public void Equation_EqGoal_Satisfy()
{
//2=2
var eq = new Equation(2, 2);
object obj;
bool result = eq.IsEqGoal(out obj);
Assert.False(result);
//3=4
eq = new Equation(3, 4);
result = eq.IsEqGoal(out obj);
Assert.False(result);
//3=5-2
var term = new Term(Expression.Add, new List<object>() { 5, -2 });
eq = new Equation(3, term);
result = eq.IsEqGoal(out obj);
Assert.False(result);
//x = x
//TODO
var variable = new Var('x');
eq = new Equation(variable, variable);
/* result = eq.IsEqGoal(out obj);
Assert.True(result);*/
//x = 2x-x
//TODO
term = new Term(Expression.Multiply, new List<object>() { 2, variable });
var term0 = new Term(Expression.Multiply, new List<object>() { -1, variable });
var term1 = new Term(Expression.Add, new List<object>() { term, term0 });
eq = new Equation(variable, term1);
/* result = eq.IsEqGoal(out obj);
Assert.True(result);*/
}
private static bool SatisfyGeneralForm(Equation equation,
out Circle circle)
{
circle = null;
var term = equation.Lhs as Term;
if (term != null && term.Op.Method.Name.Equals("Add"))
{
var lst = term.Args as List<object>;
if (lst != null && lst.Count == 3)
{
bool isNum = LogicSharp.IsNumeric(lst[2]);
if (isNum)
{
double dNum;
LogicSharp.IsDouble(lst[2], out dNum);
dNum *= -1;
object coeffX, coeffY;
bool xTerm1 = IsXSquareTerm(lst[0], out coeffX);
bool yTerm1 = IsYSquareTerm(lst[1], out coeffY);
if (xTerm1 && yTerm1)
{
var pt = new Point(coeffX, coeffY);
circle = new Circle(pt, Math.Pow(dNum, 0.5));
return true;
}
}
}
}
return false;
}
//copy constructor
public Equation(Equation eq)
{
EqLabel = eq.EqLabel;
var lhsVar = eq.Lhs as Var;
var lhsTerm = eq.Lhs as Term;
if (lhsVar != null)
{
Lhs = lhsVar.Clone();
}
else if (lhsTerm != null)
{
Lhs = lhsTerm.Clone();
}
else
{
Lhs = eq.Lhs;
}
var rhsVar = eq.Rhs as Var;
var rhsTerm = eq.Rhs as Term;
if (rhsVar != null)
{
Rhs = rhsVar.Clone();
}
else if (rhsTerm != null)
{
Rhs = rhsTerm.Clone();
}
else
{
Rhs = eq.Rhs;
}
IsGenerated = eq.IsGenerated;
}
public EqGoal(Equation eq)
: base(eq)
{
Debug.Assert(Lhs is Var);
Debug.Assert(Rhs != null);
Functor = LogicSharp.Equal()(Lhs, Rhs);
}
public void Test_Unify_3()
{
// a=2, b=a
var a = new Var("a");
var b = new Var("b");
var eqGoal = new EqGoal(a, 2);
var goalNode = new GoalNode(eqGoal);
var equation = new Equation(b, a);
object obj;
bool result = RelationLogic.ConstraintCheck(goalNode, equation, null, out obj);
Assert.True(result);
Assert.NotNull(obj);
}
public void Test_Reify_1()
{
//a = 1, a*b = -1;
//true positive
var graph = new RelationGraph();
var a = new Var("a");
var b = new Var("b");
var eqGoal = new EqGoal(a, 1);
var lhsTerm = new Term(Expression.Multiply, new List<object>() { a, b });
var equation = new Equation(lhsTerm, -1);
graph.AddNode(eqGoal);
var en = graph.AddNode(equation) as EquationNode;
Assert.NotNull(en);
Assert.True(en.Equation.CachedEntities.Count == 1);
Assert.True(graph.Nodes.Count == 3);
}
public void Test_Algebra_OneVariable_Linear_Goal_Gen_1()
{
//x = 2+3
var x = new Var('x');
var term = new Term(Expression.Add, new List<object>() { 2, 3 });
var eq = new Equation(x, term);
object obj;
bool result = eq.IsEqGoal(out obj);
Assert.True(result);
var eqGoal = obj as EqGoal;
Assert.NotNull(eqGoal);
Assert.True(eqGoal.Traces.Count == 1);
Assert.True(eqGoal.Lhs.Equals(x));
Assert.True(eqGoal.Rhs.Equals(5));
Assert.True(result);
}
/// <summary>
/// a+1=, 2+3+5=
/// </summary>
/// <param name="term"></param>
/// <param name="obj"></param>
/// <returns></returns>
public bool ConstraintSatisfy(Term term, out object obj)
{
var evalObj = term.Eval();
var generatedEq = new Equation(term, evalObj);
generatedEq.ImportTrace(term);
var evalTerm = evalObj as Term;
var evalVar = evalObj as Var;
var dict = new Dictionary<object, object>();
var connectLst = new List<GraphNode>();
if (evalTerm != null)
{
for (var i = 0; i < _nodes.Count; i++)
{
var goalNode = _nodes[i] as GoalNode;
if (goalNode != null)
{
if (evalTerm.ContainsVar((EqGoal)goalNode.Goal))
{
connectLst.Add(goalNode);
}
}
}
}
if (evalVar != null)
{
for (var i = 0; i < _nodes.Count; i++)
{
var goalNode = _nodes[i] as GoalNode;
if (goalNode != null)
{
var eqGoal = goalNode.Goal as EqGoal;
Debug.Assert(eqGoal != null);
var lhsVar = eqGoal.Lhs as Var;
Debug.Assert(lhsVar != null);
if (lhsVar.Equals(evalVar))
{
connectLst.Add(goalNode);
}
}
}
}
dict.Add(connectLst, generatedEq);
obj = dict;
return true;
}
public void Test_Arith_3()
{
//1+2+3=6
var lhs = new Term(Expression.Add, new List<object>() { 1, 2, 3 });
var equation = new Equation(lhs, 6);
bool result = equation.ContainsVar();
Assert.False(result);
Assert.True(equation.ToString().Equals("1+2+3=6"));
object outputEq;
bool? evalResult = equation.Eval(out outputEq);
Assert.NotNull(evalResult);
Assert.True(evalResult.Value);
Assert.NotNull(outputEq);
