/*
* Annotated scaffolding
*
*/
public static void FromPointsToLineSegment(LineSegmentSymbol lss)
{
var ls = lss.Shape as LineSegment;
Debug.Assert(ls != null);
var pt1Symbol = new PointSymbol(ls.Pt1);
var pt2Symbol = new PointSymbol(ls.Pt2);
string strategy;
TraceStep ts00 = new TraceStep(null, pt1Symbol, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(pt1Symbol));
TraceStep ts01 = new TraceStep(null, pt2Symbol, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(pt2Symbol));
TraceStep ts02 = null;
if (ls.Pt1.Concrete && ls.Pt2.Concrete)
{
ts02 = new TraceStep(null, lss, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(lss));
}
strategy = "Plot a Line Segment passing through two points.";
lss._innerLoop.Add(ts00);
lss._innerLoop.Add(ts01);
if (ts02 != null)
{
lss._innerLoop.Add(ts02);
}
lss.GenerateATrace(strategy);
/* string stepMetaRule = "Consider draw a line segment passing through the two points.";
string stepAppliedRule = String.Format("Draw the line segment passing through two points {0} and {1}",
pt1Symbol, pt2Symbol);
var traceStep = new TraceStep(null, lss, stepMetaRule, stepAppliedRule);
lss._innerLoop.Add(traceStep);*/
}
public void Test_OneStrategy_MultiTraceStep_Author()
{
var expr1 = new Term(Expression.Add, new List <object> {
1, 1, 1
});
var expr2 = new Term(Expression.Add, new List <object> {
2, 1
});
var ts1 = new TraceStep(expr1, expr2, null, "meta-rule todo", "rule todo");
var ts1Expr = new TraceStepExpr(ts1);
var ts2 = new TraceStep(expr2, 2, null, "meta-rule todo", "rule todo");
var ts2Expr = new TraceStepExpr(ts2);
var lst = new List <TraceStepExpr>()
{
ts1Expr, ts2Expr
};
var tuple = new Tuple <object, object>("strategy2", lst);
var lstStrategy = new List <Tuple <object, object> >();
lstStrategy.Add(tuple);
var graph = new BehaviorGraph();
graph.Insert(lstStrategy);
Assert.True(graph.Nodes.Count == 2);
var node0 = graph.Nodes[0];
Assert.Null(node0.SubGraph);
var node1 = graph.Nodes[1];
Assert.NotNull(node1.SubGraph);
Assert.True(node1.SubGraph.Nodes.Count == 3);
/////////////////////////////////////////////
// User Input, //2 steps trace
var expr3 = new Term(Expression.Add, new List <object> {
1, 2
});
var ts3 = new TraceStep(expr1, expr3, null, "meta-rule todo", "rule todo");
var ts3Expr = new TraceStepExpr(ts3);
var ts4 = new TraceStep(expr3, 2, null, "meta-rule todo", "rule todo");
var ts4Expr = new TraceStepExpr(ts4);
var lst2 = new List <TraceStepExpr>()
{
ts3Expr, ts4Expr
};
var tuple2 = new Tuple <object, object>("strategy1", lst2);
var lstStrategy2 = new List <Tuple <object, object> >();
lstStrategy2.Add(tuple2);
//Under the same strategy
graph.Update(lstStrategy2);
Assert.True(graph.Nodes.Count == 3);
Assert.True(node1.SubGraph.Nodes.Count == 3);
}
public TraceStepExpr(TraceStep ts)
{
MetaRule = ts.Rule as string;
AppliedRule = ts.AppliedRule as string;
Source = ExprG.Generate(ts.Source);
Target = ExprG.Generate(ts.Target);
//StepExpr = ExprG.Derive(Source, Target);
StepExpr = Target;
TraceStep = ts;
}
public TraceStepExpr(TraceStep ts)
{
MetaRule = ts.Rule as string;
AppliedRule = ts.AppliedRule as string;
Source = ExprG.Generate(ts.Source);
Target = ExprG.Generate(ts.Target);
//StepExpr = ExprG.Derive(Source, Target);
StepExpr = Target;
TraceStep = ts;
}
public static void FromPointPointToLine(PointSymbol ps1, PointSymbol ps2, LineSymbol ls)
{
var m = new Var("m");
var k = new Var("k");
var x = new Var("x");
var y = new Var("y");
var term = new Term(Expression.Multiply, new List <object>()
{
m, x
});
var term1 = new Term(Expression.Add, new List <object>()
{
term, k
});
var eqPattern = new Equation(y, term1);
var term2 = new Term(Expression.Multiply, new List <object>()
{
m, ps1.SymXCoordinate
});
var term22 = new Term(Expression.Add, new List <object>()
{
term2, k
});
var eqPattern1 = new Equation(ps1.SymYCoordinate, term22);
var term3 = new Term(Expression.Multiply, new List <object>()
{
m, ps2.SymXCoordinate
});
var term33 = new Term(Expression.Add, new List <object>()
{
term3, k
});
var eqPattern2 = new Equation(ps2.SymYCoordinate, term33);
string strategy = "Generate a line by substituting two given points into the line slope-intercept form y=mx+k.";
var ts0 = new TraceStep(eqPattern, eqPattern1, SubstitutionRule.SubstituteKC(), SubstitutionRule.SubstitutionStrategy,
SubstitutionRule.ApplySubstitute(eqPattern, ps1));
var ts1 = new TraceStep(eqPattern, eqPattern2, SubstitutionRule.SubstituteKC(), SubstitutionRule.SubstitutionStrategy,
SubstitutionRule.ApplySubstitute(eqPattern, ps2));
string kc = GeometryScaffold.KC_LineSlopeForm;
var ts2 = new TraceStep(null, ls, kc, "calculate m and k through the above two linear equations.",
"calculate m and k through linear equation and retrieve y=mx+k line form.");
ls._innerLoop.Add(ts0);
ls._innerLoop.Add(ts1);
ls._innerLoop.Add(ts2);
ls.GenerateATrace(strategy);
}
/// <summary>
/// Returns the current nondeterministic choice as a program trace step.
/// </summary>
/// <param name="uniqueId">Unique nondet id</param>
/// <param name="choice">Choice</param>
/// <param name="enabledMachines">Enabled machines</param>
/// <returns>TraceStep</returns>
private TraceStep GetNondeterministicChoiceTraceStep(string uniqueId, bool choice,
HashSet <Machine> enabledMachines)
{
var fingerprint = PSharpRuntime.CaptureProgramState();
var traceStep = TraceStep.CreateNondeterministicChoice(fingerprint, uniqueId,
choice, enabledMachines, PSharpRuntime.LivenessChecker.GetMonitorStatus());
Output.Debug(DebugType.Liveness, "<LivenessDebug> Captured program state '{0}' at " +
"nondeterministic choice '{1}-{2}'.", fingerprint.GetHashCode(), uniqueId, choice);
return(traceStep);
}
public void Test_OneStrategy_MultiTraceStep_UserInput()
{
var expr1 = new Term(Expression.Add, new List <object> {
1, 1, 1
});
var eq1 = new Equation(expr1, 20);
var expr2 = new Term(Expression.Add, new List <object> {
2, 1
});
var ts1 = new TraceStep(eq1, expr2, null, "meta-rule todo", "rule todo");
var ts1Expr = new TraceStepExpr(ts1);
var ts2 = new TraceStep(expr2, 2, null, "meta-rule todo", "rule todo");
var ts2Expr = new TraceStepExpr(ts2);
var lst = new List <TraceStepExpr>()
{
ts1Expr, ts2Expr
};
var tuple = new Tuple <object, object>("strategy1", lst);
var lstStrategy = new List <Tuple <object, object> >();
lstStrategy.Add(tuple);
var graph = new BehaviorGraph();
graph.Insert(lstStrategy);
Assert.True(graph.Nodes.Count == 2);
var node0 = graph.Nodes[0];
Assert.Null(node0.SubGraph);
var node1 = graph.Nodes[1];
Assert.NotNull(node1.SubGraph);
Assert.True(node1.SubGraph.Nodes.Count == 3);
/////////////////////////////////////////////
// User Input
var userExpr1 = new Term(Expression.Add, new List <object> {
1, 1, 1
});
var userEq1 = new Equation(userExpr1, 20);
var node = graph.SearchInnerLoopNode(userEq1);
Assert.NotNull(node);
var userExpr2 = new Term(Expression.Add, new List <object> {
1, 3
});
node = graph.SearchInnerLoopNode(userExpr2);
Assert.Null(node);
}
/// <summary>
/// Returns the current scheduling choice as a program trace step.
/// </summary>
/// <param name="scheduledMachine">Scheduled machine</param>
/// <param name="enabledMachines">Enabled machines</param>
/// <returns>TraceStep</returns>
private TraceStep GetSchedulingChoiceTraceStep(Machine scheduledMachine,
HashSet <Machine> enabledMachines)
{
var fingerprint = PSharpRuntime.CaptureProgramState();
var traceStep = TraceStep.CreateSchedulingChoice(fingerprint, scheduledMachine,
enabledMachines, PSharpRuntime.LivenessChecker.GetMonitorStatus());
Output.Debug(DebugType.Liveness, "<LivenessDebug> Captured program state '{0}' at " +
"scheduling choice.", fingerprint.GetHashCode());
return(traceStep);
}
/// <summary>
/// Creates a scheduling choice trace step.
/// </summary>
/// <param name="index">Index</param>
/// <param name="scheduledMachine">Scheduled machine</param>
/// <returns>TraceStep</returns>
internal static TraceStep CreateSchedulingChoice(int index, AbstractMachine scheduledMachine)
{
var traceStep = new TraceStep();
traceStep.Index = index;
traceStep.Type = TraceStepType.SchedulingChoice;
traceStep.ScheduledMachine = scheduledMachine;
traceStep.Previous = null;
traceStep.Next = null;
return traceStep;
}
/// <summary>
/// Creates a scheduling choice trace step.
/// </summary>
/// <param name="index">Index</param>
/// <param name="scheduledMachine">Scheduled machine</param>
/// <returns>TraceStep</returns>
internal static TraceStep CreateSchedulingChoice(int index, BaseMachine scheduledMachine)
{
var traceStep = new TraceStep();
traceStep.Index = index;
traceStep.Type = TraceStepType.SchedulingChoice;
traceStep.ScheduledMachine = scheduledMachine;
traceStep.Previous = null;
traceStep.Next = null;
return(traceStep);
}
/// <summary>
/// Creates a nondeterministic choice trace step.
