Add VC Arithmetic Simplification

liquidjava-verifier/src/main/java/liquidjava/rj_language/opt/VCArithmeticSimplification.java

@@ -0,0 +1,320 @@
+package liquidjava.rj_language.opt;
+
+import java.util.ArrayList;
+import java.util.List;
+
+import liquidjava.processor.SimplifiedVCImplication;
+import liquidjava.processor.VCImplication;
+import liquidjava.rj_language.Predicate;
+import liquidjava.rj_language.ast.BinaryExpression;
+import liquidjava.rj_language.ast.Expression;
+import liquidjava.rj_language.ast.GroupExpression;
+import liquidjava.rj_language.ast.Ite;
+import liquidjava.rj_language.ast.LiteralInt;
+import liquidjava.rj_language.ast.LiteralReal;
+import liquidjava.rj_language.ast.UnaryExpression;
+
+/**
+ * Simplifies VCImplication chains by applying arithmetic identities inside refinements
+ */
+public class VCArithmeticSimplification {
+
+    /**
+     * Applies the first arithmetic simplification available in a VC chain
+     */
+    public static VCImplication apply(VCImplication implication) {
+        if (implication == null)
+            return null;
+
+        return apply(implication, List.of());
+    }
+
+    private static VCImplication apply(VCImplication implication, List<Expression> nonZeroExpressions) {
+        if (implication == null)
+            return null;
+
+        Expression expression = implication.getRefinement().getExpression();
+        Expression simplified = simplify(expression, nonZeroExpressions);
+        if (!expression.equals(simplified)) {
+            VCImplication result = new SimplifiedVCImplication(implication, new Predicate(simplified), implication);
+            result.setNext(implication.getNext() == null ? null : implication.getNext().clone());
+            return result;
+        }
+
+        List<Expression> nextNoneZeroExpressions = new ArrayList<>(nonZeroExpressions);
+        addNonZeroExpression(implication.getRefinement().getExpression(), nextNoneZeroExpressions);
+
+        VCImplication next = apply(implication.getNext(), nextNoneZeroExpressions);
+        if (implication.getNext() == null || implication.getNext().equals(next))
+            return implication;
+
+        VCImplication result = implication.copyWithRefinement(implication.getRefinement().clone());
+        result.setNext(next);
+        return result;
+    }
+
+    /**
+     * Simplifies the first arithmetic identity found inside an expression
+     */
+    private static Expression simplify(Expression expression, List<Expression> nonZeroExpressions) {
+        if (expression instanceof BinaryExpression binary)
+            return simplifyBinary(binary, nonZeroExpressions);
+        if (expression instanceof UnaryExpression unary)
+            return simplifyUnary(unary, nonZeroExpressions);
+        if (expression instanceof Ite ite)
+            return simplifyIte(ite, nonZeroExpressions);
+        if (expression instanceof GroupExpression group)
+            return simplifyGroup(group, nonZeroExpressions);
+        return expression.clone();
+    }
+
+    /**
+     * Simplifies a binary expression by visiting operands before the current node
+     */
+    private static Expression simplifyBinary(BinaryExpression binary, List<Expression> nonZeroExpressions) {
+        Expression left = binary.getFirstOperand();
+        Expression simplifiedLeft = simplify(left, nonZeroExpressions);
+        if (!left.equals(simplifiedLeft))
+            return new BinaryExpression(simplifiedLeft, binary.getOperator(), binary.getSecondOperand().clone());
+
+        Expression right = binary.getSecondOperand();
+        Expression simplifiedRight = simplify(right, nonZeroExpressions);
+        if (!right.equals(simplifiedRight))
+            return new BinaryExpression(left.clone(), binary.getOperator(), simplifiedRight);
+
+        Expression simplifiedBinary = simplifyLocalBinary(left, right, binary.getOperator(), nonZeroExpressions);
+        if (simplifiedBinary != null)
+            return simplifiedBinary;
+
+        return new BinaryExpression(left.clone(), binary.getOperator(), right.clone());
+    }
+
+    /**
+     * Simplifies a unary expression by visiting its operand before the current node
+     */
+    private static Expression simplifyUnary(UnaryExpression unary, List<Expression> nonZeroExpressions) {
+        Expression operand = unary.getExpression();
+        Expression simplifiedOperand = simplify(operand, nonZeroExpressions);
+        if (!operand.equals(simplifiedOperand))
+            return new UnaryExpression(unary.getOp(), simplifiedOperand);
+
+        // -(-x) -> x
+        if ("-".equals(unary.getOp()) && isNegation(operand))
+            return negatedExpression(operand).clone();
+
+        return new UnaryExpression(unary.getOp(), operand.clone());
