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|
<!DOCTYPE html>
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<div class="slides">
<section data-id="a4661b2bbd4624c846921874ba673364"><div class="sl-block" data-block-type="text" style="width: 806px; left: 78px; top: 238px; height: auto;" data-block-id="791c2b40c03699f6fde69d16c2186a3f"><div class="sl-block-content" data-placeholder-tag="h1" data-placeholder-text="Title Text" style="z-index: 10;">
<h1><s>typeclasses</s></h1>
<p><s>also</s> bidirectional typechecking and subtyping</p>
</div></div>
<div class="sl-block" data-block-type="text" style="height: auto; width: 600px; left: 180px; top: 509.5px;" data-name="text-2840e2" data-block-id="67d13465aa6485a5c990f43539cf415f"><div class="sl-block-content" data-placeholder-tag="p" data-placeholder-text="Text" style="z-index: 11;"><p>ten slides, five minutes</p></div></div></section><section data-id="b3131b7538da110564ed88c19f88f798"><div class="sl-block" data-block-type="text" style="width: 420px; left: 29px; top: 84px; height: auto;" data-block-id="ae6fb9a98dfec970cd7c79e600eb5fe8"><div class="sl-block-content" data-placeholder-tag="h2" data-placeholder-text="Title Text" style="text-align: left; z-index: 11;"><h3>the lambda calculus</h3></div></div>
<div class="sl-block" data-block-type="text" style="width: 428px; left: 29px; top: 175px; height: auto;" data-block-id="7838a236af12095f9c2f16dcf852100a"><div class="sl-block-content" data-placeholder-tag="p" data-placeholder-text="Lorem ipsum dolor sit amet, consectetur adipiscing elit. Morbi nec metus justo. Aliquam erat volutpat." style="z-index: 13; text-align: left; line-height: 1.625;" data-has-line-height=""><ul>
<li><span style="font-size:0.9em">no time, others also did this</span></li>
<li><span style="font-size:0.9em">rust good bottom text</span></li>
<li><span style="font-size:27px">algebraic data types <<3</span></li>
<li><span style="font-size:0.9em">bidirectional typechecking</span></li>
<li><span style="font-size:0.9em"><strong>infer</strong>, <strong>check</strong>, <strong>execute</strong></span></li>
<li><span style="font-size:0.9em">bounce back and forth between infer and check</span></li>
<li><span style="font-size:0.9em">scaling, first class functions: a problem for the future</span></li>
</ul></div></div>
<div class="sl-block" data-block-type="code" style="width: 451px; height: 630px; left: 480px; top: 35px;" data-name="code-78376e" data-block-id="0241b4282f3a776e15a9e530e6d4d173"><div class="sl-block-content notranslate" data-highlight-theme="ascetic" data-code-frame="none" style="z-index: 10; border-style: solid; border-width: 1px;" data-code-wrap="true"><pre class="ocaml" style="font-size: 14px; line-height: 17px;"><code data-line-numbers="">pub type Value = u8;
pub struct Term {
pub val: Value,
pub kind: Type, // for casting
}
pub type Identifier = String;
pub type Context = HashMap<Identifier, Term>;
#[derive(Clone, PartialEq, Eq)]
pub enum Expression {
Annotation {
expr: Box<Expression>,
kind: Type
},
Constant {
term: Term
},
Variable {
id: Identifier
},
Abstraction {
param: Identifier,
func: Box<Expression>
},
Application {
func: Box<Expression>,
arg: Box<Expression>
},
Conditional {
if_cond: Box<Expression>,
if_then: Box<Expression>,
if_else: Box<Expression>
}
}
</code></pre></div></div></section><section class="stack" data-id="415287af0ae5feeb1d12a5d12ae5bdee"><section data-id="3d62bb80cc8ceab908cb8c9e8e38e89d"><div class="sl-block" data-block-type="text" style="width: 400px; left: 520px; top: 367px; height: auto;" data-block-id="7c5a36cb564fd5c7b314f0fe46b96e18"><div class="sl-block-content" data-placeholder-tag="h2" data-placeholder-text="Title Text" style="z-index: 11; text-align: center; background-color: rgb(255, 255, 255); border-style: solid; border-width: 1px; padding: 10px; --darkreader-inline-bgcolor:#181a1b;" data-darkreader-inline-bgcolor="">
<h2>parsing</h2>
<p>pegs are magic</p>
<p>very nice for simple stuff</p>
</div></div>
<div class="sl-block" data-block-type="code" style="width: 960px; height: 700px; left: 0px; top: 0px;" data-name="code-18c030" data-block-id="fbbb08031772ba21433337c8b6216bbd"><div class="sl-block-content notranslate" data-highlight-theme="xcode" data-code-frame="none" style="z-index: 10; border-style: solid; border-width: 1px;" data-code-wrap="true"><pre class="rust" style="font-size: 16px; line-height: 19px;"><code data-line-numbers="">/// Parses a lambda-calculus-like language into an AST.
