How to implement BiFunctional function that corresponds to Enum in Java?

A function accepting two parameters and returning nothing is a BiConsumer.

Your enum may implement BiConsumer:

public enum ConflictResolutionStrategy implements BiConsumer<CaseType, CaseType> {
    softResolve ((case1, case2) -> case1.update(case2)),
    hardResolve((case1, case2) -> {/* do something else */});

    private final BiConsumer<CaseType, CaseType> consumer;

    ConflictResolutionStrategy(BiConsumer<CaseType, CaseType> consumer){
        this.consumer = consumer;
    }

    @Override
    public void accept(CaseType case1, CaseType case2) {
        consumer.accept(case1, case2);
    }

}

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Suppose you have a method for processing your cases:

public void processCases(Collection<CaseType> cases, BiConsumer<CaseType, CaseType> conflictResolutionStrategy){
    // ...
}

Now you can pass in either one of your existing strategies:

processCases(cases, ConflictResolutionStrategy.softResolve);

or an inline strategy:

processCases(cases, (c1, c2) -> { /* do smth here */ });