Assert.True(outputEq.ToString().Equals("6=6"));
Assert.True(equation.Traces.Count == 1);
}
public void Test_Algebra_OneVariable_Linear_1()
{
//1+2=x
var x = new Var('x');
var lhs = new Term(Expression.Add, new List<object>() { 1, 2 });
var equation = new Equation(lhs, x);
bool result = equation.ContainsVar();
Assert.True(result);
Assert.True(equation.ToString().Equals("1+2=x"));
equation.Eval();
Assert.True(equation.CachedEntities.Count == 1);
var outputEq = equation.CachedEntities.ToList()[0] as Equation;
Assert.NotNull(outputEq);
Assert.True(outputEq.ToString().Equals("x=3"));
Assert.True(outputEq.Traces.Count == 1);
}
public void Test_Unify_1()
{
//a = 1, a*b = -1;
//true positive
var a = new Var("a");
var b = new Var("b");
var eqGoal = new EqGoal(a, 1);
var lhsTerm = new Term(Expression.Multiply, new List<object>() {a, b});
var equation = new Equation(lhsTerm, -1);
var eqNode = new EquationNode(equation);
object obj;
bool result = RelationLogic.ConstraintCheck(eqNode, eqGoal, null, out obj);
Assert.True(result);
Assert.NotNull(obj);
}
/// <summary>
/// Trace from Line General Form to Slope-Intercept Form
/// ax+by+c=0 => y=mx+b
/// </summary>
/// <param name="target"></param>
/// <returns></returns>
public static void FromLineGeneralFormToSlopeIntercept(LineSymbol ls)
{
string strategy = "Given a general form line ax+by+c=0, the slope-intercept form of it is y = -(a/b)x-c/b.";
var line = ls.Shape as Line;
Debug.Assert(line != null);
var newLS = new LineSymbol(line);
newLS.OutputType = LineType.SlopeIntercept;
var x = new Var("x");
var y = new Var("y");
var xTerm = new Term(Expression.Multiply, new List<object>() { line.A, x });
var yTerm = new Term(Expression.Multiply, new List<object>() { line.B, y });
var oldEqLeft = new Term(Expression.Add, new List<object>() { xTerm, yTerm, line.C });
var oldEq = new Equation(oldEqLeft, 0);
var invertXTerm = new Term(Expression.Multiply, new List<object>() { -1, xTerm });
var intertZ = new Term(Expression.Multiply, new List<object>() { -1, line.C });
var internalRight = new Term(Expression.Add, new List<object>() { invertXTerm, intertZ });
var internalEq = new Equation(yTerm, internalRight);
var finalXTerm = new Term(Expression.Multiply, new List<object>() { line.Slope, x });
var finalRight = new Term(Expression.Add, new List<object>() { finalXTerm, line.Intercept });
var lastEq = new Equation(yTerm, finalRight);
string step1metaRule = "Given the line general form ax+by+c=0, move x term and Constant term to the right side of equation.";
string step1AppliedRule = String.Format("Move {0}x and {1} to right side of equation.", ls.SymA, ls.SymC);
string kc = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);
var ts0 = new TraceStep(null, internalEq, kc, step1metaRule, step1AppliedRule);
ls._innerLoop.Add(ts0);
string appliedRule = string.Format("divide coefficient b in both side of equation.");
kc = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Inverse);
var ts1 = new TraceStep(null, lastEq, kc, AlgebraRule.AlgebraicStrategy, appliedRule);
ls._innerLoop.Add(ts1);
ls.GenerateATrace(strategy);
}
public void Test_Arith_2()
{
//1+2=4
var lhs = new Term(Expression.Add, new List<object>() { 1, 2 });
var equation = new Equation(lhs, 4);
bool result = equation.ContainsVar();
Assert.False(result);
Assert.True(equation.ToString().Equals("1+2=4"));
object obj = equation.Eval();
Assert.NotNull(obj);
var satisfied = obj as bool?;
Assert.NotNull(satisfied);
Assert.False(satisfied.Value);
Assert.True(equation.CachedEntities.Count == 1);
var cachedEq = equation.CachedEntities.ToList()[0] as Equation;
Assert.NotNull(cachedEq);
Assert.True(cachedEq.ToString().Equals("3=4"));
Assert.True(cachedEq.Traces.Count == 1);
}
public void Test_Algebra_OneVariable_Linear_Goal_Gen_1()
{
//x = 2+3
var x = new Var('x');
var term = new Term(Expression.Add, new List <object>()
{
2, 3
});
var eq = new Equation(x, term);
object obj;
bool result = eq.IsEqGoal(out obj);
Assert.True(result);
var eqGoal = obj as EqGoal;
Assert.NotNull(eqGoal);
Assert.True(eqGoal.Traces.Count == 1);
Assert.True(eqGoal.Lhs.Equals(x));
Assert.True(eqGoal.Rhs.Equals(5));
Assert.True(result);
}
public void Test_TwoVariables_Linear_5()
{
//y=(1/3)x
var y = new Var('y');
var x = new Var('x');
var term1 = new Term(Expression.Divide, new List <object>()
{
1, 3
});
var rhs = new Term(Expression.Multiply, new List <object>()
{
term1, x
});
var eq = new Equation(y, rhs);
object obj;
bool? result = eq.EvalEquation(out obj, true, true);
Assert.Null(result);
Assert.True(obj.ToString().Equals("-x+3y=0"));
}
public void Equation_Var_Substitution_1()
{
//a = 1, a*b = -1;
var a = new Var("a");
var b = new Var("b");
var eqGoal = new EqGoal(a, 1);
var lhsTerm = new Term(Expression.Multiply, new List<object>() { a, b });
var equation = new Equation(lhsTerm, -1);
