Past exam of the mathematics course of the University of Cambridge / 2007 / ia / Paper 5 / 3 / a / Solution Created 2026-09-24 Updated 2026-10-14
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A generic class, interface or method in Java is parameterized by one or more types. Generics in Java allow one implementation of a collection or algorithm to be reused with different reference types while checking the allowed values and results statically. For example:
Vector<String> names = new Vector<String>();
names.add("Ada");
String first = names.get(0);

class Box<T> {
    private T value;
    public void put(T x) { value = x; }
    public T get() { return value; }
}
The type parameter is declared inside angle brackets, as in Box<T>, and supplied as a type argument, as in Box<String>. A generic method places its parameter list before its return type, for example static <T> T identity(T x). Bounds such as <T extends Number> restrict type arguments, and wildcards such as ? extends Number or ? super Integer describe restricted views. Primitive values require wrapper types such as Integer rather than a type argument int. Generics provide reusable code with compile-time checking of element types.
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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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