+    }
+
+    /**
+     * Simplifies a ternary expression by visiting condition, then branch, and else branch
+     */
+    private static Expression simplifyIte(Ite ite, List<Expression> nonZeroExpressions) {
+        Expression condition = ite.getCondition();
+        Expression simplifiedCondition = simplify(condition, nonZeroExpressions);
+        if (!condition.equals(simplifiedCondition))
+            return new Ite(simplifiedCondition, ite.getThen().clone(), ite.getElse().clone());
+
+        Expression thenExpression = ite.getThen();
+        Expression simplifiedThen = simplify(thenExpression, nonZeroExpressions);
+        if (!thenExpression.equals(simplifiedThen))
+            return new Ite(condition.clone(), simplifiedThen, ite.getElse().clone());
+
+        Expression elseExpression = ite.getElse();
+        Expression simplifiedElse = simplify(elseExpression, nonZeroExpressions);
+        if (!elseExpression.equals(simplifiedElse))
+            return new Ite(condition.clone(), thenExpression.clone(), simplifiedElse);
+
+        return new Ite(condition.clone(), thenExpression.clone(), elseExpression.clone());
+    }
+
+    /**
+     * Simplifies an expression wrapped in parentheses while preserving the group node
+     */
+    private static Expression simplifyGroup(GroupExpression group, List<Expression> nonZeroExpressions) {
+        Expression expression = group.getExpression();
+        Expression simplified = simplify(expression, nonZeroExpressions);
+        if (!expression.equals(simplified))
+            return new GroupExpression(simplified);
+        return group.clone();
+    }
+
+    /**
+     * Dispatches a local binary arithmetic identity by operator
+     */
+    private static Expression simplifyLocalBinary(Expression left, Expression right, String op,
+            List<Expression> nonZeroExpressions) {
+        return switch (op) {
+        case "+" -> simplifyAddition(left, right);
+        case "-" -> simplifySubtraction(left, right);
+        case "*" -> simplifyMultiplication(left, right);
+        case "/" -> simplifyDivision(left, right, nonZeroExpressions);
+        case "%" -> simplifyModulo(left, right, nonZeroExpressions);
+        default -> null;
+        };
+    }
+
+    /**
+     * Applies addition identities involving zero and unary negation
+     */
+    private static Expression simplifyAddition(Expression left, Expression right) {
+        // x + 0 -> x
+        if (isZero(right))
+            return left.clone();
+        // 0 + x -> x
+        if (isZero(left))
+            return right.clone();
+        // x + (-x) -> 0
+        if (isNegation(right) && left.equals(negatedExpression(right)))
+            return new LiteralInt(0);
+        // (-x) + x -> 0
+        if (isNegation(left) && negatedExpression(left).equals(right))
+            return new LiteralInt(0);
+        // x + (-y) -> x - y
+        if (isNegation(right))
+            return new BinaryExpression(left.clone(), "-", negatedExpression(right).clone());
+        return null;
+    }
+
+    /**
+     * Applies subtraction identities involving zero, same operands, and unary negation
+     */
+    private static Expression simplifySubtraction(Expression left, Expression right) {
+        // x - 0 -> x
+        if (isZero(right))
+            return left.clone();
+        // 0 - x -> -x
+        if (isZero(left))
+            return new UnaryExpression("-", right.clone());
+        // x - x -> 0
+        if (left.equals(right))
+            return new LiteralInt(0);
+        // x - (-y) -> x + y
+        if (isNegation(right))
+            return new BinaryExpression(left.clone(), "+", negatedExpression(right).clone());
+        return null;
+    }
+
+    /**
+     * Applies multiplication identities involving one and zero
+     */
+    private static Expression simplifyMultiplication(Expression left, Expression right) {
+        // x * 1 -> x
+        if (isOne(right))
+            return left.clone();
+        // 1 * x -> x
+        if (isOne(left))
+            return right.clone();
+        // x * 0 -> 0
+        if (isZero(right))
+            return right.clone();
+        // 0 * x -> 0
+        if (isZero(left))
+            return left.clone();
+        return null;
+    }
+
+    /**
+     * Applies division identities, using prior non-zero premises when needed
+     */
+    private static Expression simplifyDivision(Expression left, Expression right, List<Expression> nonZeroExpressions) {
+        // x / 1 -> x
+        if (isOne(right))
+            return left.clone();
+        // 0 / x -> 0 (x != 0)
+        if (isZero(left) && isNonZero(right, nonZeroExpressions))
+            return left.clone();
+        // x / x -> 1 (x != 0)
