gistfile1.java

    /* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
     * * * * * * * * * *           Arithmetic Operations           * * * * * * * * * * * * * * 
     * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
    /*
     * Notation: OR == alt // the same
	seq + seq:
	(a; b; c) + (x; y; z) = (a+x; b+y; c+z)
	(a; b; c) + (x; y) = (a+x; b+y; c)
	(a; b) + (x; y; z) = (a+x; b+y; z)

	seq + alt: we have to promote alt to seq ==> (alt) == (alt; epsilon; epsilon; ...; epsilon) to be of the same size
	(a; b; c) + (x | y | z) = (a; b; c) + ((x | y | z); epsilon; epsilon) = (a + (x | y | z); b; c)  // a + (x | y | z) is defined in WRD + OR

	seq + wrd: we have to promote wrd to seq ===> (wrd) == (wrd; epsilon; epsilon; ...; epsilon) to be of the same size
	(a; b; c) + x = (a; b; c) + (x; epsilon; epsilon) = (a + x; b; c)  // a + x is WRD + WRD

	wrd + seq: we have to promote wrd to seq (again) ===> (wrd) == (wrd; epsilon; epsilon; ...; epsilon) to be of the same size
	x + (a; b; c) = (x; epsilon; epsilon) + (a; b; c)  = (x + a; b; c)  // a + x is WRD + WRD

	wrd + alt: we have to convert alt to wrd ===> 
	x + (a | b | c) = x + (a + b + c)  = x + a + b + c // and that's why you should have a function "Lattice sum()" that sums all the elements in a lattice and returns a WRD lattice.

	wrd + wrd: cast and sum

	alt1 + alt2: 
	Lattice resultLat = new Lattice(Lattice.OR);
	Lattice a2sum = alt2.sum(); // returns a wrd lattice that is the sum of all elements. You don't need two for loops any more
	foreach a1 in alt1:
		resultLat.vector.add(a1.plusIntInt(a2sum));
	return resultLat;

	alt + seq: we have to promote seq to alt ==> (seq) == (seq | epsilon | epsilon | ... | epsilon)
	(x | y | z) + (a; b; c) = (x | y | z) + ((a; b; c) | epsilon | epsilon) = (x + (a; b; c) | y | z) // now it is wrd + seq above


	to simplify the alt + alt function, you'll need these function for each type pair (should be generated by your script): 
	Lattice sumIntInt(); // x+y+z
	Lattice subIntInt();  // x-y-z
	Lattice timesIntInt(); // x*y*z
	Lattice divideIntInt(); // x/y/z
     */
    //The following functions perform mathematical binary and unary operations:
    public Lattice operationTemplate(Lattice secondLat, LatticeOperation op)
    {
	Lattice retVal; 
	if (this.type == WRD & secondLat.type == WRD) 
	    {
			retVal.word.element = op.process(this.word.element, secondLat.word.element);
	    }
	else if( this.type = WRD & secondLat.type == OR )// do we need the reverse of this?
	{
		// wrd + alt: we have to convert alt to wrd ===> 
		// x + (a | b | c) = x + (a + b + c)  = x + a + b + c 
		// and that's why you should have a function "Lattice sum()" 
		// that sums all the elements in a lattice and returns a WRD lattice.
		Iterator<Lattice> itr2 = secondLat.vector.iterator();
		Lattice second = itr2.next();
		if(second != null)
		{
			retVal = this.operationTemplate(second, op); // do the op for this and the first element of second lattice
		}
		while ( itr2.hasNext() ) 
	    	{	
				second = itr2.next(); 
				retVal = retVal.operationTemplate(second, op)
	    	}
	}
	else if( this.type = OR & secondLat.type == WRD )//this is the reverse of the above
	{
		Iterator<Lattice> itr1 = this.vector.iterator();
		Lattice first = itr1.next();
		if(first != null)
		{
			retVal = secondLat.operationTemplate(first, op); // do the op for this and the first element of second lattice
		}
		while ( itr1.hasNext() ) 
	    	{	
				first = itr1.next(); 
				retVal = retVal.operationTemplate(first, op)
	    	}
	}
	else if( this.type = WRD & secondLat.type == SEQ ) // do we need the reverse of this?
	{
		//wrd + seq: we have to promote wrd to seq (again) ===> (wrd) == (wrd; epsilon; epsilon; ...; epsilon) to be of the same size
		//x + (a; b; c) = (x; epsilon; epsilon) + (a; b; c)  = (x + a; b; c)  // a + x is WRD + WRD
		Iterator<Lattice> itr2 = secondLat.vector.iterator();
		Lattice temp itr2.next();
		retVal = this.operationTemplate(temp,op)
		while ( itr2.hasNext() ) 
	    	{	
				Lattice second = itr2.next(); 
				retVal.addElement(second);
	    	}		
	}
	else if( this.type = SEQ & secondLat.type == WRD ) // reverse of above
	{
		//wrd + seq: we have to promote wrd to seq (again) ===> (wrd) == (wrd; epsilon; epsilon; ...; epsilon) to be of the same size
		//x + (a; b; c) = (x; epsilon; epsilon) + (a; b; c)  = (x + a; b; c)  // a + x is WRD + WRD
		Iterator<Lattice> itr1 = this.vector.iterator();
		Lattice temp itr1.next();
		retVal = this.operationTemplate(temp,op)
		while ( secondLat.hasNext() ) 
	    	{	
				Lattice first = itr1.next(); 
				retVal.addElement(first);
	    	}			
	}
	else if( this.type == SEQ & secondLat.type == SEQ )
	{
		// 	seq + seq:
		//(a; b; c) + (x; y; z) = (a+x; b+y; c+z)
		//(a; b; c) + (x; y) = (a+x; b+y; c)
		//(a; b) + (x; y; z) = (a+x; b+y; z)
		Iterator<Lattice> itr1 = this.vector.iterator();
		Iterator<Lattice> itr2 = secondLat.vector.iterator();
		while ( itr1.hasNext() | itr2.hasNext() ) 
	    	{
			Lattice first = itr1.next();
			Lattice second = itr2.next();
			if(first != null & second != null )
				{
					retVal.vector.addElement(op.process(first,second));
		    	}	
			else if( first == null )
		    	{	
				retVal.vector.addElement(second);
		    	}
			else if( second == null )
		    	{
				retVal.vector.addElement(first);
		    	}
	    	}
	}
	else if( this.type == OR & secondLat.type == OR )
	{
		
