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//! A strongly-normalizing intermediate representation for ISLE rules. This representation is chosen
//! to closely reflect the operations we can implement in Rust, to make code generation easy.
use crate::disjointsets::DisjointSets;
use crate::error::{Error, Span};
use crate::lexer::Pos;
use crate::sema;
use crate::stablemapset::StableSet;
use std::collections::{hash_map::Entry, HashMap};
/// A field index in a tuple or an enum variant.
#[derive(Clone, Copy, Debug, Default, Eq, Hash, Ord, PartialEq, PartialOrd)]
pub struct TupleIndex(u8);
/// A hash-consed identifier for a binding, stored in a [RuleSet].
#[derive(Clone, Copy, Debug, Default, Eq, Hash, Ord, PartialEq, PartialOrd)]
pub struct BindingId(u16);
impl std::convert::TryFrom<usize> for TupleIndex {
type Error = <u8 as std::convert::TryFrom<usize>>::Error;
fn try_from(value: usize) -> Result<Self, Self::Error> {
Ok(TupleIndex(value.try_into()?))
}
}
impl std::convert::TryFrom<usize> for BindingId {
type Error = <u16 as std::convert::TryFrom<usize>>::Error;
fn try_from(value: usize) -> Result<Self, Self::Error> {
Ok(BindingId(value.try_into()?))
}
}
impl TupleIndex {
/// Get the index of this field.
pub fn index(self) -> usize {
self.0.into()
}
}
impl BindingId {
/// Get the index of this id.
pub fn index(self) -> usize {
self.0.into()
}
}
/// Bindings are anything which can be bound to a variable name in Rust. This includes expressions,
/// such as constants or function calls; but it also includes names bound in pattern matches.
#[derive(Clone, Debug, Eq, Hash, PartialEq)]
pub enum Binding {
/// Evaluates to the given integer literal.
ConstInt {
/// The constant value.
val: i128,
/// The constant's type. Unsigned types preserve the representation of `val`, not its value.
ty: sema::TypeId,
},
/// Evaluates to the given primitive Rust value.
ConstPrim {
/// The constant value.
val: sema::Sym,
},
/// One of the arguments to the top-level function.
Argument {
/// Which of the function's arguments is this?
index: TupleIndex,
},
/// The result of calling an external extractor.
Extractor {
/// Which extractor should be called?
term: sema::TermId,
/// What expression should be passed to the extractor?
parameter: BindingId,
},
/// The result of calling an external constructor.
Constructor {
/// Which constructor should be called?
term: sema::TermId,
/// What expressions should be passed to the constructor?
parameters: Box<[BindingId]>,
/// For impure constructors, a unique number for each use of this term. Always 0 for pure
/// constructors.
instance: u32,
},
/// The result of getting one value from a multi-constructor or multi-extractor.
Iterator {
/// Which expression produced the iterator that this consumes?
source: BindingId,
},
/// The result of constructing an enum variant.
MakeVariant {
/// Which enum type should be constructed?
ty: sema::TypeId,
/// Which variant of that enum should be constructed?
variant: sema::VariantId,
/// What expressions should be provided for this variant's fields?
fields: Box<[BindingId]>,
},
/// Pattern-match one of the previous bindings against an enum variant and produce a new binding
/// from one of its fields. There must be a corresponding [Constraint::Variant] for each
/// `source`/`variant` pair that appears in some `MatchVariant` binding.
MatchVariant {
/// Which binding is being matched?
source: BindingId,
/// Which enum variant are we pulling binding sites from? This is somewhat redundant with
/// information in a corresponding [Constraint]. However, it must be here so that different
/// enum variants aren't hash-consed into the same binding site.
variant: sema::VariantId,
/// Which field of this enum variant are we projecting out? Although ISLE uses named fields,
/// we track them by index for constant-time comparisons. The [sema::TypeEnv] can be used to
/// get the field names.
field: TupleIndex,
},
/// The result of constructing an Option::Some variant.