bool result = equation.Reify(eqGoal);
Assert.True(result);
Assert.True(equation.CachedEntities.Count == 1);
var cachedEq = equation.CachedEntities.ToList()[0] as Equation;
object obj;
result = cachedEq.IsEqGoal(out obj);
Assert.True(result);
var gGoal = obj as EqGoal;
Assert.NotNull(gGoal);
Assert.True(gGoal.Rhs.Equals(-1));
}
public Equation Generate(Equation currentEq, object source, object target, bool isLhs)
{
Equation cloneEq = currentEq.Clone();
if (isLhs)
{
if (!source.Equals(cloneEq.Lhs))
{
//throw new Exception("Equation.Trace.cs 1: Must be equal.");
}
cloneEq.Lhs = target;
}
else
{
if (!source.Equals(cloneEq.Rhs))
{
//throw new Exception("Equation.Trace.cs 2: Must be equal.");
}
cloneEq.Rhs = target;
}
return cloneEq;
}
public void Goal_Gen_12()
{
//-1*v = 2
var v = new Var('v');
var term = new Term(Expression.Multiply, new List <object>()
{
-1, v
});
var eq = new Equation(term, 2);
object obj;
bool result = eq.IsEqGoal(out obj);
Assert.True(result);
var gGoal = obj as EqGoal;
Assert.NotNull(gGoal);
Assert.True(gGoal.Rhs.Equals(-2));
Assert.True(gGoal.Traces.Count == 1);
}
public void Equation_Var_Substitution_2()
{
//14: a = 2, b=a
var a = new Var("a");
var b = new Var("b");
var eqGoal = new EqGoal(a, 2);
var equation = new Equation(b, a);
bool result = equation.Reify(eqGoal);
Assert.True(result);
Assert.True(equation.CachedEntities.Count == 1);
var cachedEq = equation.CachedEntities.ToList()[0] as Equation;
object obj;
result = cachedEq.IsEqGoal(out obj);
Assert.True(result);
var gGoal = obj as EqGoal;
Assert.NotNull(gGoal);
Assert.True(gGoal.Lhs.Equals(b));
Assert.True(gGoal.Rhs.Equals(2));
}
public Equation Generate(Equation currentEq, object source, object target, bool isLhs)
{
Equation cloneEq = currentEq.Clone();
if (isLhs)
{
if (!source.Equals(cloneEq.Lhs))
{
//throw new Exception("Equation.Trace.cs 1: Must be equal.");
}
cloneEq.Lhs = target;
}
else
{
if (!source.Equals(cloneEq.Rhs))
{
//throw new Exception("Equation.Trace.cs 2: Must be equal.");
}
cloneEq.Rhs = target;
}
return(cloneEq);
}
public void Test_Arith_4()
{
//1*2*3=7
var lhs = new Term(Expression.Multiply, new List <object>()
{
1, 2, 3
});
var equation = new Equation(lhs, 7);
bool result = equation.ContainsVar();
Assert.False(result);
//Assert.True(equation.ToString().Equals("2*3=7"));
object outputEq;
bool? evalResult = equation.Eval(out outputEq);
Assert.NotNull(evalResult);
Assert.False(evalResult.Value);
Assert.NotNull(outputEq);
Assert.True(outputEq.ToString().Equals("6=7"));
Assert.True(equation.Traces.Count == 1);
}
public void Test_Arith_3()
{
//1+2+3=6
var lhs = new Term(Expression.Add, new List <object>()
{
1, 2, 3
});
var equation = new Equation(lhs, 6);
bool result = equation.ContainsVar();
Assert.False(result);
Assert.True(equation.ToString().Equals("1+2+3=6"));
object outputEq;
bool? evalResult = equation.Eval(out outputEq);
Assert.NotNull(evalResult);
Assert.True(evalResult.Value);
Assert.NotNull(outputEq);
Assert.True(outputEq.ToString().Equals("6=6"));
Assert.True(equation.Traces.Count == 1);
}
public void Test_Algebra_OneVariable_Linear_1()
{
//1+2=x
var x = new Var('x');
var lhs = new Term(Expression.Add, new List <object>()
{
1, 2
});
var equation = new Equation(lhs, x);
bool result = equation.ContainsVar();
Assert.True(result);
Assert.True(equation.ToString().Equals("1+2=x"));
equation.Eval();
Assert.True(equation.CachedEntities.Count == 1);
var outputEq = equation.CachedEntities.ToList()[0] as Equation;
Assert.NotNull(outputEq);
Assert.True(outputEq.ToString().Equals("x=3"));
Assert.True(outputEq.Traces.Count == 1);
}
public void Test_TwoVariables_Linear_2()
{
//25: -2x+3y+9=0
var x = new Var('x');
var term1 = new Term(Expression.Multiply, new List <object>()
{
-2, x
});
var y = new Var('y');
var term2 = new Term(Expression.Multiply, new List <object>()
{
3, y
});
var lhs = new Term(Expression.Add, new List <object>()
{
term1, term2, 9
});
var eq = new Equation(lhs, 0);
object obj;
bool? result = eq.EvalEquation(out obj, true, true);
Assert.Null(result);
}
public Equation FindCurrentEq(Equation rootEq)
{
Equation currentEq;
if (rootEq._innerLoop.Count != 0)
{
currentEq = rootEq._innerLoop[rootEq._innerLoop.Count - 1].Target as Equation;
if (currentEq == null) throw new Exception("Must be equation here");
}
else
{
if (rootEq.Traces.Count == 0)
{
currentEq = rootEq;
}
else
{
var lastTrace = rootEq.Traces[rootEq.Traces.Count - 1].Item2 as List<TraceStep>;
Debug.Assert(lastTrace != null);
currentEq = lastTrace[lastTrace.Count - 1].Target as Equation;
}
}
return currentEq;
}
//copy constructor
public Equation(Equation eq)
{
EqLabel = eq.EqLabel;
var lhsVar = eq.Lhs as Var;
var lhsTerm = eq.Lhs as Term;
if (lhsVar != null)
{
Lhs = lhsVar.Clone();
}
else if (lhsTerm != null)
{
Lhs = lhsTerm.Clone();
}
else
