-1Yj8h9Q+QDF5FzhMs/c9+6UntbD5MkRfRwac8DoEm9ZfUBZ7tZ55YcGVAzEe4bXsdQHEk+s9S5wsOKVdZrw0tQ=="
+    },
+    "braces": {
+      "version": "3.0.2",
+      "resolved": "https://registry.npmjs.org/braces/-/braces-3.0.2.tgz",
+      "integrity": "sha512-b8um+L1RzM3WDSzvhm6gIz1yfTbBt6YTlcEKAvsmqCZZFw46z626lVj9j1yEPW33H5H+lBQpZMP1k8l+78Ha0A==",
+      "requires": {
+        "fill-range": "^7.0.1"
+      }
+    },
+    "chokidar": {
+      "version": "3.4.3",
+      "resolved": "https://registry.npmjs.org/chokidar/-/chokidar-3.4.3.tgz",
+      "integrity": "sha512-DtM3g7juCXQxFVSNPNByEC2+NImtBuxQQvWlHunpJIS5Ocr0lG306cC7FCi7cEA0fzmybPUIl4txBIobk1gGOQ==",
+      "requires": {
+        "anymatch": "~3.1.1",
+        "braces": "~3.0.2",
+        "fsevents": "~2.1.2",
+        "glob-parent": "~5.1.0",
+        "is-binary-path": "~2.1.0",
+        "is-glob": "~4.0.1",
+        "normalize-path": "~3.0.0",
+        "readdirp": "~3.5.0"
+      }
+    },
+    "commander": {
+      "version": "2.20.3",
+      "resolved": "https://registry.npmjs.org/commander/-/commander-2.20.3.tgz",
+      "integrity": "sha512-GpVkmM8vF2vQUkj2LvZmD35JxeJOLCwJ9cUkugyk2nuhbv3+mJvpLYYt+0+USMxE+oj+ey/lJEnhZw75x/OMcQ=="
+    },
+    "fill-range": {
+      "version": "7.0.1",
+      "resolved": "https://registry.npmjs.org/fill-range/-/fill-range-7.0.1.tgz",
+      "integrity": "sha512-qOo9F+dMUmC2Lcb4BbVvnKJxTPjCm+RRpe4gDuGrzkL7mEVl/djYSu2OdQ2Pa302N4oqkSg9ir6jaLWJ2USVpQ==",
+      "requires": {
+        "to-regex-range": "^5.0.1"
+      }
+    },
+    "fsevents": {
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+      "requires": {
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+      }
+    }
+  }
+}

package.json

@@ -0,0 +1,21 @@
+{
+  "name": "blag",
+  "version": "1.0.0",
+  "description": "[Go here instead](https://abby.how)",
+  "main": "index.js",
+  "dependencies": {
+    "katex": "^0.11.1",
+    "sass": "^1.28.0"
+  },
+  "devDependencies": {},
+  "scripts": {
+    "up": "stack run -- build && stack run -- deploy",
+    "watch": "stack run -- watch"
+  },
+  "repository": {
+    "type": "git",
+    "url": "[email protected]:plt-hokusai/blag.git"
+  },
+  "author": "",
+  "license": "ISC"
+}

pages/contact.md

@@ -0,0 +1,35 @@
+---
+title: Contact
+---
+Here are the easiest ways to reach me:
+
+<style>
+span#reading-length { display: none; }
+</style>
+
+<div class="contact-list">
+<div class="contact-card">
+<span class="username">@abby#4600</span>
+
+My Discord friend requests are always open. Feel free to add me for questions or comments!
+</div>
+
+<div class="contact-card">
+<span class="username">{abby}</span>
+
+<span>
+Message me directly on <a href="https://webchat.freenode.net/">Freenode</a> IRC, or join `##dependent` to talk about types!
+</span>
+</div>
+</div>
+
+If you like what I do, here are some ways you can support this blog:
+
+<div class="contact-list">
+<div class="contact-card">
+<span class="username"><a href="https://ko-fi.com/pltabby">Ko-fi</a></span>
+
+You can send me a one-time donation on Ko-Fi. Just remember not to read the name on the receipt!
+(Paypal sucks)
+</div>
+</div>

