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Previously we did this when adding new concrete type rules, but we don't have a complete rewrite system at that point yet, so there was no guarantee concrete substitution terms would be canonical. Now, perform simplification in a post-pass after completion, at the same time as simplifying rule right hand sides. Rewrite loops are recorded relating the original rule with the simplified substitutions.
646 lines
22 KiB
C++
646 lines
22 KiB
C++
//===--- KnuthBendix.cpp - Confluent completion procedure -----------------===//
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//
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// This source file is part of the Swift.org open source project
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//
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// Copyright (c) 2021 Apple Inc. and the Swift project authors
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// Licensed under Apache License v2.0 with Runtime Library Exception
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//
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// See https://swift.org/LICENSE.txt for license information
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// See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors
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//
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//===----------------------------------------------------------------------===//
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//
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// This implements completion in the rewriting system sense, not code
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// completion.
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//
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// We use a variation of the Knuth-Bendix algorithm
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// (https://en.wikipedia.org/wiki/Knuth–Bendix_completion_algorithm).
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//
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// The goal is to find 'overlapping' rules which would allow the same term to
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// be rewritten in two different ways. These two different irreducible
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// reductions are called a 'critical pair'; the completion procedure introduces
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// new rewrite rules to eliminate critical pairs by rewriting one side of the
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// pair to the other. This can introduce more overlaps with existing rules, and
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// the process iterates until fixed point.
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//
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// This implementation also extends Knuth-Bendix to introduce new _generators_,
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// in addition to new relations as in the standard algorithm. See the comment at
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// the top of RewriteSystem::processMergedAssociatedTypes() for a description.
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//
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//===----------------------------------------------------------------------===//
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#include "swift/Basic/Range.h"
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#include "llvm/Support/Debug.h"
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#include "llvm/Support/raw_ostream.h"
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#include <algorithm>
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#include <deque>
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#include <vector>
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#include "RewriteContext.h"
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#include "RewriteSystem.h"
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using namespace swift;
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using namespace rewriting;
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/// For a superclass or concrete type symbol
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///
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/// [concrete: Foo<X1, ..., Xn>]
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/// [superclass: Foo<X1, ..., Xn>]
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///
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/// Return a new symbol where the prefix T is prepended to each of the
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/// substitutions:
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///
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/// [concrete: Foo<T.X1, ..., T.Xn>]
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/// [superclass: Foo<T.X1, ..., T.Xn>]
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///
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/// Asserts if this is not a superclass or concrete type symbol.
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Symbol Symbol::prependPrefixToConcreteSubstitutions(
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const MutableTerm &prefix,
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RewriteContext &ctx) const {
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if (prefix.empty())
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return *this;
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return transformConcreteSubstitutions(
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[&](Term term) -> Term {
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MutableTerm mutTerm;
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mutTerm.append(prefix);
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mutTerm.append(term);
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return Term::get(mutTerm, ctx);
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}, ctx);
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}
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/// If we have two symbols [P:T] and [Q:T], produce a merged symbol:
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///
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/// - If P inherits from Q, this is just [P:T].
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/// - If Q inherits from P, this is just [Q:T].
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/// - If P and Q are unrelated, this is [P&Q:T].
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Symbol RewriteContext::mergeAssociatedTypes(Symbol lhs, Symbol rhs) {
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auto key = std::make_pair(lhs, rhs);
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auto found = MergedAssocTypes.find(key);
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if (found != MergedAssocTypes.end())
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return found->second;
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// Check preconditions that were established by RewriteSystem::addRule().
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assert(lhs.getKind() == Symbol::Kind::AssociatedType);
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assert(rhs.getKind() == Symbol::Kind::AssociatedType);
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assert(lhs.getName() == rhs.getName());
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assert(lhs.compare(rhs, *this) > 0);
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auto protos = lhs.getProtocols();
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auto otherProtos = rhs.getProtocols();
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// This must follow from lhs > rhs.
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assert(getProtocolSupport(protos) <= getProtocolSupport(otherProtos));
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// Compute sorted and merged list of protocols, with duplicates.
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llvm::TinyPtrVector<const ProtocolDecl *> newProtos;
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std::merge(protos.begin(), protos.end(),
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otherProtos.begin(), otherProtos.end(),
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std::back_inserter(newProtos),
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[&](const ProtocolDecl *lhs,
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const ProtocolDecl *rhs) -> int {
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return compareProtocols(lhs, rhs) < 0;
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});
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// Prune duplicates and protocols that are inherited by other
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// protocols.
