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 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 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);
}
/*
* 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 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
}
}