MakeSome {
/// Contained expression.
inner: BindingId,
},
/// Pattern-match one of the previous bindings against `Option::Some` and produce a new binding
/// from its contents. There must be a corresponding [Constraint::Some] for each `source` that
/// appears in a `MatchSome` binding. (This currently only happens with external extractors.)
MatchSome {
/// Which binding is being matched?
source: BindingId,
},
/// Pattern-match one of the previous bindings against a tuple and produce a new binding from
/// one of its fields. This is an irrefutable pattern match so there is no corresponding
/// [Constraint]. (This currently only happens with external extractors.)
MatchTuple {
/// Which binding is being matched?
source: BindingId,
/// Which tuple field are we projecting out?
field: TupleIndex,
},
}
/// Pattern matches which can fail. Some binding sites are the result of successfully matching a
/// constraint. A rule applies constraints to binding sites to determine whether the rule matches.
#[derive(Clone, Copy, Debug, Eq, Hash, Ord, PartialEq, PartialOrd)]
pub enum Constraint {
/// The value must match this enum variant.
Variant {
/// Which enum type is being matched? This is implied by the binding where the constraint is
/// applied, but recorded here for convenience.
ty: sema::TypeId,
/// Which enum variant must this binding site match to satisfy the rule?
variant: sema::VariantId,
/// Number of fields in this variant of this enum. This is recorded in the constraint for
/// convenience, to avoid needing to look up the variant in a [sema::TypeEnv].
fields: TupleIndex,
},
/// The value must equal this integer literal.
ConstInt {
/// The constant value.
val: i128,
/// The constant's type. Unsigned types preserve the representation of `val`, not its value.
ty: sema::TypeId,
},
/// The value must equal this Rust primitive value.
ConstPrim {
/// The constant value.
val: sema::Sym,
},
/// The value must be an `Option::Some`, from a fallible extractor.
Some,
}
/// A term-rewriting rule. All [BindingId]s are only meaningful in the context of the [RuleSet] that
/// contains this rule.
#[derive(Debug, Default)]
pub struct Rule {
/// Where was this rule defined?
pub pos: Pos,
/// All of these bindings must match the given constraints for this rule to apply. Note that
/// within a single rule, if a binding site must match two different constraints, then the rule
/// can never match.
constraints: HashMap<BindingId, Constraint>,
/// Sets of bindings which must be equal for this rule to match.
pub equals: DisjointSets<BindingId>,
/// These bindings are from multi-terms which need to be evaluated in this rule.
pub iterators: StableSet<BindingId>,
/// If other rules apply along with this one, the one with the highest numeric priority is
/// evaluated. If multiple applicable rules have the same priority, that's an overlap error.
pub prio: i64,
/// If this rule applies, these side effects should be evaluated before returning.
pub impure: Vec<BindingId>,
/// If this rule applies, the top-level term should evaluate to this expression.
pub result: BindingId,
}
/// Records whether a given pair of rules can both match on some input.
#[derive(Debug, Eq, PartialEq)]
pub enum Overlap {
/// There is no input on which this pair of rules can both match.
No,
/// There is at least one input on which this pair of rules can both match.
Yes {
/// True if every input accepted by one rule is also accepted by the other. This does not
/// indicate which rule is more general and in fact the rules could match exactly the same
/// set of inputs. You can work out which by comparing `total_constraints()` in both rules:
/// The more general rule has fewer constraints.
subset: bool,
},
}
/// A collection of [Rule]s, along with hash-consed [Binding]s for all of them.
#[derive(Debug, Default)]
pub struct RuleSet {
/// The [Rule]s for a single [sema::Term].
pub rules: Vec<Rule>,
/// The bindings identified by [BindingId]s within rules.
pub bindings: Vec<Binding>,
/// Intern table for de-duplicating [Binding]s.
binding_map: HashMap<Binding, BindingId>,
}
/// Construct a [RuleSet] for each term in `termenv` that has rules.
