CODEWITHSUNDEEP
typesocaml
douyu
douyu

Reputation: 2609

How can I understand OCaml user defined type?

(* Data type definitions *)
type t =
  | True
  | False
  | If of t * t * t
  | Zero
  | Succ of t
  | Pred of t
  | IsZero of t

In If of t * t * t, why use '*' to connect, and how to understand?

Upvotes: 1

Views: 69

Answers (1)

Silvio Mayolo
Silvio Mayolo

Reputation: 70397

The If constructor for your t type takes three arguments. In, say, Java, we would write it as a constructor like so

If(T a, T b, T c) { ... }

Now, we can think of a function which takes three arguments, conceptually, as a function which takes a tuple containing three things. A tuple is a sort of mathematical object which represents the "most general way" to have an ordered collection of a fixed size. So a tuple of three integers is the "most general way" (for some definition of "most", "general", and "way") to have three integers in a single data structure.

Now, category theorists call this "most general way" thing a product, in the same way we say the product of 3 and 5 is 15. You can read up on why we call it a product and what nice properties it has on Wikipedia if you like, but the basic idea is: tuples satisfy a lot of the "usual" mathematical properties of multiplication like commutativity, associativity, and distributivity over addition. So, to match this mathematical convention, OCaml uses * (the same symbol we use to multiply numbers) to indicate the "product" of types. Hence,

t * t * t

is a collection of three t values packed into a tuple in order. In Haskell, we would simply write this as (T, T, T). If you're familiar with Typescript, we would write it as [T, T, T] (tuples in Typescript are just lists where we happen to know the length and types of elements in advance). Java doesn't really have an equivalent notion to this.

Upvotes: 2

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