public static int SortOrder(this Negation f)
{
WFF i = f.inner;
if (i is AtomicWFF)
{
return(0);
}
else if (i is Biconditional)
{
return(2);
}
else if (i is Conditional)
{
return(1);
}
else if (i is Conjunction)
{
return(((Conjunction)i).arity);
}
else if (i is Disjunction)
{
return(1);
}
else if (i is Negation)
{
return(1);
}
else if (i is Quantifier)
{
return(1);
}
throw new NotImplementedException(f.GetType().ToString());
}
public static bool Decomposable(this Negation f)
{
WFF i = f.inner;
if (i is AtomicWFF)
{
return(false);
}
else if (i is Biconditional)
{
return(true);
}
else if (i is Conditional)
{
return(true);
}
else if (i is Conjunction)
{
return(true);
}
else if (i is Disjunction)
{
return(true);
}
else if (i is Negation)
{
return(true);
}
else if (i is Quantifier)
{
return(true);
}
throw new NotImplementedException(f.GetType().ToString());
}
public override Proof Find(WFF f)
{
Proof a = assumptions.Find(pl => { return(pl.line.Equals(f)); });
if (a != null)
{
return(a);
}
foreach (Proof p in steps)
{
if (p is Subproof)
{
continue;
}
a = p.Find(f);
if (a != null)
{
return(a);
}
}
if (parent == null)
{
return(null);
}
return(parent.Find(f));
}
public override Proof Find(WFF f)
{
if (line.Equals(f))
{
return(this);
}
return(null);
}
public MainForm()
{
InitializeComponent();
Icon = TruthTree2.Properties.Resources.Icon;
WFF inn = new Negation(new Predicate("A"));
WFF tmp1 = new Negation(inn);
WFF tmp2 = inn.GetNegation();
Console.WriteLine("{0}\t{1}", tmp1, tmp2);
}
public static bool Decomposable(this WFF f)
{
if (f is AtomicWFF)
{
return(Decomposable((AtomicWFF)f));
}
else if (f is ComplexWFF)
{
return(Decomposable((ComplexWFF)f));
}
throw new NotImplementedException(f.GetType().ToString());
}
public static int SortOrder(this WFF f)
{
if (f is AtomicWFF)
{
return(SortOrder((AtomicWFF)f));
}
else if (f is ComplexWFF)
{
return(SortOrder((ComplexWFF)f));
}
throw new NotImplementedException(f.GetType().ToString());
}
private List <WFF> IdentityDecompose(Identity i, WFF f)
{
if (f is AtomicWFF)
{
return(IdentityDecompose(i, (AtomicWFF)f));
}
else if (f is ComplexWFF)
{
return(IdentityDecompose(i, (ComplexWFF)f));
}
throw new NotImplementedException(f.GetType().ToString());
}
private Decomposition DecomposeWFF(WFF f)
{
if (f is AtomicWFF)
{
return(DecomposeWFF((AtomicWFF)f));
}
else if (f is ComplexWFF)
{
return(DecomposeWFF((ComplexWFF)f));
}
throw new NotImplementedException(f.GetType().ToString());
}
public Tree(List <WFF> s, Tree p = null, WFF d = null, bool rdup = true)
{
sentences = new List <WFF>();
parent = p;
decomposed = d;
children = null;
if (parent == null)
{
sentences.AddRange(s);
terms = new HashSet <Term>();
foreach (WFF f in sentences)
{
if (f == null)
{
continue;
}
terms.UnionWith(f.GetTerms());
}
}
else
{
List <WFF> all = getAllSentences();
foreach (WFF f in s)
{
if (f == null)
{
continue;
}
if (rdup)
{
if (!all.Contains(f))
{
sentences.Add(f);
all.Add(f);
}
}
else
{
sentences.Add(f);
}
}
terms = new HashSet <Term>(parent.terms);
}
}
public bool Decompose()
{
checkForCompletion();
if (State != TreeState.Incomplete)
{
return(false);
}
List <WFF> unsatisfied = getAllUnsatisfied();
unsatisfied.Sort((a, b) => { return(a.SortOrder().CompareTo(b.SortOrder())); });
if (unsatisfied.Count < 1)
{
throw new Exception("How did this even happen?");
}