/// </summary>
/// <param name="index">Index</param>
/// <param name="choice">Choice</param>
/// <returns>TraceStep</returns>
internal static TraceStep CreateNondeterministicChoice(int index, bool choice)
{
var traceStep = new TraceStep();
traceStep.Index = index;
traceStep.Type = TraceStepType.NondeterministicChoice;
traceStep.Choice = choice;
traceStep.Previous = null;
traceStep.Next = null;
return(traceStep);
}
public void Test_OneStrategy_OneTraceStep()
{
//strategy1 : 1+1->2
var expr1 = new Term(Expression.Add, new List<object>{1,1});
var ts = new TraceStep(expr1, 2, "null", "meta-rule todo", "rule todo");
var tsExpr = new TraceStepExpr(ts);
var lst = new List<TraceStepExpr>() { tsExpr};
var tuple = new Tuple<object, object>("strategy1", lst);
var lstStrategy = new List<Tuple<object, object>>();
lstStrategy.Add(tuple);
var graph = new BehaviorGraph();
graph.Insert(lstStrategy);
Assert.True(graph.Nodes.Count == 2);
var node0 = graph.Nodes[0];
Assert.Null(node0.SubGraph);
var node1 = graph.Nodes[1];
Assert.True(node0.OutEdges.Count == 1);
var edgeInfo = node0.OutEdges[0].Property as OuterLoopEdgeProperty;
Assert.NotNull(edgeInfo);
Assert.True(edgeInfo.Strategy.Equals("strategy1"));
Assert.NotNull(node1.SubGraph);
Assert.True(node1.InEdges.Count == 1);
Assert.True(node1.OutEdges.Count == 0);
Assert.True(node1.SubGraph.Nodes.Count == 2);
/////////////////////////////////////////////////////
//Search Test
var initNode = graph.RetrieveInitInnerNode();
Assert.NotNull(initNode);
int count = graph.PathFinding(initNode);
Assert.True(count == 1);
var nextObj = graph.SearchNextInnerLoopNode(initNode);
var tuple2 = nextObj as Tuple<object,object>;
Assert.NotNull(tuple2);
var nextNode = tuple2.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 0);
var prevObj = graph.SearchPrevInnerLoopNode(nextNode) as BehaviorGraphNode;
Assert.NotNull(prevObj);
count = graph.PathFinding(prevObj);
Assert.True(count == 1);
}
/// <summary>
/// Creates a fair nondeterministic choice trace step.
/// </summary>
/// <param name="index">Index</param>
/// <param name="uniqueId">Unique id</param>
/// <param name="choice">Choice</param>
/// <returns>TraceStep</returns>
internal static TraceStep CreateFairNondeterministicChoice(int index, string uniqueId, bool choice)
{
var traceStep = new TraceStep();
traceStep.Index = index;
traceStep.Type = TraceStepType.FairNondeterministicChoice;
traceStep.NondetId = uniqueId;
traceStep.Choice = choice;
traceStep.Previous = null;
traceStep.Next = null;
return(traceStep);
}
/// <summary>
/// Determines whether the specified System.Object is equal
/// to the current System.Object.
/// </summary>
/// <param name="obj">Object</param>
/// <returns>Boolean value</returns>
public override bool Equals(object obj)
{
if (obj == null)
{
return(false);
}
TraceStep mid = obj as TraceStep;
if (mid == null)
{
return(false);
}
return(this.Index == mid.Index);
}
public static void FromLineSlopeIntercetpToLineGeneralForm(LineSymbol ls)
{
var line = ls.Shape as Line;
Debug.Assert(line != null);
Debug.Assert(ls.OutputType == LineType.GeneralForm);
string step1metaRule = "Given the line slope-intercept from y=mx+b, move y term to the right side of equation.";
string step1AppliedRule = String.Format("Move y to the right side of equation");
string kc = GeometryScaffold.KC_LinePatternsTransform;
var ts = new TraceStep(ls.SlopeInterceptForm, ls.GeneralForm, kc, step1metaRule, step1AppliedRule);
string strategy = strategy_si_general;
ls._innerLoop.Add(ts);
ls.GenerateATrace(strategy);
}
//forward solving
public static void FromLineToSlope(LineSymbol ls, EqGoal goal)
{
//one strategy, one step.
var line = ls.Shape as Line;
Debug.Assert(line != null);
var lst = new List <TraceStep>();
string step1metaRule = "Given the line slope intercept form y=mx+b, the slope is m.";
string step1AppliedRule = String.Format("Given line slope-intercept form {0}, the slope is {1}.", ls.ToString(), ls.SymSlope);
string kc = GeometryScaffold.KC_LineSlopeForm;
var ts = new TraceStep(ls, goal, kc, step1metaRule, step1AppliedRule);
lst.Add(ts);
var strategy = strategy_si_slope;
var tuple = new Tuple <object, object>(strategy, lst);
goal.Traces.Add(tuple);
}
/// <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 GenerateYCacheSymbol(object obj, EqGoal goal)
{
var point = Shape as Point;
Debug.Assert(point != null);
CachedGoals.Add(new KeyValuePair<object, EqGoal>(PointAcronym.Y, goal));
if (CachedSymbols.Count == 0)
{
var gPoint = new Point(point.Label, point.XCoordinate, obj);
var gPointSymbol = new PointSymbol(gPoint);
gPointSymbol.CachedGoals.Add(new KeyValuePair<object, EqGoal>(PointAcronym.Y, goal));
CachedSymbols.Add(gPointSymbol);
gPointSymbol.Traces.AddRange(goal.Traces);
//transform goal trace
for (int i = goal.Traces.Count - 1; i >= 0; i--)
{
gPoint.Traces.Insert(0, goal.Traces[i]);
}
//Substitution trace
var rule = SubstitutionRule.ApplySubstitute();
var appliedRule = SubstitutionRule.ApplySubstitute(this, goal);
var ts = new TraceStep(this, gPointSymbol, SubstitutionRule.SubstituteKC(), rule, appliedRule);
gPointSymbol._innerLoop.Add(ts);
string strategy = "Reify a Point's y-coordinate by substituing a given fact.";
gPointSymbol.GenerateATrace(strategy);
//gPoint.Traces.Insert(0, ts);
}
else
{
foreach (ShapeSymbol ss in CachedSymbols.ToList())
{
var pt = ss.Shape as Point;
if (pt != null)
{
var yResult = LogicSharp.Reify(pt.YCoordinate, goal.ToDict());
if (!pt.YCoordinate.Equals(yResult))
{
var gPt = new Point(pt.Label, pt.XCoordinate, pt.YCoordinate);
var gPointSymbol = new PointSymbol(gPt);
//substitute
pt.YCoordinate = yResult;
ss.CachedGoals.Add(new KeyValuePair<object, EqGoal>(PointAcronym.Y, goal));
gPointSymbol.Traces.AddRange(goal.Traces);
//transform goal trace
for (int i = goal.Traces.Count - 1; i >= 0; i--)
{
pt.Traces.Insert(0, goal.Traces[i]);
}
string rule = SubstitutionRule.ApplySubstitute();
string appliedRule = SubstitutionRule.ApplySubstitute(this, goal);
var ts = new TraceStep(this, gPointSymbol, SubstitutionRule.SubstituteKC(), rule, appliedRule);
gPointSymbol._innerLoop.Add(ts);
string strategy = "Reify a Point's y-coordinate by substituing a given fact.";
gPointSymbol.GenerateATrace(strategy);
//pt.Traces.Insert(0, ts);
}
else
{
//generate
var gPoint = new Point(pt.Label, pt.XCoordinate, obj);
var gPointSymbol = new PointSymbol(gPoint);
gPointSymbol.Traces.AddRange(goal.Traces);
gPointSymbol.CachedGoals.Add(new KeyValuePair<object, EqGoal>(PointAcronym.Y, goal));
foreach (KeyValuePair<object, EqGoal> pair in ss.CachedGoals)
{
if (pair.Key.Equals(PointAcronym.X))
{
gPointSymbol.CachedGoals.Add(new KeyValuePair<object, EqGoal>(PointAcronym.X, pair.Value));
}
}
CachedSymbols.Add(gPointSymbol);
//substitute
//Add traces from pt to gPoint
for (int i = pt.Traces.Count - 1; i >= 0; i--)
{
gPoint.Traces.Insert(0, pt.Traces[i]);
}
//transform goal trace
for (int i = goal.Traces.Count - 1; i >= 0; i--)
{
gPoint.Traces.Insert(0, goal.Traces[i]);
}
var rule = SubstitutionRule.ApplySubstitute();
var appliedRule = SubstitutionRule.ApplySubstitute(this, goal);
var ts = new TraceStep(this, gPointSymbol, SubstitutionRule.SubstituteKC(), rule, appliedRule);
gPointSymbol._innerLoop.Add(ts);
string strategy = "Reify a Point's y-coordinate by substituing a given fact.";
gPointSymbol.GenerateATrace(strategy);
//gPoint.Traces.Insert(0, ts);
}
}
}
}
}
public bool Reify(EqGoal goal)
{
var lhsTerm = Lhs as Term;
var rhsTerm = Rhs as Term;
var lhsVar = Lhs as Var;
var rhsVar = Rhs as Var;
string strategy = "Reify equation's internal variable by substituing a given fact.";
if (lhsVar != null)
{
var lhsNum = LogicSharp.Reify(lhsVar, goal.ToDict());
if (lhsNum != null && !lhsNum.Equals(lhsVar))
{
var cloneEq = Clone();
cloneEq.Lhs = lhsNum;
string rule = SubstitutionRule.ApplySubstitute();
string appliedRule = SubstitutionRule.ApplySubstitute(this, cloneEq);
var ts = new TraceStep(this, cloneEq, SubstitutionRule.SubstituteKC(), rule, appliedRule);
cloneEq._innerLoop.Add(ts);
cloneEq.GenerateATrace(strategy);
CachedEntities.Add(cloneEq);
return true;
}
}
if (rhsVar != null)
{
var rhsNum = LogicSharp.Reify(rhsVar, goal.ToDict());
if (rhsNum != null && !rhsNum.Equals(lhsVar))
{
var cloneEq = Clone();
cloneEq.Rhs = rhsNum;
string rule = SubstitutionRule.ApplySubstitute();
string appliedRule = SubstitutionRule.ApplySubstitute(this, goal);
var ts = new TraceStep(this, cloneEq, SubstitutionRule.SubstituteKC(), rule, appliedRule);
cloneEq._innerLoop.Add(ts);
cloneEq.GenerateATrace(strategy);
CachedEntities.Add(cloneEq);
return true;
}
}
if(lhsTerm != null)
{
var term1 = lhsTerm.Reify(goal) as Term;
if (lhsTerm.Equals(term1) || term1 == null)
{
return false;
}
var obj = term1.Eval();
var cloneEq = Clone();
cloneEq.Lhs = obj;
string rule = SubstitutionRule.ApplySubstitute();
string appliedRule = SubstitutionRule.ApplySubstitute(this, goal);
var ts = new TraceStep(this, cloneEq, SubstitutionRule.SubstituteKC(), rule, appliedRule);
cloneEq._innerLoop.Add(ts);
cloneEq.GenerateATrace(strategy);
CachedEntities.Add(cloneEq);
return true;
}
if (rhsTerm != null)
{
object obj = rhsTerm.Reify(goal);
if (rhsTerm.Equals(obj))
{
return false;
}
var cloneEq = Clone();
cloneEq.Rhs = obj;
string rule = SubstitutionRule.ApplySubstitute();
string appliedRule = SubstitutionRule.ApplySubstitute(this, goal);
var ts = new TraceStep(this, cloneEq, SubstitutionRule.SubstituteKC(), rule, appliedRule);
cloneEq._innerLoop.Add(ts);
cloneEq.GenerateATrace(strategy);
CachedEntities.Add(cloneEq);
return true;
}
return false;
}
/*
* given m=2, k=3, y=3x+2
*/
public static void FromSlopeInterceptToLineSlopeIntercept(EqGoal slopeGoal, EqGoal interceptGoal, LineSymbol ls)
{
//1. Substitute slope and intercept properties into the line slope-intercept form y=mx+b.