{
Lhs = eq.Lhs;
}
var rhsVar = eq.Rhs as Var;
var rhsTerm = eq.Rhs as Term;
if (rhsVar != null)
{
Rhs = rhsVar.Clone();
}
else if (rhsTerm != null)
{
Rhs = rhsTerm.Clone();
}
else
{
Rhs = eq.Rhs;
}
IsGenerated = eq.IsGenerated;
}
public void Test_TwoVariables_Linear_3()
{
//25: 3y=2x-9
var y = new Var('y');
var lhs = new Term(Expression.Multiply, new List <object>()
{
3, y
});
var x = new Var('x');
var term1 = new Term(Expression.Multiply, new List <object>()
{
2, x
});
var rhs = new Term(Expression.Add, new List <object>()
{
term1, -9
});
var eq = new Equation(lhs, rhs);
object obj;
bool? result = eq.EvalEquation(out obj, true, true);
Assert.Null(result);
Assert.True(obj.ToString().Equals("-2x+3y+9=0"));
}
/// <summary>
/// if x = y, then y = x
/// </summary>
/// <param name="currentEq"></param>
/// <param name="rootEq"></param>
/// <returns></returns>
public static Equation ApplySymmetric(this Equation currentEq, Equation rootEq)
{
Equation localEq = currentEq;
object lhs = currentEq.Lhs;
object rhs = currentEq.Rhs;
if (SatisfySymmetricCondition(lhs, rhs))
{
var cloneEq = currentEq.Clone();
object tempObj = cloneEq.Lhs;
cloneEq.Lhs = cloneEq.Rhs;
cloneEq.Rhs = tempObj;
string rule = EquationsRule.Rule(EquationsRule.EquationRuleType.Symmetric);
string appliedRule = EquationsRule.Rule(
EquationsRule.EquationRuleType.Symmetric,
localEq, null);
string KC = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Symmetric);
var ts = new TraceStep(localEq, cloneEq, KC, rule, appliedRule);
rootEq._innerLoop.Add(ts);
localEq = cloneEq;
}
return localEq;
}
public void Test_TwoVariables_Linear_5()
{
//y=(1/3)x
var y = new Var('y');
var x = new Var('x');
var term1 = new Term(Expression.Divide, new List<object>() { 1, 3 });
var rhs = new Term(Expression.Multiply, new List<object>() {term1, x});
var eq = new Equation(y, rhs);
object obj;
bool? result = eq.EvalEquation(out obj, true, true);
Assert.Null(result);
Assert.True(obj.ToString().Equals("-x+3y=0"));
}
public void Test_TwoVariables_Linear_3()
{
//25: 3y=2x-9
var y = new Var('y');
var lhs = new Term(Expression.Multiply, new List<object>() {3, y});
var x = new Var('x');
var term1 = new Term(Expression.Multiply, new List<object>() {2, x});
var rhs = new Term(Expression.Add, new List<object>() {term1, -9});
var eq = new Equation(lhs, rhs);
object obj;
bool? result = eq.EvalEquation(out obj, true, true);
Assert.Null(result);
Assert.True(obj.ToString().Equals("-2x+3y+9=0"));
}
public void Test_TwoVariables_Linear_2()
{
//25: -2x+3y+9=0
var x = new Var('x');
var term1 = new Term(Expression.Multiply, new List<object>() { -2, x });
var y = new Var('y');
var term2 = new Term(Expression.Multiply, new List<object>() { 3, y });
var lhs = new Term(Expression.Add, new List<object>() { term1, term2, 9 });
var eq = new Equation(lhs, 0);
object obj;
bool? result = eq.EvalEquation(out obj, true, true);
Assert.Null(result);
}
private Equation EvalTermInEquation(Equation rootEq, bool isLhs)
{
Equation localEq = this;
object obj = isLhs ? Lhs : Rhs;
var term = obj as Term;
if (term == null)
{
return(localEq);
}
object evalResult = term.Eval();
if (evalResult.Equals(term))
{
return(localEq);
}
var cloneEq = Clone();
if (isLhs)
{
cloneEq.Lhs = evalResult;
}
else
{
cloneEq.Rhs = evalResult;
}
Equation currentEq = FindCurrentEq(rootEq);
#region Trace Transformation from term to Equation
if (term.Traces.Count != 0)
{
localEq = currentEq;
foreach (var trace in term.Traces)
{
var strategy = trace.Item1 as string;
var lst = trace.Item2 as List <TraceStep>;
foreach (var ts in lst)
{
var cloneEq2 = Generate(currentEq, ts.Source, ts.Target, isLhs);
var eqTraceStep = new TraceStep(localEq, cloneEq2, ts.KC, ts.Rule, ts.AppliedRule);
rootEq._innerLoop.Add(eqTraceStep);
localEq = cloneEq2;
}
//GenerateATrace(strategy);
}
}
if (term._innerLoop.Count != 0)
{
foreach (var ts in term._innerLoop)
{
var cloneEq1 = Generate(currentEq, ts.Source, ts.Target, isLhs);
var eqTraceStep = new TraceStep(localEq, cloneEq1, ts.KC, ts.Rule, ts.AppliedRule);
rootEq._innerLoop.Add(eqTraceStep);
localEq = cloneEq1;
}
}
#endregion
return(cloneEq);
}
private bool? EquationLaws(Equation rootEq, bool withEqRule, out object outputEq,
bool lineCheck = false)
{
/* Equation currentEq;
if (Traces.Count == 0)
{
currentEq = this;
}
else
{
var tuple = Traces[Traces.Count - 1];
var lst = tuple.Item2 as List<TraceStep>;
Debug.Assert(lst != null);
currentEq = lst[lst.Count - 1].Target as Equation;
}*/
Equation currentEq = FindCurrentEq(rootEq);
outputEq = currentEq;
Debug.Assert(currentEq != null);
bool hasChange;
do
{
hasChange = false;
Equation localEq00 = currentEq.EvalTermInEquation(rootEq, true);
if (!localEq00.Equals(currentEq))
{
hasChange = true;
currentEq = localEq00;
}
Equation localEq0 = currentEq.EvalTermInEquation(rootEq, false);
