Past exam of the mathematics course of the University of Cambridge / 2006 / ia / Paper 5 / 9 / c / Solution Created 2026-09-24 Updated 2026-10-14
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A collections library can supply a genuinely generic method in Java whose own type parameter connects the input element and the result element type:
java
static <T> java.util.List<T> oneElement(T item) {
    java.util.List<T> result = new java.util.ArrayList<T>();
    result.add(item);
    return result;
}
For example, List<String> xs = oneElement("sample"); is type-checked without a cast. The method can also construct a List<Integer> from an integer object. The standard library's Collections.singletonList is another example of this type relationship, though its returned list is unmodifiable.
The benefit is one reusable implementation with compile-time argument/result consistency. A raw List result would lose element-type information, invite unchecked calls and require casts that may fail later. Separate methods for every element type would duplicate code. Merely enclosing a concrete type in angle brackets, such as returning List<String>, does not make a method generic; the method here declares <T>. Type erasure means the guarantee is primarily a source-level type check, not a distinct runtime class for each type argument.
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Past exam of the mathematics course of the University of Cambridge / 2007 / ia / Paper 5 / 3 / b / Solution Created 2026-09-24 Updated 2026-10-14
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Replace type parameters by their erasures, normally Object or the first declared bound, and insert checked casts where an erased result is used as its former specific type. A simple generics in Java example becomes:
// Generic version
Vector<String> names = new Vector<String>();
names.add("Ada");
String s = names.get(0);

// Non-generic version
Vector names = new Vector();
names.add("Ada");
String s = (String) names.get(0);
The two fragments are alternatives, not consecutive declarations in one scope. For a user-defined Box<T>, replace fields, parameters and returns of type T by Object, and cast the retrieved result. Bounded parameters instead erase to their bound. A full translation must also preserve method dispatch where erasure changes overridden signatures, using suitable forwarding methods; this is the principle of type erasure, not simply deleting every pair of angle brackets.
The raw collection permits accidental insertion of an unrelated object, which may fail much later at a cast. The generic collection rejects such insertion during compilation, documents its contract at the declaration, and eliminates repetitive casts at use sites. The generic version catches more errors earlier and expresses the programmer's intended element type directly. Generic types are largely erased at runtime, so their advantage is static checking rather than a new runtime vector representation. The translation mechanism is specified by the Java language specification.
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