Crate polytype

A Hindley-Milner polymorphic typing system.

Examples

The basics:

// filter: (α → bool) → [α] → [α]
use polytype::{Context, Type};

let t0 = Type::Variable(0);
let tbool = Type::Constructed("bool", vec![]);
fn tlist(tp: Type) -> Type {
    Type::Constructed("list", vec![Box::new(tp)])
}

// 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:

// reduce: (β → α → β) → β → [α] → β
use polytype::{Context, Type};

let t0 = Type::Variable(0);
let t1 = Type::Variable(1);
fn tlist(tp: Type) -> Type {
    Type::Constructed("list", vec![Box::new(tp)])
}

// 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");

Macros

arrow

Creates a Type::Arrow of tp0 → tp1 → ... (convenice for nested arrows).

Structs

Arrow	An arrow (function), curried.
Context	Context is a type environment, keeping track of substitutions and type variables. Useful for unifying (and inferring) types.

Enums

Type	Represents a type in the Hindley-Milner polymorphic typing system.
UnificationError