if (!localEq0.Equals(currentEq))
{
hasChange = true;
currentEq = localEq0;
}
bool? satisfiable = Satisfy(currentEq);
if (satisfiable != null)
{
if (rootEq._innerLoop.Count != 0)
{
rootEq.GenerateATrace(EquationsRule.EqStrategy);
}
outputEq = currentEq;
return satisfiable.Value;
}
var localEq000 = currentEq.ApplyTransitive2(rootEq, withEqRule, lineCheck);
if (!localEq000.Equals(currentEq))
{
hasChange = true;
currentEq = localEq000 as Equation;
}
var localObj1 = currentEq.ApplyTransitive(rootEq, withEqRule, lineCheck);
var localEq1 = localObj1 as Equation;
var localEqLst = localObj1 as List<Equation>;
if (localEqLst != null)
{
if (rootEq._innerLoop.Count != 0)
{
rootEq.GenerateATrace(EquationsRule.EqStrategy);
}
outputEq = localEqLst;
return null;
}
if (localEq1 != null && !localEq1.Equals(currentEq))
{
hasChange = true;
currentEq = localEq1;
}
var localEq2 = localEq1.ApplySymmetric(rootEq);
if (!localEq2.Equals(localEq1))
{
hasChange = true;
currentEq = localEq2;
}
} while (hasChange);
if (rootEq._innerLoop.Count != 0)
{
rootEq.GenerateATrace(EquationsRule.EqStrategy);
}
outputEq = currentEq;
return null;
}
public void Goal_Gen_3()
{
//x=(-1)*0
var x = new Var('x');
var term = new Term(Expression.Multiply, new List<object>() { -1, 0 });
var eq = new Equation(x, term);
object obj;
bool result = eq.IsEqGoal(out obj);
Assert.True(result);
var goal = obj as EqGoal;
Assert.NotNull(goal);
Assert.True(goal.Rhs.Equals(0));
}
/// <summary>
/// if x = y and y = z, then x = z
/// if x = y, then x + a = y + a
/// if x^2 = y^2, then x = y
/// if x = y, then ax = ay
/// ax = ay -> x=y
/// </summary>
/// <param name="goal"></param>
/// <param name="gGoal"></param>
/// <returns></returns>
public static object ApplyTransitive(this Equation currentEq, Equation rootEq, bool withEqRule,
bool lineCheck = false)
{
Equation localEq = currentEq;
object lhs = currentEq.Lhs;
object rhs = currentEq.Rhs;
if (!withEqRule)
{
return(localEq);
}
//Power Inverse
if (SatisfyTransitiveCondition2(lhs, rhs))
{
#region Condition2
var cloneEq = currentEq.Clone();
var cloneEq2 = currentEq.Clone();
var lhsTerm = cloneEq.Lhs as Term;
Debug.Assert(lhsTerm != null);
var cloneLst = lhsTerm.Args as List <object>;
Debug.Assert(cloneLst != null);
cloneEq.Lhs = cloneLst[0];
cloneEq.Rhs = new Term(Expression.Power, new List <object>()
{
cloneEq.Rhs, 0.5
});
var lhsTerm2 = cloneEq2.Lhs as Term;
Debug.Assert(lhsTerm2 != null);
var cloneLst2 = lhsTerm2.Args as List <object>;
Debug.Assert(cloneLst2 != null);
cloneEq2.Lhs = cloneLst2[0];
var internal1 = new Term(Expression.Power, new List <object>()
{
cloneEq2.Rhs, 0.5
});
cloneEq2.Rhs = new Term(Expression.Multiply, new List <object>()
{
-1, internal1
});
string rule = EquationsRule.Rule(EquationsRule.EquationRuleType.Transitive);
string appliedRule = EquationsRule.Rule(
EquationsRule.EquationRuleType.Transitive,
localEq, null);
string KC = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);
var ts = new TraceStep(localEq, cloneEq, KC, rule, appliedRule);
rootEq._innerLoop.Add(ts);
//localEq = cloneEq;
var lst = new List <Equation>();
lst.Add(cloneEq);
lst.Add(cloneEq2);
return(lst);
#endregion
}
if (!lineCheck)
{
//Add Inverse
if (SatifyTransitiveCondition0(lhs, rhs))
{
#region condition0
var cloneEq = currentEq.Clone();
var rhsTerm = new Term(Expression.Add, new List <object>()
{
cloneEq.Rhs
});
var lhsTerm = cloneEq.Lhs as Term;
Debug.Assert(lhsTerm != null);
var lst = lhsTerm.Args as List <object>;
Debug.Assert(lst != null);
for (int i = 0; i < lst.Count; i++)
{
var temp = lst[i];
bool isNumber = LogicSharp.IsNumeric(temp);
if (isNumber)
{
var inverseRhs = new Term(Expression.Multiply, new List <object>()
{
-1, temp
});
lst.Remove(temp);
var rhsArgLst = rhsTerm.Args as List <object>;
Debug.Assert(rhsArgLst != null);
rhsArgLst.Add(inverseRhs);
break;
}
var term = temp as Term;
if (term != null && !term.ContainsVar())
{
var inverseRhs = new Term(Expression.Multiply, new List <object>()
{
-1, temp
});
lst.Remove(i);
var rhsArgLst = rhsTerm.Args as List <object>;
Debug.Assert(rhsArgLst != null);
rhsArgLst.Add(inverseRhs);
break;
}
}
cloneEq.Rhs = rhsTerm;
if (lst.Count == 1)
{
cloneEq.Lhs = lst[0];
}
string rule = EquationsRule.Rule(EquationsRule.EquationRuleType.Transitive);
string appliedRule = EquationsRule.Rule(
EquationsRule.EquationRuleType.Transitive,
localEq, null);
string KC = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);
var traceStep = new TraceStep(localEq, cloneEq, KC, rule, appliedRule);
rootEq._innerLoop.Add(traceStep);
localEq = cloneEq;
return(localEq);
#endregion
}
}
else
{
if (SatisfyTransitiveCondition1(lhs, rhs))
{
#region Condition1
var cloneEq = currentEq.Clone();
var inverseRhs = new Term(Expression.Multiply, new List <object>()
{
-1, rhs
});
var lhsTerm = cloneEq.Lhs as Term;
