commit 1adcb66891f342483c3eb59b34190af8cfd9a22b
Author: prescientmoon <git@moonythm.dev>
Date:   Tue Apr 29 17:10:58 2025 +0200

    Start working on the slides

diff --git a/.gitignore b/.gitignore
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+++ b/.gitignore
@@ -0,0 +1,2 @@
+iotas.pdf
+result
diff --git a/flake.lock b/flake.lock
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--- /dev/null
+++ b/flake.lock
@@ -0,0 +1,82 @@
+{
+  "nodes": {
+    "flake-utils": {
+      "inputs": {
+        "systems": "systems"
+      },
+      "locked": {
+        "lastModified": 1731533236,
+        "narHash": "sha256-l0KFg5HjrsfsO/JpG+r7fRrqm12kzFHyUHqHCVpMMbI=",
+        "owner": "numtide",
+        "repo": "flake-utils",
+        "rev": "11707dc2f618dd54ca8739b309ec4fc024de578b",
+        "type": "github"
+      },
+      "original": {
+        "owner": "numtide",
+        "repo": "flake-utils",
+        "type": "github"
+      }
+    },
+    "nixpkgs": {
+      "locked": {
+        "lastModified": 1744932701,
+        "narHash": "sha256-fusHbZCyv126cyArUwwKrLdCkgVAIaa/fQJYFlCEqiU=",
+        "owner": "nixos",
+        "repo": "nixpkgs",
+        "rev": "b024ced1aac25639f8ca8fdfc2f8c4fbd66c48ef",
+        "type": "github"
+      },
+      "original": {
+        "owner": "nixos",
+        "ref": "nixos-unstable",
+        "repo": "nixpkgs",
+        "type": "github"
+      }
+    },
+    "root": {
+      "inputs": {
+        "flake-utils": "flake-utils",
+        "nixpkgs": "nixpkgs",
+        "typix": "typix"
+      }
+    },
+    "systems": {
+      "locked": {
+        "lastModified": 1681028828,
+        "narHash": "sha256-Vy1rq5AaRuLzOxct8nz4T6wlgyUR7zLU309k9mBC768=",
+        "owner": "nix-systems",
+        "repo": "default",
+        "rev": "da67096a3b9bf56a91d16901293e51ba5b49a27e",
+        "type": "github"
+      },
+      "original": {
+        "owner": "nix-systems",
+        "repo": "default",
+        "type": "github"
+      }
+    },
+    "typix": {
+      "inputs": {
+        "nixpkgs": [
+          "nixpkgs"
+        ]
+      },
+      "locked": {
+        "lastModified": 1745311617,
+        "narHash": "sha256-rSwSFTy7E+/i+V2IB6GT4eP07r0XPoKlq/GbNYhakkw=",
+        "owner": "loqusion",
+        "repo": "typix",
+        "rev": "bc85fe6c66247893e8ff3e5d15166276caaf26eb",
+        "type": "github"
+      },
+      "original": {
+        "owner": "loqusion",
+        "repo": "typix",
+        "type": "github"
+      }
+    }
+  },
+  "root": "root",
+  "version": 7
+}
diff --git a/flake.nix b/flake.nix
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index 0000000..6606d15
--- /dev/null
+++ b/flake.nix
@@ -0,0 +1,66 @@
+{
+  inputs = {
+    nixpkgs.url = "github:nixos/nixpkgs/nixos-unstable";
+    flake-utils.url = "github:numtide/flake-utils";
+
+    typix = {
+      url = "github:loqusion/typix";
+      inputs.nixpkgs.follows = "nixpkgs";
+    };
+  };
+
+  outputs =
+    inputs:
+    inputs.flake-utils.lib.eachSystem (with inputs.flake-utils.lib.system; [ x86_64-linux ]) (
+      system:
+      let
+        pkgs = inputs.nixpkgs.legacyPackages.${system};
+        typixLib = inputs.typix.lib.${system};
+        lib = pkgs.lib;
+
+        src = lib.fileset.toSource {
+          root = ./.;
+          fileset = lib.fileset.unions [
+            ./images
+            ./iotas.typ
+          ];
+        };
+
+        commonArgs = handout: {
+          typstSource = "iotas.typ";
+          fontPaths = [ "${pkgs.cascadia-code}/share/fonts/truetype" ];
+          virtualPaths = [ ];
+          unstable_typstPackages = [
+            {
+              name = "polylux";