pub fn parse_str(input: &str) -> Result<Expression, peg::error::ParseError<peg::str::LineCol>>{
// this is kinda gross
// i miss my nim pegs
peg::parser!{
grammar lambda() for str {
rule identifier() -> String
= i:['a'..='z' | 'A'..='Z' | '0'..='9']+ {
i.iter().collect::<String>()
}
rule constant() -> Expression
= p:"-"? c:['0'..='9']+ {
let value = c.iter().collect::<String>().parse::<Value>().unwrap();
Expression::Constant {
term: Term {
val: if let Some(_) = p {
value.wrapping_neg()
} else {
value
},
kind: Type::Empty
}
}
}
rule primitive() -> Type
= k:$("empty" / "unit" / "bool" / "nat" / "int") {
match k {
"empty" => Type::Empty,
"unit" => Type::Unit,
"bool" => Type::Boolean,
"nat" => Type::Natural,
"int" => Type::Integer,
_ => Type::Empty
}
}
rule function() -> Type = "(" f:kind() " "* "->" " "* t:kind() ")" {
Type::Function { from: Box::new(f), to: Box::new(t) }
}
rule kind() -> Type
= k:(function() / primitive()) {
k
}
rule annotation() -> Expression
= e:(conditional() / abstraction() / application() / constant() / variable()) " "* ":" " "* k:kind() {
Expression::Annotation {
expr: Box::new(e),
kind: k
}
}
rule variable() -> Expression
= v:identifier() {
Expression::Variable {
id: v
}
}
rule abstraction() -> Expression
= ("λ" / "lambda") " "* p:identifier() " "* "." " "* f:expression() {
Expression::Abstraction {
param: p,
func: Box::new(f)
}
}
rule application() -> Expression
= "(" f:(annotation() / abstraction()) ")" " "* a:expression() {
Expression::Application {
func: Box::new(f),
arg: Box::new(a)
}
}
rule conditional() -> Expression
= "if" " "+ c:expression() " "+ "then" " "+ t:expression() " "+ "else" " "+ e:expression() {
Expression::Conditional {
if_cond: Box::new(c),
if_then: Box::new(t),
if_else: Box::new(e)
}
}
pub rule expression() -> Expression
= e:(conditional() / annotation() / abstraction() / application() / constant() / variable()) {
e
}
pub rule ast() -> Vec<Expression>
= expression() ** ("\n"+)
}
}
return lambda::expression(input.trim());
}</code></pre></div></div></section><section data-id="b571280a25332e373ef4c198d796bf9e"><div class="sl-block" data-block-type="text" style="width: 400px; left: 520px; top: 396px; height: auto;" data-block-id="4304ebe755544fa0129f72a9b727e2eb"><div class="sl-block-content" data-placeholder-tag="h2" data-placeholder-text="Title Text" style="z-index: 11; text-align: center; background-color: rgb(255, 255, 255); border-style: solid; border-width: 1px; padding: 10px; --darkreader-inline-bgcolor:#181a1b;" data-darkreader-inline-bgcolor="">
<h2>oh god</h2>
<p>why did i decide to do this<br></p>
</div></div>
<div class="sl-block" data-block-type="code" style="width: 960px; height: 700px; left: 0px; top: 0px;" data-name="code-18c030" data-block-id="a053327817730688c30270bd7790eaec"><div class="sl-block-content notranslate" data-highlight-theme="xcode" data-code-frame="none" style="z-index: 10; border-style: solid; border-width: 1px;" data-code-wrap="true"><pre class="rust" style="font-size: 16px; line-height: 19px;"><code data-line-numbers="">/// Parses a simple language with bracket-based indentation and end-of-term semicolons.
