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use crate::{Name, Type, TypeScheme, Variable};
use indexmap::IndexMap;
use std::{cell::RefCell, collections::HashMap, error, fmt};
/// Errors during unification.
#[derive(Debug, Clone, PartialEq)]
pub enum UnificationError<N: Name = &'static str> {
/// `Occurs` happens when occurs checks fail (i.e. a type variable is
/// unified recursively). The id of the bad type variable is supplied.
Occurs(Variable),
/// `Failure` happens when symbols or type variants don't unify because of
/// structural differences.
Failure(Type<N>, Type<N>),
}
impl<N: Name> fmt::Display for UnificationError<N> {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> Result<(), fmt::Error> {
match *self {
UnificationError::Occurs(v) => write!(f, "Occurs({})", v),
UnificationError::Failure(ref t1, ref t2) => {
write!(f, "Failure({}, {})", t1.show(false), t2.show(false))
}
}
}
}
impl<N: Name + fmt::Debug> error::Error for UnificationError<N> {
fn description(&self) -> &'static str {
"unification failed"
}
}
/// A type environment. Useful for reasoning about [`Type`]s (e.g unification,
/// type inference).
///
/// Contexts track substitutions and generate fresh type variables.
///
/// [`Type`]: enum.Type.html
#[derive(Debug, Clone, PartialEq, Eq)]
pub struct Context<N: Name = &'static str> {
/// A set of constraints mapping from [`Variable`]s to [`Type`]s.
///
/// [`Type`]: enum.Type.html
/// [`Variable`]: type.Variable.html
pub(crate) substitution: IndexMap<Variable, Type<N>>,
/// Some operations on [`Type`]s, notably [`apply`] and [`apply_mut`]
/// perform path compression as they operate. Path compression is a
/// technique commonly used in [Union-Find data structures]. We apply it
/// here so that whenever a chain of substitutions is traversed, each
/// variable is updated to point to its ultimate value. For example, the
/// chain:
///
/// `t0 ↦ t1`, `t1 ↦ t2`, and `t2 ↦ int`
///
/// becomes
///
/// `t0 ↦ int`, `t1 ↦ int`, and `t2 ↦ int`
///
/// Rather than updating the actual mappings, `Context` maintains this cache
/// of compressed mappings.
///
/// [Union-Find data structure]: https://en.wikipedia.org/wiki/Disjoint-set_data_structure
/// [`Type`]: enum.Type.html
/// [`apply`]: enum.Type.html#method.apply
/// [`apply_mut`]: enum.Type.html#method.apply_mut
pub(crate) path_compression_cache: RefCell<HashMap<Variable, Type<N>>>,
/// A counter used to generate fresh [`Variable`]s
///
/// [`Variable`]: type.Variable.html
next: Variable,
}
impl<N: Name> Default for Context<N> {
fn default() -> Self {
Context {
substitution: IndexMap::new(),
path_compression_cache: RefCell::new(HashMap::new()),
next: 0,
}
}
}
impl<N: Name> Context<N> {
/// The substitution managed by the context.
pub fn substitution(&self) -> &IndexMap<Variable, Type<N>> {
&self.substitution
}
/// The number of constraints in the substitution.
pub fn len(&self) -> usize {
self.substitution.len()
}
/// `true` if the substitution has any constraints, else `false`.
pub fn is_empty(&self) -> bool {
self.substitution.is_empty()
}
/// Clears the substitution managed by the context.