if (lhsTerm != null)
{
var cloneLst = lhsTerm.Args as List <object>;
Debug.Assert(cloneLst != null);
if (lhsTerm.Op.Method.Name.Equals("Add"))
{
cloneLst.Add(inverseRhs);
}
else
{
cloneEq.Lhs = new Term(Expression.Add, new List <object>()
{
lhs, inverseRhs
});
}
}
else
{
cloneEq.Lhs = new Term(Expression.Add, new List <object>()
{
lhs, inverseRhs
});
}
cloneEq.Rhs = 0;
string rule = EquationsRule.Rule(EquationsRule.EquationRuleType.Transitive);
string appliedRule = EquationsRule.Rule(
EquationsRule.EquationRuleType.Transitive,
localEq, null);
string KC = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);
var traceStep = new TraceStep(localEq, cloneEq, KC, rule, appliedRule);
rootEq._innerLoop.Add(traceStep);
localEq = cloneEq;
#endregion
}
}
//Mutliply Inverse
if (SatisfyTransitiveCondition3(lhs, rhs))
{
#region condition3
var cloneEq = currentEq.Clone();
var rhsTerm = new Term(Expression.Multiply, new List <object>()
{
cloneEq.Rhs
});
var lhsTerm = cloneEq.Lhs as Term;
Debug.Assert(lhsTerm != null);
var lst = lhsTerm.Args as List <object>;
Debug.Assert(lst != null);
for (int i = 0; i < lst.Count; i++)
{
var temp = lst[i];
bool isNumber = LogicSharp.IsNumeric(temp);
if (isNumber)
{
var inverseRhs = new Term(Expression.Divide, new List <object>()
{
1, temp
});
lst.Remove(temp);
var rhsArgLst = rhsTerm.Args as List <object>;
Debug.Assert(rhsArgLst != null);
rhsArgLst.Add(inverseRhs);
break;
}
var term = temp as Term;
if (term != null && !term.ContainsVar())
{
var inverseRhs = new Term(Expression.Divide, new List <object>()
{
1, temp
});
lst.Remove(i);
var rhsArgLst = rhsTerm.Args as List <object>;
Debug.Assert(rhsArgLst != null);
rhsArgLst.Add(inverseRhs);
break;
}
}
cloneEq.Rhs = rhsTerm;
if (lst.Count == 1)
{
cloneEq.Lhs = lst[0];
}
string rule = EquationsRule.Rule(EquationsRule.EquationRuleType.Transitive);
string appliedRule = EquationsRule.Rule(
EquationsRule.EquationRuleType.Transitive,
localEq, null);
string KC = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);
var traceStep = new TraceStep(localEq, cloneEq, KC, rule, appliedRule);
rootEq._innerLoop.Add(traceStep);
localEq = cloneEq;
return(localEq);
#endregion
}
//Divide Inverse
if (SatisfyTransitiveCondition4(lhs, rhs))
{
#region condition4
var cloneEq = currentEq.Clone();
var lhsTerm = cloneEq.Lhs as Term;
Debug.Assert(lhsTerm != null);
var lst = lhsTerm.Args as List <object>;
Debug.Assert(lst != null);
Debug.Assert(lst.Count == 2);
bool numerator = LogicSharp.IsNumeric(lst[0]);
bool deNumerator = LogicSharp.IsNumeric(lst[1]);
if (deNumerator)
{
var rhsTerm = new Term(Expression.Multiply, new List <object>()
{
lst[1], cloneEq.Rhs
});
var newEq = new Equation(lst[0], rhsTerm);
string rule = EquationsRule.Rule(EquationsRule.EquationRuleType.Transitive);
string appliedRule = EquationsRule.Rule(
EquationsRule.EquationRuleType.Transitive,
localEq, newEq);
string KC = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);
var traceStep = new TraceStep(localEq, newEq, KC, rule, appliedRule);
rootEq._innerLoop.Add(traceStep);
localEq = newEq;
return(localEq);
}
if (numerator)
{
var rhsTerm = new Term(Expression.Divide, new List <object>()
{
lst[0], cloneEq.Rhs
});
var newEq = new Equation(lst[1], rhsTerm);
string rule = EquationsRule.Rule(EquationsRule.EquationRuleType.Transitive);
string appliedRule = EquationsRule.Rule(
EquationsRule.EquationRuleType.Transitive,
localEq, newEq);
string KC = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);
var traceStep = new TraceStep(localEq, newEq, KC, rule, appliedRule);
rootEq._innerLoop.Add(traceStep);
localEq = newEq;
return(localEq);
}
#endregion
}
return(localEq);
}
public void Goal_Gen_6()
{
// d^2 = (1.0-4.0)^2+(2.0-6.0)^2
// d>0
object pt1XCoord = 1.0;
object pt1YCoord = 2.0;
object pt2XCoord = 4.0;
object pt2YCoord = 6.0;
var variable = new Var('d');
var lhs = new Term(Expression.Power, new List<object>() { variable, 2.0 });
var term1 = new Term(Expression.Subtract, new List<object>() { pt1XCoord, pt2XCoord });
var term11 = new Term(Expression.Power, new List<object>() { term1, 2.0 });
var term2 = new Term(Expression.Subtract, new List<object>() { pt1YCoord, pt2YCoord });
var term22 = new Term(Expression.Power, new List<object>() { term2, 2.0 });
var rhs = new Term(Expression.Add, new List<object>() { term11, term22 });
//var obj = rhs.Eval();
//Assert.True(obj.Equals(25));
var eq = new Equation(lhs, rhs);
object obj;
bool result = eq.IsEqGoal(out obj);
Assert.True(result);
var lst = obj as List<object>;
Assert.NotNull(lst);
Assert.True(lst.Count == 2);
//Trace Verify
var gGoal = lst[0] as EqGoal;
Assert.NotNull(gGoal);
Assert.True(gGoal.Traces.Count == 1);
var steps = gGoal.Traces[0].Item2 as List<TraceStep>;
Assert.NotNull(steps);
Assert.True(steps.Count == 7);
var lastStep = steps[6];