pages/index.html

@@ -0,0 +1,13 @@
+---
+title: Home
+---
+
+<p>
+  You've reached Abigail's blog, a place where I exposit and reflect on programming languages and type theory.
+  Here's the posts I've written recently:
+</p>
+
+<h2>Posts</h2>
+$partial("templates/post-list.html")$
+
+<p>…or you can find more in the <a href="/archive.html">archives</a>.</p>

pages/oss.md

@@ -0,0 +1,14 @@
+---
+title: Open-source Licenses
+---
+
+<style>
+span#reading-length { display: none; }
+</style>
+
+This blog redistributes (parts of) the following free software projects:
+
+* **KaTeX** is a fast JavaScript library for rendering LaTeX on the client. I use it to pre-generate amazing looking mathematics at compile time. **KaTeX is licensed under the terms of the MIT license, with a copy available [here](/static/licenses/LICENSE.KaTeX)**.
+
+
+* **Fantasque Sans Mono** is the programming font I've used for the past 3 years, including on this website. **Fantasque Sans Mono is distributed under the terms of the Open Font License (OFL), with a copy available [here](/static/licenses/LICENSE.FantasqueSansMono)**.

pages/posts/2016-08-17-parsec.md

@@ -0,0 +1,308 @@
+---
+title: You could have invented Parsec
+date: August 17, 2016 01:29 AM
+---
+
+As most of us should know, [Parsec](https://hackage.haskell.org/package/parsec)
+is a relatively fast, lightweight monadic parser combinator library.
+
+In this post I aim to show that monadic parsing is not only useful, but a simple
+concept to grok.
+
+We shall implement a simple parsing library with instances of common typeclasses
+of the domain, such as Monad, Functor and Applicative, and some example
+combinators to show how powerful this abstraction really is.
+
+---
+
+Getting the buzzwords out of the way, being _monadic_ just means that Parsers
+instances of `Monad`{.haskell}. Recall the Monad typeclass, as defined in
+`Control.Monad`{.haskell},
+
+```haskell
+class Applicative m => Monad m where
+  return :: a -> m a
+  (>>=)  :: m a -> (a -> m b) -> m b
+  {- Some fields omitted -}
+```
+
+How can we fit a parser in the above constraints? To answer that, we must first
+define what a parser _is_.
+
+A naïve implementation of the `Parser`{.haskell} type would be a simple type
+synonym.
+
+```haskell
+type Parser a = String -> (a, String)
+```
+
+This just defines that a parser is a function from a string to a result pair
+with the parsed value and the resulting stream. This would mean that parsers are
+just state transformers, and if we define it as a synonym for the existing mtl
+`State`{.haskell} monad, we get the Monad, Functor and Applicative instances for
+free!  But alas, this will not do.
+
+Apart from modeling the state transformation that a parser expresses, we need a
+way to represent failure. You already know that `Maybe a`{.haskell} expresses
+failure, so we could try something like this:
+
+```haskell
+type Parser a = String -> Maybe (a, String)
+```
+
+But, as you might have guessed, this is not the optimal representation either:
+`Maybe`{.haskell} _does_ model failure, but in a way that is lacking. It can
+only express that a computation was successful or that it failed, not why it
+failed. We need a way to fail with an error message. That is, the
+`Either`{.haskell} monad.
+
+```haskell
+type Parser e a = String -> Either e (a, String)
+```
+
+Notice how we have the `Maybe`{.haskell} and `Either`{.haskell} outside the
+tuple, so that when an error happens we stop parsing immediately. We could
