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#define QUANTIFIER_WARNINGS
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using Microsoft.Boogie;
using System.Diagnostics.Contracts;
//FIXME Generated triggers should be _triggers
//FIXME: When scoring, do not consider old(x) to be higher than x.
namespace Microsoft.Dafny.Triggers {
class QuantifierWithTriggers {
internal QuantifierExpr quantifier;
internal List<TriggerTerm> CandidateTerms;
internal List<TriggerCandidate> Candidates;
internal List<TriggerCandidate> RejectedCandidates;
internal bool AllowsLoops { get { return TriggerUtils.AllowsMatchingLoops(quantifier); } }
internal bool CouldSuppressLoops { get; set; }
internal QuantifierWithTriggers(QuantifierExpr quantifier) {
this.quantifier = quantifier;
this.RejectedCandidates = new List<TriggerCandidate>();
}
internal void TrimInvalidTriggers() {
Contract.Requires(CandidateTerms != null);
Contract.Requires(Candidates != null);
Candidates = TriggerUtils.Filter(Candidates, tr => tr.MentionsAll(quantifier.BoundVars), tr => { }).ToList();
}
}
class QuantifiersCollection {
readonly ErrorReporter reporter;
readonly List<QuantifierWithTriggers> quantifiers;
internal QuantifiersCollection(IEnumerable<QuantifierExpr> quantifiers, ErrorReporter reporter) {
this.reporter = reporter;
this.quantifiers = quantifiers.Select(q => new QuantifierWithTriggers(q)).ToList();
}
internal void ComputeTriggers(TriggersCollector triggersCollector) {
CollectAndShareTriggers(triggersCollector);
TrimInvalidTriggers();
BuildDependenciesGraph();
SuppressMatchingLoops();
SelectTriggers();
}
private bool SubsetGenerationPredicate(List<TriggerTerm> terms, TriggerTerm additionalTerm) {
// Simple formulas like [P0(i) && P1(i) && P2(i) && P3(i) && P4(i)] yield very
// large numbers of multi-triggers, most of which are useless. This filter
// restricts subsets of terms so that we only generate sets of terms where each
// element contributes at least one variable. In the example above, we'll only
// get 5 triggers.
return additionalTerm.Variables.Where(v => !terms.Any(t => t.Variables.Contains(v))).Any();
}
//FIXME document that this assumes that the quantifiers live in the same context and share the same variables
void CollectAndShareTriggers(TriggersCollector triggersCollector) {
var pool = quantifiers.SelectMany(q => triggersCollector.CollectTriggers(q.quantifier));
var distinctPool = pool.Deduplicate(TriggerTerm.Eq);
var multiPool = TriggerUtils.AllNonEmptySubsets(distinctPool, SubsetGenerationPredicate).Select(candidates => new TriggerCandidate(candidates)).ToList();
foreach (var q in quantifiers) {
q.CandidateTerms = distinctPool; //Candidate terms are immutable: no copy needed
q.Candidates = multiPool.Select(candidate => new TriggerCandidate(candidate)).ToList();
}
}
private void TrimInvalidTriggers() {
foreach (var q in quantifiers) {
q.TrimInvalidTriggers();
}
}
void BuildDependenciesGraph() {
// FIXME: Think more about multi-quantifier dependencies
//class QuantifierDependency {
// QuantifierWithTriggers Cause;
// QuantifierWithTriggers Consequence;
// List<TriggerCandidate> Triggers;
// List<Expression> MatchingTerm;
//}
}
void SuppressMatchingLoops() {
// NOTE: This only looks for self-loops; that is, loops involving a single
// quantifier.
// For a given quantifier q, we introduce a triggering relation between trigger
// candidates by writing t1 → t2 if instantiating q from t1 introduces a ground
// term that matches t2. Then, we notice that this relation is transitive, since
// all triggers yield the same set of terms. This means that any matching loop
// t1 → ... → t1 can be reduced to a self-loop t1 → t1. Detecting such
// self-loops is then only a matter of finding terms in the body of the
// quantifier that match a given trigger.