Assert.NotNull(lastStep);
}
public Query(Equation eq)
: base(eq)
{
}
private bool?EquationLaws(Equation rootEq, bool withEqRule, out object outputEq,
bool lineCheck = false)
{
/* Equation currentEq;
* if (Traces.Count == 0)
* {
* currentEq = this;
* }
* else
* {
* var tuple = Traces[Traces.Count - 1];
* var lst = tuple.Item2 as List<TraceStep>;
* Debug.Assert(lst != null);
* currentEq = lst[lst.Count - 1].Target as Equation;
* }*/
Equation currentEq = FindCurrentEq(rootEq);
outputEq = currentEq;
Debug.Assert(currentEq != null);
bool hasChange;
do
{
hasChange = false;
Equation localEq00 = currentEq.EvalTermInEquation(rootEq, true);
if (!localEq00.Equals(currentEq))
{
hasChange = true;
currentEq = localEq00;
}
Equation localEq0 = currentEq.EvalTermInEquation(rootEq, false);
if (!localEq0.Equals(currentEq))
{
hasChange = true;
currentEq = localEq0;
}
bool?satisfiable = Satisfy(currentEq);
if (satisfiable != null)
{
if (rootEq._innerLoop.Count != 0)
{
rootEq.GenerateATrace(EquationsRule.EqStrategy);
}
outputEq = currentEq;
return(satisfiable.Value);
}
var localEq000 = currentEq.ApplyTransitive2(rootEq, withEqRule, lineCheck);
if (!localEq000.Equals(currentEq))
{
hasChange = true;
currentEq = localEq000 as Equation;
}
var localObj1 = currentEq.ApplyTransitive(rootEq, withEqRule, lineCheck);
var localEq1 = localObj1 as Equation;
var localEqLst = localObj1 as List <Equation>;
if (localEqLst != null)
{
if (rootEq._innerLoop.Count != 0)
{
rootEq.GenerateATrace(EquationsRule.EqStrategy);
}
outputEq = localEqLst;
return(null);
}
if (localEq1 != null && !localEq1.Equals(currentEq))
{
hasChange = true;
currentEq = localEq1;
}
var localEq2 = localEq1.ApplySymmetric(rootEq);
if (!localEq2.Equals(localEq1))
{
hasChange = true;
currentEq = localEq2;
}
} while (hasChange);
if (rootEq._innerLoop.Count != 0)
{
rootEq.GenerateATrace(EquationsRule.EqStrategy);
}
outputEq = currentEq;
return(null);
}
public void Test_Algebra_TwoVariables_Quadratic_1()
{
//a^2+b^2=25
object pt1XCoord = new Var("a");
object pt2XCoord = new Var('b');
//var term1 = new Term(Expression.Add, new List<object>() { pt1XCoord, pt2XCoord });
var term11 = new Term(Expression.Power, new List<object>() { pt1XCoord, 2.0 });
//var term2 = new Term(Expression.Add, new List<object>() { pt1YCoord, pt2YCoord });
var term22 = new Term(Expression.Power, new List<object>() { pt2XCoord, 2.0 });
var rhs = new Term(Expression.Add, new List<object>() { term11, term22 });
var eq = new Equation(rhs, 25);
eq.Eval();
Assert.True(eq.CachedEntities.Count == 1);
var outputEq = eq.CachedEntities.ToList()[0];
Assert.True(outputEq.Equals(eq));
}
public void Goal_Gen_7()
{
//a^2 = 25
// 25 = (a-3.0)^2+(6.0-3.0)^2
object pt1XCoord = new Var("a");
object pt1YCoord = 6.0;
object pt2XCoord = -3.0;
object pt2YCoord = -3.0;
var term1 = new Term(Expression.Add, new List<object>() { pt1XCoord, pt2XCoord });
var term11 = new Term(Expression.Power, new List<object>() { term1, 2.0 });
var term2 = new Term(Expression.Add, new List<object>() { pt1YCoord, pt2YCoord });
var term22 = new Term(Expression.Power, new List<object>() { term2, 2.0 });
var rhs = new Term(Expression.Add, new List<object>() { term11, term22 });
var eq = new Equation(rhs, 25);
object obj;
bool result = eq.IsEqGoal(out obj);
Assert.True(result);
var lst = obj as List<object>;
Assert.NotNull(lst);
Assert.True(lst.Count == 2);
var gGoal1 = lst[0] as EqGoal;
Assert.NotNull(gGoal1);
Assert.True(gGoal1.Traces.Count == 1);
}
public void Goal_Gen_6()
{
// d^2 = (1.0-4.0)^2+(2.0-6.0)^2
// d>0
object pt1XCoord = 1.0;
object pt1YCoord = 2.0;
object pt2XCoord = 4.0;
object pt2YCoord = 6.0;
var variable = new Var('d');
var lhs = new Term(Expression.Power, new List <object>()
{
variable, 2.0
});
var term1 = new Term(Expression.Subtract, new List <object>()
{
pt1XCoord, pt2XCoord
});
var term11 = new Term(Expression.Power, new List <object>()
{
term1, 2.0
});
var term2 = new Term(Expression.Subtract, new List <object>()
{
pt1YCoord, pt2YCoord
});
var term22 = new Term(Expression.Power, new List <object>()
{
term2, 2.0
});
var rhs = new Term(Expression.Add, new List <object>()
{
term11, term22
});
//var obj = rhs.Eval();
//Assert.True(obj.Equals(25));
var eq = new Equation(lhs, rhs);
object obj;
bool result = eq.IsEqGoal(out obj);
Assert.True(result);
var lst = obj as List <object>;
Assert.NotNull(lst);
Assert.True(lst.Count == 2);
//Trace Verify
var gGoal = lst[0] as EqGoal;
Assert.NotNull(gGoal);
Assert.True(gGoal.Traces.Count == 1);
var steps = gGoal.Traces[0].Item2 as List <TraceStep>;
Assert.NotNull(steps);
Assert.True(steps.Count == 7);
var lastStep = steps[6];
Assert.NotNull(lastStep);
}
public void Goal_Gen_8()
{
double value = 5.0d;
var v = new Var("v");
var term1_1 = new Term(Expression.Multiply, new List<object>() { -1, 5.0 });
