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ok we're back to rust

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Michael Zhang 2023-11-01 23:46:22 -05:00
parent f85b5d6785
commit 809c25c8bc
17 changed files with 1347 additions and 118 deletions
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3
.gitignore vendored
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@ -9,4 +9,5 @@ node_modules
lib/bs
__tests__/**/*.mjs
src/**/*.mjs
src/**/*.mjs
target

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Makefile Normal file
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.PHONY: doc
doc:
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12
bidir/Cargo.toml Normal file
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[package]
name = "bidir"
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edition = "2021"
# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
[dependencies]
anyhow = "1.0.75"
im = "15.1.0"
lazy_static = "1.4.0"
parking_lot = "0.12.1"

57
bidir/bidir.ts
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@ -1,57 +0,0 @@
import { isTypeInContext } from "./contexts";
import { ContextEntry, Term, Type } from "./data";
function check(
ctx: ContextEntry[],
term: Term,
type: Type
): [boolean, ContextEntry[]] {
switch (term.kind) {
case "var":
break;
case "unit":
return [type.kind === "unit", ctx];
case "lambda": {
// Get A and B first
if (type.kind !== "arrow") return [false, ctx];
const { input: A, output: B } = type;
}
case "app":
break;
case "annot":
break;
}
}
function synthesize(ctx: ContextEntry[], term: Term): [Type, ContextEntry[]] {
switch (term.kind) {
case "var": {
const res = lookupTypeVariable(ctx, term.name);
if (!res) throw new Error("wtf?");
return [res, ctx];
}
case "unit":
return [{ kind: "unit" }, ctx];
case "lambda": {
}
case "app":
break;
case "annot": {
// Require that the type exists
if (!isTypeInContext(term.type, ctx))
throw new Error("type doesn't exist");
// Require that the term checks against the type
const [result, outputCtx] = check(ctx, term.term, term.type);
if (!result) throw new Error("invalid annotation: term doesn't check");
return [term.type, outputCtx];
}
}
}
function synthesizeApp(
ctx: ContextEntry[],
funcType: Type,
term: Term
): [Type, ContextEntry[]] {}

18
bidir/contexts.ts
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@ -1,18 +0,0 @@
// Helper functions for dealing with contexts
import { ContextEntry, Type } from "./data";
import { isEqual } from "lodash";
/** Γ |- A (is the given type in this context?) */
export function isTypeInContext(type: Type, ctx: ContextEntry[]): boolean {
for (const entry of ctx) {
switch (entry.kind) {
case "termAnnot":
if (isEqual(entry.type, type)) return true;
break;
default:
continue;
}
}
return false;
}

42
bidir/data.ts
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@ -1,42 +0,0 @@
/**
* Terms e ::= x | () | λx. e | e e | (e : A)
* Types A, B, C ::= 1 | α | ^α | ∀α. A | A → B
* Monotypes τ, σ ::= 1 | α | ^α | τ → σ
* Contexts Γ, ∆, Θ ::= · | Γ, α | Γ, x : A
* | Γ, ^α | Γ, ^α = τ | Γ, I^α
* Complete Contexts Ω ::= · | Ω, α | Ω, x : A
* | Ω, ^α = τ | Ω, I^
*/
export type Term =
| { kind: "var"; name: string }
| { kind: "unit" }
| { kind: "lambda"; name: string; body: Term }
| { kind: "app"; func: Term; arg: Term }
| { kind: "annot"; term: Term; type: Type };
export type Type =
| { kind: "unit" }
| { kind: "var"; name: string }
| { kind: "existential"; name: string }
| { kind: "poly"; name: string; type: Type }
| { kind: "arrow"; input: Type; output: Type };
export type Monotype =
| { kind: "unit" }
| { kind: "var"; name: string }
| { kind: "existential"; name: string }
| { kind: "arrow"; input: Monotype; output: Monotype };
export type ContextEntry =
| { kind: "typeVar"; name: string }
| { kind: "termAnnot"; name: string; type: Type }
| { kind: "existentialVar"; name: string }
| { kind: "existentialSolved"; name: string; type: Monotype }
| { kind: "marker"; name: string };
export type CompleteContextEntry =
| { kind: "typeVar"; name: string }
| { kind: "termAnnot"; name: string; type: Type }
| { kind: "existentialSolved"; name: string; type: Monotype }
| { kind: "marker"; name: string };