///
/// # Examples
///
/// ```
/// # use polytype::{Type, Context, ptp, tp};
/// let mut ctx = Context::default();
///
/// // Get a fresh variable
/// let t0 = ctx.new_variable();
/// let t1 = ctx.new_variable();
///
/// let clean = ctx.clone();
///
/// if let Type::Variable(N) = t0 {
/// ctx.extend(N, tp![t1]);
/// let dirty = ctx.clone();
///
/// ctx.clean();
///
/// assert_eq!(clean, ctx);
/// assert_ne!(clean, dirty);
/// }
/// ```
pub fn clean(&mut self) {
self.substitution.clear();
self.path_compression_cache.get_mut().clear();
}
/// Removes previous substitutions added to the `Context` until there are only `n` remaining.
pub fn rollback(&mut self, n: usize) {
self.path_compression_cache.get_mut().clear();
if n == 0 {
self.substitution.clear();
} else {
while n < self.substitution.len() {
self.substitution.pop();
}
}
}
/// Create a new substitution for [`Type::Variable`] number `v` to the
/// [`Type`] `t`.
///
/// [`Type`]: enum.Type.html
/// [`Type::Variable`]: enum.Type.html#variant.Variable
pub fn extend(&mut self, v: Variable, t: Type<N>) {
if v >= self.next {
self.next = v + 1
}
self.substitution.insert(v, t);
}
/// Create a new [`Type::Variable`] from the next unused number.
///
/// # Examples
///
/// ```
/// # use polytype::{Type, Context, ptp, tp};
/// let mut ctx = Context::default();
///
/// // Get a fresh variable
/// let t0 = ctx.new_variable();
/// assert_eq!(t0, Type::Variable(0));
///
/// // Instantiating a polytype will yield new variables
/// let t = ptp!(0, 1; @arrow[tp!(0), tp!(1), tp!(1)]);
/// let t = t.instantiate(&mut ctx);
/// assert_eq!(t.to_string(), "t1 → t2 → t2");
///
/// // Get another fresh variable
/// let t3 = ctx.new_variable();
/// assert_eq!(t3, Type::Variable(3));
/// ```
///
/// [`Type::Variable`]: enum.Type.html#variant.Variable
pub fn new_variable(&mut self) -> Type<N> {
self.next += 1;
Type::Variable(self.next - 1)
}
/// Create constraints within the context that ensure `t1` and `t2`
/// unify.
///
/// # Examples
///
/// ```
/// # use polytype::{Context, tp};
/// let mut ctx = Context::default();
///
/// let t1 = tp!(@arrow[tp!(int), tp!(0)]);
/// let t2 = tp!(@arrow[tp!(1), tp!(bool)]);
/// ctx.unify(&t1, &t2).expect("unifies");
///
/// let t1 = t1.apply(&ctx);
/// let t2 = t2.apply(&ctx);
/// assert_eq!(t1, t2); // int → bool
/// ```
///
/// Unification errors leave the context unaffected. A
/// [`UnificationError::Failure`] error happens when symbols don't match:
///
/// ```
/// # use polytype::{Context, UnificationError, tp};
/// let mut ctx = Context::default();
///
/// let t1 = tp!(@arrow[tp!(int), tp!(0)]);
/// let t2 = tp!(@arrow[tp!(bool), tp!(1)]);
/// let res = ctx.unify(&t1, &t2);
///
/// if let Err(UnificationError::Failure(left, right)) = res {
/// // failed to unify t1 with t2.
/// assert_eq!(left, tp!(int));
/// assert_eq!(right, tp!(bool));
/// } else { unreachable!() }
/// ```
///
/// An [`UnificationError::Occurs`] error happens when the same type
/// variable occurs in both types in a circular way. Ensure you
/// [`instantiate`][] your types properly, so type variables don't overlap
/// unless you mean them to.
///
/// ```
/// # use polytype::{Context, UnificationError, tp};
/// let mut ctx = Context::default();
///
/// let t1 = tp!(1);
/// let t2 = tp!(@arrow[tp!(bool), tp!(1)]);
/// let res = ctx.unify(&t1, &t2);
///
/// if let Err(UnificationError::Occurs(v)) = res {
/// // failed to unify t1 with t2 because of circular type variable occurrence.
/// // t1 would have to be bool -> bool -> ... ad infinitum.
