357 lines
16 KiB
Typst
357 lines
16 KiB
Typst
// 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[
|
||
#set align(horizon)
|
||
= 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)
|
||
#grid(columns:(auto, auto), gutter:20pt, [
|
||
= The #S#K#I combinators
|
||
#v(1em)
|
||
#set text(size: 23pt)
|
||
#set align(horizon)
|
||
|
||
Any term in the $clam$-calculus can be written using nothing but the #S#K combinators.
|
||
|
||
#show: later
|
||
For example $#I := #S #K #S$.
|
||
],[
|
||
#set align(horizon+center)
|
||
#uncover(2)[
|
||
#image("images/ithinkshespartoftheskteam.jpg", height:80%)
|
||
]
|
||
])
|
||
]
|
||
|
||
#slide[
|
||
#set text(size: 25pt)
|
||
= A combinator to conquer them all
|
||
#v(1em)
|
||
#grid(columns:(auto, auto), gutter: 5pt,[
|
||
#set text(size: 18pt)
|
||
|
||
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)))
|
||
$
|
||
],[
|
||
#align(horizon)[
|
||
#uncover(2)[
|
||
#image("images/alwayshasbeenallfunctions.jpg")
|
||
]
|
||
]
|
||
])
|
||
]
|
||
|
||
#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)
|
||
#uncover(2)[
|
||
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[
|
||
#set page(margin:5pt)
|
||
#align(center+horizon)[
|
||
#set text(size: 18pt)
|
||
#grid(columns:(35%,35%),
|
||
gutter:5pt,
|
||
[
|
||
#set align(top)
|
||
#image("images/slides-qrcode.png", height:50%)
|
||
Slide repository
|
||
],
|
||
[
|
||
#set align(top)
|
||
#image("images/challenge-qrcode.png", height:50%)
|
||
The riddle from my team's previous presentation
|
||
]
|
||
)
|
||
|
||
#set text(size: 35pt)
|
||
✨ Thanks You! ✨
|
||
]
|
||
]
|
||
|
||
#slide[ #show:later ]
|