pub fn build(termenv: &sema::TermEnv) -> (Vec<(sema::TermId, RuleSet)>, Vec<Error>) {
let mut errors = Vec::new();
let mut term = HashMap::new();
for rule in termenv.rules.iter() {
term.entry(rule.root_term)
.or_insert_with(RuleSetBuilder::default)
.add_rule(rule, termenv, &mut errors);
}
// The `term` hash map may return terms in any order. Sort them to ensure that we produce the
// same output every time when given the same ISLE source. Rules are added to terms in `RuleId`
// order, so it's not necessary to sort within a `RuleSet`.
let mut result: Vec<_> = term
.into_iter()
.map(|(term, builder)| (term, builder.rules))
.collect();
result.sort_unstable_by_key(|(term, _)| *term);
(result, errors)
}
impl RuleSet {
/// Returns the [BindingId] corresponding to the given [Binding] within this rule-set, if any.
pub fn find_binding(&self, binding: &Binding) -> Option<BindingId> {
self.binding_map.get(binding).copied()
}
}
impl Binding {
/// Returns the binding sites which must be evaluated before this binding.
pub fn sources(&self) -> &[BindingId] {
match self {
Binding::ConstInt { .. } => &[][..],
Binding::ConstPrim { .. } => &[][..],
Binding::Argument { .. } => &[][..],
Binding::Extractor { parameter, .. } => std::slice::from_ref(parameter),
Binding::Constructor { parameters, .. } => ¶meters[..],
Binding::Iterator { source } => std::slice::from_ref(source),
Binding::MakeVariant { fields, .. } => &fields[..],
Binding::MatchVariant { source, .. } => std::slice::from_ref(source),
Binding::MakeSome { inner } => std::slice::from_ref(inner),
Binding::MatchSome { source } => std::slice::from_ref(source),
Binding::MatchTuple { source, .. } => std::slice::from_ref(source),
}
}
}
impl Constraint {
/// Return the nested [Binding]s from matching the given [Constraint] against the given [BindingId].
pub fn bindings_for(self, source: BindingId) -> Vec<Binding> {
match self {
// These constraints never introduce any bindings.
Constraint::ConstInt { .. } | Constraint::ConstPrim { .. } => vec![],
Constraint::Some => vec![Binding::MatchSome { source }],
Constraint::Variant {
variant, fields, ..
} => (0..fields.0)
.map(TupleIndex)
.map(|field| Binding::MatchVariant {
source,
variant,
field,
})
.collect(),
}
}
}
impl Rule {
/// Returns whether a given pair of rules can both match on some input, and if so, whether
/// either matches a subset of the other's inputs. If this function returns `No`, then the two
/// rules definitely do not overlap. However, it may return `Yes` in cases where the rules can't
/// overlap in practice, or where this analysis is not yet precise enough to decide.
pub fn may_overlap(&self, other: &Rule) -> Overlap {
// Two rules can't overlap if, for some binding site in the intersection of their
// constraints, the rules have different constraints: an input can't possibly match both
// rules then. If the rules do overlap, and one has a subset of the constraints of the
// other, then the less-constrained rule matches every input that the more-constrained rule
// matches, and possibly more. We test for both conditions at once, with the observation
// that if the intersection of two sets is equal to the smaller set, then it's a subset. So
// the outer loop needs to go over the rule with fewer constraints in order to correctly
// identify if it's a subset of the other rule. Also, that way around is faster.
let (small, big) = if self.constraints.len() <= other.constraints.len() {
(self, other)
} else {
(other, self)
};
// TODO: nonlinear constraints complicate the subset check
// For the purpose of overlap checking, equality constraints act like other constraints, in
// that they can cause rules to not overlap. However, because we don't have a concrete
// pattern to compare, the analysis to prove that is complicated. For now, we approximate
// the result. If either rule has nonlinear constraints, conservatively report that neither
// is a subset of the other. Note that this does not disagree with the doc comment for
// `Overlap::Yes { subset }` which says to use `total_constraints` to disambiguate, since if
// we return `subset: true` here, `equals` is empty for both rules, so `total_constraints()`
// equals `constraints.len()`.
let mut subset = small.equals.is_empty() && big.equals.is_empty();
for (binding, a) in small.constraints.iter() {
if let Some(b) = big.constraints.get(binding) {
if a != b {
// If any binding site is constrained differently by both rules then there is
// no input where both rules can match.
return Overlap::No;
}
// Otherwise both are constrained in the same way at this binding site. That doesn't
// rule out any possibilities for what inputs the rules accept.