////////////////////////////////////////////////////////
var ts0 = new TraceStep(null, slopeGoal, GeometryScaffold.KC_LineSlopeForm, PlottingRule.PlottingStrategy, PlottingRule.Plot(slopeGoal));
var ts1 = new TraceStep(null, interceptGoal, GeometryScaffold.KC_LineInterceptForm, PlottingRule.PlottingStrategy, PlottingRule.Plot(interceptGoal));
ls._innerLoop.Add(ts0);
var abstractLs = new Line(ls.Shape.Label, slopeGoal.Lhs, interceptGoal.Lhs);
var abstractLss = new LineSymbol(abstractLs);
var internalLs = new Line(ls.Shape.Label, ls.SymSlope, interceptGoal.Lhs);
var internalLss = new LineSymbol(internalLs);
var traceStep1 = new TraceStep(abstractLss, internalLss, SubstitutionRule.SubstituteKC(), SubstitutionRule.SubstitutionStrategy, SubstitutionRule.ApplySubstitute(abstractLss, slopeGoal));
ls._innerLoop.Add(traceStep1);
ls._innerLoop.Add(ts1);
/*
var rule = "Substitute given property to line slope-intercept form.";
var appliedRule1 = string.Format("Substitute slope={0} into y=mx+b", ls.SymSlope);
var appliedRule2= string.Format("Substitute intercept={0} into y=mx+b", ls.SymIntercept);*/
var traceStep2 = new TraceStep(internalLss, ls, SubstitutionRule.SubstituteKC(), SubstitutionRule.SubstitutionStrategy, SubstitutionRule.ApplySubstitute(internalLss, interceptGoal));
ls._innerLoop.Add(traceStep2);
string strategy = "Substitute slope and intercept properties into the line slope-intercept form y = mx + b.";
ls.GenerateATrace(strategy);
}
public static void FromPointSlopeToLine(PointSymbol ps, EqGoal goal, LineSymbol ls)
{
string strategy = "Substitute point and slope property into line form.";
// 1. Substitute slope property into the line slope-intercept form.
// 2. Calculate the line intercept by substituting the point into line pattern.
//////////////////////////////////////////////////////////////////////
string strategy1 = "Substitute slope property into the line slope-intercept form.";
var m = new Var("m");
var k = new Var("k");
var x = new Var("x");
var y = new Var("y");
var term = new Term(Expression.Multiply, new List<object>() {m, x});
var term1 = new Term(Expression.Add, new List<object>() {term, k});
var eqPattern = new Equation(y, term1);
var term2 = new Term(Expression.Multiply, new List<object>() {goal.Rhs,x});
var term3 = new Term(Expression.Add, new List<object>() {term2, k});
var eqInternal1 = new Equation(y, term3);
var appliedRule1 = SubstitutionRule.ApplySubstitute(eqPattern, goal);
var ts0 = new TraceStep(eqPattern, eqInternal1, SubstitutionRule.SubstituteKC(), strategy1, appliedRule1);
ls._innerLoop.Add(ts0);
//////////////////////////////////////////////////////////////////////
var point = ps.Shape as Point;
Debug.Assert(point != null);
string strategy2 = "Calculate the line intercept by substituting the point into line pattern.";
var term4 = new Term(Expression.Multiply, new List<object>() { goal.Rhs, point.XCoordinate});
var term5 = new Term(Expression.Add, new List<object>() {term4, k});
var eqinternal2 = new Equation(point.YCoordinate, term5);
object obj;
bool result = eqinternal2.IsEqGoal(out obj);
var eqGoal = obj as EqGoal;
Debug.Assert(eqGoal != null);
var gTuple = eqGoal.Traces[0];
var gLst = gTuple.Item2 as List<TraceStep>;
Debug.Assert(gLst != null);
ls._innerLoop.AddRange(gLst);
var appliedRule2 = SubstitutionRule.ApplySubstitute(eqInternal1, ps);
var ts = new TraceStep(eqInternal1, ls, SubstitutionRule.SubstituteKC(), strategy2, appliedRule2);
ls._innerLoop.Add(ts);
ls.GenerateATrace(strategy);
}
/*
* Automatic scaffolding
*
* Distance function (x-x0)^2+(y-y0)^2 = d^2
*
* Forward chaining to derive d.
* Backward chaining to derive other four parameters.
*/
private static Tuple<object, object> DistanceSubstitution(LineSegmentSymbol lss)
{
var ls = lss.Shape as LineSegment;
var lst = new List<TraceStep>();
string step1metaRule = "The Distance Function between two points it: d^2=(x0-x1)^2+(y0-y1)^2";
string step1AppliedRule = String.Format(
"Substitute two points into the distance function d^2=({0}-{1})^2+({2}-{3})^2",
ls.Pt1.XCoordinate.ToString(),
ls.Pt2.XCoordinate.ToString(),
ls.Pt1.YCoordinate.ToString(),
ls.Pt2.YCoordinate.ToString());
var pt1X = new Var("x0");
var pt1Y = new Var("y0");
var pt2X = new Var("x1");
var pt2Y = new Var("y1");
var term1_1 = new Term(Expression.Subtract, new List<object>() { pt1X, pt2X });
var term11_1 = new Term(Expression.Power, new List<object>() { term1_1, 2.0 });
var term2_1 = new Term(Expression.Subtract, new List<object>() { pt1Y, pt2Y });
var term22_1 = new Term(Expression.Power, new List<object>() { term2_1, 2.0 });
var rhs_1 = new Term(Expression.Add, new List<object>() { term11_1, term22_1 });
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>() { ls.Pt1.XCoordinate, ls.Pt2.XCoordinate });
var term11 = new Term(Expression.Power, new List<object>() { term1, 2.0 });
var term2 = new Term(Expression.Subtract, new List<object>() { ls.Pt1.YCoordinate, ls.Pt2.YCoordinate });
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(lhs, rhs);
var old_eq = new Equation(lhs, rhs_1);
var trace = new TraceStep(old_eq, eq, GeometryScaffold.KC_Distance, step1metaRule, step1AppliedRule);
lst.Add(trace);
string strategy = "Substitute two points coordinates into the distance function.";
var newTuple = new Tuple<object, object>(strategy, lst);
return newTuple;
}
public static object ApplyTransitive2(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;
//Divide Transform
object newLhs, newRhs;
if (SatisfyTransitiveCondition5(lhs, rhs, out newLhs, out newRhs))
{
var cloneEq = currentEq.Clone();
var newEq = new Equation(newLhs, newRhs);
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;
}
return localEq;
}
/// <summary>
/// Creates a nondeterministic choice trace step.
/// </summary>
/// <param name="index">Index</param>
/// <param name="choice">Choice</param>
/// <returns>TraceStep</returns>
internal static TraceStep CreateNondeterministicChoice(int index, bool choice)
{
var traceStep = new TraceStep();
traceStep.Index = index;
traceStep.Type = TraceStepType.NondeterministicChoice;
traceStep.Choice = choice;
traceStep.Previous = null;
traceStep.Next = null;
return traceStep;
}
public static void LineSlopeIntercepToGraph(LineSymbol ls)
{
string strategy = strategy_graphing;
//Plotting shapes
//1. plotting Y-Intercept
//2. plotting X-Intercept
//3. plotting the line
//////////////////////////////////////////////////////////////
// Step 1:
var pt = new Point(0, ls.SymIntercept);
var ptSym = new PointSymbol(pt);
var ts0 = new TraceStep(null, ptSym, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ptSym));
ls._innerLoop.Add(ts0);
//////////////////////////////////////////////////////////////
// Step 2:
var line = ls.Shape as Line;
Debug.Assert(line != null);
Equation eq;
if (line.B == null)
{
}
else
{
var x = new Var("x");
//step 2.1
var term = new Term(Expression.Multiply, new List<object>() { line.Slope, x });
var term1 = new Term(Expression.Add, new List<object>() { term, line.Intercept });
eq = new Equation(term1, 0);
object obj;
EqGoal gGoal = null;
bool result = eq.IsEqGoal(out obj);
if (result)
{
gGoal = obj as EqGoal;
}
if (gGoal != null)
{
double dX;
LogicSharp.IsDouble(gGoal.Rhs, out dX);
var pt1 = new Point(dX, 0);
var ptSym1 = new PointSymbol(pt1);
var ts1 = new TraceStep(null, ptSym1, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ptSym1));
ls._innerLoop.Add(ts1);
}
}
/////////////////////////////////////////////////////////////////
const string step1MetaRule = "Given the line slope-intercept form y=mx+b, plot the line by passing points (0,b) and (-b/m,0).";
string step1AppliedRule = String.Format("Plotting the line passing through (0,{0}) and ({1},0) ", ls.SymIntercept, ls.SymC);
//var ts = new TraceStep(null, ls.SlopeInterceptForm, step1MetaRule, step1AppliedRule);
string kc = GeometryScaffold.KC_LineGraphing;
var ts = new TraceStep(null, ls, kc, step1MetaRule, step1AppliedRule);
ls._innerLoop.Add(ts);
//////////////////////////////////////////////////////////////////
ls.GenerateATrace(strategy);
}
public void CacheC(object obj, EqGoal goal)
{
CachedGoals.Add(new KeyValuePair<object, EqGoal>(LineAcronym.C, goal));
if (CachedSymbols.Count == 0)
{
var line = Shape as Line;
Debug.Assert(line != null);
#region generate new object
var gLine = new Line(line.Label, line.A, line.B, obj);
var gLineSymbol = new LineSymbol(gLine);
gLineSymbol.CachedGoals.Add(new KeyValuePair<object, EqGoal>(LineAcronym.C, goal));
CachedSymbols.Add(gLineSymbol);
//Transform goal trace
for (int i = goal.Traces.Count - 1; i >= 0; i--)
{
gLine.Traces.Insert(0, goal.Traces[i]);
}
//Substitution trace
string rule = SubstitutionRule.ApplySubstitute();
string appliedRule = SubstitutionRule.ApplySubstitute(this, goal);
string kc = SubstitutionRule.SubstituteKC();
var ts = new TraceStep(this, gLineSymbol, kc, rule, appliedRule);
gLine._innerLoop.Add(ts);
gLine.GenerateATrace(SubstitutionRule.SubstitutionStrategy);
//gLine.Traces.Insert(0, ts);
#endregion
}
else
{
#region Iterate existing point object
foreach (ShapeSymbol ss in CachedSymbols.ToList())
{
var line = ss.Shape as Line;
if (line != null)
{
var cResult = LogicSharp.Reify(line.C, goal.ToDict());
if (!line.C.Equals(cResult))
{
var gline = new Line(line.Label, line.A, line.B, line.C);
var gLineSymbol = new LineSymbol(gline);
//substitute
line.C = cResult;
ss.CachedGoals.Add(new KeyValuePair<object, EqGoal>(LineAcronym.C, goal));
//transform goal trace
for (int i = goal.Traces.Count - 1; i >= 0; i--)
{
line.Traces.Insert(0, goal.Traces[i]);
}
string rule = SubstitutionRule.ApplySubstitute();
string appliedRule = SubstitutionRule.ApplySubstitute(gLineSymbol, goal);
string kc = SubstitutionRule.SubstituteKC();
var ts = new TraceStep(gLineSymbol, ss, kc, rule, appliedRule);
//line.Traces.Insert(0, ts);
line._innerLoop.Add(ts);
line.GenerateATrace(SubstitutionRule.SubstitutionStrategy);
}
else
{
//generate
var gLine = new Line(line.Label, line.A, line.B, obj);
var gLineSymbol = new LineSymbol(gLine);
gLineSymbol.CachedGoals.Add(new KeyValuePair<object, EqGoal>(LineAcronym.C, goal));
foreach (KeyValuePair<object, EqGoal> pair in ss.CachedGoals)
{
if (pair.Key.Equals(LineAcronym.A))
{
gLineSymbol.CachedGoals.Add(new KeyValuePair<object, EqGoal>(LineAcronym.A, pair.Value));
}
else if (pair.Key.Equals(LineAcronym.B))
{
gLineSymbol.CachedGoals.Add(new KeyValuePair<object, EqGoal>(LineAcronym.B, pair.Value));
}
}
CachedSymbols.Add(gLineSymbol);
//substitute
//Add traces from line to gLine
for (int i = line.Traces.Count - 1; i >= 0; i--)
{
gLine.Traces.Insert(0, line.Traces[i]);
}
//transform goal trace
for (int i = goal.Traces.Count - 1; i >= 0; i--)
{
gLine.Traces.Insert(0, goal.Traces[i]);
}
string rule = SubstitutionRule.ApplySubstitute();
string appliedRule = SubstitutionRule.ApplySubstitute(gLineSymbol, goal);
string kc = SubstitutionRule.SubstituteKC();
var ts = new TraceStep(ss, gLineSymbol, kc, rule, appliedRule);
gLine._innerLoop.Add(ts);
gLine.GenerateATrace(SubstitutionRule.SubstitutionStrategy);
//gLine.Traces.Insert(0, ts);
}
}
}
#endregion
}
}
/*
* Automatic scaffolding
*
* Distance function (x-x0)^2+(y-y0)^2 = d^2
*
* Forward chaining to derive d.
