private Block RelatedTheorems()
{
string firstContent = FirstBlock.GetContent(true).ToString(),
secondContent = SecondBlock.GetContent(true).ToString();
bool isConjunctive = Logic.IsConjunction;
if (firstContent == secondContent)
{
return(FirstBlock.IsNegated != SecondBlock.IsNegated ?
new Block(isConjunctive ? "false" : "true") : // complement
FirstBlock); // idempotent
}
switch (firstContent)
{
case "true": return(isConjunctive ? SecondBlock : new Block("true")); // identity
case "false": return(isConjunctive ? new Block("false") : SecondBlock); // annulment
}
return(secondContent switch
{
"true" => isConjunctive ? FirstBlock : new Block("true"), // identity
"false" => isConjunctive ? new Block("false") : SecondBlock, // annulment
_ => ConcatStoredBlocks(),
});
/// <summary>
/// a<=>b into (a=>b)&(b=>a) into ((~a||b)&(a||~b)) (Prioritize CNF over DNF)
/// Warning: This method is one directional, do not use this to convert a logic block into <=>
/// </summary>
/// <param name="logicBlock"></param>
/// <returns>The block passed to this method</returns>
public override Block Translate()
{
if (FirstBlock == null || SecondBlock == null)
{
ThrowErrorOnFirstCheck();
}
if (!Logic.IsBiconditional)
{
return(ConcatStoredBlocks());
}
Block cloneFirstBlock = new Block(FirstBlock.GetContent(true).ToString(), FirstBlock.IsNegated),
cloneSecondBlock = new Block(SecondBlock.GetContent(true).ToString(), SecondBlock.IsNegated);
// (~a||b)
FirstBlock.SetNegation(!FirstBlock.IsNegated)
.InsertBack(new Block(PropositionalLogic.Disjunction))
.InsertBack(SecondBlock);
// (a||~b)
cloneFirstBlock
.InsertBack(new Block(PropositionalLogic.Disjunction))
.InsertBack(cloneSecondBlock.SetNegation(!cloneFirstBlock.IsNegated));
// ((~a||b)&(a||~b))
var nested = new Block(FirstBlock);
nested.InsertBack(new Block(PropositionalLogic.Conjunction))
.InsertBack(new Block(cloneFirstBlock));
return(nested);
}
/// <summary>
/// Only a||(b&c) <=> (a||b)&(a||c) is available to prioritize CNF over DNF
/// </summary>
/// <param name="logicBlock"></param>
/// <returns>A block containing nested contents, which are distributed from original one</returns>
public override Block Translate()
{
if (FirstBlock == null || Logic == null || SecondBlock == null)
{
ThrowErrorOnFirstCheck();
}
bool isFirstNormal = FirstBlock.ContentType == ContentType.Normal,
isSecondNormal = SecondBlock.ContentType == ContentType.Normal;
// from left to right instead of expanding from the least to the most symbols
// no point in taking a&b or similars into consideration
if (!isFirstNormal || !isSecondNormal)
{
var logic = Logic.ToString();
// swap places: (a&b)||c into c||(a&b) locally
if (isSecondNormal)
{
(FirstBlock, SecondBlock) = (SecondBlock, FirstBlock);
}
// a&(b||c) like
if (FirstBlock.ContentType == ContentType.Normal)
{
return(Distribute(
FirstBlock.IsNegated,
FirstBlock.GetContent(true).ToString(),
SecondBlock.GetContent() as Block));
}
// (a||b)&(c||d) like
if (FirstBlock.ContentType == ContentType.Nested)
{
BlockIterator.ForEach(FirstBlock.GetContent() as Block, (currentBlock) =>
{
if (currentBlock.ContentType == ContentType.Normal)
{
Distribute(
currentBlock.IsNegated,
currentBlock.GetContent(true).ToString(),
SecondBlock.GetContent() as Block
);
}
});
return(FirstBlock.GetContent() as Block);
}
}
return(ConcatStoredBlocks());
}