// Of course, each trigger that actually appears in the body of the quantifier
// yields a trivial self-loop (e.g. P(i) in [∀ i {P(i)} ⋅ P(i)]), so we
// ignore this type of loops. In fact, we ignore any term in the body of the
// quantifier that matches one of the terms of the trigger (this ensures that
// [∀ x {f(x), f(f(x))} ⋅ f(x) = f(f(x))] is not a loop). And we even
// ignore terms that almost match a trigger term, modulo a single variable
// (this ensures that [∀ x y {a(x, y)} ⋅ a(x, y) == a(y, x)] is not a loop).
// This ignoring logic is implemented by the CouldCauseLoops method.
foreach (var q in quantifiers) {
var looping = new List<TriggerCandidate>();
var loopingSubterms = q.Candidates.ToDictionary(candidate => candidate, candidate => candidate.LoopingSubterms(q.quantifier).ToList());
var safe = TriggerUtils.Filter(
q.Candidates,
c => !loopingSubterms[c].Any(),
c => {
looping.Add(c);
c.Annotation = "loops with " + loopingSubterms[c].MapConcat(t => Printer.ExprToString(t.Expr), ", ");
}).ToList();
q.CouldSuppressLoops = safe.Count > 0;
if (!q.AllowsLoops && q.CouldSuppressLoops) {
q.Candidates = safe;
q.RejectedCandidates.AddRange(looping);
}
}
}
void SelectTriggers() {
//FIXME
}
private void CommitOne(QuantifierWithTriggers q, bool addHeader) {
var errorLevel = ErrorLevel.Info;
var msg = new StringBuilder();
var indent = addHeader ? " " : " "; //FIXME if multiline messages were properly supported, this indentation wouldn't be needed
if (!TriggerUtils.NeedsAutoTriggers(q.quantifier)) { //FIXME: matchingloop and autotriggers attributes are passed down to Boogie
msg.AppendFormat("Not generating triggers for {{{0}}}.", Printer.ExprToString(q.quantifier.Term)).AppendLine();
// FIXME This shouldn't be printed for autoReqs. (see autoReq.dfy)
// FIXME typeQuantifier?
} else {
if (addHeader) {
msg.AppendFormat("For expression {{{0}}}:", Printer.ExprToString(q.quantifier.Term)).AppendLine();
}
foreach (var candidate in q.Candidates) { //FIXME make this _trigger instead of trigger
q.quantifier.Attributes = new Attributes("trigger", candidate.Terms.Select(t => t.Expr).ToList(), q.quantifier.Attributes);
}
AddTriggersToMessage("Selected triggers:", q.Candidates, msg, indent);
AddTriggersToMessage("Rejected triggers:", q.RejectedCandidates, msg, indent, true);
#if QUANTIFIER_WARNINGS
string WARN = (msg.Length > 0 ? indent : "") + (DafnyOptions.O.UnicodeOutput ? "⚠ " : "(!) "); //FIXME set unicodeoutput in extension
if (!q.CandidateTerms.Any()) {
errorLevel = ErrorLevel.Warning;
msg.Append(WARN).AppendLine("No terms found to trigger on.");
} else if (!q.Candidates.Any()) {
errorLevel = ErrorLevel.Warning;
msg.Append(WARN).AppendLine("No trigger covering all quantified variables found.");
} else if (!q.CouldSuppressLoops && !q.AllowsLoops) {
errorLevel = ErrorLevel.Warning;
msg.Append(WARN).AppendLine("Suppressing loops would leave this expression without triggers.");
}
#endif
}
if (msg.Length > 0) {
reporter.Message(MessageSource.Rewriter, errorLevel, q.quantifier.tok, msg.ToString().TrimEnd("\r\n".ToCharArray()));
}
}
private static void AddTriggersToMessage<T>(string header, List<T> triggers, StringBuilder msg, string indent, bool newlines = false) {
if (triggers.Any()) {
msg.Append(indent).Append(header);
if (triggers.Count == 1) {
msg.Append(" ");
} else if (triggers.Count > 1) {
msg.AppendLine().Append(indent).Append(" ");
}
var separator = newlines && triggers.Count > 1 ? Environment.NewLine + indent + " " : ", ";
msg.AppendLine(String.Join(separator, triggers));
}
}
internal void CommitTriggers() {
foreach (var q in quantifiers) {
CommitOne(q, quantifiers.Count > 1);
}
}
}
}
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