science

Nominal type system

Nominal type system is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Nominal type system rather than just read about it. In short: In computer science, a type system is nominal (also called nominative or name-based) if compatibility and equivalence of data types is determined by explicit declarations and/or the name of the types. Nominal systems are used to determine whether types are equivalent, as well as whether a type is a subtype of another.

Key takeaways

Nominal type system belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Nominal type system to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Nominal type system from memory before moving on to harder problems.

Reference excerpt

In computer science, a type system is nominal (also called nominative or name-based) if compatibility and equivalence of data types is determined by explicit declarations and/or the name of the types. Nominal systems are used to determine whether types are equivalent, as well as whether a type is a subtype of another. Nominal type systems contrast with structural systems, where comparisons are based on the structure of the types in question and do not require explicit declarations.

Nominal typing Nominal typing means that two variables are type-compatible if and only if their declarations name the same type. For example, in C, two struct types with different names in the same translation unit are never considered compatible, even if they have identical field declarations. However, C also allows a typedef declaration, which introduces an alias for an existing type. These are merely syntactic and do not differentiate the type from its alias for the purpose of type checking. This feature, present in many languages, can result in a loss of type safety when (for example) the same primitive integer type is used in two semantically distinct ways. Haskell provides the C-style syntactic alias in the form of the type declaration, as well as the newtype declaration that does introduce a new, distinct type, isomorphic to an existing type.

Nominal subtyping In a similar fashion, nominal subtyping means that one type is a subtype of another if and only if it is explicitly declared to be so in its definition. Nominally-typed languages typically enforce the requirement that declared subtypes be structurally compatible (though Eiffel allows non-compatible subtypes to be declared). However, subtypes which are structurally compatible "by accident", but not declared as subtypes, are not considered to be subtypes. C++, C#, Java, Kotlin, Objective-C, Delphi, Swift, Julia, and Rust all use mostly both nominal typing and subtyping. Some nominally-subtyped languages, such as Java and C#, allow classes to be declared final (or sealed in C# terminology), indicating that no further subtyping is permitted.

Comparison Nominal typing is useful at preventing accidental type equivalence, which allows better type-safety than structural typing. The cost is a reduced flexibility, as, for example, nominal typing does not allow new super-types to be created without modification of the existing subtypes.

See also Structural type system Abstract type Type system

References

Sources Pierce, Benjamin C. (2002). "§19.3 Nominal and Structural Type Systems". Types and Programming Languages. MIT Press. pp. 253–. ISBN 0-262-16209-1.

External links c2.com: Nominative and structural typing

Worked examples

Example 1 — a first encounter with Nominal type system

Start with the simplest possible case. Write down what Nominal type system claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Nominal type system before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Nominal type system ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Nominal type system

In research: Nominal type system appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Nominal type system in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Nominal type system is common in secondary-school and first-year university syllabi. It links to neighbouring topics Type systems, so understanding it makes those chapters shorter.
In everyday life: Look for Nominal type system outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Nominal type system in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Nominal type system means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Nominal type system out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Nominal type system in simple terms?

Why does Nominal type system matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Nominal type system?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Nominal type system.