var term1 = new Term(Expression.Add, new List<object>() { 2.0, term1_1 });
var term11 = new Term(Expression.Power, new List<object>() { term1, 2.0 });
var term2_2 = new Term(Expression.Multiply, new List<object>() { -1, v });
var term2 = new Term(Expression.Add, new List<object>() { 4, term2_2 });
var term22 = new Term(Expression.Power, new List<object>() { term2, 2.0 });
var rhs = new Term(Expression.Add, new List<object>() { term11, term22 });
var lhs = new Term(Expression.Power, new List<object>() { value, 2.0 });
var eq = new Equation(lhs, rhs);
object obj;
bool result = eq.IsEqGoal(out obj);
Assert.True(result);
var lst = obj as List<object>;
Assert.NotNull(lst);
Assert.True(lst.Count == 2);
}
private Equation EvalTermInEquation(Equation rootEq, bool isLhs)
{
Equation localEq = this;
object obj = isLhs ? Lhs : Rhs;
var term = obj as Term;
if (term == null) return localEq;
object evalResult = term.Eval();
if (evalResult.Equals(term)) return localEq;
var cloneEq = Clone();
if (isLhs)
{
cloneEq.Lhs = evalResult;
}
else
{
cloneEq.Rhs = evalResult;
}
Equation currentEq = FindCurrentEq(rootEq);
#region Trace Transformation from term to Equation
if (term.Traces.Count != 0)
{
localEq = currentEq;
foreach (var trace in term.Traces)
{
var strategy = trace.Item1 as string;
var lst = trace.Item2 as List<TraceStep>;
foreach (var ts in lst)
{
var cloneEq2 = Generate(currentEq, ts.Source, ts.Target, isLhs);
var eqTraceStep = new TraceStep(localEq, cloneEq2, ts.KC, ts.Rule, ts.AppliedRule);
rootEq._innerLoop.Add(eqTraceStep);
localEq = cloneEq2;
}
//GenerateATrace(strategy);
}
}
if (term._innerLoop.Count != 0)
{
foreach (var ts in term._innerLoop)
{
var cloneEq1 = Generate(currentEq, ts.Source, ts.Target, isLhs);
var eqTraceStep = new TraceStep(localEq, cloneEq1, ts.KC, ts.Rule, ts.AppliedRule);
rootEq._innerLoop.Add(eqTraceStep);
localEq = cloneEq1;
}
}
#endregion
return cloneEq;
}
public void Goal_Gen_9()
{
double value = 5.0d;
var v = new Var("v");
var term1_1 = new Term(Expression.Multiply, new List<object>() { -1, 5.0 });
var term1 = new Term(Expression.Subtract, new List<object>() { 2.0, 5.0 });
var term11 = new Term(Expression.Power, new List<object>() { term1, 2.0 });
var term2_2 = new Term(Expression.Multiply, new List<object>() { -1, v });
var term2 = new Term(Expression.Subtract, new List<object>() { 4, v });
var term22 = new Term(Expression.Power, new List<object>() { term2, 2.0 });
var rhs = new Term(Expression.Add, new List<object>() { term11, term22 });
var lhs = new Term(Expression.Power, new List<object>() { value, 2.0 });
var eq = new Equation(lhs, rhs);
object obj;
bool result = eq.IsEqGoal(out obj);
Assert.False(result);
//do not use substract when dealing with variable. use add instead.
}
/// <summary>
/// The Reflexive Property states that for every real number x, x = x.
/// </summary>
/// <param name="equation"></param>
/// <returns>True: Satisfy, False: Un-satisfy, null: </returns>
private bool? Satisfy(Equation equation)
{
bool lhsNumeric = LogicSharp.IsNumeric(equation.Lhs);
bool rhsNumeric = LogicSharp.IsNumeric(equation.Rhs);
if (lhsNumeric && rhsNumeric)
{
return equation.Lhs.Equals(equation.Rhs);
}
var leftVar = equation.Lhs as Var;
var rightVar = equation.Rhs as Var;
if (leftVar != null && rightVar != null)
{
bool result = leftVar.Equals(rightVar);
if (result) return true;
return null;
}
/* var leftTerm = equation.Lhs as Term;
var rightTerm = equation.Rhs as Term;
if (leftTerm != null && rightTerm != null)
{
return leftTerm.Equals(rightTerm);
}*/
return null;
}
public void Test_TwoVariables_Linear_1()
{
//2x+3y-1=0
var x = new Var("x");
var term1 = new Term(Expression.Multiply, new List<object>() { 2, x });
var y = new Var("y");
var term2 = new Term(Expression.Multiply, new List<object>() { 3, y });
var term = new Term(Expression.Add, new List<object>() { term1, term2, -1 });
var equation = new Equation(term, 0);
object obj;
bool? result = equation.Eval(out obj, false);
Assert.Null(result);
var outputEq = obj as Equation;
Assert.NotNull(outputEq);
Assert.True(outputEq.Equals(equation));
result = equation.Eval(out obj, true);
Assert.Null(result);
outputEq = obj as Equation;
Assert.NotNull(outputEq);
Assert.False(outputEq.Equals(equation));
Assert.True(outputEq.ToString().Equals("2x+3y=1"));
}
/// <summary>
/// Inverse Properties
/// 1. For any number a, there exists a number x such that a+x=0.
/// 2. If a is any number except 0, there exists a number x such that ax = 1.
/// </summary>
/// <param name="currentEq"></param>
/// <param name="rootEq"></param>
/// <returns></returns>
public static bool ApplyInverse(this Equation currentEq, Equation rootEq)
{
return(false);
}
protected Shape(Equation equation) : base(equation)
{
Coordinate = CoordinateSystemType.Cartesian;
Repr = RepresentationType.Explicit;
}
