public static void Run()
{
Sym inf = new SymInf();
Sym loose4 = new SymLoose(4);
Sym loose5 = new SymLoose(5);
Sym divs3left = new SymDivs(1, 3, 0, 0);
var semi = new ConveyorSR();
Console.WriteLine("Starting unit tests...");
TestEq <Sym>("Left additive identity", semi.Add(inf, loose4), loose4);
TestEq <Sym>("Right additive identity", semi.Add(loose4, inf), loose4);
TestEq <Sym>("Left multiplicative zero", semi.Mult(inf, loose4), inf);
TestEq <Sym>("Right multiplicative zero", semi.Mult(loose4, inf), inf);
TestEq <Sym>("Left multiplicative identity", semi.Mult(new SymLoose(0), loose4), loose4);
TestEq <Sym>("Right multiplicative identity", semi.Mult(loose4, new SymLoose(0)), loose4);
TestEq <Sym>("Sym.Add", semi.Add(loose4, loose4), loose4);
TestEq <Sym>("Loose 4 add Loose 5", semi.Add(loose4, loose5), loose4);
TestEq <Sym>("Loose 5 add Loose 4", semi.Add(loose5, loose4), loose4);
TestEq <Sym>("Loose 4 (X) Loose 5", semi.Mult(loose4, loose5), new SymLoose(9));
TestEq <Sym>("Loose 5 (X) Divs 1 3 0 0", semi.Mult(loose5, new SymDivs(1, 3, 0, 0)), new SymDivs(1, 8, 0, 0));
TestEq <Sym>("Divs 1 3 0 0 (X) Loose 5", semi.Mult(new SymDivs(1, 3, 0, 0), loose5), new SymDivs(1, 3, 0, 5));
Console.WriteLine("Done unit tests...");
}
static void Main(string[] args)
{
PropertyTests.Run(100);
return;
// UnitTests.Run();
// return;
var testcase = ReadInput();
var d = testcase.NumDividers;
// An H-predicate that allows a count to be up to a certain amount
var upToHP = new UpToNPred(d);
var multMap = new List <List <Tuple <int, int> > >();
for (int i = 0; i <= d + 1; i++)
{
var range = Enumerable.Range(0, i + 1)
.Select(x => new Tuple <int, int>(x, i - x))
.ToList();
multMap.Add(range);
}
var conveyorSR = new ConveyorSR();
// Embed the UpToNPred H-predicate into ConveyorNR [Emoto theorem 14]
INestedReducer <Sym, Marked <int, bool> > conveyorNR = new ConveyorNR();
INestedReducer <LiftedSet <Sym, int>, Marked <int, bool> > nested =
new LiftedNestedReducer <Sym, int, Marked <int, bool> >(conveyorNR, upToHP, multMap);
var marks = new List <bool> {
true, false
};
// All-mark the lifted nested reducer with T, F and run the
// resulting list homomorphism [Emoto lemma 18]
IListHomomorphism <LiftedSet <Sym, int>, int> marked =
new AllMarked <bool, LiftedSet <Sym, int>, int>(marks, nested);
LiftedSet <Sym, int> result = ListHomomorphism.Run(marked, testcase.Prices);
var final = upToHP.Symbols()
.Where(upToHP.Accept)
.Select(i => result.coefficients.ElementAt(i))
.Aggregate(conveyorSR.Add)
.Price;
Console.WriteLine("{0}", final);
}
public static void Run(int count)
{
var r = new Random();
var conveyorSR = new ConveyorSR();
/*
* var aa = new SymDivs(17, 5, 10, 13);
* var bb = new SymDivs(9, 9, 5, 15);
* var cc = new SymDivs(13, 16, 5, 5);
*
* Console.WriteLine("Debug: {0} {1} {2}", aa, bb, cc);
* Console.WriteLine("b (+) c = {0}", conveyorSR.Add(bb, cc));
* Console.WriteLine("a (X) b = {0}", conveyorSR.Mult(aa, bb));
* Console.WriteLine("a (X) c = {0}", conveyorSR.Mult(aa, cc));
*
* Console.WriteLine("a (X) (b + c) = {0}", conveyorSR.Mult(aa, conveyorSR.Add(bb, cc)));
* Console.WriteLine("a (X) b (+) (a (X) c) = {0}", conveyorSR.Add(conveyorSR.Mult(aa, bb),
* conveyorSR.Mult(aa, cc)));
*/
Console.WriteLine("Starting property tests");
/* Associativity of ConveyorSR.Add over Sym */
for (int i = 1; i <= count; i++)
{
Sym a = RandomSym(r);
Sym b = RandomSym(r);
Sym c = RandomSym(r);
var p = conveyorSR.Add(a, conveyorSR.Add(b, c));
var q = conveyorSR.Add(conveyorSR.Add(a, b), c);
if (!p.Equals(q))
{
Console.WriteLine("{3} Found non-associative triple of Syms under addition: {0}, {1}, {2}",
a.ToString(),
b.ToString(),
c.ToString(),
i);
}
}
/* Associativity of ConveyorSR.Mult over Sym */
for (int i = 1; i <= count; i++)
{
Sym a = RandomSym(r);
Sym b = RandomSym(r);
Sym c = RandomSym(r);
var p = conveyorSR.Mult(a, conveyorSR.Mult(b, c));
var q = conveyorSR.Mult(conveyorSR.Mult(a, b), c);
if (!p.Equals(q))
{
Console.WriteLine("{3} Found non-associative triple of Syms under multiplication: {0}, {1}, {2} --- {4}, {5}",
a.ToString(),
b.ToString(),
c.ToString(),
i,
p,
q);
}
}
/* Left-distributivity of ConveyorSR over Sym */
for (int i = 1; i <= count; i++)
{
Sym a = RandomSym(r);
Sym b = RandomSym(r);
Sym c = RandomSym(r);
var p = conveyorSR.Mult(a, conveyorSR.Add(b, c));
var q = conveyorSR.Add(conveyorSR.Mult(a, b), conveyorSR.Mult(a, c));
if (!p.Equals(q))
{
Console.WriteLine("{3} Found non-left-distributive triple of Syms: {0}, {1}, {2} --- {4}, {5}",
a.ToString(),
b.ToString(),
c.ToString(),
i,
p,
q);
}
}
/* Right-distributivity of ConveyorSR over Sym */
for (int i = 1; i <= count; i++)
{
Sym a = RandomSym(r);
Sym b = RandomSym(r);
Sym c = RandomSym(r);
var p = conveyorSR.Mult(conveyorSR.Add(a, b), c);
var q = conveyorSR.Add(conveyorSR.Mult(a, c), conveyorSR.Mult(b, c));
if (!p.Equals(q))
{
Console.WriteLine("{3} Found non-right-distributive triple of Syms: {0}, {1}, {2}",
a.ToString(),
b.ToString(),
c.ToString(),
i);
}
}
Console.WriteLine("Done property tests");
}
