public Expr DisjointnessExpr(string domainName, HashSet <Variable> scope)
{
LinearDomain domain = linearDomains[domainName];
BoundVariable partition = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, string.Format("partition_{0}", domainName), new MapType(Token.NoToken, new List <TypeVariable>(), new List <Type> {
domain.elementType
}, Microsoft.Boogie.Type.Int)));
Expr disjointExpr = Expr.True;
int count = 0;
foreach (Variable v in scope)
{
IdentifierExpr ie = new IdentifierExpr(Token.NoToken, v);
Expr e = new NAryExpr(Token.NoToken, new FunctionCall(domain.mapConstInt), new List <Expr> {
new LiteralExpr(Token.NoToken, Microsoft.Basetypes.BigNum.FromInt(count++))
});
e = new NAryExpr(Token.NoToken, new FunctionCall(domain.mapEqInt), new List <Expr> {
new IdentifierExpr(Token.NoToken, partition), e
});
e = new NAryExpr(Token.NoToken, new FunctionCall(domain.mapImpBool), new List <Expr> {
v.TypedIdent.Type is MapType ? ie : Singleton(ie, domainName), e
});
e = Expr.Binary(BinaryOperator.Opcode.Eq, e, new NAryExpr(Token.NoToken, new FunctionCall(domain.mapConstBool), new List <Expr> {
Expr.True
}));
disjointExpr = Expr.Binary(BinaryOperator.Opcode.And, e, disjointExpr);
}
var expr = new ExistsExpr(Token.NoToken, new List <Variable> {
partition
}, disjointExpr);
expr.Resolve(new ResolutionContext(null));
expr.Typecheck(new TypecheckingContext(null));
return(expr);
}
// Parse an sequence of add/subtract operators
Expr ParseMultiplyDivide()
{
// Parse the left hand side
var lhs = ParsePowers();
while (true)
{
// Work out the operator
BinaryOp op;
switch (_tokenizer.Current.Token)
{
case Token.Multiply:
op = BinaryOp.Multiply;
break;
case Token.Divide:
op = BinaryOp.Divide;
break;
default:
// Binary operator not found.
return(lhs);
}
// Skip the operator
_tokenizer.MoveNext();
// Parse the right hand side of the expression
var rhs = ParsePowers();
// Create a binary node and use it as the left-hand side from now on
switch (op)
{
case BinaryOp.Multiply:
case BinaryOp.Divide:
lhs = Expr.Binary(op, lhs, rhs);
break;
default:
throw new NotSupportedException();
}
}
}
private async Task <Expr> ParseEquation(Expr e)
{
var pExpr = e;
do
{
var pExpr2 = await ParseExpr();
var pExprTmp = Expr.Binary(ETypeExpr.Equal, pExpr, pExpr2);
pExpr = pExprTmp;
if (mTokenizer.EOF || mTokenizer.EOL)
{
break;
}
} while (mTokenizer.Token == ETokenType.Equal);
return(pExpr);
}
static void TestBinaryFunctions()
{
Console.ForegroundColor = ConsoleColor.White;
Console.WriteLine("Test Binary Functions:");
Console.ForegroundColor = ConsoleColor.Gray;
VariableExpr a = "a", b = "b";
double x = 5, y = 2;
string fstr = $"f({x},{y})", fpstr = $"f'({x},{y})";
Console.ForegroundColor = ConsoleColor.Yellow;
Console.Write($"{"f",-12} ");
Console.ForegroundColor = ConsoleColor.Cyan;
Console.Write($"{"f'",-28} ");
Console.ForegroundColor = ConsoleColor.Magenta;
Console.Write($"{fstr,-22} ");
Console.ForegroundColor = ConsoleColor.Green;
Console.Write($"{fpstr,-28}");
Console.WriteLine();
foreach (var op in Enum.GetValues(typeof(BinaryOp)) as BinaryOp[])
{
if (op == BinaryOp.Undefined)
{
continue;
}
var f_expr = Expr.Binary(op, a, b);
var dfda = f_expr.Partial(a);
var f = f_expr[a, b];
var fp = dfda[a, b];
Console.ForegroundColor = ConsoleColor.Yellow;
Console.Write($"{f_expr,-12} ");
Console.ForegroundColor = ConsoleColor.Cyan;
Console.Write($"{dfda,-28:g4} ");
Console.ForegroundColor = ConsoleColor.Magenta;
Console.Write($"{f(x,y),-22:g4} ");
Console.ForegroundColor = ConsoleColor.Green;
Console.Write($"{fp(x,y),-28:g4}");
Console.WriteLine();
}
Console.WriteLine();
}