* Backward chaining to derive other four parameters.
*/
private static Tuple <object, object> DistanceSubstitution(LineSegmentSymbol lss)
{
var ls = lss.Shape as LineSegment;
var lst = new List <TraceStep>();
string step1metaRule = "The Distance Function between two points it: d^2=(x0-x1)^2+(y0-y1)^2";
string step1AppliedRule = String.Format(
"Substitute two points into the distance function d^2=({0}-{1})^2+({2}-{3})^2",
ls.Pt1.XCoordinate.ToString(),
ls.Pt2.XCoordinate.ToString(),
ls.Pt1.YCoordinate.ToString(),
ls.Pt2.YCoordinate.ToString());
var pt1X = new Var("x0");
var pt1Y = new Var("y0");
var pt2X = new Var("x1");
var pt2Y = new Var("y1");
var term1_1 = new Term(Expression.Subtract, new List <object>()
{
pt1X, pt2X
});
var term11_1 = new Term(Expression.Power, new List <object>()
{
term1_1, 2.0
});
var term2_1 = new Term(Expression.Subtract, new List <object>()
{
pt1Y, pt2Y
});
var term22_1 = new Term(Expression.Power, new List <object>()
{
term2_1, 2.0
});
var rhs_1 = new Term(Expression.Add, new List <object>()
{
term11_1, term22_1
});
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>()
{
ls.Pt1.XCoordinate, ls.Pt2.XCoordinate
});
var term11 = new Term(Expression.Power, new List <object>()
{
term1, 2.0
});
var term2 = new Term(Expression.Subtract, new List <object>()
{
ls.Pt1.YCoordinate, ls.Pt2.YCoordinate
});
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(lhs, rhs);
var old_eq = new Equation(lhs, rhs_1);
var trace = new TraceStep(old_eq, eq, GeometryScaffold.KC_Distance, step1metaRule, step1AppliedRule);
lst.Add(trace);
string strategy = "Substitute two points coordinates into the distance function.";
var newTuple = new Tuple <object, object>(strategy, lst);
return(newTuple);
}
public void GenerateYCacheSymbol(object obj, EqGoal goal)
{
var point = Shape as Point;
Debug.Assert(point != null);
CachedGoals.Add(new KeyValuePair <object, EqGoal>(PointAcronym.Y, goal));
if (CachedSymbols.Count == 0)
{
var gPoint = new Point(point.Label, point.XCoordinate, obj);
var gPointSymbol = new PointSymbol(gPoint);
gPointSymbol.CachedGoals.Add(new KeyValuePair <object, EqGoal>(PointAcronym.Y, goal));
CachedSymbols.Add(gPointSymbol);
gPointSymbol.Traces.AddRange(goal.Traces);
//transform goal trace
for (int i = goal.Traces.Count - 1; i >= 0; i--)
{
gPoint.Traces.Insert(0, goal.Traces[i]);
}
//Substitution trace
var rule = SubstitutionRule.ApplySubstitute();
var appliedRule = SubstitutionRule.ApplySubstitute(this, goal);
var ts = new TraceStep(this, gPointSymbol, SubstitutionRule.SubstituteKC(), rule, appliedRule);
gPointSymbol._innerLoop.Add(ts);
string strategy = "Reify a Point's y-coordinate by substituing a given fact.";
gPointSymbol.GenerateATrace(strategy);
//gPoint.Traces.Insert(0, ts);
}
else
{
foreach (ShapeSymbol ss in CachedSymbols.ToList())
{
var pt = ss.Shape as Point;
if (pt != null)
{
var yResult = LogicSharp.Reify(pt.YCoordinate, goal.ToDict());
if (!pt.YCoordinate.Equals(yResult))
{
var gPt = new Point(pt.Label, pt.XCoordinate, pt.YCoordinate);
var gPointSymbol = new PointSymbol(gPt);
//substitute
pt.YCoordinate = yResult;
ss.CachedGoals.Add(new KeyValuePair <object, EqGoal>(PointAcronym.Y, goal));
gPointSymbol.Traces.AddRange(goal.Traces);
//transform goal trace
for (int i = goal.Traces.Count - 1; i >= 0; i--)
{
pt.Traces.Insert(0, goal.Traces[i]);
}
string rule = SubstitutionRule.ApplySubstitute();
string appliedRule = SubstitutionRule.ApplySubstitute(this, goal);
var ts = new TraceStep(this, gPointSymbol, SubstitutionRule.SubstituteKC(), rule, appliedRule);
gPointSymbol._innerLoop.Add(ts);
string strategy = "Reify a Point's y-coordinate by substituing a given fact.";
gPointSymbol.GenerateATrace(strategy);
//pt.Traces.Insert(0, ts);
}
else
{
//generate
var gPoint = new Point(pt.Label, pt.XCoordinate, obj);
var gPointSymbol = new PointSymbol(gPoint);
gPointSymbol.Traces.AddRange(goal.Traces);
gPointSymbol.CachedGoals.Add(new KeyValuePair <object, EqGoal>(PointAcronym.Y, goal));
foreach (KeyValuePair <object, EqGoal> pair in ss.CachedGoals)
{
if (pair.Key.Equals(PointAcronym.X))
{
gPointSymbol.CachedGoals.Add(new KeyValuePair <object, EqGoal>(PointAcronym.X, pair.Value));
}
}
CachedSymbols.Add(gPointSymbol);
//substitute
//Add traces from pt to gPoint
for (int i = pt.Traces.Count - 1; i >= 0; i--)
{
gPoint.Traces.Insert(0, pt.Traces[i]);
}
//transform goal trace
for (int i = goal.Traces.Count - 1; i >= 0; i--)
{
gPoint.Traces.Insert(0, goal.Traces[i]);
}
var rule = SubstitutionRule.ApplySubstitute();
var appliedRule = SubstitutionRule.ApplySubstitute(this, goal);
var ts = new TraceStep(this, gPointSymbol, SubstitutionRule.SubstituteKC(), rule, appliedRule);
gPointSymbol._innerLoop.Add(ts);
string strategy = "Reify a Point's y-coordinate by substituing a given fact.";
gPointSymbol.GenerateATrace(strategy);
//gPoint.Traces.Insert(0, ts);
}
}
}
}
}
public void CacheC(object obj, EqGoal goal)
{
CachedGoals.Add(new KeyValuePair <object, EqGoal>(LineAcronym.C, goal));
if (CachedSymbols.Count == 0)
{
var line = Shape as Line;
Debug.Assert(line != null);
#region generate new object
var gLine = new Line(line.Label, line.A, line.B, obj);
var gLineSymbol = new LineSymbol(gLine);
gLineSymbol.CachedGoals.Add(new KeyValuePair <object, EqGoal>(LineAcronym.C, goal));
CachedSymbols.Add(gLineSymbol);
//Transform goal trace
for (int i = goal.Traces.Count - 1; i >= 0; i--)
{
gLine.Traces.Insert(0, goal.Traces[i]);
}
//Substitution trace
string rule = SubstitutionRule.ApplySubstitute();
string appliedRule = SubstitutionRule.ApplySubstitute(this, goal);
string kc = SubstitutionRule.SubstituteKC();
var ts = new TraceStep(this, gLineSymbol, kc, rule, appliedRule);
gLine._innerLoop.Add(ts);
gLine.GenerateATrace(SubstitutionRule.SubstitutionStrategy);
//gLine.Traces.Insert(0, ts);
#endregion
}
else
{
#region Iterate existing point object
foreach (ShapeSymbol ss in CachedSymbols.ToList())
{
var line = ss.Shape as Line;
if (line != null)
{
var cResult = LogicSharp.Reify(line.C, goal.ToDict());
if (!line.C.Equals(cResult))
{
var gline = new Line(line.Label, line.A, line.B, line.C);
var gLineSymbol = new LineSymbol(gline);
//substitute
line.C = cResult;
ss.CachedGoals.Add(new KeyValuePair <object, EqGoal>(LineAcronym.C, goal));
//transform goal trace
for (int i = goal.Traces.Count - 1; i >= 0; i--)
{
line.Traces.Insert(0, goal.Traces[i]);
}
string rule = SubstitutionRule.ApplySubstitute();
string appliedRule = SubstitutionRule.ApplySubstitute(gLineSymbol, goal);
string kc = SubstitutionRule.SubstituteKC();
var ts = new TraceStep(gLineSymbol, ss, kc, rule, appliedRule);
//line.Traces.Insert(0, ts);
line._innerLoop.Add(ts);
line.GenerateATrace(SubstitutionRule.SubstitutionStrategy);
}
else
{
//generate
var gLine = new Line(line.Label, line.A, line.B, obj);
var gLineSymbol = new LineSymbol(gLine);
gLineSymbol.CachedGoals.Add(new KeyValuePair <object, EqGoal>(LineAcronym.C, goal));
foreach (KeyValuePair <object, EqGoal> pair in ss.CachedGoals)
{
if (pair.Key.Equals(LineAcronym.A))
{
gLineSymbol.CachedGoals.Add(new KeyValuePair <object, EqGoal>(LineAcronym.A, pair.Value));
}
else if (pair.Key.Equals(LineAcronym.B))
{
gLineSymbol.CachedGoals.Add(new KeyValuePair <object, EqGoal>(LineAcronym.B, pair.Value));
}
}
CachedSymbols.Add(gLineSymbol);
//substitute
//Add traces from line to gLine
for (int i = line.Traces.Count - 1; i >= 0; i--)
{
gLine.Traces.Insert(0, line.Traces[i]);
}
//transform goal trace
for (int i = goal.Traces.Count - 1; i >= 0; i--)
{
gLine.Traces.Insert(0, goal.Traces[i]);
}
string rule = SubstitutionRule.ApplySubstitute();
string appliedRule = SubstitutionRule.ApplySubstitute(gLineSymbol, goal);
string kc = SubstitutionRule.SubstituteKC();
var ts = new TraceStep(ss, gLineSymbol, kc, rule, appliedRule);
gLine._innerLoop.Add(ts);
gLine.GenerateATrace(SubstitutionRule.SubstitutionStrategy);
//gLine.Traces.Insert(0, ts);
}
}
}
#endregion
}
}
public static void FromLineSlopeIntercetpToLineGeneralForm(LineSymbol ls)
{
var line = ls.Shape as Line;
Debug.Assert(line != null);