+              version = "0.4.0";
+              hash = "sha256-4owP2KiyaaASS1YZ0Hs58k6UEVAqsRR3YdGF26ikosk=";
+            }
+          ];
+
+          typstOpts.format = "pdf";
+          typstOpts.input = "HANDOUT=${if handout then "true" else "false"}";
+        };
+
+        buildPresentation = handout: typixLib.buildTypstProject ((commonArgs handout) // { inherit src; });
+
+        presentation = pkgs.linkFarm "coles-presentation" [
+          {
+            path = buildPresentation false;
+            name = "slides.pdf";
+          }
+          {
+            path = buildPresentation true;
+            name = "handout.pdf";
+          }
+        ];
+      in
+      {
+        devShell = pkgs.mkShell {
+          nativeBuildInputs = [ pkgs.typst ];
+        };
+
+        packages.default = presentation;
+      }
+    );
+}
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diff --git a/images/final-slide-fbp.png b/images/final-slide-fbp.png
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diff --git a/images/iota-manuscript.png b/images/iota-manuscript.png
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diff --git a/iotas.typ b/iotas.typ
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--- /dev/null
+++ b/iotas.typ
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+// Get Polylux from the official package repository
+#import "@preview/polylux:0.4.0": *
+
+#set page(paper: "presentation-16-9")
+#set text(size: 20pt, font: "Cascadia Code")
+
+#enable-handout-mode(json(bytes(sys.inputs.at("HANDOUT", default:"false"))))
+
+#slide[
+  #set page(fill:rgb(245,169,184))
+  #set text(fill: white, size:35pt)
+  #set align(horizon+center)
+  = (｡ι‿ι｡) Church-encoding text into iotas
+]
+
+#let clam = [#text(fill: rgb(60,150,180), $#sym.lambda$)]
+#let cdot = [#text(fill: rgb(60,150,180), $.$)]
+#let la(a, b) = [#clam #a #cdot #{h(0.5em)} #b]
+#let S = text(fill: rgb(255, 41, 155), $#math.op("S")$)
+#let K = text(fill:green,$#math.op("K")$)
+#let I = text(fill:rgb(145,145,145),$#math.op("I")$)
+#let zero = text(fill:rgb(145,145,145),$#math.op("zero")$)
+#let succ = text(fill:purple,$#math.op("succ")$)
+#let nil = text(fill:red,$#math.op("nil")$)
+#let cons = text(fill:orange,$#math.op("cons")$)
+#let iota = text(fill: purple, $#sym.iota$)
+#let nats = text(fill: red, $ℕ$)
+#let char(c) = text(fill:green, raw("'" + c + "'"))
+
+
+#slide[
+  #set text(size: 25pt)
+  = The backstory
+  #v(1em)
+  #set text(size: 18pt)
+
+  // They say that a peculiar QR code was lying on the final slide of our bachelor prep presentation. A promise of a prize, awaiting those about to scan the code. None lingered long enough to pierce the iota-veiled puzzle, but worry not, for the meaning of the runes shall soon reveal itself to those who seek it.
+
+  #align(center+horizon)[
+  #grid(columns:(45%, 45%),
+    [
+      #image("images/final-slide-fbp.png", height: 50%)
+      A mysterious QR code...
+    ],
+    align(bottom+right)[
+      #show: later
+      #v(3em)
+      ...leading to peculiar runes
+      #image("images/iota-manuscript.png", height: 50%)
+    ]
+  )
+  ]
+]
+
+#slide[
+  = The $clam$-calculus
+  #v(1em)
+
+  1. Lamdas: instead of $x ↦ ...$ we write $la(x,...)$
+
+  #show: later
+  #v(0.15em)
+
+  2. Variable references: for example $la(x, x)$ denotes the identity.
+
+  #show: later
+  #v(0.15em)
+
+  3. Function applications: instead of $f(x)$ we write $f x$.
+]
+
+
+#slide[
+  #set text(size: 25pt)
+  = Multi-parameter functions
+  #v(1em)
+  #set text(size: 23pt)
+
+  Problem: no products
+  $
+  f &: nats #sym.times nats -> nats \
+  f &: (a, b) ↦ a + b
+  $
+
+  #show: later
+  Solution: currying!