/// assert_eq!(v, 1);
/// } else { unreachable!() }
/// ```
///
/// [`UnificationError::Failure`]: enum.UnificationError.html#variant.Failure
/// [`UnificationError::Occurs`]: enum.UnificationError.html#variant.Occurs
/// [`instantiate`]: enum.Type.html#method.instantiate
pub fn unify(&mut self, t1: &Type<N>, t2: &Type<N>) -> Result<(), UnificationError<N>> {
let rollback_n = self.substitution.len();
let t1 = t1.apply(self);
let t2 = t2.apply(self);
let result = self.unify_internal(t1, t2);
if result.is_err() {
self.rollback(rollback_n);
}
result
}
/// Like [`unify`], but may affect the context even under failure. Hence, use this if you
/// discard the context upon failure.
///
/// [`unify`]: #method.unify
pub fn unify_fast(
&mut self,
mut t1: Type<N>,
mut t2: Type<N>,
) -> Result<(), UnificationError<N>> {
t1.apply_mut(self);
t2.apply_mut(self);
self.unify_internal(t1, t2)
}
/// unify_internal may mutate the context even with an error. The context on
/// which it's called should be discarded if there's an error.
fn unify_internal(&mut self, t1: Type<N>, t2: Type<N>) -> Result<(), UnificationError<N>> {
if t1 == t2 {
return Ok(());
}
match (t1, t2) {
(Type::Variable(v), t2) => {
if t2.occurs(v) {
Err(UnificationError::Occurs(v))
} else {
self.extend(v, t2);
Ok(())
}
}
(t1, Type::Variable(v)) => {
if t1.occurs(v) {
Err(UnificationError::Occurs(v))
} else {
self.extend(v, t1);
Ok(())
}
}
(Type::Constructed(n1, a1), Type::Constructed(n2, a2)) => {
if n1 != n2 {
Err(UnificationError::Failure(
Type::Constructed(n1, a1),
Type::Constructed(n2, a2),
))
} else {
for (mut t1, mut t2) in a1.into_iter().zip(a2) {
t1.apply_mut(self);
t2.apply_mut(self);
self.unify_internal(t1, t2)?;
}
Ok(())
}
}
}
}
/// Confines the substitution to those which act on the given variables.
///
/// # Examples
///
/// ```
/// # use polytype::{Context, tp};
/// let mut ctx = Context::default();
/// let v0 = ctx.new_variable();
/// let v1 = ctx.new_variable();
/// ctx.unify(&v0, &tp!(int));
/// ctx.unify(&v1, &tp!(bool));
///
/// {
/// let sub = ctx.substitution();
/// assert_eq!(sub.len(), 2);
/// assert_eq!(sub[&0], tp!(int));
/// assert_eq!(sub[&1], tp!(bool));
/// }
///
/// // confine the substitution to v1
/// ctx.confine(&[1]);
/// let sub = ctx.substitution();
/// assert_eq!(sub.len(), 1);
/// assert_eq!(sub[&1], tp!(bool));
/// ```
pub fn confine(&mut self, keep: &[Variable]) {
let mut substitution = IndexMap::new();
for v in keep {
substitution.insert(*v, self.substitution[v].clone());
}
self.substitution = substitution;
}
/// Merge two type contexts.
///
/// Every [`Type`] ([`TypeScheme`]) that corresponds to the `other` context
/// must be reified using [`ContextChange::reify_type`]
/// ([`ContextChange::reify_typescheme`]). Any [`Variable`] in `sacreds`
/// will not be changed by the context (i.e. reification will ignore it).