for (int a = 0; a < unsatisfied.Count; a++)
{
Decomposition dec = DecomposeWFF(unsatisfied[a]);
if (dec == null)
{
continue;
}
children = dec.getTrees(this);
if (children == null)
{
continue;
}
decomposed = dec.decomposed;
return(true);
}
return(false);
}
internal static void AddTree(this Subproof p, Tree t)
{
if (t == null)
{
throw new ArgumentNullException();
}
if (t.State != TreeState.Closed)
{
throw new InvalidOperationException();
}
if (t.decomposed == null)
{
// Something got a contradiction here, find out what
List <WFF> all = t.getAllSentences();
WFF c1 = null;
WFF c2 = null;
for (int a = 0; a < all.Count; a++)
{
if (all[a] is Negation)
{
Negation n = (Negation)all[a];
if (n.inner is Identity)
{
Identity i = (Identity)n.inner;
if (i.left.Equals(i.right))
{
c1 = all[a];
break;
}
}
}
else if (all[a] is Contradiction)
{
c1 = all[a];
break;
}
bool found = false;
for (int b = a + 1; b < all.Count; b++)
{
if (all[a].Equals(all[b].GetNegation()) || all[b].Equals(all[a].GetNegation()))
{
c1 = all[a];
c2 = all[b];
found = true;
break;
}
}
if (found)
{
break;
}
}
Proof p1 = p.Find(c1);
if (p1 == null)
{
throw new InvalidOperationException("p1");
}
if (c2 == null)
{
p.steps.Add(new ProofLine(new Contradiction(), Rule.ContradictionIntro, p1));
}
else
{
Proof p2 = p.Find(c2);
if (p2 == null)
{
throw new InvalidOperationException("p2");
}
p.steps.Add(new ProofLine(new Contradiction(), Rule.ContradictionIntro, p1, p2));
}
return;
}
Proof d = p.Find(t.decomposed);
if (t.decomposed is Biconditional)
{
// Add the steps for Equiv
Biconditional b = (Biconditional)t.decomposed;
Disjunction equ = new Disjunction(
new Conjunction(b.left, b.right),
new Conjunction(b.left.GetNegation(), b.right.GetNegation()));
ProofLine equp = new ProofLine(equ, Rule.Equivalence, d);
p.steps.Add(equp);
ProofLine plleft = new ProofLine(equ.disjuncts[0], Rule.Assumption);
Subproof left = new Subproof();
left.parent = p;
left.assumptions.Add(plleft);
left.steps.Add(new ProofLine(b.left, Rule.AndElim, plleft));
left.steps.Add(new ProofLine(b.right, Rule.AndElim, plleft));
AddTree(left, t.children[0]);
p.steps.Add(left);
ProofLine plright = new ProofLine(equ.disjuncts[1], Rule.Assumption);
Subproof right = new Subproof();
right.parent = p;
right.assumptions.Add(plright);
right.steps.Add(new ProofLine(b.left.GetNegation(), Rule.AndElim, plright));
right.steps.Add(new ProofLine(b.right.GetNegation(), Rule.AndElim, plright));
AddTree(right, t.children[1]);
p.steps.Add(right);
p.steps.Add(new ProofLine(new Contradiction(), Rule.OrElim, equp, left, right));
}
else if (t.decomposed is Conditional)
{
// Add the steps for Impl
Conditional c = (Conditional)t.decomposed;
Disjunction imp = new Disjunction(c.antecedent.GetNegation(), c.consequent);
ProofLine impp = new ProofLine(imp, Rule.Implication, d);
p.steps.Add(impp);
Proof[] steps = new Proof[t.children.Length + 1];
steps[0] = impp;
for (int a = 0; a < t.children.Length; a++)
{
steps[a + 1] = new Subproof();
Subproof s = (Subproof)steps[a + 1];
s.parent = p;
s.assumptions.Add(new ProofLine(t.children[a].sentences[0], Rule.Assumption));
AddTree(s, t.children[a]);
p.steps.Add(s);
}
p.steps.Add(new ProofLine(new Contradiction(), Rule.OrElim, steps));
}
else if (t.decomposed is Conjunction)
{
foreach (WFF f in t.children[0].sentences)
{