#[allow(unused_variables)]
pub fn parse_lang(input: &str) -> Result<Vec<Expression>, peg::error::ParseError<peg::str::LineCol>> {
peg::parser! {
grammar puck() for str {
// whitespace
rule w() = ("\n" / " ")+
// todo: multiple parameters pls
rule abs() -> Expression
= "func" w() n:ident() w()? "(" p:ident() ")"
w()? ":" w()? k:function() w() "=" w() "{" w() f:expr() w() "}" {
Expression::Annotation {
expr: Box::new(Expression::Abstraction { param: p, func: Box::new(f) }),
kind: k
}
}
// fixme: this requires, uh, refactoring the ast...
rule app() -> Expression
= f:ident() "(" a:expr() ")" {
Expression::Application {
func: Box::new(Expression::Variable {
id: f
}),
arg: Box::new(a)
}
}
rule cond() -> Expression
= "if" w() c:expr() w() "=" w() "{" w() t:expr() w() "};" w()
"else" w() "=" w() "{" w() e:expr() w() "}" {
Expression::Conditional {
if_cond: Box::new(c),
if_then: Box::new(t),
if_else: Box::new(e)
}
}
// fixme: cannot say e:(expr()), left-recursion issue
rule ann() -> Expression
= e:(cond() / abs() / app() / cons() / var()) w()? ":" w() k:kind() {
Expression::Annotation {
expr: Box::new(e),
kind: k
}
}
// identifiers
rule ident() -> String = i:['a'..='z' | 'A'..='Z' | '0'..='9']+ {
i.iter().collect::<String>()
}
rule var() -> Expression
= v:ident() {
Expression::Variable {
id: v
}
}
// constants
rule cons() -> Expression = p:"-"? c:['0'..='9']+ {
let value = c.iter().collect::<String>().parse::<Value>().unwrap();
Expression::Constant {
term: Term {
val: if let Some(_) = p {
value.wrapping_neg()
} else {
value
},
kind: Type::Empty // fixme
}
}
}
// types
rule primitive() -> Type = k:$("empty" / "unit" / "bool" / "nat" / "int") {
match k {
"empty" => Type::Empty,
"unit" => Type::Unit,
"bool" => Type::Boolean,
"nat" => Type::Natural,
"int" => Type::Integer,
_ => Type::Empty // never happens
}
}
// fixme: parenthesis necessary, left-recursion issue
rule function() -> Type = "(" w()? f:kind() w()? "->" w()? t:kind() w()? ")" {
Type::Function { from: Box::new(f), to: Box::new(t) }
}
// todo: records, etc
rule kind() -> Type
= k:(function() / primitive()) {
k
}
pub rule expr() -> Expression
= e:(ann() / cond() / abs() / app() / cons() / var()) ";" {
e
}
pub rule file() -> Vec<Expression>
= expr() ++ "\n"
}
}
return puck::file(input);
}
</code></pre></div></div></section><section data-id="5b7407362576e3330ce5a041db94c4f6"><div class="sl-block" data-block-type="code" style="width: 372px; height: 315px; left: 28px; top: 350px;" data-name="code-fec34b" data-block-id="0465bb1bf164ad420888c724cd3d6956">
<div class="sl-block-content notranslate" data-highlight-theme="ascetic" data-code-frame="none" style="z-index: 11; border-style: solid; border-width: 1px;" data-code-wrap="true">
<pre class="nim" style="font-size: 16px; line-height: 19px;"><code data-line-numbers="">func negate(x): (bool -> bool) =
if x: 0
else: 1
func fib(x): (int -> int) =
if eq(x, 0):
0
else:
if eq(x, 1):
1
else: # comment
add(fib(sub(x, 1)),
fib(sub(x, 2)))
negate(negate(1))
fib(5)
</code></pre>
</div>
</div>
<div class="sl-block" data-block-type="code" style="width: 511px; height: 630px; left: 434.5px; top: 35px;" data-block-id="6a738ee3f5ae23601928ee4c798bf6f2" data-name="code-729f31">
<div class="sl-block-content notranslate" data-highlight-theme="ascetic" data-code-frame="none" style="z-index: 10; border-style: solid; border-width: 1px;" data-code-wrap="true">
<pre class="none" style="font-size: 16px; line-height: 19px;"><code data-line-numbers="">/// Converts a whitespace-indented language
/// into a bracketed language for PEG matching.
pub fn lex(input: &str) ->
Result<String, &'static str> {
#[derive(Eq, PartialEq)]
enum Previous {
Start,
Block,
Line,
}
struct State {
blank: bool, // entirely whitespace so far?
level: usize, // current indentation level
count: usize, // current whitespace count
previous: Previous,
comment: bool // current line a comment?