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llvm::TinyPtrVector<const ProtocolDecl *> minimalProtos;
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for (const auto *newProto : newProtos) {
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auto inheritsFrom = [&](const ProtocolDecl *thisProto) {
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if (thisProto == newProto)
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return true;
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const auto &inherited = getInheritedProtocols(thisProto);
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return std::find(inherited.begin(),
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inherited.end(),
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newProto) != inherited.end();
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};
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if (std::find_if(minimalProtos.begin(), minimalProtos.end(),
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inheritsFrom)
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== minimalProtos.end()) {
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minimalProtos.push_back(newProto);
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}
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}
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// The two input sets are minimal already, so the merged set
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// should have at least as many elements as the smallest
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// input set.
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assert(minimalProtos.size() >= std::min(protos.size(), otherProtos.size()));
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// The merged set cannot contain more elements than the union
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// of the two sets.
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assert(minimalProtos.size() <= protos.size() + otherProtos.size());
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auto result = Symbol::forAssociatedType(minimalProtos, lhs.getName(), *this);
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auto inserted = MergedAssocTypes.insert(std::make_pair(key, result));
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assert(inserted.second);
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(void) inserted;
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return result;
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}
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/// Consider the following example:
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///
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/// protocol P1 { associatedtype T : P1 }
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/// protocol P2 { associatedtype T : P2 }
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/// struct G<T : P1 & P2> {}
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///
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/// We start with these rewrite rules:
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///
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/// [P1].T => [P1:T]
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/// [P2].T => [P2:T]
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/// [P1:T].[P1] => [P1:T]
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/// [P2:T].[P1] => [P2:T]
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/// τ_0_0.[P1] => τ_0_0
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/// τ_0_0.[P2] => τ_0_0
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/// τ_0_0.T => τ_0_0.[P1:T]
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/// τ_0_0.[P2:T] => τ_0_0.[P1:T]
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///
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/// The completion procedure ends up adding an infinite series of rules of the
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/// form
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///
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/// τ_0_0.[P1:T].[P2] => τ_0_0.[P1:T]
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/// τ_0_0.[P1:T].[P2:T] => τ_0_0.[P1:T].[P1:T]
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///
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/// τ_0_0.[P1:T].[P1:T].[P2] => τ_0_0.[P1:T].[P1:T]
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/// τ_0_0.[P1:T].[P1:T].[P2:T] => τ_0_0.[P1:T].[P1:T].[P1:T]
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///
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/// τ_0_0.[P1:T].[P1:T].[P1:T].[P2] => τ_0_0.[P1:T].[P1:T].[P1.T]
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/// τ_0_0.[P1:T].[P1:T].[P1:T].[P2:T] => τ_0_0.[P1:T].[P1:T].[P1:T].[P1.T]
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///
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/// The difficulty here stems from the fact that an arbitrary sequence of
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/// [P1:T] following a τ_0_0 is known to conform to P2, but P1:T itself
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/// does not conform to P2.
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///
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/// We use a heuristic to compute a completion in this case by using
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/// merged associated type terms.
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///
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/// The key is the following rewrite rule:
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///
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/// τ_0_0.[P2:T] => τ_0_0.[P1:T]
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///
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/// When we add this rule, we introduce a new merged symbol [P1&P2:T] and
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/// a new rule:
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///
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/// τ_0_0.[P1:T] => τ_0_0.[P1&P2:T]
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///
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/// We also look for any existing rules of the form [P1:T].[Q] => [P1:T]
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/// or [P2:T].[Q] => [P2:T], and introduce a new rule:
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///
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/// [P1&P2:T].[Q] => [P1&P2:T]
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///
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/// In the above example, we have such a rule for Q == P1 and Q == P2, so
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/// in total we end up adding the following four rules:
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///
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/// τ_0_0.[P1:T] => τ_0_0.[P1&P2:T]
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/// [P1&P2:T].[P1] => [P1&P2:T]
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/// [P1&P2:T].[P2] => [P1&P2:T]
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///
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/// Intuitively, since the conformance requirements on the merged term
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/// are not prefixed by the root τ_0_0, they apply at any level; we've
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/// "tied off" the recursion, and the rewrite system is now convergent.