} else {
// The `big` rule's inputs are a subset of the `small` rule's inputs if every
// constraint in `small` is exactly matched in `big`. But we found a counterexample.
subset = false;
}
}
Overlap::Yes { subset }
}
/// Returns the total number of binding sites which this rule constrains, with either a concrete
/// pattern or an equality constraint.
pub fn total_constraints(&self) -> usize {
// Because of `normalize_equivalence_classes`, these two sets don't overlap, so the size of
// the union is the sum of their sizes.
self.constraints.len() + self.equals.len()
}
/// Returns the constraint that the given binding site must satisfy for this rule to match, if
/// there is one.
pub fn get_constraint(&self, source: BindingId) -> Option<Constraint> {
self.constraints.get(&source).copied()
}
fn set_constraint(
&mut self,
source: BindingId,
constraint: Constraint,
) -> Result<(), UnreachableError> {
match self.constraints.entry(source) {
Entry::Occupied(entry) => {
if entry.get() != &constraint {
return Err(UnreachableError {
pos: self.pos,
constraint_a: *entry.get(),
constraint_b: constraint,
});
}
}
Entry::Vacant(entry) => {
entry.insert(constraint);
}
}
Ok(())
}
}
#[derive(Debug)]
struct UnreachableError {
pos: Pos,
constraint_a: Constraint,
constraint_b: Constraint,
}
#[derive(Debug, Default)]
struct RuleSetBuilder {
current_rule: Rule,
impure_instance: u32,
unreachable: Vec<UnreachableError>,
rules: RuleSet,
}
impl RuleSetBuilder {
fn add_rule(&mut self, rule: &sema::Rule, termenv: &sema::TermEnv, errors: &mut Vec<Error>) {
self.impure_instance = 0;
self.current_rule.pos = rule.pos;
self.current_rule.prio = rule.prio;
self.current_rule.result = rule.visit(self, termenv);
if termenv.terms[rule.root_term.index()].is_partial() {
self.current_rule.result = self.dedup_binding(Binding::MakeSome {
inner: self.current_rule.result,
});
}
self.normalize_equivalence_classes();
let rule = std::mem::take(&mut self.current_rule);
if self.unreachable.is_empty() {
self.rules.rules.push(rule);
} else {
// If this rule can never match, drop it so it doesn't affect overlap checking.
errors.extend(
self.unreachable
.drain(..)
.map(|err| Error::UnreachableError {
msg: format!(
"rule requires binding to match both {:?} and {:?}",
err.constraint_a, err.constraint_b
),
span: Span::new_single(err.pos),
}),
)
}
}
/// Establish the invariant that a binding site can have a concrete constraint in `constraints`,
/// or an equality constraint in `equals`, but not both. This is useful because overlap checking
/// is most effective on concrete constraints, and also because it exposes more rule structure
/// for codegen.
///
/// If a binding site is constrained and also required to be equal to another binding site, then
/// copy the constraint and push the equality inside it. For example:
/// - `(term x @ 2 x)` is rewritten to `(term 2 2)`
/// - `(term x @ (T.A _ _) x)` is rewritten to `(term (T.A y z) (T.A y z))`
/// In the latter case, note that every field of `T.A` has been replaced with a fresh variable
/// and each of the copies are set equal.
///
/// If several binding sites are supposed to be equal but they each have conflicting constraints
/// then this rule is unreachable. For example, `(term x @ 2 (and x 3))` requires both arguments
/// to be equal but also requires them to match both 2 and 3, which can't happen for any input.