+instead have them inside the tuple for better error reporting, but that's out of
+scope for a simple blag post.
+
+This is pretty close to the optimal representation, but there are still some
+warts things to address: `String`{.haskell} is a bad representation for textual
+data, so ideally you'd have your own `Stream`{.haskell} class that has instances
+for things such as `Text`{.haskell}, `ByteString`{.haskell} and
+`String`{.haskell}.
+
+One issue, however, is more glaring: You _can't_ define typeclass instances for
+type synonyms! The fix, however, is simple: make `Parser`{.haskell} a newtype.
+
+```haskell
+newtype Parser a
+  = Parser { parse :: String -> Either String (a, String) }
+```
+
+---
+
+Now that that's out of the way, we can actually get around to instancing some
+typeclasses.
+
+Since the AMP landed in GHC 7.10 (base 4.8), the hierarchy of the Monad
+typeclass is as follows:
+
+```haskell
+class Functor (m :: * -> *) where
+class Functor m     => Applicative m where
+class Applicative m => Monad m where
+```
+
+That is, we need to implement Functor and Applicative before we can actually
+implement Monad.
+
+We shall also add an `Alternative`{.haskell} instance for expressing choice.
+
+First we need some utility functions, such as `runParser`{.haskell}, that runs a
+parser from a given stream.
+
+```haskell
+runParser :: Parser a -> String -> Either String a
+runParser (Parser p) s = fst <$> p s
+```
+
+We could also use function for modifying error messages. For convenience, we
+make this an infix operator, `<?>`{.haskell}.
+
+```haskell
+(<?>) :: Parser a -> String -> Parser a
+(Parser p) <?> err = Parser go where
+  go s = case p s of
+    Left _ -> Left err
+    Right x -> return x
+infixl 2 <?>
+```
+
+
+`Functor`
+=======
+
+Remember that Functor models something that can be mapped over (technically,
+`fmap`-ed over).
+
+We need to define semantics for `fmap` on Parsers. A sane implementation would
+only map over the result, and keeping errors the same. This is a homomorphism,
+and follows the Functor laws.
+
+However, since we can't modify a function in place, we need to return a new
+parser that applies the given function _after_ the parsing is done.
+
+```haskell
+instance Functor Parser where
+  fn `fmap` (Parser p) = Parser go where
+    go st = case p st of
+      Left e            -> Left e
+      Right (res, str') -> Right (fn res, str')
+```
+
+### `Applicative`
+
+While Functor is something that can be mapped over, Applicative defines
+semantics for applying a function inside a context to something inside a
+context.
+
+The Applicative class is defined as
+
+```haskell
+class Functor m => Applicative m where
+  pure  :: a -> m a
+  (<*>) :: f (a -> b) -> f a -> f b
+```
+
+Notice how the `pure`{.haskell} and the `return`{.haskell} methods are
+equivalent, so we only have to implement one of them.
+
+Let's go over this by parts.
+
+```haskell
+instance Applicative Parser where
+  pure x = Parser $ \str -> Right (x, str)
+```
+
+The `pure`{.haskell} function leaves the stream untouched, and sets the result
+to the given value.
+
+The `(<*>)`{.haskell} function needs to to evaluate and parse the left-hand side
+to get the in-context function to apply it.
+
+```haskell
+  (Parser p) <*> (Parser p') = Parser go where
+    go st = case p st of
+      Left e -> Left e
+      Right (fn, st') -> case p' st' of
+        Left e' -> Left e'
+        Right (v, st'') -> Right (fn v, st'')
+```
+
+### `Alternative`
+
+Since the only superclass of Alternative is Applicative, we can instance it