}
let indent_size: usize = 2;
let mut state = State {
blank: true,
level: 0,
count: 0,
previous: Previous::Start,
comment: false
};
let mut buffer = String::new();
let mut result = String::new();
// wow lexers are hard
for c in input.chars() {
match c {
'\n' => {
if !buffer.is_empty() {
if state.count == state.level {
if state.previous !=
Previous::Start {
result.push(';');
result.push('\n');
}
state.previous = Previous::Line;
} else if state.level + indent_size
== state.count {
result.push(' ');
result.push('{');
result.push('\n');
state.level = state.count;
state.previous = Previous::Line;
} else if state.count >
state.level + indent_size {
return Err("invalid indent jump");
} else if state.count % indent_size
!= 0 {
return Err("incorrect indent offset");
} else if state.level > state.count {
while state.level > state.count {
if state.previous ==
Previous::Line {
result.push(';');
}
state.level -= indent_size;
result.push('\n');
result.push_str(
&" ".repeat(state.level));
result.push('}');
result.push(';');
state.previous = Previous::Block;
}
result.push('\n');
} else {
return Err("unknown indentation");
}
result.push_str(
&" ".repeat(state.count));
result.push_str(&buffer);
state.count = 0;
state.comment = false;
buffer.clear();
}
state.blank = true;
},
' ' if state.blank => {
state.count += 1;
},
'#' => {
state.blank = false;
state.comment = true;
},
_ => {
if state.blank {
state.blank = false;
}
if !state.comment {
buffer.push(c);
}
},
}
}
if state.previous == Previous::Line {
result.push(';');
}
while state.level != 0 {
state.level -= 2;
result.push('\n');
result.push_str(&" ".repeat(state.level));
result.push('}');
result.push(';');
}
return Ok(result);
}</code></pre>
</div>
</div>
<div class="sl-block" data-block-type="text" style="width: 384px; left: 28px; top: 106px; height: auto;" data-block-id="91eb6fbcf652855c2504b2ff23e1e2ce" data-name="text-a739f8">
<div class="sl-block-content" data-placeholder-tag="h2" data-placeholder-text="Title Text" style="text-align: left; z-index: 12;"><h3>don't write a parser</h3></div>
</div>
<div class="sl-block" data-block-type="text" style="width: 384px; left: 28px; top: 202px; height: auto;" data-block-id="b0c9d472583c05a21d1f5ee7082ba525" data-name="text-64290a">
<div class="sl-block-content" data-placeholder-tag="p" data-placeholder-text="Lorem ipsum dolor sit amet, consectetur adipiscing elit. Proin urna odio, aliquam vulputate faucibus id, elementum lobortis felis. Mauris urna dolor, placerat ac sagittis quis." style="text-align: left; z-index: 13;"><p>i now fully appreciate the role of lexers, whitespace and PEGs do <em>*not*</em> mix</p></div>
</div></section></section><section class="stack" data-id="078cbf3544989234f99f58c5eaf385c4"><section data-id="a2ec09b9df8f881193e02b67d9d34a6f"><div class="sl-block" data-block-type="text" style="width: 864px; left: 39.5px; top: 66px; height: auto;" data-block-id="5c70c5419a4fffc36f326389f04919b1"><div class="sl-block-content" data-placeholder-tag="h2" data-placeholder-text="Title Text" style="text-align: left; z-index: 11;"><h2>subtyping</h2></div></div>
<div class="sl-block" data-block-type="code" style="width: 881px; height: 508px; left: 39.5px; top: 160px;" data-name="code-b4c850" data-block-id="f43d7b497a44cc7a79f9799f8c957bc7"><div class="sl-block-content notranslate" data-highlight-theme="github-gist" data-code-frame="none" style="z-index: 10; border-style: solid; border-width: 1px;" data-code-wrap="true"><pre style="font-size: 16px; line-height: 19px;" class="cpp"><code data-line-numbers="">/// The subtyping relation between any two types.
