Hazel markets itself as an "Elm/ML-like functional programming language". From the previous example of map, it should be apparent just how close to OCaml the language is.

It turns out that a majority of the transpiler is a transformation of syntax. Take a simple ADT for an arithmetic programming language.

type expr =
  | Float of float
  | Add of expr * expr
  | Sub of expr * expr
  | Mul of expr * expr
  | Div of expr * expr

And when we run hazel_of_ocaml over this OCaml type declaration.

type expr =
  + Float(Float)
  + Add((expr, expr))
  + Sub((expr, expr))
  + Mul((expr, expr))
  + Div((expr, expr))
 in ?

Not much has changed expect some syntax. Hazel does not have a notion of top-level expression so hazel_of_ocaml wraps the program into one set of value bindings. For the most part, Hazel acts as a subset of the pure, functional part of OCaml. At the time of writing, this subset is fairly limited with no support for modules or labelled records out of the box (there are plenty of development branches with these features).

If we try out the same map function but written in OCaml and transpiled to Hazel we get.

let rec map f = function
  | [] -> []
  | x :: xs -> f x :: map f xs

Which becomes the following hazel program.

let map = fun f -> fun x1 -> case x1
  | [] => []
  | x :: xs => f(x) :: map(f)(xs)
end in ?

We could have a field day discussing the syntax of OCaml and Hazel (parentheses for function arguments, well-scoped cases for pattern-matching, a different arrow for pattern-matching etc.). What would be more interesting is taking a look at how to handle polymorphism in Hazel.

Hazel has explicit polymorphism. So far, we have not seen it as we have let the types have holes in them. The map function in OCaml has the following type.

val map : 
  ('a -> 'b) -> 'a list -> 'b list

We must remind ourselves (by reading Craig's excellent blogpost on the matter) that in OCaml

... type variables in signatures are implicitly universally-quantified

So in reality, we have that map has the following type.

val map : ∀ a b. (a ->  b) -> a list -> b list

In Hazel, we have to explicitly type our map function to be polymorphic. Not only does this mean the type annotation requires universally quantified type variables, but we must also perform type application wherever we choose to apply the map function (whether that be recursively or somewhere later in our program).

let map : forall a -> forall b -> (a -> b) -> [a] -> [b] =
  typfun a -> typfun b -> fun f -> fun xs -> case xs
    | [] => []
    | x :: xs => f (x) :: map@<a>@<b>(f)(xs) 
end in
map@<Int>@<Int>(fun x -> ?)([1, 2, 3])

forall introduces a universally quantified type variable into our type annotation, and typfun introduces it into the function itself (à la System F). Type application requires @<T> where T is some type. This allows hazel to quite easily support higher rank polymorphism, but we will not worry too much about that.

Most often, OCaml users interact with prenex polymorphism (rank-1) where the universal quantifiers are at the front of the type. OCaml does support quantifiers inside certain types like records.

What this means for the transpiler is that we can reuse OCaml's type inference to safely instantiate the correct type annotations and type applications in Hazel! To do this, hazel_of_ocaml uses Merlin to inspect the type of the function in either a value binding or at the point of a function application.

Take a simple, polymorphic length function.

let rec length = function
 | [] -> 0
 | _ :: xs -> 1 + length xs

let int_len = length [ 1; 2; 3 ]
let str_len = length [ "only"; "two" ]

When we run this through hazel_of_ocaml with the -type flag we get.

let length : forall a -> [a] -> Int = typfun a -> fun x1 -> case x1
  | [] => 0
  | _ :: xs => 1 + length@<a>(xs)
end in
let int_len : Int = length@<Int>(1 :: 2 :: [3]) in
let str_len : Int = length@<String>("only" :: ["two"])
in ?

hazel_of_ocaml has correctly instantiated the type for length inside the recursive function and then in each case with the integer list and the string list.