Debug.Assert(ls.OutputType == LineType.GeneralForm);
string step1metaRule = "Given the line slope-intercept from y=mx+b, move y term to the right side of equation.";
string step1AppliedRule = String.Format("Move y to the right side of equation");
string kc = GeometryScaffold.KC_LinePatternsTransform;
var ts = new TraceStep(ls.SlopeInterceptForm, ls.GeneralForm, kc, step1metaRule, step1AppliedRule);
string strategy = strategy_si_general;
ls._innerLoop.Add(ts);
ls.GenerateATrace(strategy);
}
//forward solving
public static void FromLineToIntercept(LineSymbol ls, EqGoal goal)
{
var line = ls.Shape as Line;
Debug.Assert(line != null);
var lst = new List<TraceStep>();
string step1metaRule = "Given the line slope intercept form y=mx+K, the y-intercept is K.";
string step1AppliedRule = String.Format("Given line slope-intercept form {0}, the slope is {1}.", ls.ToString(), ls.SymIntercept);
string kc = GeometryScaffold.KC_LineInterceptForm;
var ts = new TraceStep(ls, goal, kc, step1metaRule, step1AppliedRule);
lst.Add(ts);
var strategy = strategy_si_intercept;
var tuple = new Tuple<object, object>(strategy, lst);
goal.Traces.Add(tuple);
}
/// <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_OneStrategy_MultiTraceStep()
{
var expr1 = new Term(Expression.Add, new List<object> { 1, 1 , 1});
var expr2 = new Term(Expression.Add, new List<object> {2, 1} );
var ts1 = new TraceStep(expr1, expr2, "null", "meta-rule todo", "rule todo");
var ts1Expr = new TraceStepExpr(ts1);
var ts2 = new TraceStep(expr2, 2, "null", "meta-rule todo", "rule todo");
var ts2Expr = new TraceStepExpr(ts2);
var lst = new List<TraceStepExpr>() { ts1Expr,ts2Expr};
var tuple = new Tuple<object, object>("strategy1", lst);
var lstStrategy = new List<Tuple<object, object>>();
lstStrategy.Add(tuple);
var graph = new BehaviorGraph();
graph.Insert(lstStrategy);
Assert.True(graph.Nodes.Count == 2);
var node0 = graph.Nodes[0];
Assert.Null(node0.SubGraph);
var node1 = graph.Nodes[1];
Assert.NotNull(node1.SubGraph);
Assert.True(node1.SubGraph.Nodes.Count == 3);
Assert.True(node1.OutEdges.Count == 0);
/////////////////////////////////////////////////////
//Search Test
var initNode = graph.RetrieveInitInnerNode();
Assert.NotNull(initNode);
int count = graph.PathFinding(initNode);
Assert.True(count == 2);
var nextObj = graph.SearchNextInnerLoopNode(initNode);
var tuple2 = nextObj as Tuple<object, object>;
Assert.NotNull(tuple2);
var nextNode = tuple2.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 1);
var nextObj2 = graph.SearchNextInnerLoopNode(nextNode);
var tuple3 = nextObj2 as Tuple<object, object>;
Assert.NotNull(tuple3);
var nextNode2 = tuple3.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode2);
count = graph.PathFinding(nextNode2);
Assert.True(count == 0);
}
/// <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 static void FromPointSlopeToLine(PointSymbol ps, EqGoal goal, LineSymbol ls)
{
string strategy = "Substitute point and slope property into line form.";
// 1. Substitute slope property into the line slope-intercept form.
// 2. Calculate the line intercept by substituting the point into line pattern.
//////////////////////////////////////////////////////////////////////
string strategy1 = "Substitute slope property into the line slope-intercept form.";
var m = new Var("m");
var k = new Var("k");
var x = new Var("x");
var y = new Var("y");
var term = new Term(Expression.Multiply, new List <object>()
{
m, x
});
var term1 = new Term(Expression.Add, new List <object>()
{
term, k
});
var eqPattern = new Equation(y, term1);
var term2 = new Term(Expression.Multiply, new List <object>()
{
goal.Rhs, x
});
var term3 = new Term(Expression.Add, new List <object>()
{
term2, k
});
var eqInternal1 = new Equation(y, term3);
var appliedRule1 = SubstitutionRule.ApplySubstitute(eqPattern, goal);
var ts0 = new TraceStep(eqPattern, eqInternal1, SubstitutionRule.SubstituteKC(), strategy1, appliedRule1);
ls._innerLoop.Add(ts0);
//////////////////////////////////////////////////////////////////////
var point = ps.Shape as Point;
Debug.Assert(point != null);
string strategy2 = "Calculate the line intercept by substituting the point into line pattern.";
var term4 = new Term(Expression.Multiply, new List <object>()
{
goal.Rhs, point.XCoordinate
});
var term5 = new Term(Expression.Add, new List <object>()
{
term4, k
});
var eqinternal2 = new Equation(point.YCoordinate, term5);
object obj;
bool result = eqinternal2.IsEqGoal(out obj);
var eqGoal = obj as EqGoal;
Debug.Assert(eqGoal != null);
var gTuple = eqGoal.Traces[0];
var gLst = gTuple.Item2 as List <TraceStep>;
Debug.Assert(gLst != null);
ls._innerLoop.AddRange(gLst);
var appliedRule2 = SubstitutionRule.ApplySubstitute(eqInternal1, ps);
var ts = new TraceStep(eqInternal1, ls, SubstitutionRule.SubstituteKC(), strategy2, appliedRule2);
ls._innerLoop.Add(ts);
ls.GenerateATrace(strategy);
}
public void Test_MultiStrategy_1()
{
//strategy1: 1->2, 2->3
var ts1 = new TraceStep(1, 2, "null", "TODO1", "TODO2");
var ts1Expr = new TraceStepExpr(ts1);
var ts2 = new TraceStep(2, 3, "null", "TODO2", "TODO3");
var ts2Expr = new TraceStepExpr(ts2);
var lst1 = new List<TraceStepExpr>() { ts1Expr, ts2Expr };
var tuple1 = new Tuple<object, object>("strategy1", lst1);
//strategy2: 2->3, 3->5, 5->7
var ts3 = new TraceStep(2, 3, null, "TODO", "TODO1");
var ts3Expr = new TraceStepExpr(ts3);
var ts4 = new TraceStep(3, 5, null, "TODO2", "TODO5");
var ts4Expr = new TraceStepExpr(ts4);
var ts5 = new TraceStep(5, 7, null,"Test1", "test23");
var ts5Expr = new TraceStepExpr(ts5);
var lst2 = new List<TraceStepExpr>() {ts3Expr, ts4Expr, ts5Expr};
var tuple2 = new Tuple<object, object>("strategy2", lst2);
var lstStrategy = new List<Tuple<object, object>>();
lstStrategy.Add(tuple1);
lstStrategy.Add(tuple2);
var graph = new BehaviorGraph();
graph.Insert(lstStrategy);
Assert.True(graph.Nodes.Count == 3);
var node1 = graph.Nodes[1];
Assert.True(node1.OutEdges.Count == 1);
var node2 = graph.Nodes[2];
Assert.True(node2.InEdges.Count == 1);
Assert.True(node2.OutEdges.Count == 0);
Assert.NotNull(node1.SubGraph);
Assert.True(node1.SubGraph.Nodes.Count == 3);
Assert.NotNull(node2.SubGraph);
Assert.True(node2.SubGraph.Nodes.Count == 4);
/////////////////////////////////////////////////////
//Search Test
var initNode = graph.RetrieveInitInnerNode();
Assert.NotNull(initNode);
int count = graph.PathFinding(initNode);
Assert.True(count == 5);
var nextObj = graph.SearchNextInnerLoopNode(initNode);
var tuple5 = nextObj as Tuple<object, object>;
Assert.NotNull(tuple5);
var nextNode = tuple5.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 4);
nextObj = graph.SearchNextInnerLoopNode(nextNode);
tuple5 = nextObj as Tuple<object, object>;
Assert.NotNull(tuple5);
nextNode = tuple5.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 3);
var index = graph.SearchOuterLoopNodeIndex(nextNode);
Assert.True(index == 1);
nextObj = graph.SearchNextInnerLoopNode(nextNode);
tuple5 = nextObj as Tuple<object, object>;
Assert.NotNull(tuple5);
nextNode = tuple5.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 2);
index = graph.SearchOuterLoopNodeIndex(nextNode);
Assert.True(index == 2);
nextObj = graph.SearchNextInnerLoopNode(nextNode);
tuple5 = nextObj as Tuple<object, object>;
Assert.NotNull(tuple5);
nextNode = tuple5.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 1);
index = graph.SearchOuterLoopNodeIndex(nextNode);
Assert.True(index == 2);
nextObj = graph.SearchNextInnerLoopNode(nextNode);
tuple5 = nextObj as Tuple<object, object>;
Assert.NotNull(tuple5);
nextNode = tuple5.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 0);
index = graph.SearchOuterLoopNodeIndex(nextNode);
Assert.True(index == 2);
var prevNode = graph.SearchPrevInnerLoopNode(nextNode) as BehaviorGraphNode;
Assert.NotNull(prevNode);
count = graph.PathFinding(prevNode);
Assert.True(count == 1);
var strateties = graph.SearchAllOuterEdgeInfos();
Assert.True(strateties.Count == 2);
}
/// <summary>
/// Creates a fair nondeterministic choice trace step.
