/// <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>
/// a->b <=> (~a||b)
/// </summary>
/// <param name="logicBlock"></param>
/// <returns>The block passed to this method</returns>
public override Block Translate()
{
if (FirstBlock == null || SecondBlock == null)
{
ThrowErrorOnFirstCheck();
}
// elimination
if (Logic.IsImplication)
{
FirstBlock.SetNegation(!FirstBlock.IsNegated)
.InsertBack(new Block(PropositionalLogic.Disjunction))
.InsertBack(SecondBlock);
return(FirstBlock);
}
// reverse elimination
// ~a||b into a=>b and a||~b into b=>a
// accepting either one of them is negated, not both true or both false => XOR is the best choice
if (Logic.IsDisjunction && (FirstBlock.IsNegated ^ SecondBlock.IsNegated))
{
FirstBlock = FirstBlock.IsNegated ? FirstBlock : SecondBlock;
SecondBlock = FirstBlock.IsNegated ? SecondBlock : FirstBlock;
FirstBlock.SetNegation(!FirstBlock.IsNegated)
.InsertBack(new Block(PropositionalLogic.Implication))
.InsertBack(SecondBlock);
return(FirstBlock);
}
return(ConcatStoredBlocks());
}
protected override void Layout()
{
Renderman renderer = Element.Document.Renderer;
ComputedStyle computed = Element.Style.Computed;
// Get the top left inner corner (inside margin and border):
int width = computed.PaddedWidth;
int height = computed.PaddedHeight;
int top = computed.OffsetTop + computed.BorderTop;
int left = computed.OffsetLeft + computed.BorderLeft;
// Is it clipped?
if (renderer.IsInvisible(left, top, width, height))
{
// Totally not visible.
return;
}
// Ensure we have a batch (doesn't change graphics or font thus both nulls):
SetupBatch(null, null);
Add();
// Using firstblock as our block here.
// Set the UV to that of the solid block colour pixel:
FirstBlock.SetSolidColourUV();
// Set the (overlay) colour:
FirstBlock.SetColour(BackingColour);
// And finally sort out the verts:
FirstBlock.SetClipped(renderer.ClippingBoundary, new BoxRegion(left, top, width, height), renderer, computed.ZIndex - 0.006f);
}
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(),
});
public override void Paint()
{
if (FirstBlock == null)
{
// This can happen if an animation is requesting that a now offscreen element gets painted only.
return;
}
FirstBlock.SetColour(BackingColour);
FirstBlock.Paint();
}
/// <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());
}