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void RewriteSystem::processMergedAssociatedTypes() {
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if (MergedAssociatedTypes.empty())
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return;
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unsigned i = 0;
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// Chase the end of the vector, since addRule() might add new elements below.
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while (i < MergedAssociatedTypes.size()) {
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// Copy the entry out, since addRule() might add new elements below.
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auto entry = MergedAssociatedTypes[i++];
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if (Debug.contains(DebugFlags::Merge)) {
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llvm::dbgs() << "## Processing associated type merge with ";
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llvm::dbgs() << entry.rhs << ", ";
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llvm::dbgs() << entry.lhsSymbol << ", ";
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llvm::dbgs() << entry.mergedSymbol << "\n";
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}
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// If we have X.[P2:T] => Y.[P1:T], add a new rule:
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// X.[P1:T] => X.[P1&P2:T]
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MutableTerm lhs(entry.rhs);
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// Build the term X.[P1&P2:T].
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MutableTerm rhs(entry.rhs);
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rhs.back() = entry.mergedSymbol;
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// Add the rule X.[P1:T] => X.[P1&P2:T].
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addRule(lhs, rhs);
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// Collect new rules here so that we're not adding rules while traversing
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// the trie.
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SmallVector<std::pair<MutableTerm, MutableTerm>, 2> inducedRules;
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// Look for conformance requirements on [P1:T] and [P2:T].
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auto visitRule = [&](unsigned ruleID) {
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const auto &otherRule = getRule(ruleID);
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const auto &otherLHS = otherRule.getLHS();
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if (otherLHS.size() == 2 &&
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otherLHS[1].getKind() == Symbol::Kind::Protocol) {
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if (otherLHS[0] == entry.lhsSymbol ||
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otherLHS[0] == entry.rhs.back()) {
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// We have a rule of the form
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//
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// [P1:T].[Q] => [P1:T]
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//
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// or
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//
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// [P2:T].[Q] => [P2:T]
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if (Debug.contains(DebugFlags::Merge)) {
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llvm::dbgs() << "### Lifting conformance rule " << otherRule << "\n";
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}
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// We know that [P1:T] or [P2:T] conforms to Q, therefore the
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// merged type [P1&P2:T] must conform to Q as well. Add a new rule
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// of the form:
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//
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// [P1&P2:T].[Q] => [P1&P2:T]
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//
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MutableTerm newLHS;
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newLHS.add(entry.mergedSymbol);
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newLHS.add(otherLHS[1]);
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MutableTerm newRHS;
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newRHS.add(entry.mergedSymbol);
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inducedRules.emplace_back(newLHS, newRHS);
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}
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}
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};
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// Visit rhs first to preserve the ordering of protocol requirements in the
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// the property map. This is just for aesthetic purposes in the debug dump,
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// it doesn't change behavior.
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Trie.findAll(entry.rhs.back(), visitRule);
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Trie.findAll(entry.lhsSymbol, visitRule);
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// Now add the new rules.
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for (const auto &pair : inducedRules)
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addRule(pair.first, pair.second);
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}
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MergedAssociatedTypes.clear();
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}
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/// Check if we have a rule of the form
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///
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/// X.[P1:T] => X.[P2:T]
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///
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/// If so, record this rule for later. We'll try to merge the associated
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/// types in RewriteSystem::processMergedAssociatedTypes().
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void RewriteSystem::checkMergedAssociatedType(Term lhs, Term rhs) {
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// FIXME: Figure out 3-cell representation for merged associated types
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if (RecordLoops ||
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!Context.getASTContext().LangOpts.RequirementMachineMergedAssociatedTypes)
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return;
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if (lhs.size() == rhs.size() &&
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std::equal(lhs.begin(), lhs.end() - 1, rhs.begin()) &&
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lhs.back().getKind() == Symbol::Kind::AssociatedType &&
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rhs.back().getKind() == Symbol::Kind::AssociatedType &&
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lhs.back().getName() == rhs.back().getName()) {
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if (Debug.contains(DebugFlags::Merge)) {
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llvm::dbgs() << "## Associated type merge candidate ";
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llvm::dbgs() << lhs << " => " << rhs << "\n\n";
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}
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auto mergedSymbol = Context.mergeAssociatedTypes(lhs.back(), rhs.back());
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if (Debug.contains(DebugFlags::Merge)) {
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llvm::dbgs() << "### Merged symbol " << mergedSymbol << "\n";
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}
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// We must have mergedSymbol <= rhs < lhs, therefore mergedSymbol != lhs.