+without a Monad instance defined. We do, however, need an import of
+`Control.Applicative`{.haskell}.
+
+```haskell
+instance Alternative Parser where
+  empty = Parser $ \_ -> Left "empty parser"
+  (Parser p) <|> (Parser p') = Parser go where
+    go st = case p st of
+      Left _  -> p' st
+      Right x -> Right x
+```
+
+### `Monad`
+
+After almost a thousand words, one would be excused for forgetting we're
+implementing a _monadic_ parser combinator library. That means, we need an
+instance of the `Monad`{.haskell} typeclass.
+
+Since we have an instance of Applicative, we don't need an implementation of
+return: it is equivalent to `pure`, save for the class constraint.
+
+```haskell
+instance Monad Parser where
+  return = pure
+```
+
+
+The `(>>=)`{.haskell} implementation, however, needs a bit more thought. Its
+type signature is
+
+```haskell
+(>>=) :: m a -> (a -> m b) -> m b
+```
+
+That means we need to extract a value from the Parser monad and apply it to the
+given function, producing a new Parser.
+
+```haskell
+  (Parser p) >>= f = Parser go where
+    go s = case p s of
+      Left e -> Left e
+      Right (x, s') -> parse (f x) s'
+```
+
+While some people think that the `fail`{.haskell} is not supposed to be in the
+Monad typeclass, we do need an implementation for when pattern matching fails.
+It is also convenient to use `fail`{.haskell} for the parsing action that
+returns an error with a given message.
+
+```haskell
+  fail m = Parser $ \_ -> Left m
+```
+
+---
+
+We now have a `Parser`{.haskell} monad, that expresses a parsing action. But, a
+parser library is no good when actual parsing is made harder than easier. To
+make parsing easier, we define _combinators_, functions that modify a parser in
+one way or another.
+
+But first, we should get some parsing functions.
+
+### any, satisfying
+
+`any` is the parsing action that pops a character off the stream and returns
+that. It does no further parsing at all.
+
+```haskell
+any :: Parser Char
+any = Parser go where
+  go []     = Left "any: end of file"
+  go (x:xs) = Right (x,xs)
+```
+
+`satisfying` tests the parsed value against a function of type `Char ->
+Bool`{.haskell} before deciding if it's successful or a failure.
+
+```haskell
+satisfy :: (Char -> Bool) -> Parser Char
+satisfy f = d
+  x <- any
+  if f x
+    then return x
+    else fail "satisfy: does not satisfy"
+```
+
+We use the `fail`{.haskell} function defined above to represent failure.
+
+### `oneOf`, `char`
+
+These functions are defined in terms of `satisfying`, and parse individual
+characters.
+
+```haskell
+char :: Char -> Parser Char
+char c = satisfy (c ==) <?> "char: expected literal " ++ [c]
+
+oneOf :: String -> Parser Char
+oneOf s = satisfy (`elem` s) <?> "oneOf: expected one of '" ++ s ++ "'"
+```
+
+### `string`
+
+This parser parses a sequence of characters, in order.
+
+```haskell
+string :: String -> Parser String
+string [] = return []
+string (x:xs) = do
+  char   x
+  string xs
+  return $ x:xs
+```
+
+---
+
+And that's it! In a few hundred lines, we have built a working parser combinator
+library with Functor, Applicative, Alternative, and Monad instances. While it's
+not as complex or featureful as Parsec in any way, it is powerful enough to
+define grammars for simple languages.
+
+[A transcription](/static/Parser.hs) ([with syntax
+highlighting](/static/Parser.hs.html)) of this file is available as runnable
+Haskell. The transcription also features some extra combinators for use.