private void MergeCells(Cell l, Cell r)
{
l.Expr = Expr.Binary(l.TypeOp, l.Expr, r.Expr);
l.TypeOp = r.TypeOp;
}
public LinearDomain(Program program, string domainName, Type elementType)
{
this.elementType = elementType;
this.axioms = new List <Axiom>();
MapType mapTypeBool = new MapType(Token.NoToken, new List <TypeVariable>(), new List <Type> {
this.elementType
}, Type.Bool);
MapType mapTypeInt = new MapType(Token.NoToken, new List <TypeVariable>(), new List <Type> {
this.elementType
}, Type.Int);
this.mapOrBool = new Function(Token.NoToken, "linear_" + domainName + "_MapOr",
new List <Variable> {
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "a", mapTypeBool), true),
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "b", mapTypeBool), true)
},
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "c", mapTypeBool), false));
if (CommandLineOptions.Clo.UseArrayTheory)
{
this.mapOrBool.AddAttribute("builtin", "MapOr");
}
else
{
BoundVariable a = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "a", mapTypeBool));
IdentifierExpr aie = new IdentifierExpr(Token.NoToken, a);
BoundVariable b = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "b", mapTypeBool));
IdentifierExpr bie = new IdentifierExpr(Token.NoToken, b);
BoundVariable x = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", elementType));
IdentifierExpr xie = new IdentifierExpr(Token.NoToken, x);
var mapApplTerm = new NAryExpr(Token.NoToken, new FunctionCall(mapOrBool), new List <Expr> {
aie, bie
});
var lhsTerm = new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List <Expr> {
mapApplTerm, xie
});
var rhsTerm = Expr.Binary(BinaryOperator.Opcode.Or,
new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List <Expr> {
aie, xie
}),
new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List <Expr> {
bie, xie
}));
var axiomExpr = new ForallExpr(Token.NoToken, new List <TypeVariable>(), new List <Variable> {
a, b
}, null,
new Trigger(Token.NoToken, true, new List <Expr> {
mapApplTerm
}),
new ForallExpr(Token.NoToken, new List <Variable> {
x
}, Expr.Binary(BinaryOperator.Opcode.Eq, lhsTerm, rhsTerm)));
axiomExpr.Typecheck(new TypecheckingContext(null));
axioms.Add(new Axiom(Token.NoToken, axiomExpr));
}
this.mapImpBool = new Function(Token.NoToken, "linear_" + domainName + "_MapImp",
new List <Variable> {
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "a", mapTypeBool), true),
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "b", mapTypeBool), true)
},
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "c", mapTypeBool), false));
if (CommandLineOptions.Clo.UseArrayTheory)
{
this.mapImpBool.AddAttribute("builtin", "MapImp");
}
else
{
BoundVariable a = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "a", mapTypeBool));
IdentifierExpr aie = new IdentifierExpr(Token.NoToken, a);
BoundVariable b = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "b", mapTypeBool));
IdentifierExpr bie = new IdentifierExpr(Token.NoToken, b);
BoundVariable x = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", elementType));
IdentifierExpr xie = new IdentifierExpr(Token.NoToken, x);
var mapApplTerm = new NAryExpr(Token.NoToken, new FunctionCall(mapImpBool), new List <Expr> {
aie, bie
});
var lhsTerm = new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List <Expr> {
mapApplTerm, xie
});
var rhsTerm = Expr.Binary(BinaryOperator.Opcode.Imp,
new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List <Expr> {
aie, xie
}),
new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List <Expr> {
bie, xie
}));
var axiomExpr = new ForallExpr(Token.NoToken, new List <TypeVariable>(), new List <Variable> {
