public static void MyPlaygroundForL1Expressions()
{
var rules = new RuleSet();
var p = rules.Define1("p");
var q = rules.Define1("q");
// Axioms
// rules += x => p(x) | q(x) | !p("c");
rules += x => p(x) | q(x);
rules += x => !p(x) | q(x);
rules += x => p(x) | !q(x);
// Conclusion
rules.Prove(p("c") & q("c"));
}
public static void OldMainExample()
{
var rules = new RuleSet();
var isType = rules.Define1("is a type");
var extends = rules.Define2("extends");
var isPof = rules.Define2("is parent of");
// Axioms
rules += (X, Y) => (extends(Y, X) & isType(X) & isType(Y)) > isPof(X, Y);
// Factum
rules += isType("C1");
rules += isType("C2");
rules += extends("C1", "C2");
// Conclusion
rules.Prove(isPof("C2", "C1")); // should be true
}
public static void ExtendsBelongs()
{
var rules = new RuleSet();
var isType = rules.Define1("is a type");
var extends = rules.Define2("extends");
var belongs = rules.Define2("belongs");
// Axioms
rules += (X, Y, P) => (extends(Y, X) & isType(X) & isType(Y) & belongs(P, X)) > belongs(P, Y);
// Factum
rules += isType("C1");
rules += isType("C2");
rules += extends("C1", "C2");
rules += belongs("P1", "C2");
// Conclusion
rules.Prove(belongs("P1", "C1"));
}
public static void AdContrary()
{
var rules = new RuleSet();
var p = rules.Define1("p");
var q = rules.Define1("q");
// Axioms
rules += x => p(x) > q(x);
// Factum
rules += !q("c");
// Conclusion
rules.Prove(!p("c"));
// rules.Prove(!p("c") | q("c"));
}
public static void ExampleOfHighlyInefficientResolution()
{
var rules = new RuleSet();
var p = rules.Define1("p");
var q = rules.Define1("q");
// Axioms
rules += x => p(x) | q(x);
rules += x => !p(x) | q(x);
rules += x => p(x) | !q(x);
// Conclusion
rules.Prove(p("c") & q("c"));
}
public static void SyntaxDemo()
{
var rules = new RuleSet();
var isType = rules.Define1("is a type");
var extends = rules.Define2("extends");
var isPof = rules.Define2("is parent of");
// Axioms
rules += (X, Y) => (extends(Y, X) & isType(X) & isType(Y)) > isPof(X, Y);
// Factum
rules += isType("C1");
rules += isType("C2");
rules += extends("C1", "C2");
// Conclusion
rules.Prove(isPof("C2", "C1")); // should be true
// Extensions (to demonstrate additional capabilites)
var toString = (!isType("dog") & isType("Object")).ToString();
rules += !isType("dog") & isType("Object");
// TODO. definition is incomplete, since no function calls are allowed in predicates
var equals = rules.Define2("equals");
rules += x => isType(x) > (extends(x, "Object") | equals(x, "Object"));
}
public static void AritySimplifierDemo()
{
var rules = new RuleSet();
var term = rules.Define1("term");
var node =
(
(
term("o1")
& term("o2")
& term("o3")
& term("o4")
)
| term("oo1")
| term("oo2")
)
& term("ooo1");
var expr = new L1Expression(node);
expr.Traverse(new TreeDumper());
expr.Xform(new AritySimplifier());
expr.Traverse(new AstValidator());
expr.Traverse(new TreeDumper());
}
public static void CnfDemoMain2()
{
var rules = new RuleSet();
var isType = rules.Define1("term");
rules += (isType("c1") & isType("c2") & isType("c3")) | isType("d1") | isType("d2");
var expression = rules.Factum[0];
expression.Traverse(new TreeDumper());
expression.Xform(new CnfTransformer());
expression.Traverse(new TreeDumper());
}
public static void CnfDemoMain()
{
var rules = new RuleSet();
var p = rules.Define1("P");
var q = rules.Define1("Q");
var r = rules.Define1("R");
var s = rules.Define1("S");
// p.24 of the book, p.13 of the scan
rules += (p("x") & (q("x") > r("x"))) > s("x");
var expression = rules.Factum[0];
expression.Traverse(new TreeDumper());
expression.Xform(new CnfTransformer());
expression.Traverse(new AstValidator());
expression.Traverse(new TreeDumper());
}