///
/// We could do this incrementally, while building the rule. The implementation is nearly
/// identical but, having tried both ways, it's slightly easier to think about this as a
/// separate pass. Also, batching up this work should be slightly faster if there are multiple
/// binding sites set equal to each other.
fn normalize_equivalence_classes(&mut self) {
// First, find all the constraints that need to be copied to other binding sites in their
// respective equivalence classes. Note: do not remove these constraints here! Yes, we'll
// put them back later, but we rely on still having them around so that
// `set_constraint` can detect conflicting constraints.
let mut deferred_constraints = Vec::new();
for (&binding, &constraint) in self.current_rule.constraints.iter() {
if let Some(root) = self.current_rule.equals.find_mut(binding) {
deferred_constraints.push((root, constraint));
}
}
// Pick one constraint and propagate it through its equivalence class. If there are no
// errors then it doesn't matter what order we do this in, because that means that any
// redundant constraints on an equivalence class were equal. We can write equal values into
// the constraint map in any order and get the same result. If there were errors, we aren't
// going to generate code from this rule, so order only affects how conflicts are reported.
while let Some((current, constraint)) = deferred_constraints.pop() {
// Remove the entire equivalence class and instead add copies of this constraint to
// every binding site in the class. If there are constraints on other binding sites in
// this class, then when we try to copy this constraint to those binding sites,
// `set_constraint` will check that the constraints are equal and record an appropriate
// error otherwise.
//
// Later, we'll re-visit those other binding sites because they're still in
// `deferred_constraints`, but `set` will be empty because we already deleted the
// equivalence class the first time we encountered it.
let set = self.current_rule.equals.remove_set_of(current);
if let Some((&base, rest)) = set.split_first() {
let mut defer = |this: &Self, binding| {
// We're adding equality constraints to binding sites that may not have had
// one already. If that binding site already had a concrete constraint, then
// we need to "recursively" propagate that constraint through the new
// equivalence class too.
if let Some(constraint) = this.current_rule.get_constraint(binding) {
deferred_constraints.push((binding, constraint));
}
};
// If this constraint introduces nested binding sites, make the fields of those
// binding sites equal instead. Arbitrarily pick one member of `set` to set all the
// others equal to. If there are existing constraints on the new binding sites, copy
// those around the new equivalence classes too.
let base_fields = self.set_constraint(base, constraint);
base_fields.iter().for_each(|&x| defer(self, x));
for &b in rest {
for (&x, y) in base_fields.iter().zip(self.set_constraint(b, constraint)) {
defer(self, y);
self.current_rule.equals.merge(x, y);
}
}
}
}
}
fn dedup_binding(&mut self, binding: Binding) -> BindingId {
if let Some(binding) = self.rules.binding_map.get(&binding) {
*binding
} else {
let id = BindingId(self.rules.bindings.len().try_into().unwrap());
self.rules.bindings.push(binding.clone());
self.rules.binding_map.insert(binding, id);
id
}
}
fn set_constraint(&mut self, input: BindingId, constraint: Constraint) -> Vec<BindingId> {
if let Err(e) = self.current_rule.set_constraint(input, constraint) {
self.unreachable.push(e);
}
constraint
.bindings_for(input)
.into_iter()
.map(|binding| self.dedup_binding(binding))
.collect()
}
}
impl sema::PatternVisitor for RuleSetBuilder {
type PatternId = BindingId;
fn add_match_equal(&mut self, a: BindingId, b: BindingId, _ty: sema::TypeId) {
// If both bindings represent the same binding site, they're implicitly equal.