a, b
}, null,
new Trigger(Token.NoToken, true, new List <Expr> {
mapApplTerm
}),
new ForallExpr(Token.NoToken, new List <Variable> {
x
}, Expr.Binary(BinaryOperator.Opcode.Eq, lhsTerm, rhsTerm)));
axiomExpr.Typecheck(new TypecheckingContext(null));
axioms.Add(new Axiom(Token.NoToken, axiomExpr));
}
this.mapConstBool = new Function(Token.NoToken, "linear_" + domainName + "_MapConstBool",
new List <Variable> {
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "b", Type.Bool), true)
},
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "c", mapTypeBool), false));
if (CommandLineOptions.Clo.UseArrayTheory)
{
this.mapConstBool.AddAttribute("builtin", "MapConst");
}
else
{
BoundVariable x = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", elementType));
IdentifierExpr xie = new IdentifierExpr(Token.NoToken, x);
var trueTerm = new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1),
new List <Expr> {
new NAryExpr(Token.NoToken, new FunctionCall(mapConstBool), new List <Expr> {
Expr.True
}), xie
});
var trueAxiomExpr = new ForallExpr(Token.NoToken, new List <Variable> {
x
}, trueTerm);
trueAxiomExpr.Typecheck(new TypecheckingContext(null));
axioms.Add(new Axiom(Token.NoToken, trueAxiomExpr));
var falseTerm = new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1),
new List <Expr> {
new NAryExpr(Token.NoToken, new FunctionCall(mapConstBool), new List <Expr> {
Expr.False
}), xie
});
var falseAxiomExpr = new ForallExpr(Token.NoToken, new List <Variable> {
x
}, Expr.Unary(Token.NoToken, UnaryOperator.Opcode.Not, falseTerm));
falseAxiomExpr.Typecheck(new TypecheckingContext(null));
axioms.Add(new Axiom(Token.NoToken, falseAxiomExpr));
}
this.mapEqInt = new Function(Token.NoToken, "linear_" + domainName + "_MapEq",
new List <Variable> {
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "a", mapTypeInt), true),
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "b", mapTypeInt), true)
},
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "c", mapTypeBool), false));
if (CommandLineOptions.Clo.UseArrayTheory)
{
this.mapEqInt.AddAttribute("builtin", "MapEq");
}
else
{
BoundVariable a = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "a", mapTypeInt));
IdentifierExpr aie = new IdentifierExpr(Token.NoToken, a);
BoundVariable b = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "b", mapTypeInt));
IdentifierExpr bie = new IdentifierExpr(Token.NoToken, b);
BoundVariable x = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", elementType));
IdentifierExpr xie = new IdentifierExpr(Token.NoToken, x);
var mapApplTerm = new NAryExpr(Token.NoToken, new FunctionCall(mapEqInt), new List <Expr> {
aie, bie
});
var lhsTerm = new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List <Expr> {
mapApplTerm, xie
});
var rhsTerm = Expr.Binary(BinaryOperator.Opcode.Eq,
new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List <Expr> {
aie, xie
}),
new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List <Expr> {
bie, xie
}));
var axiomExpr = new ForallExpr(Token.NoToken, new List <TypeVariable>(), new List <Variable> {
a, b
}, null,
new Trigger(Token.NoToken, true, new List <Expr> {
mapApplTerm
}),
new ForallExpr(Token.NoToken, new List <Variable> {
x
}, Expr.Binary(BinaryOperator.Opcode.Eq, lhsTerm, rhsTerm)));
axiomExpr.Typecheck(new TypecheckingContext(null));
axioms.Add(new Axiom(Token.NoToken, axiomExpr));
}
this.mapConstInt = new Function(Token.NoToken, "linear_" + domainName + "_MapConstInt",
new List <Variable> {
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "b", Type.Int), true)
},