///
/// # Examples
///
/// Without sacred variables, which assumes that all type variables between the contexts are
/// distinct:
///
/// ```
/// # use polytype::{Type, Context, ptp, tp};
/// let mut ctx = Context::default();
/// let a = ctx.new_variable();
/// let b = ctx.new_variable();
/// ctx.unify(&Type::arrow(a, b), &tp!(@arrow[tp!(int), tp!(bool)])).unwrap();
/// // ctx uses t0 and t1
///
/// let mut ctx2 = Context::default();
/// let pt = ptp!(0, 1; @arrow[tp!(0), tp!(1)]);
/// let mut t = pt.instantiate(&mut ctx2);
/// ctx2.extend(0, tp!(bool));
/// assert_eq!(t.apply(&ctx2).to_string(), "bool → t1");
/// // ctx2 uses t0 and t1
///
/// let ctx_change = ctx.merge(ctx2, vec![]);
/// // rewrite all terms under ctx2 using ctx_change
/// ctx_change.reify_type(&mut t);
/// assert_eq!(t.to_string(), "t2 → t3");
/// assert_eq!(t.apply(&ctx).to_string(), "bool → t3");
///
/// assert_eq!(ctx.new_variable(), tp!(4));
/// ```
///
/// With sacred variables, which specifies which type variables are equivalent in both
/// contexts:
///
/// ```
/// # use polytype::{Type, Context, tp};
/// let mut ctx = Context::default();
/// let a = ctx.new_variable();
/// let b = ctx.new_variable();
/// ctx.unify(&Type::arrow(a, b), &tp!(@arrow[tp!(int), tp!(bool)])).unwrap();
/// // ctx uses t0 and t1
///
/// let mut ctx2 = Context::default();
/// let a = ctx2.new_variable();
/// let b = ctx2.new_variable();
/// let mut t = Type::arrow(a, b);
/// ctx2.extend(0, tp!(bool));
/// assert_eq!(t.apply(&ctx2).to_string(), "bool → t1");
/// // ctx2 uses t0 and t1
///
/// // t1 from ctx2 is preserved *and* constrained by ctx
/// let ctx_change = ctx.merge(ctx2, vec![1]);
/// // rewrite all terms under ctx2 using ctx_change
/// ctx_change.reify_type(&mut t);
/// assert_eq!(t.to_string(), "t2 → t1");
/// assert_eq!(t.apply(&ctx).to_string(), "bool → bool");
///
/// assert_eq!(ctx.new_variable(), tp!(4));
/// ```
/// [`ContextChange::reify_type`]: struct.ContextChange.html#method.reify_type
/// [`ContextChange::reify_typescheme`]: struct.ContextChange.html#method.reify_typescheme
/// [`Type`]: enum.Type.html
/// [`TypeScheme`]: enum.TypeScheme.html
/// [`Variable`]: type.TypeScheme.html
pub fn merge(&mut self, other: Context<N>, sacreds: Vec<Variable>) -> ContextChange {
let delta = self.next;
for (v, tp) in other.substitution {
self.substitution.insert(delta + v, tp);
}
// this is intentionally wasting variable space when there are sacreds:
self.next += other.next;
ContextChange { delta, sacreds }
}
}
/// Allow types to be reified for use in a different context. See [`Context::merge`].
///
/// [`Context::merge`]: struct.Context.html#method.merge
pub struct ContextChange {
delta: usize,
sacreds: Vec<Variable>,
}
impl ContextChange {
/// Reify a [`Type`] for use under a merged [`Context`].
///
/// [`Type`]: enum.Type.html
/// [`Context`]: struct.Context.html
pub fn reify_type(&self, tp: &mut Type) {
match tp {
Type::Constructed(_, args) => {
for arg in args {
self.reify_type(arg)
}
}
Type::Variable(n) if self.sacreds.contains(n) => (),
Type::Variable(n) => *n += self.delta,
}
}
/// Reify a [`TypeScheme`] for use under a merged [`Context`].
///
/// [`TypeScheme`]: enum.TypeScheme.html
/// [`Context`]: struct.Context.html
pub fn reify_typescheme(&self, tpsc: &mut TypeScheme) {
match tpsc {
TypeScheme::Monotype(tp) => self.reify_type(tp),
TypeScheme::Polytype { variable, body } => {
*variable += self.delta;
self.reify_typescheme(body);
}
}
}
}