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assert(lhs.back() != mergedSymbol &&
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"Left hand side should not already end with merged symbol?");
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assert(mergedSymbol.compare(rhs.back(), Context) <= 0);
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assert(rhs.back().compare(lhs.back(), Context) < 0);
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// If the merge didn't actually produce a new symbol, there is nothing else
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// to do.
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if (rhs.back() == mergedSymbol) {
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if (Debug.contains(DebugFlags::Merge)) {
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llvm::dbgs() << "### Skipping\n";
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}
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return;
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}
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MergedAssociatedTypes.push_back({rhs, lhs.back(), mergedSymbol});
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}
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}
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/// Compute a critical pair from the left hand sides of two rewrite rules,
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/// where \p rhs begins at \p from, which must be an iterator pointing
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/// into \p lhs.
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///
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/// The resulting pair is pushed onto \p result only if it is non-trivial,
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/// that is, the left hand side and right hand side are not equal.
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///
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/// Returns true if the pair was non-trivial, false if it was trivial.
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///
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/// There are two cases:
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///
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/// 1) lhs == TUV -> X, rhs == U -> Y. The overlapped term is TUV;
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/// applying lhs and rhs, respectively, yields the critical pair
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/// (X, TYV).
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///
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/// 2) lhs == TU -> X, rhs == UV -> Y. The overlapped term is once
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/// again TUV; applying lhs and rhs, respectively, yields the
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/// critical pair (XV, TY).
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///
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/// If lhs and rhs have identical left hand sides, either case could
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/// apply, but we arbitrarily pick case 1.
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///
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/// There is also an additional wrinkle. If we're in case 2, and the
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/// last symbol of V is a superclass or concrete type symbol A, we prepend
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/// T to each substitution of A.
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///
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/// For example, suppose we have the following two rules:
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///
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/// A.B -> C
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/// B.[concrete: Foo<X>] -> B
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///
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/// The overlapped term is A.B.[concrete: Foo<X>], so the critical pair
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/// is (C.[concrete: Foo<A.X>], A.B). We prepended 'A' to the
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/// concrete substitution 'X' to get 'A.X'; the new concrete term
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/// is now rooted at the same level as A.B in the rewrite system,
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/// not just B.
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bool
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RewriteSystem::computeCriticalPair(ArrayRef<Symbol>::const_iterator from,
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const Rule &lhs, const Rule &rhs,
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std::vector<std::pair<MutableTerm,
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MutableTerm>> &pairs,
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std::vector<RewritePath> &paths,
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std::vector<RewriteLoop> &loops) const {
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auto end = lhs.getLHS().end();
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if (from + rhs.getLHS().size() < end) {
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// lhs == TUV -> X, rhs == U -> Y.
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// Note: This includes the case where the two rules have exactly
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// equal left hand sides; that is, lhs == U -> X, rhs == U -> Y.
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//
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// In this case, T and V are both empty.
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// Compute the terms T and V.
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MutableTerm t(lhs.getLHS().begin(), from);
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MutableTerm v(from + rhs.getLHS().size(), lhs.getLHS().end());
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// Compute the term TYV.
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MutableTerm tyv(t);
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tyv.append(rhs.getRHS());
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tyv.append(v);
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MutableTerm x(lhs.getRHS());
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// Compute a path from X to TYV: (X => TUV) ⊗ T.(U => Y).V
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RewritePath path;
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// (1) First, apply the left hand side rule in the reverse direction:
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//
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// (X => TUV)
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path.add(RewriteStep::forRewriteRule(/*startOffset=*/0,
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/*endOffset=*/0,
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getRuleID(lhs),
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/*inverse=*/true));
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// (2) Now, apply the right hand side in the forward direction:
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//
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// T.(U => Y).V
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path.add(RewriteStep::forRewriteRule(t.size(), v.size(),
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getRuleID(rhs),
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/*inverse=*/false));
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// If X == TYV, we have a trivial overlap.
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if (x == tyv) {
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loops.emplace_back(x, path);
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return false;
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}
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// Add the pair (X, TYV).
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pairs.emplace_back(x, tyv);
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paths.push_back(path);
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} else {
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// lhs == TU -> X, rhs == UV -> Y.
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// Compute the terms T and V.