pub fn subtype(is: &Type, of: &Type) -> bool {
match (is, of) {
(Type::Record(is_fields), Type::Record(of_fields)) => {
// width, depth, and permutation
for (key, of_value) in of_fields {
match is_fields.get(key) {
Some(is_value) => if !subtype(is_value, of_value) {
return false;
},
None => return false
}
}
return true;
},
(Type::Function { from: is_from, to: is_to },
Type::Function { from: of_from, to: of_to }) => {
subtype(of_from, is_from) && subtype(is_to, of_to)
}
(Type::Natural, Type::Integer) => true, // obviously not, but let's pretend
(_, Type::Empty) => true,
(Type::Error, _) => true,
(_, _) if is == of => true,
(_, _) => false,
}
}
</code></pre></div></div></section><section data-id="185642af785c80a8e89f91ed87071041"><div class="sl-block" data-block-type="text" style="width: 413px; left: 29px; top: 84px; height: auto;" data-block-id="509cdb304125bcb536707476b3659024"><div class="sl-block-content" data-placeholder-tag="h2" data-placeholder-text="Title Text" style="text-align: left; z-index: 11;"><h3>advanced ish types</h3></div></div>
<div class="sl-block" data-block-type="text" style="width: 413px; left: 29px; top: 165px; height: auto;" data-block-id="74b007d99173637ef45f94e4d8ee8230"><div class="sl-block-content" data-placeholder-tag="p" data-placeholder-text="Lorem ipsum dolor sit amet, consectetur adipiscing elit. Morbi nec metus justo. Aliquam erat volutpat." style="z-index: 13; text-align: left; line-height: 1.625;" data-has-line-height=""><ul>
<li>function types</li>
<li>structs/records/products: three types for the price of one! <span style="font-size:0.5em">(note: remove this, this isn't funny)</span>
</li>
<li>subtyping determined with a <strong>subtype</strong> function</li>
<li>drop-in replacement for type equality (<strong>==</strong>) in impl</li>
<li>if branches must be mutual subtypes</li>
</ul></div></div>
<div class="sl-block" data-block-type="code" style="width: 451px; height: 548.5px; left: 480px; top: 109.5px;" data-name="code-365804" data-block-id="6b0a245087a60ebd891520e52e03c50f"><div class="sl-block-content notranslate" data-highlight-theme="ascetic" data-code-frame="none" style="z-index: 10; border-style: solid; border-width: 1px;"><pre class="ocaml" style="font-size: 16px; line-height: 19px;"><code data-line-numbers="">pub type Identifier = String;
pub type Context =
HashMap<Identifier, Term>;
pub type Value = u64;
#[derive(Debug, Clone, PartialEq, Eq)]
pub enum Type {
Empty, // top
Error, // bottom
Unit,
Boolean,
Natural,
Integer,
// Float,
// String,
Enum(Vec<Type>),
Record(HashMap<Identifier, Type>),
Function{from: Box<Type>,
to: Box<Type>
},
}
#[derive(Debug, Clone, PartialEq, Eq)]
pub struct Term {
pub val: Value,
pub kind: Type,
}
</code></pre></div></div></section></section><section data-id="395e68419b49e56ae2c9503f9349949b"><div class="sl-block" data-block-type="text" style="width: 864px; left: 30px; top: 58px; height: auto;" data-block-id="fca8471a1c5e254df842c59786968a72"><div class="sl-block-content" data-placeholder-tag="h1" style="font-size: 200%; text-align: left; z-index: 10;" data-placeholder-text="Text"><h2>future plans<br>
</h2></div></div>
<div class="sl-block" data-block-type="text" style="height: auto; width: 850px; left: 30px; top: 245px;" data-name="text-419f61" data-block-id="03c292be5839e649ed825dbb51b4ed96"><div class="sl-block-content" data-placeholder-tag="p" data-placeholder-text="Text" style="z-index: 11;"><ul>
<li>complete and test subtyping</li>
<li>extend system with additional higher-level types
<ul>
<li>enums</li>
<li>actually distinct naturals and integers</li>
<li>floats</li>
<li>strings (ugh), vecs, collections of data</li>
</ul>
</li>
<li>type classes (still really want to implement), needs:
<ul>
<li>a global context + first class functions</li>
<li>resolving functions via identifiers</li>
</ul>
</li>
<li>then, write another parser</li>
</ul></div></div></section><section data-id="0d1b641e07aaf095303a30707be1be28"><div class="sl-block" data-block-type="text" style="width: 864px; left: 30px; top: 58px; height: auto;" data-block-id="7d75ef11e0b5935bc5066a155bf24992"><div class="sl-block-content" data-placeholder-tag="h1" style="font-size: 200%; text-align: left; z-index: 10;" data-placeholder-text="Text">
<h1>Questions?<br>
</h1>
<p>no</p>
</div></div></section><section data-id="9c412ee29000e2ef5c0d519c9144e8ab"><div class="sl-block" data-block-type="text" style="width: 910px; left: 25px; top: 299.5px; height: auto;" data-block-id="ca2a2bc628d05d54fbc85e432d1d9f09"><div class="sl-block-content" data-placeholder-tag="p" data-placeholder-text="Text" style="z-index: 11; line-height: 2.6;" data-has-line-height=""><h3><a href="https://www.youtube.com/watch?v=dQw4w9WgXcQ" target="_blank">https://github.com/j-james/chrysanthemum</a></h3></div></div></section>
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