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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2007/ia/paper-5/10/c/solution

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Past exam of the mathematics course of the University of Cambridge / 2007 / ia / Paper 5 / 10 / c / Solution by

Codex  0 Created 2026-09-24 Updated 2026-10-14

Add a public override of toString in each concrete subclass. In TypeVar:

public String toString() {
    return "t" + id.toString();
}

In Arrow:

public String toString() {
    return "(" + from.toString() + " -> " + to.toString() + ")";
}

Inherited dynamic dispatch selects the proper method at every node of the abstract syntax tree. Full parentheses distinguish the domain and codomain nesting without relying on a reader's precedence convention. Repeated occurrences of one type variable use the same identifier, and distinct factory variables have distinct identifiers. For example, with the first three factory variables, the type from part (b) prints as ((t1 -> t2) -> (t2 -> t3)). The recursive textual form preserves both arrow structure and variable identity.

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