		// alt1 + alt2: 
		// Lattice resultLat = new Lattice(Lattice.OR);
		// Lattice a2sum = alt2.sum(); // returns a wrd lattice that is the sum of all elements. You don't need two for loops any more
		// foreach a1 in alt1:
		// resultLat.vector.add(a1.plusIntInt(a2sum));
		// return resultLat;
		Lattice sum = this.sumTemplate(secondLat,op);
		Iterator<Lattice> itr1 = this.vector.iterator();
		while ( itr1.hasNext() ) 
	    	{	
				Lattice first = itr1.next(); // we get the rhs first value
				retVall.vector.add(op.process(first,sum));
	    	}
	}
	else if( this.type == OR & secondLat.type == SEQ ) // the first one defines the behavior
	{
		//alt + seq: we have to promote seq to alt ==> (seq) == (seq | epsilon | epsilon | ... | epsilon)
		//(x | y | z) + (a; b; c) = (x | y | z) + ((a; b; c) | epsilon | epsilon) = (x + (a; b; c) | y | z) // now it is wrd + seq above
		Iterator<Lattice> itr1 = this.vector.iterator();
		Iterator<Lattice> itr2 = secondLat.vector.iterator();
		Lattice second = itr2.next();
		Lattice first = itr1.next()
		retVal.type = OR;
		retVal = second.operationTemplate(this, op); //a+(x|y|z)	
		while( itr2.hasNext() )
		{
			second = itr2.next();
			retVal.vector.add( second );
		}		
	}
	else if( this.type ==SEQ & secondLat.type == OR ) // the first one defines the behavior
	{
		// seq + alt: we have to promote alt to seq ==> (alt) == (alt; epsilon; epsilon; ...; epsilon) to be of the same size
		//(a; b; c) + (x | y | z) = (a; b; c) + ((x | y | z); epsilon; epsilon) = (a + (x | y | z); b; c)  // a + (x | y | z) is defined in WRD + OR
		Iterator<Lattice> itr1 = this.vector.iterator();
		Iterator<Lattice> itr2 = secondLat.vector.iterator();
		Lattice second = itr2.next();
		Lattice first = itr1.next()
		retVal.type = SEQ;
		retVal = first.operationTemplate(second, op); //a+(x|y|z)	
		while( itr1.hasNext() )
		{
			first = itr1.next();
			retVal.vector.add( first );
		}
	
	}	
	return retVal;
	    
    }
    /*****************************************************************************************/
    final public Lattice sumTemplate(Lattice lattice, LatticeOperation op)
    {
     // apply the operation to each element in the lattice 
    	Lattice retVal;
    	Iterator<Lattice> iter = lattice.vector.iterator();
    	Lattice temp;
    	while( iter.hasNext() )
    	{
    		temp = iter.next();// this is left to right evaluation
    		op.process(retVal,temp);
    	}
    	return retVal;
    }