pages/posts/2016-08-23-hasochism.lhs

@@ -0,0 +1,331 @@
+---
+title: Dependent types in Haskell - Sort of
+date: August 23, 2016
+---
+
+**Warning**: An intermediate level of type-fu is necessary for understanding
+*this post.
+
+The glorious Glasgow Haskell Compilation system, since around version 6.10 has
+had support for indexed type familes, which let us represent functional
+relationships between types. Since around version 7, it has also supported
+datatype-kind promotion, which lifts arbitrary data declarations to types. Since
+version 8, it has supported an extension called `TypeInType`, which unifies the
+kind and type level.
+
+With this in mind, we can implement the classical dependently-typed example:
+Length-indexed lists, also called `Vectors`{.haskell}.
+
+----
+
+> {-# LANGUAGE TypeInType #-}
+
+`TypeInType` also implies `DataKinds`, which enables datatype promotion, and
+`PolyKinds`, which enables kind polymorphism.
+
+`TypeOperators` is needed for expressing type-level relationships infixly, and
+`TypeFamilies` actually lets us define these type-level functions.
+
+> {-# LANGUAGE TypeOperators #-}
+> {-# LANGUAGE TypeFamilies #-}
+
+Since these are not simple-kinded types, we'll need a way to set their kind
+signatures[^kind] explicitly. We'll also need Generalized Algebraic Data Types
+(or GADTs, for short) for defining these types.
+
+> {-# LANGUAGE KindSignatures #-}
+> {-# LANGUAGE GADTs #-}
+
+Since GADTs which couldn't normally be defined with regular ADT syntax can't
+have deriving clauses, we also need `StandaloneDeriving`.
+
+> {-# LANGUAGE StandaloneDeriving #-}
+
+> module Vector where
+> import Data.Kind
+
+----
+
+Natural numbers
+===============
+
+We could use the natural numbers (and singletons) implemented in `GHC.TypeLits`,
+but since those are not defined inductively, they're painful to use for our
+purposes.
+
+Recall the definition of natural numbers proposed by Giuseppe Peano in his
+axioms: **Z**ero is a natural number, and the **s**uccessor of a natural number
+is also a natural number.
+
+If you noticed the bold characters at the start of the words _zero_ and
+_successor_, you might have already assumed the definition of naturals to be
+given by the following GADT:
+
+< data Nat where
+<   Z :: Nat
+<   S :: Nat -> Nat
+
+This is fine if all you need are natural numbers at the _value_ level, but since
+we'll be parametrising the Vector type with these, they have to exist at the
+type level. The beauty of datatype promotion is that any promoted type will
+exist at both levels: A kind with constructors as its inhabitant types, and a
+type with constructors as its... constructors.
+
+Since we have TypeInType, this declaration was automatically lifted, but we'll
+use explicit kind signatures for clarity.
+
+> data Nat :: Type where
+>   Z :: Nat
+>   S :: Nat -> Nat
+
+The `Type` kind, imported from `Data.Kind`, is a synonym for the `*` (which will
+eventually replace the latter).
+
+Vectors
+=======
+
+Vectors, in dependently-typed languages, are lists that apart from their content
+encode their size along with their type.
+
+If we assume that lists can not have negative length, and an empty vector has
+length 0, this gives us a nice inductive definition using the natural number
+~~type~~ kind[^kinds]
+
+ > 1. An empty vector of `a` has size `Z`{.haskell}.
+ > 2. Adding an element to the front of a vector of `a` and length `n` makes it
+ > have length `S n`{.haskell}.
+
+We'll represent this in Haskell as a datatype with a kind signature of `Nat ->
+Type -> Type` - That is, it takes a natural number (remember, these were
+automatically lifted to kinds), a regular type, and produces a regular type.
+Note that, `->` still means a function at the kind level.
+
+> data Vector :: Nat -> Type -> Type where
+
+Or, without use of `Type`,
+
+< data Vector :: Nat -> * -> * where
+
+We'll call the empty vector `Nil`{.haskell}. Remember, it has size
+`Z`{.haskell}.
+
+>  Nil :: Vector Z a
+
+Also note that type variables are implicit in the presence of kind signatures:
+They are assigned names in order of appearance.
+
+Consing onto a vector, represented by the infix constructor `:|`, sets its
+length to the successor of the existing length, and keeps the type of elements
+intact.
+
+>  (:|) :: a -> Vector x a -> Vector (S x) a
+
+Since this constructor is infix, we also need a fixidity declaration. For
+consistency with `(:)`, cons for regular lists, we'll make it right-associative
+with a precedence of `5`.
+
+> infixr 5 :|
+
+We'll use derived `Show`{.haskell} and `Eq`{.haskell} instances for
+`Vector`{.haskell}, for clarity reasons. While the derived `Eq`{.haskell} is
+fine, one would prefer a nicer `Show`{.haskell} instance for a
+production-quality library.
+
+> deriving instance Show a => Show (Vector n a)
+