+  $
+  g &: nats -> nats -> nats \
+  g &: a ↦ (b ↦ a + b)
+  $
+
+  #align(bottom)[
+  #set text(size: 11pt)
+  Note: the two are equivalent in a sense because something something adjoint functors, don't worry about it.
+  ]
+]
+
+#slide[
+  #set text(size: 25pt)
+  = The #S#K#I combinators
+  #v(1em)
+  #set text(size: 35pt)
+
+  #align(horizon)[$
+  #I &:= la(x,x) \
+  #K &:= la(a,la(b, a)) \
+  #S &:= la(f, la(a, la(c, (f c) (a c))))
+  $]
+]
+
+#slide[
+  #set text(size: 25pt)
+  = The #S#K#I combinators
+  #v(1em)
+  #set text(size: 23pt)
+
+  - Any term in the $clam$-calculus can be written using nothing but the #S#K combinators. #later[For example $#I := #S #K #S$.
+
+  #align(horizon+center)[
+    #image("images/ithinkshespartoftheskteam.jpg", width:40%)
+  ]
+]
+]
+
+#slide[
+  #set text(size: 25pt)
+  = A combinator to conquer them all
+  #v(1em)
+  #set text(size: 20pt)
+
+  Enter, the $iota$-combinator!
+  $ iota := la(x, x #S #K) = #S (#S #I (#K #S))(#K #K). $
+
+  #show:later
+
+  We can then define the #S#K#I combinators in terms of $iota$:
+  $
+  #I &= iota iota \
+  #K &= iota( iota (iota iota)) \
+  #S &= iota(iota(iota(iota iota)))
+  $
+]
+
+#slide[
+  #set text(size: 25pt)
+  = Defining $nats$
+  #v(1em)
+  #set text(size: 20pt)
+
+  #set align(horizon)
+  - Problem: we normally define $nats$ using $zero$ and $succ$, but we have neither of those things.
+  - Solution: ask the person using the numbers to provide them!
+]
+
+#slide[
+  #set text(size: 25pt)
+  = Defining $nats$
+  #v(1em)
+  #set text(size: 20pt)
+
+  Example: instead of defining $1 := succ(zero)$, let $ 1 := la(zero, la(succ, succ " " zero)). $
+
+  #show:later
+  We can keep going!
+  $
+  2 &:= la(zero, la(succ, succ (succ " " zero)) ) \
+  3 &:= la(zero, la(succ,succ( succ (succ " " zero)))) \
+  4 &:= la(zero, la(succ,succ(succ( succ (succ " " zero)))))\
+  dots.v " " &
+  $
+
+]
+
+#slide[
+  #set text(size: 25pt)
+  = Working with $nats$
+  #v(1em)
+  #set text(size: 18pt)
+
+  How do we define addition?
+  1. The function takes two arguments: $la(a, la(b, ...))$
+  #show:later
+  2. The result is also a natural: $la(a, la(b, la(zero, la(succ, ...))))$
+  // #show:later
+  // 3. The result likely involves $a$: $la(a, la(b, la(zero, la(succ, a " " ? " " ?))))$
+  #show:later
+  3. Idea — return $a$, but with its concept of "$zero$" defined as the natural given by $b$: $la(a, la(b, la(zero, la(succ, a " " (b " " zero " " succ) " " succ))))$
+
+ $ a + b := la(zero, la(succ, a " " (b " " zero " " succ) " " succ)). $
+]
+
+#slide[
+  #set text(size: 30pt)
+  = Ordered lists
+  #v(1em)
+  #set text(size: 20pt)
+
+  #align(horizon)[
+  Ordered lists are surprisingly similar to $nats$. We need:
+    - The empty list (call it $nil$)
+    - A way to go from $a_1, a_2, ..., a_n$ to $x, a_1, a_2, ..., a_n$ (call it $cons$)
+
+    #show:later
+    Example: We can write $[1, 2, 3]$ as $ la(nil, la(cons, cons " " 1 " " (cons " " 2 " " (cons " " 3 " " nil)))) $
+  ]
+
+  #align(bottom)[
+  #set text(size: 11pt)
+  Note: the naturals are essentially just ordered lists of the unit type, but don't worry about that.