+        if (left.equals(right) && isNonZero(right, nonZeroExpressions))
+            return new LiteralInt(1);
+        return null;
+    }
+
+    /**
+     * Applies modulo identities, using prior non-zero premises when needed
+     */
+    private static Expression simplifyModulo(Expression left, Expression right, List<Expression> nonZeroExpressions) {
+        // x % 1 -> 0
+        if (isOne(right))
+            return new LiteralInt(0);
+        // x % x -> 0 (x != 0)
+        if (left.equals(right) && isNonZero(right, nonZeroExpressions))
+            return new LiteralInt(0);
+        return null;
+    }
+
+    /**
+     * Records direct non-zero premises from equalities and inequalities
+     */
+    private static void addNonZeroExpression(Expression expression, List<Expression> nonZeroExpressions) {
+        if (!(expression instanceof BinaryExpression binary))
+            return;
+
+        Expression left = binary.getFirstOperand();
+        Expression right = binary.getSecondOperand();
+        if ("!=".equals(binary.getOperator())) {
+            // x != 0 -> x is non-zero
+            if (isZero(right))
+                nonZeroExpressions.add(left.clone());
+            // 0 != x -> x is non-zero
+            if (isZero(left))
+                nonZeroExpressions.add(right.clone());
+        } else if ("==".equals(binary.getOperator())) {
+            // x == n && n != 0 -> x is non-zero
+            if (isNumericLiteral(right) && !isZero(right))
+                nonZeroExpressions.add(left.clone());
+            // n == x && n != 0 -> x is non-zero
+            if (isNumericLiteral(left) && !isZero(left))
+                nonZeroExpressions.add(right.clone());
+        }
+    }
+
+    /**
+     * Checks whether a previous premise recorded an expression as non-zero
+     */
+    private static boolean isNonZero(Expression expression, List<Expression> nonZeroExpressions) {
+        return nonZeroExpressions.stream().anyMatch(e -> e.equals(expression));
+    }
+
+    /**
+     * Checks whether an expression is a numeric zero literal
+     */
+    private static boolean isZero(Expression expression) {
+        if (expression instanceof LiteralInt literal)
+            return literal.getValue() == 0;
+        if (expression instanceof LiteralReal literal)
+            return literal.getValue() == 0.0;
+        return false;
+    }
+
+    /**
+     * Checks whether an expression is a numeric literal
+     */
+    private static boolean isNumericLiteral(Expression expression) {
+        return expression instanceof LiteralInt || expression instanceof LiteralReal;
+    }
+
+    /**
+     * Checks whether an expression is a numeric one literal
+     */
+    private static boolean isOne(Expression expression) {
+        if (expression instanceof LiteralInt literal)
+            return literal.getValue() == 1;
+        if (expression instanceof LiteralReal literal)
+            return literal.getValue() == 1.0;
+        return false;
+    }
+
+    /**
+     * Checks whether an expression is unary negation
+     */
+    private static boolean isNegation(Expression expression) {
+        return expression instanceof UnaryExpression unary && "-".equals(unary.getOp());
+    }
+
+    /**
+     * Returns the operand of a unary negation expression
+     */
+    private static Expression negatedExpression(Expression expression) {
+        return ((UnaryExpression) expression).getExpression();
+    }
+}

liquidjava-verifier/src/main/java/liquidjava/rj_language/opt/VCSimplification.java

@@ -1,12 +1,18 @@
 package liquidjava.rj_language.opt;
 
+import java.util.List;
+import java.util.function.UnaryOperator;
+
 import liquidjava.processor.VCImplication;
 
 /**
  * Simplifies VCImplication chains by applying various simplification steps
  */
 public class VCSimplification {
 
+    private static final List<UnaryOperator<VCImplication>> PASSES = List.of(VCSubstitution::apply, VCFolding::apply,
+            VCArithmeticSimplification::apply);
+
     /**
      * Applies all available simplification steps to a VC chain until a fixed point is reached
      */
@@ -31,11 +37,11 @@ public static VCImplication simplifyOnce(VCImplication implication) {
         if (implication == null)
             return null;
 
-        // first try to apply substitution, then folding
-        VCImplication substituted = VCSubstitution.apply(implication);
-        if (!implication.equals(substituted))
-            return substituted;
-
-        return VCFolding.apply(implication);
+        for (UnaryOperator<VCImplication> pass : PASSES) {
+            VCImplication simplified = pass.apply(implication);
+            if (!implication.equals(simplified))
+                return simplified;
+        }
+        return implication;
     }
 }