/// </summary>
/// <param name="index">Index</param>
/// <param name="uniqueId">Unique id</param>
/// <param name="choice">Choice</param>
/// <returns>TraceStep</returns>
internal static TraceStep CreateFairNondeterministicChoice(int index, string uniqueId, bool choice)
{
var traceStep = new TraceStep();
traceStep.Index = index;
traceStep.Type = TraceStepType.FairNondeterministicChoice;
traceStep.NondetId = uniqueId;
traceStep.Choice = choice;
traceStep.Previous = null;
traceStep.Next = null;
return traceStep;
}
public void Test_OneStrategy_OneTraceStep_Author()
{
//1+1->2
var expr1 = new Term(Expression.Add, new List <object> {
1, 1
});
var ts = new TraceStep(expr1, 2, "null", "meta-rule todo", "rule todo");
var tsExpr = new TraceStepExpr(ts);
var lst = new List <TraceStepExpr>()
{
tsExpr
};
var tuple = new Tuple <object, object>("strategy1", lst);
var lstStrategy = new List <Tuple <object, object> >();
lstStrategy.Add(tuple);
var graph = new BehaviorGraph();
graph.Insert(lstStrategy);
Assert.True(graph.Nodes.Count == 2);
var node0 = graph.Nodes[0];
Assert.Null(node0.SubGraph);
var node1 = graph.Nodes[1];
Assert.NotNull(node1.SubGraph);
Assert.True(node1.SubGraph.Nodes.Count == 2);
/////////////////////////////////////////////
//4-1->2
var expr2 = new Term(Expression.Add, new List <object> {
4, 1
});
// User Input, //wrong step
var ts1 = new TraceStep(expr2, 2);
var ts1Expr = new TraceStepExpr(ts1);
var tsLst = new List <TraceStepExpr>()
{
ts1Expr
};
var tuple2 = new Tuple <object, object>("strategy1", tsLst);
var lst44 = new List <Tuple <object, object> >()
{
tuple2
};
bool matchResult = graph.Match(lst44);
Assert.True(matchResult);
graph.Update(lst44);
Assert.True(graph.Nodes.Count == 2);
Assert.True(node1.SubGraph.Nodes.Count == 3);
/////////////////////////////////////////////
//test search
var initNode = graph.RetrieveInitInnerNode();
Assert.NotNull(initNode);
var innerState = initNode.State as InnerLoopBehaviorState;
Assert.NotNull(innerState);
Assert.True(innerState.UserKnowledge.ToString().Equals("1+1"));
Assert.True(initNode.InEdges.Count == 0);
Assert.True(initNode.OutEdges.Count == 1);
int count = graph.PathFinding(initNode);
Assert.True(count == 1);
var nextObj = graph.SearchNextInnerLoopNode(initNode);
var tuple22 = nextObj as Tuple <object, object>;
Assert.NotNull(tuple22);
var nextNode = tuple22.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 0);
}
public void Test_OneStrategy_MultiTraceStep_Author()
{
var expr1 = new Term(Expression.Add, new List<object> { 1, 1, 1 });
var expr2 = new Term(Expression.Add, new List<object> { 2, 1 });
var ts1 = new TraceStep(expr1, expr2, null, "meta-rule todo", "rule todo");
var ts1Expr = new TraceStepExpr(ts1);
var ts2 = new TraceStep(expr2, 2, null, "meta-rule todo", "rule todo");
var ts2Expr = new TraceStepExpr(ts2);
var lst = new List<TraceStepExpr>() { ts1Expr, ts2Expr };
var tuple = new Tuple<object, object>("strategy2", lst);
var lstStrategy = new List<Tuple<object, object>>();
lstStrategy.Add(tuple);
var graph = new BehaviorGraph();
graph.Insert(lstStrategy);
Assert.True(graph.Nodes.Count == 2);
var node0 = graph.Nodes[0];
Assert.Null(node0.SubGraph);
var node1 = graph.Nodes[1];
Assert.NotNull(node1.SubGraph);
Assert.True(node1.SubGraph.Nodes.Count == 3);
/////////////////////////////////////////////
// User Input, //2 steps trace
var expr3 = new Term(Expression.Add, new List<object> { 1, 2 });
var ts3 = new TraceStep(expr1, expr3, null, "meta-rule todo", "rule todo");
var ts3Expr = new TraceStepExpr(ts3);
var ts4 = new TraceStep(expr3, 2, null, "meta-rule todo", "rule todo");
var ts4Expr = new TraceStepExpr(ts4);
var lst2 = new List<TraceStepExpr>() { ts3Expr, ts4Expr };
var tuple2 = new Tuple<object, object>("strategy1", lst2);
var lstStrategy2 = new List<Tuple<object, object>>();
lstStrategy2.Add(tuple2);
//Under the same strategy
graph.Update(lstStrategy2);
Assert.True(graph.Nodes.Count == 3);
Assert.True(node1.SubGraph.Nodes.Count == 3);
}
public void Test_OneStrategy_OneTraceStep()
{
//strategy1 : 1+1->2
var expr1 = new Term(Expression.Add, new List <object> {
1, 1
});
var ts = new TraceStep(expr1, 2, "null", "meta-rule todo", "rule todo");
var tsExpr = new TraceStepExpr(ts);
var lst = new List <TraceStepExpr>()
{
tsExpr
};
var tuple = new Tuple <object, object>("strategy1", lst);
var lstStrategy = new List <Tuple <object, object> >();
lstStrategy.Add(tuple);
var graph = new BehaviorGraph();
graph.Insert(lstStrategy);
Assert.True(graph.Nodes.Count == 2);
var node0 = graph.Nodes[0];
Assert.Null(node0.SubGraph);
var node1 = graph.Nodes[1];
Assert.True(node0.OutEdges.Count == 1);
var edgeInfo = node0.OutEdges[0].Property as OuterLoopEdgeProperty;
Assert.NotNull(edgeInfo);
Assert.True(edgeInfo.Strategy.Equals("strategy1"));
Assert.NotNull(node1.SubGraph);
Assert.True(node1.InEdges.Count == 1);
Assert.True(node1.OutEdges.Count == 0);
Assert.True(node1.SubGraph.Nodes.Count == 2);
/////////////////////////////////////////////////////
//Search Test
var initNode = graph.RetrieveInitInnerNode();
Assert.NotNull(initNode);
int count = graph.PathFinding(initNode);
Assert.True(count == 1);
var nextObj = graph.SearchNextInnerLoopNode(initNode);
var tuple2 = nextObj as Tuple <object, object>;
Assert.NotNull(tuple2);
var nextNode = tuple2.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 0);
var prevObj = graph.SearchPrevInnerLoopNode(nextNode) as BehaviorGraphNode;
Assert.NotNull(prevObj);
count = graph.PathFinding(prevObj);
Assert.True(count == 1);
}
/// <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 Test_OneStrategy_MultiTraceStep()
{
var expr1 = new Term(Expression.Add, new List <object> {
1, 1, 1
});
var expr2 = new Term(Expression.Add, new List <object> {
2, 1
});
var ts1 = new TraceStep(expr1, expr2, "null", "meta-rule todo", "rule todo");
var ts1Expr = new TraceStepExpr(ts1);
var ts2 = new TraceStep(expr2, 2, "null", "meta-rule todo", "rule todo");
var ts2Expr = new TraceStepExpr(ts2);
var lst = new List <TraceStepExpr>()
{
ts1Expr, ts2Expr
};
var tuple = new Tuple <object, object>("strategy1", lst);
var lstStrategy = new List <Tuple <object, object> >();
lstStrategy.Add(tuple);
var graph = new BehaviorGraph();
graph.Insert(lstStrategy);
Assert.True(graph.Nodes.Count == 2);
var node0 = graph.Nodes[0];
Assert.Null(node0.SubGraph);
var node1 = graph.Nodes[1];
Assert.NotNull(node1.SubGraph);
Assert.True(node1.SubGraph.Nodes.Count == 3);
Assert.True(node1.OutEdges.Count == 0);
/////////////////////////////////////////////////////
//Search Test
var initNode = graph.RetrieveInitInnerNode();
Assert.NotNull(initNode);
int count = graph.PathFinding(initNode);
Assert.True(count == 2);
var nextObj = graph.SearchNextInnerLoopNode(initNode);
var tuple2 = nextObj as Tuple <object, object>;
Assert.NotNull(tuple2);
var nextNode = tuple2.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 1);
var nextObj2 = graph.SearchNextInnerLoopNode(nextNode);
var tuple3 = nextObj2 as Tuple <object, object>;
Assert.NotNull(tuple3);
var nextNode2 = tuple3.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode2);
count = graph.PathFinding(nextNode2);
Assert.True(count == 0);
}
public void Test_OneStrategy_MultiTraceStep_UserInput()
{
var expr1 = new Term(Expression.Add, new List<object> { 1, 1, 1 });
var eq1 = new Equation(expr1, 20);
var expr2 = new Term(Expression.Add, new List<object> { 2, 1 });
var ts1 = new TraceStep(eq1, expr2, null, "meta-rule todo", "rule todo");
var ts1Expr = new TraceStepExpr(ts1);
var ts2 = new TraceStep(expr2, 2, null, "meta-rule todo", "rule todo");
var ts2Expr = new TraceStepExpr(ts2);
var lst = new List<TraceStepExpr>() { ts1Expr, ts2Expr };
var tuple = new Tuple<object, object>("strategy1", lst);
var lstStrategy = new List<Tuple<object, object>>();
lstStrategy.Add(tuple);
var graph = new BehaviorGraph();
graph.Insert(lstStrategy);
Assert.True(graph.Nodes.Count == 2);
var node0 = graph.Nodes[0];
Assert.Null(node0.SubGraph);
var node1 = graph.Nodes[1];
Assert.NotNull(node1.SubGraph);
Assert.True(node1.SubGraph.Nodes.Count == 3);
/////////////////////////////////////////////
// User Input
var userExpr1 = new Term(Expression.Add, new List<object> { 1, 1, 1 });
var userEq1 = new Equation(userExpr1, 20);
var node = graph.SearchInnerLoopNode(userEq1);
Assert.NotNull(node);
var userExpr2 = new Term(Expression.Add, new List<object> { 1, 3 });
node = graph.SearchInnerLoopNode(userExpr2);
Assert.Null(node);
}
public static void FromPointPointToLine(PointSymbol ps1, PointSymbol ps2, LineSymbol ls)
{
var m = new Var("m");
var k = new Var("k");
var x = new Var("x");
var y = new Var("y");
var term = new Term(Expression.Multiply, new List<object>() { m, x });
var term1 = new Term(Expression.Add, new List<object>() { term, k });
var eqPattern = new Equation(y, term1);
var term2 = new Term(Expression.Multiply, new List<object>() {m, ps1.SymXCoordinate});
var term22 = new Term(Expression.Add, new List<object>() {term2, k});
var eqPattern1 = new Equation(ps1.SymYCoordinate, term22);
var term3 = new Term(Expression.Multiply, new List<object>() {m, ps2.SymXCoordinate});
var term33 = new Term(Expression.Add, new List<object>() { term3, k });
var eqPattern2 = new Equation(ps2.SymYCoordinate, term33);
string strategy = "Generate a line by substituting two given points into the line slope-intercept form y=mx+k.";
var ts0 = new TraceStep(eqPattern, eqPattern1, SubstitutionRule.SubstituteKC(),SubstitutionRule.SubstitutionStrategy,
