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Asked: 2026-05-31T02:20:51+00:00

I understand what a datatype is (intuitively). But I need the formal definition. I

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I understand what a datatype is (intuitively). But I need the formal definition. I don’t understand if it is a set or it’s the names ‘int’ ‘float’ etc. The formal definition found on wikipedia is confusing.

In computer programming, a data type is a classification identifying one of various types of data, such as floating-point, integer, or Boolean, that determines the possible values for that type; the operations that can be done on values of that type; the meaning of the data; and the way values of that type can be stored.

Can anyone help me with that?

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  1. Editorial Team

    Yep. What that’s saying is that a data type has three pieces:

    1. The various possible values. So, for example, an eight bit signed integer might have -127..128. This of that as a set of values V.

    2. The operations: so an 8-bit signed integer might have +, -, * (multiply), and / (divide). The full definition would define those as functions from V into V, or possible as a function from V into float for division.

    3. The way it’s stored — I sort of gave it away when I said “eight bit signed integer”. The other detail is that I’m assuming a specific representation by the way I showed the range of values.

    You might, if you’re into object oriented programming, notice that this is very much like the definition of a class, which is defined by the storage used by each object, adn the methods of the class. Providing those parts for some arbitrary thing, but not inheritance rules, gives you what’s called an abstract data type.

    Update

    @Appy, there’s some room for differences in the formalities. I was a little subtle because it was late and I was suddenly uncertain if I’d assumed one’s complement or two’s complement — of course it’s two’s complement. So interpretation is included in my description. Abstractly, though, you’d say it is a algebraic structure T=(V,O) where V is a set of values, O a set of functions from V into some arbitrary type — remember ‘==’ for example will be a function eq:V × V → {0,1} so you can’t expect every operation to be into V.

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