polytype

A Hindley-Milner polymorphic typing system. Implements type inference via unification.

Usage

toml [dependencies] polytype = "1.0"

Provided by polytype are the Type enum and the Context struct.

The basics:

```rust // filter: (α → bool) → [α] → [α]

[macro_use] extern crate polytype;

use polytype::{Context, Type};

fn tlist(tp: Type) -> Type { Type::Constructed("list", vec![Box::new(tp)]) }

fn main() { let t0 = Type::Variable(0); let tbool = Type::Constructed("bool", vec![]);

// the filter type
let t = arrow![
    arrow![t0.clone(), tbool],
    tlist(t0.clone()),
    tlist(t0.clone()),
];

assert!(t.is_polymorphic());
assert_eq!(format!("{}", &t),
           "(t0 → bool) → list(t0) → list(t0)");

// we can substitute t0 using a type context:
let mut ctx = Context::default();

let tint = Type::Constructed("int", vec![]);
ctx.unify(&t0, &tint).expect("unifies");

let t = t.apply(&ctx);
assert!(!t.is_polymorphic());
assert_eq!(format!("{}", &t),
           "(int → bool) → list(int) → list(int)");

} ```

More about instantiation, and unification:

```rust // reduce: (β → α → β) → β → [α] → β

[macro_use] extern crate polytype;

use polytype::{Context, Type};

fn tlist(tp: Type) -> Type { Type::Constructed("list", vec![Box::new(tp)]) }

fn main() { let t0 = Type::Variable(0); let t1 = Type::Variable(1);

// the reduce type
let t = arrow![
    arrow![
        t1.clone(),
        t0.clone(),
        t1.clone(),
    ],
    t1.clone(),
    tlist(t0.clone()),
    t1.clone(),
];

assert!(t.is_polymorphic());
assert_eq!(format!("{}", &t),
           "(t1 → t0 → t1) → t1 → list(t0) → t1");

let tint = Type::Constructed("int", vec![]);
let tplus = arrow![tint.clone(), tint.clone(), tint.clone()];  // e.g. add two ints
assert_eq!(format!("{}", &tplus), "int → int → int");

// instantiate polymorphic types within our context so new type variables will be distinct
let mut ctx = Context::default();
let t = t.instantiate_indep(&mut ctx);

// by unifying, we can ensure valid function application and infer what gets returned
let treturn = ctx.new_variable();
ctx.unify(
    &t,
    &arrow![
        tplus.clone(),
        tint.clone(),
        tlist(tint.clone()),
        treturn.clone(),
    ],
).expect("unifies");
assert_eq!(treturn.apply(&ctx), tint.clone());  // inferred return: int

// now that unification has happened with ctx, we can see what form reduce takes
let t = t.apply(&ctx);
assert_eq!(format!("{}", t),
           "(int → int → int) → int → list(int) → int");

} ```