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using Microsoft.Boogie;
using System;
using System.Collections.Generic;
using System.Diagnostics.Contracts;
using System.Linq;
using System.Text;
namespace Microsoft.Dafny.Triggers {
class QuantifierSplitter : BottomUpVisitor {
/// This cache was introduced because some statements (notably calc) return the same SubExpression multiple times.
/// This ended up causing an inconsistent situation when the calc statement's subexpressions contained the same quantifier
/// twice: on the first pass that quantifier got its SplitQuantifiers generated, and on the the second pass these
/// split quantifiers got re-split, creating a situation where the direct children of a split quantifier were
/// also split quantifiers.
private Dictionary<QuantifierExpr, List<Expression>> splits = new Dictionary<QuantifierExpr, List<Expression>>();
private static BinaryExpr.Opcode FlipOpcode(BinaryExpr.Opcode opCode) {
if (opCode == BinaryExpr.Opcode.And) {
return BinaryExpr.Opcode.Or;
} else if (opCode == BinaryExpr.Opcode.Or) {
return BinaryExpr.Opcode.And;
} else {
throw new ArgumentException();
}
}
// NOTE: If we wanted to split quantifiers as far as possible, it would be
// enough to put the formulas in DNF (for foralls) or CNF (for exists).
// Unfortunately, this would cause ill-behaved quantifiers to produce
// exponentially many smaller quantifiers. Thus we only do one step of
// distributing, which takes care of the usual precondition case:
// forall x :: P(x) ==> (Q(x) && R(x))
private static UnaryOpExpr Not(Expression expr) {
return new UnaryOpExpr(expr.tok, UnaryOpExpr.Opcode.Not, expr) { Type = expr.Type };
}
private static Attributes CopyAttributes(Attributes source) {
if (source == null) {
return null;
} else {
return new Attributes(source.Name, source.Args, CopyAttributes(source.Prev));
}
}
internal static IEnumerable<Expression> SplitExpr(Expression expr, BinaryExpr.Opcode separator) {
expr = expr.Resolved;
var unary = expr as UnaryOpExpr;
var binary = expr as BinaryExpr;
if (unary != null && unary.Op == UnaryOpExpr.Opcode.Not) {
foreach (var e in SplitExpr(unary.E, FlipOpcode(separator))) { yield return Not(e); }
} else if (binary != null && binary.Op == separator) {
foreach (var e in SplitExpr(binary.E0, separator)) { yield return e; }
foreach (var e in SplitExpr(binary.E1, separator)) { yield return e; }
} else if (binary != null && binary.Op == BinaryExpr.Opcode.Imp && separator == BinaryExpr.Opcode.Or) {
foreach (var e in SplitExpr(Not(binary.E0), separator)) { yield return e; }
foreach (var e in SplitExpr(binary.E1, separator)) { yield return e; }
} else {
yield return expr;
}
}
internal static IEnumerable<Expression> SplitAndStich(BinaryExpr pair, BinaryExpr.Opcode separator) {
foreach (var e1 in SplitExpr(pair.E1, separator)) {
// Notice the token. This makes triggers/splitting-picks-the-right-tokens.dfy possible
yield return new BinaryExpr(e1.tok, pair.Op, pair.E0, e1) { ResolvedOp = pair.ResolvedOp, Type = pair.Type };
}
}
internal static IEnumerable<Expression> SplitQuantifier(QuantifierExpr quantifier) {
var body = quantifier.Term;
var binary = body as BinaryExpr;
if (quantifier is ForallExpr) {
IEnumerable<Expression> stream;
if (binary != null && (binary.Op == BinaryExpr.Opcode.Imp || binary.Op == BinaryExpr.Opcode.Or)) {
stream = SplitAndStich(binary, BinaryExpr.Opcode.And);
} else {
stream = SplitExpr(body, BinaryExpr.Opcode.And);
}
foreach (var e in stream) {
var tok = new NestedToken(quantifier.tok, e.tok);
yield return new ForallExpr(tok, quantifier.TypeArgs, quantifier.BoundVars, quantifier.Range, e, CopyAttributes(quantifier.Attributes)) { Type = quantifier.Type };
}
} else if (quantifier is ExistsExpr) {
IEnumerable<Expression> stream;
if (binary != null && binary.Op == BinaryExpr.Opcode.And) {
stream = SplitAndStich(binary, BinaryExpr.Opcode.Or);
} else {
stream = SplitExpr(body, BinaryExpr.Opcode.Or);
}
foreach (var e in stream) {
var tok = new NestedToken(quantifier.tok, e.tok);
yield return new ExistsExpr(tok, quantifier.TypeArgs, quantifier.BoundVars, quantifier.Range, e, CopyAttributes(quantifier.Attributes)) { Type = quantifier.Type };
}
} else {
yield return quantifier;
}
}
private static bool AllowsSplitting(QuantifierExpr quantifier) {
bool splitAttr = true;
return !Attributes.ContainsBool(quantifier.Attributes, "split", ref splitAttr) || splitAttr;
}
protected override void VisitOneExpr(Expression expr) {
var quantifier = expr as QuantifierExpr;
if (quantifier != null) {
Contract.Assert(quantifier.SplitQuantifier == null);
if (!splits.ContainsKey(quantifier) && AllowsSplitting(quantifier)) {
splits[quantifier] = SplitQuantifier(quantifier).ToList();
}
}
}
protected override void VisitOneStmt(Statement stmt) {
Contract.Requires(stmt != null);
if (stmt is ForallStmt) {
ForallStmt s = (ForallStmt)stmt;
if (s.ForallExpressions != null) {
foreach (Expression expr in s.ForallExpressions) {
VisitOneExpr(expr);
}
}
}
}
/// <summary>
/// See comments above definition of splits for reason why this method exists
/// </summary>
internal void Commit() {
foreach (var quantifier in splits.Keys) {
quantifier.SplitQuantifier = splits[quantifier];
}
}
}
}
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