if a != b {
self.current_rule.equals.merge(a, b);
}
}
fn add_match_int(&mut self, input: BindingId, ty: sema::TypeId, val: i128) {
let bindings = self.set_constraint(input, Constraint::ConstInt { val, ty });
debug_assert_eq!(bindings, &[]);
}
fn add_match_prim(&mut self, input: BindingId, _ty: sema::TypeId, val: sema::Sym) {
let bindings = self.set_constraint(input, Constraint::ConstPrim { val });
debug_assert_eq!(bindings, &[]);
}
fn add_match_variant(
&mut self,
input: BindingId,
input_ty: sema::TypeId,
arg_tys: &[sema::TypeId],
variant: sema::VariantId,
) -> Vec<BindingId> {
let fields = TupleIndex(arg_tys.len().try_into().unwrap());
self.set_constraint(
input,
Constraint::Variant {
fields,
ty: input_ty,
variant,
},
)
}
fn add_extract(
&mut self,
input: BindingId,
_input_ty: sema::TypeId,
output_tys: Vec<sema::TypeId>,
term: sema::TermId,
infallible: bool,
multi: bool,
) -> Vec<BindingId> {
let source = self.dedup_binding(Binding::Extractor {
term,
parameter: input,
});
// If the extractor is fallible, build a pattern and constraint for `Some`
let source = if multi {
self.current_rule.iterators.insert(source);
self.dedup_binding(Binding::Iterator { source })
} else if infallible {
source
} else {
let bindings = self.set_constraint(source, Constraint::Some);
debug_assert_eq!(bindings.len(), 1);
bindings[0]
};
// If the extractor has multiple outputs, create a separate binding for each
match output_tys.len().try_into().unwrap() {
0 => vec![],
1 => vec![source],
outputs => (0..outputs)
.map(TupleIndex)
.map(|field| self.dedup_binding(Binding::MatchTuple { source, field }))
.collect(),
}
}
}
impl sema::ExprVisitor for RuleSetBuilder {
type ExprId = BindingId;
fn add_const_int(&mut self, ty: sema::TypeId, val: i128) -> BindingId {
self.dedup_binding(Binding::ConstInt { val, ty })
}
fn add_const_prim(&mut self, _ty: sema::TypeId, val: sema::Sym) -> BindingId {
self.dedup_binding(Binding::ConstPrim { val })
}
fn add_create_variant(
&mut self,
inputs: Vec<(BindingId, sema::TypeId)>,
ty: sema::TypeId,
variant: sema::VariantId,
) -> BindingId {
self.dedup_binding(Binding::MakeVariant {
ty,
variant,
fields: inputs.into_iter().map(|(expr, _)| expr).collect(),
})
}
fn add_construct(
&mut self,
inputs: Vec<(BindingId, sema::TypeId)>,
_ty: sema::TypeId,
term: sema::TermId,
pure: bool,
infallible: bool,
multi: bool,
) -> BindingId {
let instance = if pure {
0
} else {
self.impure_instance += 1;
self.impure_instance
};
let source = self.dedup_binding(Binding::Constructor {
term,
parameters: inputs.into_iter().map(|(expr, _)| expr).collect(),
instance,
});
// If the constructor is fallible, build a pattern for `Some`, but not a constraint. If the
// constructor is on the right-hand side of a rule then its failure is not considered when
// deciding which rule to evaluate. Corresponding constraints are only added if this
// expression is subsequently used as a pattern; see `expr_as_pattern`.
let source = if multi {
self.current_rule.iterators.insert(source);
self.dedup_binding(Binding::Iterator { source })
} else if infallible {
source
} else {
self.dedup_binding(Binding::MatchSome { source })
};
if !pure {
self.current_rule.impure.push(source);
}
source
}
}
impl sema::RuleVisitor for RuleSetBuilder {
type PatternVisitor = Self;
type ExprVisitor = Self;
type Expr = BindingId;
fn add_arg(&mut self, index: usize, _ty: sema::TypeId) -> BindingId {
let index = TupleIndex(index.try_into().unwrap());
self.dedup_binding(Binding::Argument { index })
}
fn add_pattern<F: FnOnce(&mut Self)>(&mut self, visitor: F) {
visitor(self)
}
fn add_expr<F>(&mut self, visitor: F) -> BindingId
where
F: FnOnce(&mut Self) -> sema::VisitedExpr<Self>,
{
visitor(self).value
}
fn expr_as_pattern(&mut self, expr: BindingId) -> BindingId {
let mut todo = vec![expr];
while let Some(expr) = todo.pop() {
let expr = &self.rules.bindings[expr.index()];
todo.extend_from_slice(expr.sources());
if let &Binding::MatchSome { source } = expr {
let _ = self.set_constraint(source, Constraint::Some);
}
}
expr
}
fn pattern_as_expr(&mut self, pattern: BindingId) -> BindingId {
pattern
}
}