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MutableTerm t(lhs.getLHS().begin(), from);
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MutableTerm v(rhs.getLHS().begin() + (lhs.getLHS().end() - from),
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rhs.getLHS().end());
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// Compute the term XV.
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MutableTerm xv(lhs.getRHS());
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xv.append(v);
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// Compute the term TY.
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MutableTerm ty(t);
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ty.append(rhs.getRHS());
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// Compute a path from XV to TY: (X => TU).V ⊗ (σ - T) ⊗ T.(UV => Y)
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RewritePath path;
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// (1) First, apply the left hand side rule in the reverse direction:
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//
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// (X => TU).V
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path.add(RewriteStep::forRewriteRule(/*startOffset=*/0, v.size(),
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getRuleID(lhs),
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/*inverse=*/true));
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// (2) Next, if the right hand side rule ends with a concrete type symbol,
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// perform the concrete type adjustment:
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//
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// (σ - T)
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if (xv.back().hasSubstitutions() &&
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!xv.back().getSubstitutions().empty() &&
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t.size() > 0) {
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path.add(RewriteStep::forAdjustment(t.size(), /*endOffset=*/0,
|
||
/*inverse=*/true));
|
||
|
||
xv.back() = xv.back().prependPrefixToConcreteSubstitutions(
|
||
t, Context);
|
||
}
|
||
|
||
// (3) Finally, apply the right hand side in the forward direction:
|
||
//
|
||
// T.(UV => Y)
|
||
path.add(RewriteStep::forRewriteRule(t.size(), /*endOffset=*/0,
|
||
getRuleID(rhs),
|
||
/*inverse=*/false));
|
||
|
||
// If XV == TY, we have a trivial overlap.
|
||
if (xv == ty) {
|
||
loops.emplace_back(xv, path);
|
||
return false;
|
||
}
|
||
|
||
// Add the pair (XV, TY).
|
||
pairs.emplace_back(xv, ty);
|
||
paths.push_back(path);
|
||
}
|
||
|
||
return true;
|
||
}
|
||
|
||
/// Computes the confluent completion using the Knuth-Bendix algorithm.
|
||
///
|
||
/// Returns a pair consisting of a status and number of iterations executed.
|
||
///
|
||
/// The status is CompletionResult::MaxIterations if we exceed \p maxIterations
|
||
/// iterations.
|
||
///
|
||
/// The status is CompletionResult::MaxDepth if we produce a rewrite rule whose
|
||
/// left hand side has a length exceeding \p maxDepth.
|
||
///
|
||
/// Otherwise, the status is CompletionResult::Success.
|
||
std::pair<CompletionResult, unsigned>
|
||
RewriteSystem::computeConfluentCompletion(unsigned maxIterations,
|
||
unsigned maxDepth) {
|
||
assert(Initialized);
|
||
assert(!Minimized);
|
||
|
||
// Complete might already be set, if we're re-running completion after
|
||
// adding new rules in the property map's concrete type unification procedure.
|
||
Complete = 1;
|
||
|
||
unsigned steps = 0;
|
||
|
||
bool again = false;
|
||
|
||
std::vector<std::pair<MutableTerm, MutableTerm>> resolvedCriticalPairs;
|
||
std::vector<RewritePath> resolvedPaths;
|
||
std::vector<RewriteLoop> resolvedLoops;
|
||
|
||
do {
|
||
// For every rule, looking for other rules that overlap with this rule.
|
||
for (unsigned i = 0, e = Rules.size(); i < e; ++i) {
|
||
const auto &lhs = getRule(i);
|
||
if (lhs.isSimplified())
|
||
continue;
|
||
|
||
// Look up every suffix of this rule in the trie using findAll(). This
|
||
// will find both kinds of overlap:
|
||
//
|
||
// 1) rules whose left hand side is fully contained in [from,to)
|
||
// 2) rules whose left hand side has a prefix equal to [from,to)
|
||
auto from = lhs.getLHS().begin();
|
||
auto to = lhs.getLHS().end();
|
||
while (from < to) {
|
||
Trie.findAll(from, to, [&](unsigned j) {
|
||
const auto &rhs = getRule(j);
|
||
if (rhs.isSimplified())
|
||
return;
|
||
|
||
if (from == lhs.getLHS().begin()) {
|
||
// While every rule will have an overlap of the first kind
|
||
// with itself, it's not useful to consider since the
|
||
// resulting critical pair is always trivial.
