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 * Copyright (c) 2013, SRI International
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 * Licensed under the The BSD 3-Clause License;
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 * Redistributions of source code must retain the above copyright
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package com.sri.ai.grinder.sgdpllt.theory.differencearithmetic;

import static com.sri.ai.expresso.helper.Expressions.makeSymbol;
import static com.sri.ai.grinder.sgdpllt.library.FunctorConstants.MINUS;
import static com.sri.ai.grinder.sgdpllt.theory.differencearithmetic.DifferenceArithmeticLiteralSide.makeDifferenceArithmeticLiteralNonZeroSideOfLiteralEquivalentTo;

import java.util.ArrayList;
import java.util.Collections;
import java.util.Set;

import com.google.common.annotations.Beta;
import com.sri.ai.expresso.api.Expression;
import com.sri.ai.expresso.helper.Expressions;
import com.sri.ai.grinder.sgdpllt.api.Context;
import com.sri.ai.grinder.sgdpllt.library.number.Plus;
import com.sri.ai.grinder.sgdpllt.theory.differencearithmetic.DifferenceArithmeticLiteralSide.DifferenceArithmeticLiteralSideException;

/**
 * A collection of methods for manipulating difference arithmetic literals.
 *
 * @author braz
 *
 */
@Beta
public class DifferenceArithmeticUtil {

	/**
	 * Simplify a difference arithmetic literal.
	 * @param expression
	 * @param theory TODO
	 * @param context TODO
	 * @return
	 */
	public static Expression simplify(Expression expression, DifferenceArithmeticTheory theory, Context context) {
		Expression result;
		
		try {
			if (theory.isLiteralOrBooleanConstant(expression, context)) {
				DifferenceArithmeticLiteralSide literalSide = makeDifferenceArithmeticLiteralNonZeroSideOfLiteralEquivalentTo(expression);
				ArrayList leftHandSideArguments  = new ArrayList(literalSide.getPositives());
				ArrayList rightHandSideArguments = new ArrayList(literalSide.getNegatives()); // negatives in the left-hand side (all elements in term are supposed to be there) move to right-hand side as positives
				if (literalSide.getConstant() >= 0) {
					leftHandSideArguments.add(makeSymbol(literalSide.getConstant()));
				}
				else {
					rightHandSideArguments.add(makeSymbol(-literalSide.getConstant()));
				}
				result = Expressions.apply(expression.getFunctor(), Plus.make(leftHandSideArguments), Plus.make(rightHandSideArguments));
				if (result.equals(expression)) {
					result = expression; // make sure to return the same instance if there has been no change, as simplifiers rely on that to know something didn't change
				}
			}
			else {
				result = expression;
			}
		}
		catch (DifferenceArithmeticLiteralSideException exception) {
			result = expression;
		}

		return result;
	}

	/**
	 * Returns an expression equivalent to difference arithmetic expression numericalComparison in which terms are cancelled out,
	 * numerical constants are summed together, and the given variable occurs alone in one of the sides.
	 * Terms on the side opposite to the variable are sorted according to their natural order.
	 * @param variable
	 * @param numericalComparison
	 * @return
	 * @throws Error
	 */
	public static Expression isolateVariable(Expression variable, Expression numericalComparison) throws Error {
		Expression result;

		try {
			DifferenceArithmeticLiteralSide literalSide = makeDifferenceArithmeticLiteralNonZeroSideOfLiteralEquivalentTo(numericalComparison);

			Set positiveVariables = literalSide.getPositives();
			Set negativeVariables = literalSide.getNegatives();
			int constant = literalSide.getConstant();

			// now isolate variable:

			// create array for all the arguments of the sum that is going to be on the side opposite to the variable
			ArrayList sumArguments = new ArrayList(positiveVariables.size() + negativeVariables.size() -1 + 1); // minus variable, plus constant
			if (positiveVariables.contains(variable)) {
				for (Expression positiveVariable : positiveVariables) { // variable will be on left-hand side: invert signs of everybody else (negative variables become positive)
					if ( ! positiveVariable.equals(variable)) {
						sumArguments.add(Expressions.apply(MINUS, positiveVariable));
					}
				}
				for (Expression negativeVariable : negativeVariables) {
					sumArguments.add(negativeVariable);
				}
				sumArguments.add(makeSymbol(-constant));

				if (positiveVariables.contains(variable)) { // check again, since variable may have been canceled out
					Expression oppositeSide = Plus.make(sumArguments);
					result = Expressions.apply(numericalComparison.getFunctor(), variable, oppositeSide);
				}
				else {
					throw new Error("Trying to isolate " + variable + " in " + numericalComparison + " but it gets canceled out");
				}
			}
			else {
				for (Expression positiveVariable : positiveVariables) { // variable will be on right-hand side: everybody else stays on left-hand side and keeps their sign (negative variables get the negative sign in their representation)
					sumArguments.add(positiveVariable);
				}
				for (Expression negativeVariable : negativeVariables) {
					if ( ! negativeVariable.equals(variable)) {
						sumArguments.add(Expressions.apply(MINUS, negativeVariable));
					}
				}
				sumArguments.add(makeSymbol(constant));

				Collections.sort(sumArguments); // this increases readability and normalization.

				if (negativeVariables.contains(variable)) { // check again, since variable may have been canceled out
					Expression oppositeSide = Plus.make(sumArguments);
					result = Expressions.apply(numericalComparison.getFunctor(), oppositeSide, variable);
				}
				else {
					throw new Error("Trying to isolate " + variable + " in " + numericalComparison + " but it gets canceled out");
				}
			}

			if (result.equals(numericalComparison)) {
				result = numericalComparison; // make sure to return the same instance if there has been no change, as simplifiers rely on that to know something didn't change
			}
		}
		catch (DifferenceArithmeticLiteralSideException exception) {
			throw new Error("Trying to isolate " + variable + " in " + numericalComparison + " but the latter is not a valid difference arithmetic literal");
		}

		return result;
	}
}