How to write the list in OCaml?

Question

If I want to write list.ml in OCaml,

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Q1

which way is correct?

type 'a list = 
  | Nil
  | Cons of 'a * ('a list)

or

type 'a list = 
  | Nil
  | Cons of 'a * 'a list

Any differences?

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Q2

Also, how do I define the Cons inside the type definition as :: ?

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Q3

How do I define Nil inside the type definition as [] ?

Answer 1

Q1 - There is no difference; each has two parameters associated to Cons . Although, Cons of ('a * 'a list) is different since it has one parameter, a tuple. You will come across that as an important distinction if you construct a tuple and try to wrap it in Cons as in, let x = a,Nil in Cons x . The choice depends on how you plan on constructing elements or some semantics of the data. In this particular case, no parenthesis should be used.

Q2 - You cannot use : as the first character of infix function names as it is a keyword in the language -- :: is also a keyword regardless. In general infix operators can be defined with parenthesis around the function name and there is a special set of symbols allowed,

let (!!) a b = Cons( a,b )

Q3 - This would require naming an identifier [] , as in let [] = Nil . Those characters are not allowed in the naming conventions (see same link as above) as they are also individually keywords.