p.steps.Add(new ProofLine(f, Rule.AndElim, d));
}
AddTree(p, t.children[0]);
}
else if (t.decomposed is Disjunction)
{
Proof[] steps = new Proof[t.children.Length + 1];
steps[0] = d;
for (int a = 0; a < t.children.Length; a++)
{
steps[a + 1] = new Subproof();
Subproof s = (Subproof)steps[a + 1];
s.parent = p;
s.assumptions.Add(new ProofLine(t.children[a].sentences[0], Rule.Assumption));
AddTree(s, t.children[a]);
p.steps.Add(s);
}
p.steps.Add(new ProofLine(new Contradiction(), Rule.OrElim, steps));
}
else if (t.decomposed is Existential)
{
Subproof sub = new Subproof();
sub.parent = p;
sub.assumptions.Add(new ProofLine(t.children[0].sentences[0], Rule.Assumption));
AddTree(sub, t.children[0]);
p.steps.Add(sub);
p.steps.Add(new ProofLine(new Contradiction(), Rule.ExistentialElim, d, sub));
}
else if (t.decomposed is Identity)
{
// Need to add some way to find the other source
foreach (WFF f in t.children[0].sentences)
{
p.steps.Add(new ProofLine(f, Rule.EqualsElim, d));
}
AddTree(p, t.children[0]);
}
else if (t.decomposed is Negation)
{
Negation n = (Negation)t.decomposed;
if (n.inner is Biconditional)
{
// I really hope there is a better way for this one
// Add the steps for DeM and Equiv
Biconditional b = (Biconditional)n.inner;
ProofLine equ = new ProofLine(new Negation(new Conjunction(new Disjunction(b.left.GetNegation(), b.right), new Disjunction(b.left, b.right.GetNegation()))), Rule.Equivalence, d);
p.steps.Add(equ);
ProofLine dem = new ProofLine(new Disjunction(new Negation(new Disjunction(b.left.GetNegation(), b.right)), new Negation(new Disjunction(b.left, b.right.GetNegation()))), Rule.DeMorgans, equ);
p.steps.Add(dem);
Subproof left = new Subproof();
left.parent = p;
ProofLine plleft = new ProofLine(new Negation(new Disjunction(b.left.GetNegation(), b.right)), Rule.Assumption);
left.assumptions.Add(plleft);
ProofLine demleft = new ProofLine(new Conjunction(b.left, b.right.GetNegation()), Rule.DeMorgans, plleft);
left.steps.Add(demleft);
left.steps.Add(new ProofLine(b.left, Rule.AndElim, demleft));
left.steps.Add(new ProofLine(b.right.GetNegation(), Rule.AndElim, demleft));
AddTree(left, t.children[1]);
p.steps.Add(left);
Subproof right = new Subproof();
right.parent = p;
ProofLine plright = new ProofLine(new Negation(new Disjunction(b.left, b.right.GetNegation())), Rule.Assumption);
right.assumptions.Add(plright);
ProofLine demright = new ProofLine(new Conjunction(b.left.GetNegation(), b.right), Rule.DeMorgans, plright);
right.steps.Add(demright);
right.steps.Add(new ProofLine(b.left.GetNegation(), Rule.AndElim, demright));
right.steps.Add(new ProofLine(b.right, Rule.AndElim, demright));
AddTree(right, t.children[0]);
p.steps.Add(right);
p.steps.Add(new ProofLine(new Contradiction(), Rule.OrElim, dem, left, right));
}
else if (n.inner is Conditional)
{
// Add the steps for DeM and Impl
Conditional c = (Conditional)n.inner;
ProofLine imp = new ProofLine(new Negation(new Disjunction(c.antecedent.GetNegation(), c.consequent)), Rule.Implication, d);
p.steps.Add(imp);
ProofLine dem = new ProofLine(new Conjunction(c.antecedent, c.consequent.GetNegation()), Rule.DeMorgans, imp);
p.steps.Add(dem);
p.steps.Add(new ProofLine(c.antecedent, Rule.AndElim, dem));
p.steps.Add(new ProofLine(c.consequent.GetNegation(), Rule.AndElim, dem));
AddTree(p, t.children[0]);
}
else if (n.inner is Conjunction)