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "c", mapTypeInt), false));
if (CommandLineOptions.Clo.UseArrayTheory)
{
this.mapConstInt.AddAttribute("builtin", "MapConst");
}
else
{
BoundVariable a = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "a", Type.Int));
IdentifierExpr aie = new IdentifierExpr(Token.NoToken, a);
BoundVariable x = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", elementType));
IdentifierExpr xie = new IdentifierExpr(Token.NoToken, x);
var lhsTerm = new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List <Expr> {
new NAryExpr(Token.NoToken, new FunctionCall(mapConstInt), new List <Expr> {
aie
}), xie
});
var axiomExpr = new ForallExpr(Token.NoToken, new List <Variable> {
a, x
}, Expr.Binary(BinaryOperator.Opcode.Eq, lhsTerm, aie));
axiomExpr.Typecheck(new TypecheckingContext(null));
axioms.Add(new Axiom(Token.NoToken, axiomExpr));
}
foreach (var axiom in axioms)
{
axiom.Expr.Resolve(new ResolutionContext(null));
axiom.Expr.Typecheck(new TypecheckingContext(null));
}
}
public Expr MakeModPow2(Expr lhs, Expr rhs)
{
return(Expr.Binary(BinaryOperator.Opcode.Mod, lhs, rhs));
}
// Parse a leaf node
// (For the moment this is just a number)
Expr ParseLeaf()
{
// Is it a number?
if (_tokenizer.Current.Token == Token.Number)
{
var node = Expr.Number(_tokenizer.Current.Number);
_tokenizer.MoveNext();
return(node);
}
// Bracket?
if (_tokenizer.Current.Token == Token.OpenBracket)
{
// array
// Skip '['
_tokenizer.MoveNext();
var elements = new List <Expr>();
while (true)
{
// Parse argument and add to list
elements.Add(ParseAddSubtract());
// Is there another argument?
if (_tokenizer.Current.Token == Token.Comma)
{
_tokenizer.MoveNext();
continue;
}
// Get out
break;
}
// Check and skip ')'
if (_tokenizer.Current.Token != Token.CloseBracket)
{
throw new SyntaxException("Missing close bracket");
}
_tokenizer.MoveNext();
return(Expr.FromArray(elements));
}
// Parenthesis?
if (_tokenizer.Current.Token == Token.OpenParens)
{
// Skip '('
_tokenizer.MoveNext();
// Parse a top-level expression
var node = ParseAddSubtract();
// Check and skip ')'
if (_tokenizer.Current.Token != Token.CloseParens)
{
throw new SyntaxException("Missing close parenthesis");
}
_tokenizer.MoveNext();
// Return
return(node);
}
// Variable
if (_tokenizer.Current.Token == Token.Identifier)
{
// Capture the name and skip it
var name = _tokenizer.Current.Identifier;
_tokenizer.MoveNext();
// Parens indicate a function call, otherwise just a variable
if (_tokenizer.Current.Token != Token.OpenParens)
{
return(Expr.VariableOrConst(name));
}
else
{
// Function call
// Skip parens
_tokenizer.MoveNext();
// Parse arguments
var arguments = new List <Expr>();
while (true)
{
// Parse argument and add to list
arguments.Add(ParseAddSubtract());
// Is there another argument?
if (_tokenizer.Current.Token == Token.Comma)
{
_tokenizer.MoveNext();
continue;
}
// Get out
break;
}
// Check and skip ')'
if (_tokenizer.Current.Token != Token.CloseParens)
{
throw new SyntaxException("Missing close parenthesis");
}
_tokenizer.MoveNext();
// Create the function call node
switch (arguments.Count)
{
case 1:
if (FindOperation(name, out UnaryOp uop))
{
return(Expr.Unary(uop, arguments[0]));
}
throw new ArgumentException($"Invalid unary function {name}");
case 2:
if (FindOperation(name, out BinaryOp bop))
{
return(Expr.Binary(bop, arguments[0], arguments[1]));
}
throw new ArgumentException($"Invalid binary function {name}");
default:
throw new SyntaxException("Invalid number of arguments");
}
}
}
// Don't Understand
throw new SyntaxException($"Unexpected token: {_tokenizer.Current.Token}");
}