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use anyhow::{bail, Result};
use crate::{
data::{ctx_lookup_type, Context, ContextEntry, Term, Type},
gensym::gensym_prefix,
};
// Figure 8. Applying a context, as a substitution, to a type
pub fn app_ctx(ctx: &Context, ty: &Type) -> Type {
match ty {
Type::Existential(_) => todo!(),
Type::Polytype(_, _) => todo!(),
Type::Arrow(a, b) => Type::Arrow(Box::new(app_ctx(ctx, a)), Box::new(app_ctx(ctx, b))),
_ => ty.clone(),
}
}
// Figure 9. Algorithmic subtyping
/// Under input context Γ , type A is a subtype of B, with output context ∆
pub fn subtype(ctx: &Context, a: &Type, b: &Type) -> Result<Context> {
println!("subtype(ctx = {ctx:?}, a = {a:?}, b = {b:?})");
match (a, b) {
// <:Unit rule
(Type::Unit, Type::Unit) => Ok(ctx.clone()),
// <:Var rule
(Type::Var(x), Type::Var(y)) if x == y => {
// Ensure that the name exists in the context
if !ctx.iter().any(|entry| match entry {
ContextEntry::ExistentialVar(z) if x == z => true,
_ => false,
}) {
bail!("name {x} not in context");
}
Ok(ctx.clone())
}
(Type::Existential(_), Type::Unit) => todo!(),
(Type::Existential(_), Type::Var(_)) => todo!(),
(Type::Existential(_), Type::Existential(_)) => todo!(),
(Type::Existential(_), Type::Polytype(_, _)) => todo!(),
(Type::Existential(_), Type::Arrow(_, _)) => todo!(),
(Type::Polytype(_, _), Type::Unit) => todo!(),
(Type::Polytype(_, _), Type::Var(_)) => todo!(),
(Type::Polytype(_, _), Type::Existential(_)) => todo!(),
(Type::Polytype(_, _), Type::Polytype(_, _)) => todo!(),
(Type::Polytype(_, _), Type::Arrow(_, _)) => todo!(),
(Type::Arrow(_, _), Type::Unit) => todo!(),
(Type::Arrow(_, _), Type::Var(_)) => todo!(),
(Type::Arrow(_, _), Type::Existential(_)) => todo!(),
(Type::Arrow(_, _), Type::Polytype(_, _)) => todo!(),
(Type::Arrow(_, _), Type::Arrow(_, _)) => todo!(),
_ => bail!("subtyping relation failed"),
}
}
// Figure 10. Instantiation
// Figure 11. Algorithmic typing
pub fn typecheck(ctx: &Context, term: &Term, ty: &Type) -> Result<Context> {
println!("typecheck(ctx = {ctx:?}, term = {term:?}, ty = {ty:?})");
match (term, ty) {
// 1I rule
(Term::Unit, Type::Unit) => Ok(ctx.clone()),
// ∀I rule
(e, Type::Polytype(x, tyA)) => todo!(),
// →I rule
(Term::Lam(x, e), Type::Arrow(ty_a, ty_b)) => {
let mut aug_ctx = ctx.clone();
todo!()
}
// Sub rule
(term, ty) => {
let (ty_a, ctx_theta) = synthesize(ctx, term)?;
let a = app_ctx(&ctx_theta, &ty_a);
let b = app_ctx(&ctx_theta, ty);
let ctx_delta = subtype(&ctx_theta, &a, &b)?;
Ok(ctx_delta)
}
}
}
pub fn synthesize(ctx: &Context, term: &Term) -> Result<(Type, Context)> {
println!("synthesize(ctx = {ctx:?}, term = {term:?}");
match term {
// Var rule
Term::Var(name) => {
let ty = match ctx_lookup_type(ctx, name) {
Some(v) => v,
None => bail!("could not find name {name}"),
};
Ok((ty, ctx.clone()))
}
// 1I⇒ rule
Term::Unit => Ok((Type::Unit, ctx.clone())),
// Anno rule
Term::Annot(_, _) => todo!(),
// →I⇒ rule
Term::Lam(x, e) => {
let mut aug_ctx = ctx.clone();
let ex_a = gensym_prefix("ex");
let ex_b = gensym_prefix("ex");
aug_ctx.push_back(ContextEntry::TypeVar(ex_a.clone()));
aug_ctx.push_back(ContextEntry::TypeVar(ex_b.clone()));
aug_ctx.push_back(ContextEntry::TermAnnot(x.clone(), Type::Var(ex_a.clone())));
let res = typecheck(&aug_ctx, &e, &Type::Var(ex_b.clone()));
Ok((
Type::Arrow(
Box::new(Type::Existential(ex_a)),
Box::new(Type::Existential(ex_b)),
),
ctx.clone(),
))
}
// →E rule
Term::App(e1, e2) => {
let (tyA, out_ctx) = synthesize(ctx, e1)?;
todo!()
}
}
}