{
// Add the steps for DeM
Conjunction i = (Conjunction)n.inner;
List <WFF> neg = new List <WFF>();
foreach (WFF f in i.conjuncts)
{
neg.Add(f.GetNegation());
}
Disjunction dem = new Disjunction(neg.ToArray());
ProofLine demp = new ProofLine(dem, Rule.DeMorgans, d);
p.steps.Add(demp);
Proof[] steps = new Proof[t.children.Length + 1];
steps[0] = demp;
for (int a = 0; a < t.children.Length; a++)
{
steps[a + 1] = new Subproof();
Subproof s = (Subproof)steps[a + 1];
s.parent = p;
s.assumptions.Add(new ProofLine(t.children[a].sentences[0], Rule.Assumption));
AddTree(s, t.children[a]);
p.steps.Add(s);
}
p.steps.Add(new ProofLine(new Contradiction(), Rule.OrElim, steps));
}
else if (n.inner is Disjunction)
{
// Add the steps for DeM
Disjunction i = (Disjunction)n.inner;
List <WFF> neg = new List <WFF>();
foreach (WFF f in i.disjuncts)
{
neg.Add(f.GetNegation());
}
Conjunction dem = new Conjunction(neg.ToArray());
ProofLine demp = new ProofLine(dem, Rule.DeMorgans, d);
p.steps.Add(demp);
foreach (WFF f in t.children[0].sentences)
{
p.steps.Add(new ProofLine(f, Rule.AndElim, demp));
}
AddTree(p, t.children[0]);
}
else if (n.inner is Existential)
{
// Add the steps for DeM
p.steps.Add(new ProofLine(t.children[0].sentences[0], Rule.DeMorgans, d));
AddTree(p, t.children[0]);
}
else if (n.inner is Negation)
{
p.steps.Add(new ProofLine(t.children[0].sentences[0], Rule.NotElim, d));
AddTree(p, t.children[0]);
}
else if (n.inner is Universal)
{
// Add the steps for DeM
p.steps.Add(new ProofLine(t.children[0].sentences[0], Rule.DeMorgans, d));
AddTree(p, t.children[0]);
}
}
else if (t.decomposed is Universal)
{
foreach (WFF f in t.children[0].sentences)
{
p.steps.Add(new ProofLine(f, Rule.UniversalElim, d));
}
AddTree(p, t.children[0]);
}
}
public Universal(Variable v, WFF s)
{
variable = v;
scope = s;
}
public Existential(Variable v, WFF s)
{
variable = v;
scope = s;
}
internal Decomposition(WFF d, params List <WFF>[] c)
{
decomposed = d;
decomposition = c;
}
public ProofLine(WFF l, Rule r, params Proof[] s)
{
line = l;
rule = r;
reasons = new List <Proof>(s);
}
private void bParse_Click(object sender, EventArgs e)
{
premises = new List <WFF>();
rtbPremisesOut.Text = "";
foreach (string l in rtbPremisesIn.Text.Trim().Split('\n'))
{
if (l.Length < 1)
{
continue;
}
WFF f = Parser.parseString(l.Trim());
if (f != null)
{
premises.Add(f);
rtbPremisesOut.AppendText(f + "\n");
}
else
{
MessageBox.Show(string.Format("Error parsing premise {{{0}}}", l.Trim()));
rtbPremisesOut.Text = "";
return;
}
}
conclusion = Parser.parseString(rtbConclusionIn.Text);
if (conclusion == null)
{
MessageBox.Show(string.Format("Error parsing conclusion {{{0}}}", rtbConclusionIn.Text));
rtbPremisesOut.Text = "";
return;
}
rtbConclusionOut.Text = String.Format("{0}", conclusion);
List <WFF> sentences = new List <WFF>(premises);
sentences.Add(conclusion.GetNegation());
worker = new Worker <Tree>(
() =>
{
Tree t = new Tree(sentences);
t.Satisfy();
return(t);
});
worker.WorkFinished += workComplete;
tree = null;
proof = null;
setStatus("Initialized");
setEnabled(bParse, true);
setEnabled(bSatisfy, true);
setEnabled(bStop, false);
setEnabled(bShowTree, false);
setEnabled(bShowProof, false);
setEnabled(bSaveTree, false);
setEnabled(bSaveProof, false);
setTab(1);
}
public abstract Proof Find(WFF f);