SubstitutionRule.ApplySubstitute(eqPattern, ps1));
var ts1 = new TraceStep(eqPattern, eqPattern2, SubstitutionRule.SubstituteKC(),SubstitutionRule.SubstitutionStrategy,
SubstitutionRule.ApplySubstitute(eqPattern, ps2));
string kc = GeometryScaffold.KC_LineSlopeForm;
var ts2 = new TraceStep(null, ls, kc, "calculate m and k through the above two linear equations.",
"calculate m and k through linear equation and retrieve y=mx+k line form.");
ls._innerLoop.Add(ts0);
ls._innerLoop.Add(ts1);
ls._innerLoop.Add(ts2);
ls.GenerateATrace(strategy);
}
public void Test_MultiStrategy_1()
{
//strategy1: 1->2, 2->3
var ts1 = new TraceStep(1, 2, "null", "TODO1", "TODO2");
var ts1Expr = new TraceStepExpr(ts1);
var ts2 = new TraceStep(2, 3, "null", "TODO2", "TODO3");
var ts2Expr = new TraceStepExpr(ts2);
var lst1 = new List <TraceStepExpr>()
{
ts1Expr, ts2Expr
};
var tuple1 = new Tuple <object, object>("strategy1", lst1);
//strategy2: 2->3, 3->5, 5->7
var ts3 = new TraceStep(2, 3, null, "TODO", "TODO1");
var ts3Expr = new TraceStepExpr(ts3);
var ts4 = new TraceStep(3, 5, null, "TODO2", "TODO5");
var ts4Expr = new TraceStepExpr(ts4);
var ts5 = new TraceStep(5, 7, null, "Test1", "test23");
var ts5Expr = new TraceStepExpr(ts5);
var lst2 = new List <TraceStepExpr>()
{
ts3Expr, ts4Expr, ts5Expr
};
var tuple2 = new Tuple <object, object>("strategy2", lst2);
var lstStrategy = new List <Tuple <object, object> >();
lstStrategy.Add(tuple1);
lstStrategy.Add(tuple2);
var graph = new BehaviorGraph();
graph.Insert(lstStrategy);
Assert.True(graph.Nodes.Count == 3);
var node1 = graph.Nodes[1];
Assert.True(node1.OutEdges.Count == 1);
var node2 = graph.Nodes[2];
Assert.True(node2.InEdges.Count == 1);
Assert.True(node2.OutEdges.Count == 0);
Assert.NotNull(node1.SubGraph);
Assert.True(node1.SubGraph.Nodes.Count == 3);
Assert.NotNull(node2.SubGraph);
Assert.True(node2.SubGraph.Nodes.Count == 4);
/////////////////////////////////////////////////////
//Search Test
var initNode = graph.RetrieveInitInnerNode();
Assert.NotNull(initNode);
int count = graph.PathFinding(initNode);
Assert.True(count == 5);
var nextObj = graph.SearchNextInnerLoopNode(initNode);
var tuple5 = nextObj as Tuple <object, object>;
Assert.NotNull(tuple5);
var nextNode = tuple5.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 4);
nextObj = graph.SearchNextInnerLoopNode(nextNode);
tuple5 = nextObj as Tuple <object, object>;
Assert.NotNull(tuple5);
nextNode = tuple5.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 3);
var index = graph.SearchOuterLoopNodeIndex(nextNode);
Assert.True(index == 1);
nextObj = graph.SearchNextInnerLoopNode(nextNode);
tuple5 = nextObj as Tuple <object, object>;
Assert.NotNull(tuple5);
nextNode = tuple5.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 2);
index = graph.SearchOuterLoopNodeIndex(nextNode);
Assert.True(index == 2);
nextObj = graph.SearchNextInnerLoopNode(nextNode);
tuple5 = nextObj as Tuple <object, object>;
Assert.NotNull(tuple5);
nextNode = tuple5.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 1);
index = graph.SearchOuterLoopNodeIndex(nextNode);
Assert.True(index == 2);
nextObj = graph.SearchNextInnerLoopNode(nextNode);
tuple5 = nextObj as Tuple <object, object>;
Assert.NotNull(tuple5);
nextNode = tuple5.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 0);
index = graph.SearchOuterLoopNodeIndex(nextNode);
Assert.True(index == 2);
var prevNode = graph.SearchPrevInnerLoopNode(nextNode) as BehaviorGraphNode;
Assert.NotNull(prevNode);
count = graph.PathFinding(prevNode);
Assert.True(count == 1);
var strateties = graph.SearchAllOuterEdgeInfos();
Assert.True(strateties.Count == 2);
}
public void Test_OneStrategy_OneTraceStep_Author()
{
//1+1->2
var expr1 = new Term(Expression.Add, new List<object> { 1, 1 });
var ts = new TraceStep(expr1, 2, "null", "meta-rule todo", "rule todo");
var tsExpr = new TraceStepExpr(ts);
var lst = new List<TraceStepExpr>() { tsExpr };
var tuple = new Tuple<object, object>("strategy1", lst);
var lstStrategy = new List<Tuple<object, object>>();
lstStrategy.Add(tuple);
var graph = new BehaviorGraph();
graph.Insert(lstStrategy);
Assert.True(graph.Nodes.Count == 2);
var node0 = graph.Nodes[0];
Assert.Null(node0.SubGraph);
var node1 = graph.Nodes[1];
Assert.NotNull(node1.SubGraph);
Assert.True(node1.SubGraph.Nodes.Count == 2);
/////////////////////////////////////////////
//4-1->2
var expr2 = new Term(Expression.Add, new List<object> { 4, 1 });
// User Input, //wrong step
var ts1 = new TraceStep(expr2, 2);
var ts1Expr = new TraceStepExpr(ts1);
var tsLst = new List<TraceStepExpr>() { ts1Expr };
var tuple2 = new Tuple<object, object>("strategy1", tsLst);
var lst44 = new List<Tuple<object, object>>() { tuple2 };
bool matchResult = graph.Match(lst44);
Assert.True(matchResult);
graph.Update(lst44);
Assert.True(graph.Nodes.Count == 2);
Assert.True(node1.SubGraph.Nodes.Count == 3);
/////////////////////////////////////////////
//test search
var initNode = graph.RetrieveInitInnerNode();
Assert.NotNull(initNode);
var innerState = initNode.State as InnerLoopBehaviorState;
Assert.NotNull(innerState);
Assert.True(innerState.UserKnowledge.ToString().Equals("1+1"));
Assert.True(initNode.InEdges.Count == 0);
Assert.True(initNode.OutEdges.Count == 1);
int count = graph.PathFinding(initNode);
Assert.True(count == 1);
var nextObj = graph.SearchNextInnerLoopNode(initNode);
var tuple22 = nextObj as Tuple<object, object>;
Assert.NotNull(tuple22);
var nextNode = tuple22.Item2 as BehaviorGraphNode;
Assert.NotNull(nextNode);
count = graph.PathFinding(nextNode);
Assert.True(count == 0);
}
public static void FromPointsToMidPoint(PointSymbol ps1, PointSymbol ps2, PointSymbol midPoint)
{
//1. plot the ps1, ps2 and the line
//2. generate x coordinate
//3. generate y coordinate
//4. generate point (x,y)
string strategy;
var ts00 = new TraceStep(null, ps1, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ps1));
var ts01 = new TraceStep(null, ps2, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ps2));
var ls = LineBinaryRelation.Unify(ps1, ps2) as LineSymbol;
var ts02 = new TraceStep(null, ls, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ls));
strategy = "Plot the given two points and the connected line.";
midPoint._innerLoop.Add(ts00);
midPoint._innerLoop.Add(ts01);
midPoint._innerLoop.Add(ts02);
midPoint.GenerateATrace(strategy);
////////////////////////////////////////////////
var xCoord = new Var("x");
var pt1 = ps1.Shape as Point;
Debug.Assert(pt1 != null);
var pt2 = ps2.Shape as Point;
Debug.Assert(pt2 != null);
var term1 = new Term(Expression.Add, new List<object>(){pt1.XCoordinate, pt2.XCoordinate});
var term2 = new Term(Expression.Divide, new List<object>(){term1, 2});
var eq = new Equation(xCoord, term2);
/////////////////////////////////////////////////
object obj;
bool result = eq.IsEqGoal(out obj);
EqGoal goal1 = null;
if (result)
{
goal1 = obj as EqGoal;
Debug.Assert(goal1!=null);
Debug.Assert(goal1.Traces.Count == 1);
var currentTrace = goal1.Traces.ToList()[0];
strategy = "Generate x coordinate of midpoint.";
var newTrace = new Tuple<object, object>(strategy, currentTrace.Item2);
midPoint.Traces.Add(newTrace);
}
//////////////////////////////////////////////////
var yCoord = new Var("y");
term1 = new Term(Expression.Add, new List<object>() { pt1.YCoordinate, pt2.YCoordinate });
term2 = new Term(Expression.Divide, new List<object>() { term1, 2 });
var eq1 = new Equation(yCoord, term2);
result = eq1.IsEqGoal(out obj);
EqGoal goal2 = null;
if (result)
{
goal2 = obj as EqGoal;
Debug.Assert(goal2 != null);
Debug.Assert(goal2.Traces.Count == 1);
var currentTrace1 = goal2.Traces.ToList()[0];
strategy = "Generate y coordinate of midpoint.";
var newTrace = new Tuple<object, object>(strategy, currentTrace1.Item2);
midPoint.Traces.Add(newTrace);
}
//////////////////////////////////////////////////////
var ps = new Point(xCoord, yCoord);
var psym = new PointSymbol(ps);
var mid = midPoint.Shape as Point;
Debug.Assert(mid != null);
var ps_inter1 = new Point(mid.XCoordinate, yCoord);
var psym_inter1 = new PointSymbol(ps_inter1);
var metaRule = "Consider substitute generate x coordinate into the point form.";
var appliedRule = SubstitutionRule.ApplySubstitute(goal1, psym);
var ts1 = new TraceStep(psym, psym_inter1, null, metaRule, appliedRule);
metaRule = "Consider substitute generate y coordinate into the point form.";
appliedRule = SubstitutionRule.ApplySubstitute(goal2, psym_inter1);
var ts2 = new TraceStep(psym_inter1, midPoint, null, metaRule, appliedRule);
strategy = "Generate point (x,y) by subsitute generated x and y.";
midPoint._innerLoop.Add(ts1);
midPoint._innerLoop.Add(ts2);
midPoint.GenerateATrace(strategy);
}
public static void LineSlopeIntercepToGraph(LineSymbol ls)
{
string strategy = strategy_graphing;
//Plotting shapes
//1. plotting Y-Intercept
//2. plotting X-Intercept
//3. plotting the line
//////////////////////////////////////////////////////////////
// Step 1:
var pt = new Point(0, ls.SymIntercept);
var ptSym = new PointSymbol(pt);
var ts0 = new TraceStep(null, ptSym, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ptSym));
ls._innerLoop.Add(ts0);
//////////////////////////////////////////////////////////////
// Step 2:
var line = ls.Shape as Line;
Debug.Assert(line != null);
Equation eq;
if (line.B == null)
{
}
else
{
var x = new Var("x");
//step 2.1
var term = new Term(Expression.Multiply, new List <object>()
{
line.Slope, x
});