|
||
if (i == j)
|
||
return;
|
||
|
||
// If the first rule's left hand side is a proper prefix
|
||
// of the second rule's left hand side, don't do anything.
|
||
//
|
||
// We will find the 'opposite' overlap later, where the two
|
||
// rules are swapped around. Then it becomes an overlap of
|
||
// the first kind, and will be handled as such.
|
||
if (rhs.getLHS().size() > lhs.getLHS().size())
|
||
return;
|
||
}
|
||
|
||
// We don't have to consider the same pair of rules more than once,
|
||
// since those critical pairs were already resolved.
|
||
if (!CheckedOverlaps.insert(std::make_pair(i, j)).second)
|
||
return;
|
||
|
||
// Try to repair the confluence violation by adding a new rule.
|
||
if (computeCriticalPair(from, lhs, rhs,
|
||
resolvedCriticalPairs,
|
||
resolvedPaths,
|
||
resolvedLoops)) {
|
||
if (Debug.contains(DebugFlags::Completion)) {
|
||
const auto &pair = resolvedCriticalPairs.back();
|
||
const auto &path = resolvedPaths.back();
|
||
|
||
llvm::dbgs() << "$ Overlapping rules: (#" << i << ") ";
|
||
llvm::dbgs() << lhs << "\n";
|
||
llvm::dbgs() << " -vs- (#" << j << ") ";
|
||
llvm::dbgs() << rhs << ":\n";
|
||
llvm::dbgs() << "$$ First term of critical pair is "
|
||
<< pair.first << "\n";
|
||
llvm::dbgs() << "$$ Second term of critical pair is "
|
||
<< pair.second << "\n\n";
|
||
|
||
llvm::dbgs() << "$$ Resolved via path: ";
|
||
path.dump(llvm::dbgs(), pair.first, *this);
|
||
llvm::dbgs() << "\n\n";
|
||
}
|
||
} else {
|
||
if (Debug.contains(DebugFlags::Completion)) {
|
||
const auto &loop = resolvedLoops.back();
|
||
|
||
llvm::dbgs() << "$ Trivially overlapping rules: (#" << i << ") ";
|
||
llvm::dbgs() << lhs << "\n";
|
||
llvm::dbgs() << " -vs- (#" << j << ") ";
|
||
llvm::dbgs() << rhs << ":\n";
|
||
|
||
llvm::dbgs() << "$$ Loop: ";
|
||
loop.dump(llvm::dbgs(), *this);
|
||
llvm::dbgs() << "\n\n";
|
||
}
|
||
}
|
||
});
|
||
|
||
++from;
|
||
}
|
||
}
|
||
|
||
simplifyLeftHandSides();
|
||
|
||
assert(resolvedCriticalPairs.size() == resolvedPaths.size());
|
||
|
||
again = false;
|
||
for (unsigned index : indices(resolvedCriticalPairs)) {
|
||
const auto &pair = resolvedCriticalPairs[index];
|
||
const auto &path = resolvedPaths[index];
|
||
|
||
// Check if we've already done too much work.
|
||
if (Rules.size() > maxIterations)
|
||
return std::make_pair(CompletionResult::MaxIterations, steps);
|
||
|
||
if (!addRule(pair.first, pair.second, &path))
|
||
continue;
|
||
|
||
// Check if the new rule is too long.
|
||
if (Rules.back().getDepth() > maxDepth)
|
||
return std::make_pair(CompletionResult::MaxDepth, steps);
|
||
|
||
// Only count a 'step' once we add a new rule.
|
||
++steps;
|
||
again = true;
|
||
}
|
||
|
||
for (const auto &loop : resolvedLoops) {
|
||
recordRewriteLoop(loop);
|
||
}
|
||
|
||
resolvedCriticalPairs.clear();
|
||
resolvedPaths.clear();
|
||
resolvedLoops.clear();
|
||
|
||
simplifyRightHandSidesAndSubstitutions();
|
||
|
||
// If the added rules merged any associated types, process the merges now
|
||
// before we continue with the completion procedure. This is important
|
||
// to perform incrementally since merging is required to repair confluence
|
||
// violations.
|
||
processMergedAssociatedTypes();
|
||
} while (again);
|
||
|
||
assert(MergedAssociatedTypes.empty() &&
|
||
"Should have processed all merge candidates");
|
||
|
||
return std::make_pair(CompletionResult::Success, steps);
|
||
}
|