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The Checker Framework enhances Java’s type system to make it more powerful and useful. This lets software developers detect and prevent errors in their Java programs. The Checker Framework includes compiler plug-ins ("checkers") that find bugs or verify their absence. It also permits you to write your own compiler plug-ins.

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package org.checkerframework.qualframework.poly;

import org.checkerframework.qualframework.base.QualifierHierarchy;

/** A binary operation for combining qualifiers of type {@code Q}.
 */
public interface CombiningOperation {
    /** Apply the operation to two qualifiers, producing a new qualifier.  The
     * operation is expected to be commutative and associative.
     */
    Q combine(Q a, Q b);

    /** The identity element for this operation.  It should always be the case
     * that {@code op.combine(op.identity(), x)} is equivalent to {@code x}.
     */
    Q identity();

    /** The least-upper-bound operation over a qualifier hierarchy.
     */
    public static class Lub implements CombiningOperation {
        QualifierHierarchy hierarchy;

        public Lub(QualifierHierarchy hierarchy) {
            this.hierarchy = hierarchy;
        }

        @Override
        public Q combine(Q a, Q b) {
            return hierarchy.leastUpperBound(a, b);
        }

        @Override
        public Q identity() {
            return hierarchy.getBottom();
        }

        @Override
        public boolean equals(Object o) {
            if (o == null || o.getClass() != this.getClass()) {
                return false;
            }
            @SuppressWarnings("rawtypes")
            Lub other = (Lub)o;
            return this.hierarchy.equals(other.hierarchy);
        }

        @Override
        public int hashCode() {
            return this.hierarchy.hashCode();
        }

        @Override
        public String toString() {
            return "Lub";
        }
    }

    /** The greatest-lower-bound operation over a qualifier hierarchy.
     */
    public static class Glb implements CombiningOperation  {
        QualifierHierarchy hierarchy;

        public Glb(QualifierHierarchy hierarchy) {
            this.hierarchy = hierarchy;
        }

        @Override
        public Q combine(Q a, Q b) {
            return hierarchy.greatestLowerBound(a, b);
        }

        @Override
        public Q identity() {
            return hierarchy.getTop();
        }

        @Override
        public boolean equals(Object o) {
            if (o == null || o.getClass() != this.getClass()) {
                return false;
            }
            @SuppressWarnings("rawtypes")
            Glb other = (Glb)o;
            return this.hierarchy.equals(other.hierarchy);
        }

        @Override
        public int hashCode() {
            return this.hierarchy.hashCode();
        }

        @Override
        public String toString() {
            return "Glb";
        }
    }
}