var term1 = new Term(Expression.Add, new List <object>()
{
term, line.Intercept
});
eq = new Equation(term1, 0);
object obj;
EqGoal gGoal = null;
bool result = eq.IsEqGoal(out obj);
if (result)
{
gGoal = obj as EqGoal;
}
if (gGoal != null)
{
double dX;
LogicSharp.IsDouble(gGoal.Rhs, out dX);
var pt1 = new Point(dX, 0);
var ptSym1 = new PointSymbol(pt1);
var ts1 = new TraceStep(null, ptSym1, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ptSym1));
ls._innerLoop.Add(ts1);
}
}
/////////////////////////////////////////////////////////////////
const string step1MetaRule = "Given the line slope-intercept form y=mx+b, plot the line by passing points (0,b) and (-b/m,0).";
string step1AppliedRule = String.Format("Plotting the line passing through (0,{0}) and ({1},0) ", ls.SymIntercept, ls.SymC);
//var ts = new TraceStep(null, ls.SlopeInterceptForm, step1MetaRule, step1AppliedRule);
string kc = GeometryScaffold.KC_LineGraphing;
var ts = new TraceStep(null, ls, kc, step1MetaRule, step1AppliedRule);
ls._innerLoop.Add(ts);
//////////////////////////////////////////////////////////////////
ls.GenerateATrace(strategy);
}
public static void FromPointsToMidPoint(PointSymbol ps1, PointSymbol ps2, PointSymbol midPoint)
{
//1. plot the ps1, ps2 and the line
//2. generate x coordinate
//3. generate y coordinate
//4. generate point (x,y)
string strategy;
var ts00 = new TraceStep(null, ps1, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ps1));
var ts01 = new TraceStep(null, ps2, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ps2));
var ls = LineBinaryRelation.Unify(ps1, ps2) as LineSymbol;
var ts02 = new TraceStep(null, ls, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ls));
strategy = "Plot the given two points and the connected line.";
midPoint._innerLoop.Add(ts00);
midPoint._innerLoop.Add(ts01);
midPoint._innerLoop.Add(ts02);
midPoint.GenerateATrace(strategy);
////////////////////////////////////////////////
var xCoord = new Var("x");
var pt1 = ps1.Shape as Point;
Debug.Assert(pt1 != null);
var pt2 = ps2.Shape as Point;
Debug.Assert(pt2 != null);
var term1 = new Term(Expression.Add, new List <object>()
{
pt1.XCoordinate, pt2.XCoordinate
});
var term2 = new Term(Expression.Divide, new List <object>()
{
term1, 2
});
var eq = new Equation(xCoord, term2);
/////////////////////////////////////////////////
object obj;
bool result = eq.IsEqGoal(out obj);
EqGoal goal1 = null;
if (result)
{
goal1 = obj as EqGoal;
Debug.Assert(goal1 != null);
Debug.Assert(goal1.Traces.Count == 1);
var currentTrace = goal1.Traces.ToList()[0];
strategy = "Generate x coordinate of midpoint.";
var newTrace = new Tuple <object, object>(strategy, currentTrace.Item2);
midPoint.Traces.Add(newTrace);
}
//////////////////////////////////////////////////
var yCoord = new Var("y");
term1 = new Term(Expression.Add, new List <object>()
{
pt1.YCoordinate, pt2.YCoordinate
});
term2 = new Term(Expression.Divide, new List <object>()
{
term1, 2
});
var eq1 = new Equation(yCoord, term2);
result = eq1.IsEqGoal(out obj);
EqGoal goal2 = null;
if (result)
{
goal2 = obj as EqGoal;
Debug.Assert(goal2 != null);
Debug.Assert(goal2.Traces.Count == 1);
var currentTrace1 = goal2.Traces.ToList()[0];
strategy = "Generate y coordinate of midpoint.";
var newTrace = new Tuple <object, object>(strategy, currentTrace1.Item2);
midPoint.Traces.Add(newTrace);
}
//////////////////////////////////////////////////////
var ps = new Point(xCoord, yCoord);
var psym = new PointSymbol(ps);
var mid = midPoint.Shape as Point;
Debug.Assert(mid != null);
var ps_inter1 = new Point(mid.XCoordinate, yCoord);
var psym_inter1 = new PointSymbol(ps_inter1);
var metaRule = "Consider substitute generate x coordinate into the point form.";
var appliedRule = SubstitutionRule.ApplySubstitute(goal1, psym);
var ts1 = new TraceStep(psym, psym_inter1, null, metaRule, appliedRule);
metaRule = "Consider substitute generate y coordinate into the point form.";
appliedRule = SubstitutionRule.ApplySubstitute(goal2, psym_inter1);
var ts2 = new TraceStep(psym_inter1, midPoint, null, metaRule, appliedRule);
strategy = "Generate point (x,y) by subsitute generated x and y.";
midPoint._innerLoop.Add(ts1);
midPoint._innerLoop.Add(ts2);
midPoint.GenerateATrace(strategy);
}
/*
* Automatic scaffolding
*
* Distance function (x-x0)^2+(y-y0)^2 = d^2
*
* Forward chaining to derive d.
* Backward chaining to derive other four parameters.
*/
private static Tuple <object, object> SlopeSubstitution(Point pt1, Point pt2, double value)
{
//out strategy
string strategy = "Substitute two points and slope value into the slope function.";
//1. Substitute two points into the line slope function.
//2. Substitute slope property into the line slope function.
var lst = new List <TraceStep>();
///////////////////////////////////////////////////////////////////
var variable = new Var('m');
//1.
string step1metaRule = "Consider the Line Slope Function: m=(y1-y0)/(x1-x0)";
string step1AppliedRule = String.Format(
"Substitute two points value into the slope function {0}=({1}-{2})/({3}-{4})",
variable,
pt2.YCoordinate.ToString(),
pt1.YCoordinate.ToString(),
pt2.XCoordinate.ToString(),
pt1.XCoordinate.ToString());
/* var pt1X = new Var("x0");
* var pt1Y = new Var("y0");
* var pt2X = new Var("x1");
* var pt2Y = new Var("y1");*/
/* var term1_1 = new Term(Expression.Subtract, new List<object>() { pt1X, pt2X });
* var term2_1 = new Term(Expression.Subtract, new List<object>() { pt1Y, pt2Y });
* var rhs_1 = new Term(Expression.Divide, new List<object>() { term2_1, term1_1 });
*
* var old_eq = new Equation(variable, rhs_1);*/
var term1_11 = new Term(Expression.Subtract, new List <object>()
{
pt2.XCoordinate, pt1.XCoordinate
});
var term2_11 = new Term(Expression.Subtract, new List <object>()
{
pt2.YCoordinate, pt1.YCoordinate
});
var rhs_11 = new Term(Expression.Divide, new List <object>()
{
term1_11, term2_11
});
var eq = new Equation(variable, rhs_11);
string kc = GeometryScaffold.KC_LineSlopeForm;
var trace1 = new TraceStep(null, eq, kc, step1metaRule, step1AppliedRule);
//lst.Add(trace1);
lst.Add(trace1);
///////////////////////////////////////////////////////////////////////////
//2.
var newEq = new Equation(value, rhs_11);
string step2metaRule = "Substitute slope property into the Line Slope Function: m=(y1-y0)/(x1-x0)";
string step2AppliedRule = String.Format(
"Substitute slope value into the slope function {0}=({1}-{2})/({3}-{4})",
value,
pt2.YCoordinate.ToString(),
pt1.YCoordinate.ToString(),
pt2.XCoordinate.ToString(),
pt1.XCoordinate.ToString());
kc = SubstitutionRule.SubstituteKC();
var trace2 = new TraceStep(null, newEq, kc, step2metaRule, step2AppliedRule);
//lst.Add(trace1);
lst.Add(trace2);
////////////////////////////////////////////////////////////////////////////
var newTuple = new Tuple <object, object>(strategy, lst);
return(newTuple);
}
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;
}
/*
* Automatic scaffolding
*
* Distance function (x-x0)^2+(y-y0)^2 = d^2
*
* Forward chaining to derive d.
* Backward chaining to derive other four parameters.
*/
private static Tuple<object, object> SlopeSubstitution(Point pt1, Point pt2, double value)
{
//out strategy
string strategy = "Substitute two points and slope value into the slope function.";
//1. Substitute two points into the line slope function.
//2. Substitute slope property into the line slope function.
var lst = new List<TraceStep>();
///////////////////////////////////////////////////////////////////
var variable = new Var('m');
//1.
string step1metaRule = "Consider the Line Slope Function: m=(y1-y0)/(x1-x0)";
string step1AppliedRule = String.Format(
"Substitute two points value into the slope function {0}=({1}-{2})/({3}-{4})",
variable,
pt2.YCoordinate.ToString(),
pt1.YCoordinate.ToString(),
pt2.XCoordinate.ToString(),
pt1.XCoordinate.ToString());
/* var pt1X = new Var("x0");
var pt1Y = new Var("y0");
var pt2X = new Var("x1");
var pt2Y = new Var("y1");*/
/* var term1_1 = new Term(Expression.Subtract, new List<object>() { pt1X, pt2X });
var term2_1 = new Term(Expression.Subtract, new List<object>() { pt1Y, pt2Y });
var rhs_1 = new Term(Expression.Divide, new List<object>() { term2_1, term1_1 });
var old_eq = new Equation(variable, rhs_1);*/
var term1_11 = new Term(Expression.Subtract, new List<object>() { pt2.XCoordinate, pt1.XCoordinate });
var term2_11 = new Term(Expression.Subtract, new List<object>() { pt2.YCoordinate, pt1.YCoordinate });
var rhs_11 = new Term(Expression.Divide, new List<object>() { term1_11, term2_11 });
var eq = new Equation(variable, rhs_11);
string kc = GeometryScaffold.KC_LineSlopeForm;
var trace1 = new TraceStep(null, eq, kc, step1metaRule, step1AppliedRule);
//lst.Add(trace1);
lst.Add(trace1);
///////////////////////////////////////////////////////////////////////////
//2.
var newEq = new Equation(value, rhs_11);
string step2metaRule = "Substitute slope property into the Line Slope Function: m=(y1-y0)/(x1-x0)";
string step2AppliedRule = String.Format(
"Substitute slope value into the slope function {0}=({1}-{2})/({3}-{4})",
value,
pt2.YCoordinate.ToString(),
pt1.YCoordinate.ToString(),
pt2.XCoordinate.ToString(),
pt1.XCoordinate.ToString());
kc = SubstitutionRule.SubstituteKC();
var trace2 = new TraceStep(null, newEq, kc, step2metaRule, step2AppliedRule);
//lst.Add(trace1);
lst.Add(trace2);
////////////////////////////////////////////////////////////////////////////
var newTuple = new Tuple<object, object>(strategy, lst);
return newTuple;
}