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use im::Vector;
#[derive(Debug, Clone)]
pub enum Term {
Unit,
Var(String),
Lam(String, Box<Term>),
App(Box<Term>, Box<Term>),
Annot(Box<Term>, Type),
}
#[derive(Debug, Clone)]
pub enum Type {
Unit,
Var(String),
Existential(String),
Polytype(String, Box<Type>),
Arrow(Box<Type>, Box<Type>),
}
#[derive(Debug, Clone)]
pub enum Monotype {
Unit,
Var(String),
Existential(String),
Arrow(Box<Monotype>, Box<Monotype>),
}
pub type Context = Vector<ContextEntry>;
#[derive(Debug, Clone)]
pub enum ContextEntry {
TypeVar(String),
TermAnnot(String, Type),
ExistentialVar(String),
ExistentialSolved(String, Monotype),
Marker(String),
}
#[derive(Debug, Clone)]
pub enum CompleteContextEntry {
TypeVar(String),
TermAnnot(String, Type),
ExistentialSolved(String, Monotype),
Marker(String),
}
pub fn ctx_lookup_type(ctx: &Context, name: impl AsRef<str>) -> Option<Type> {
ctx.iter().find_map(|entry| match entry {
ContextEntry::TermAnnot(n, t) if n == name.as_ref() => Some(t.clone()),
_ => None,
})
}

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use lazy_static::lazy_static;
use parking_lot::Mutex;
lazy_static! {
static ref CTR: Mutex<usize> = Mutex::new(0);
}
pub fn gensym() -> String {
gensym_prefix("var")
}
pub fn gensym_prefix(prefix: impl AsRef<str>) -> String {
let mut g = CTR.lock();
let ctr = *g;
*g += 1;
drop(g);
format!("{}{}", prefix.as_ref(), ctr)
}

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mod bidir;
mod data;
mod gensym;
#[cfg(test)]
mod tests;

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use anyhow::{bail, Result};
use im::Vector;
use crate::{bidir::synthesize, data::Term};
#[test]
fn test_id() -> Result<()> {
let id = Term::Lam("x".to_owned(), Box::new(Term::Var("x".to_owned())));
let ctx = Vector::new();
let (ty, out_ctx) = synthesize(&ctx, &id)?;
// bail!("Output: {ty:?} in context {out_ctx:?}");
Ok(())
}

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tab_spaces = 2