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use std::collections::HashMap;
use crate::syntax::{Label, V};
/// Stores a pair of variables: a normal one and one
/// that corresponds to the alpha-normalized version of the first one.
/// Equality is up to alpha-equivalence (compares on the second one only).
#[derive(Clone, Eq)]
pub struct AlphaVar {
normal: V<Label>,
alpha: V<()>,
}
// Exactly like a Label, but equality returns always true.
// This is so that ValueKind equality is exactly alpha-equivalence.
#[derive(Clone, Eq)]
pub struct Binder {
name: Label,
}
pub(crate) trait Shift: Sized {
// Shift an expression to move it around binders without changing the meaning of its free
// variables. Shift by 1 to move an expression under a binder. Shift by -1 to extract an
// expression from under a binder, if the expression does not refer to that bound variable.
// Returns None if delta was negative and the variable was free in the expression.
fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self>;
fn over_binder<T>(&self, x: T) -> Option<Self>
where
T: Into<AlphaVar>,
{
self.shift(-1, &x.into())
}
fn under_binder<T>(&self, x: T) -> Self
where
T: Into<AlphaVar>,
{
// Can't fail since delta is positive
self.shift(1, &x.into()).unwrap()
}
fn under_multiple_binders(&self, shift_map: &HashMap<Label, usize>) -> Self
where
Self: Clone,
{
let mut v = self.clone();
for (x, n) in shift_map {
v = v.shift(*n as isize, &x.into()).unwrap();
}
v
}
}
pub(crate) trait Subst<S> {
fn subst_shift(&self, var: &AlphaVar, val: &S) -> Self;
}
impl AlphaVar {
pub(crate) fn to_var_maybe_alpha(&self, alpha: bool) -> V<Label> {
if alpha {
V("_".into(), self.alpha.idx())
} else {
self.normal.clone()
}
}
}
impl Binder {
pub(crate) fn new(name: Label) -> Self {
Binder { name }
}
pub(crate) fn to_label_maybe_alpha(&self, alpha: bool) -> Label {
if alpha {
"_".into()
} else {
self.to_label()
}
}
pub(crate) fn to_label(&self) -> Label {
self.clone().into()
}
}
impl Shift for AlphaVar {
fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
Some(AlphaVar {
normal: self.normal.shift(delta, &var.normal)?,
alpha: self.alpha.shift(delta, &var.alpha)?,
})
}
}
/// Equality up to alpha-equivalence
impl std::cmp::PartialEq for AlphaVar {
fn eq(&self, other: &Self) -> bool {
self.alpha == other.alpha
}
}
/// Equality up to alpha-equivalence
impl std::cmp::PartialEq for Binder {
fn eq(&self, _other: &Self) -> bool {
true
}
}
impl std::fmt::Debug for AlphaVar {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
write!(f, "AlphaVar({}, {})", self.normal, self.alpha.1)
}
}
impl std::fmt::Debug for Binder {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
write!(f, "Binder({})", &self.name)
}
}
impl<'a> From<&'a Label> for AlphaVar {
fn from(x: &'a Label) -> AlphaVar {
AlphaVar {
normal: V(x.clone(), 0),
alpha: V((), 0),
}
}
}
impl From<Binder> for AlphaVar {
fn from(x: Binder) -> AlphaVar {
AlphaVar {
normal: V(x.into(), 0),
alpha: V((), 0),
}
}
}
impl<'a> From<&'a Binder> for AlphaVar {
fn from(x: &'a Binder) -> AlphaVar {
x.clone().into()
}
}
impl From<Binder> for Label {
fn from(x: Binder) -> Label {
x.name
}
}
|