+  ]
+]
+
+#slide[
+  #grid(columns:(auto, auto),
+    gutter: 10pt,
+  [
+#set text(size: 23pt)
+#v(1em)
+= The general principle
+#v(1em)
+#set text(size: 25pt)
+
+    #align(horizon)[
+    - We can encode any inductively defined structure into the $clam$-calculus this way
+    - Named after the logician *Alonzo Church*
+    ]
+  ],
+  image("images/alonzo-church.jpg", height:100%)
+  )
+]
+
+#slide[
+  #set text(size: 30pt)
+  = Encoding text as iotas
+  #v(1em)
+  #set text(size: 25pt)
+  #align(horizon)[
+    - Strings of text are nothing but ordered lists of characters.
+    - Characters can be represented as naturals (indices inside some alphabet)
+  ]
+]
+
+#slide[
+  #set text(size: 30pt)
+  = Encoding text as iotas
+  #v(1em)
+  #set text(size: 25pt)
+  #align(horizon)[
+    1. Take the input string, and church-encode it:
+    $ #text(fill:green,```"meow"```) -> #image("images/un-executed-church-encoding.png",height:3em) $
+    #show:later
+    2. Normalize (evaluate) the output:
+  #set text(size: 15pt)
+    ```λλ1(λλ1(1(1(1(1(1(1(1(1(1(1(1 0))))))))))))(1(λλ1(1(1(1 0))))(1(λλ1(1(1(1(1(1(1(1(1(1(1(1(1(1 0))))))))))))))(1(λλ1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1 0)))))))))))))))))))))) 0)))```
+
+  // #set text(size: 10pt)
+// Without expanding the naturals, the above is essentially
+    // $ la(nil,la(cons,cons " " #char("m") " " (cons " " #char("e") " " (cons " " #char("o") " " (cons " " #char("w") " " nil))))) $
+  ]
+]
+#slide[
+  #set text(size: 30pt)
+  = Encoding text as iotas
+  #v(1em)
+  #set text(size: 25pt)
+  #align(horizon)[
+    3. Convert to #S#K combinators
+  #set text(size: 15pt)
+    ```S(S(KS)(S(KK)(SI(K(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(KI)))))))))))))))))(S(S(KS)(S(KK)(SI(K(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(KI)))))))))(S(S(KS)(S(KK)(SI(K(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(KI)))))))))))))))))))(S(S(KS)(S(KK)(SI(K(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(S(S(KS)(S(KK)I))(KI)))))))))))))))))))))))))))(KI))))```
+  ]
+]
+
+#slide[
+  #set text(size: 20pt)
+  = The final result
+  #set text(size: 9pt)
+  #align(horizon)[
+```ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ι(ι(ι(ιι)))(ιι)(ι(ι(ιι))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ιι))(ιι))))))))))))))))))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ι(ι(ι(ιι)))(ιι)(ι(ι(ιι))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ιι))(ιι))))))))))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ι(ι(ι(ιι)))(ιι)(ι(ι(ιι))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ιι))(ιι))))))))))))))))))))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ι(ι(ι(ιι)))(ιι)(ι(ι(ιι))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ι(ιι)))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ι(ιι)))))(ι(ι(ι(ιι)))(ι(ι(ιι))(ι(ι(ιι))))(ιι)))(ι(ι(ιι))(ιι))))))))))))))))))))))))))))(ι(ι(ιι))(ιι)))))```
+  ]
+]
+
+#slide[
+  #set page(fill:rgb(245,169,184))
+  #set text(fill: white)
+  #align(center+horizon)[
+  #set text(size: 35pt)
+  = But like, isn't this kinda useless
+  ]
+
+  #show: later
+  #align(center+bottom)[
+  ...well yeah, the final result kinda is ;-;\
+  ...but the individual components aren't!
+  ]
+]
+
+
+#slide[
+  #align(horizon)[
+  #grid(columns:(auto, auto), gutter: 5pt,[
+      #set text(size: 20pt)
+      = The silver lining
+      #v(1em)
+      #set text(size: 18pt)
+      #align(horizon)[
+      - The $clam$-calculus itself is extremely important!
+      - Many functional programming languages (Haskell, Lean, etc) have it at their very core!
+      ]
+    ],align(bottom+right)[
+      // #show: later
+      #image("images/fpmentioned.jpg", height: 100%)
+    ]
+  )
+  ]
+]
+
+#slide[
+  #align(center+horizon)[
+  #set text(size: 35pt)
+  ✨ Thanks You! ✨
+  ]
+]
+
+#slide[ #show:later ]