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Writing a Lisp, Part 6: Primitives 1

December 27, 2016

Last time we added environments to our Lisp, but they are not much use in their current state - there’s no way to interact with them from inside the REPL. So this time we’re going to add a primitive, val, to define variables. We’ll use val like so:

(val x 5) ;; Returns: 5
x         ;; Returns: 5
(val x 7) ;; Returns: 7
x         ;; Returns: 7

Here, val changes the apparent value of x, but not by modifying the contents; instead it will make a new binding in the current scope. Essentially just a wrapper for bind. So the environment starts off as () or nil, then looks like ((x . 5)), then ((x . 7) (x . 5)).

We’ll implement val much in the same way we implemented if — a case in match:

let rec eval_sexp sexp env =
    match sexp with
    [...]
    | Pair(Symbol "if", Pair(cond, Pair(iftrue, Pair(iffalse, Nil)))) ->
            eval_sexp (eval_if cond iftrue iffalse) env
    | Pair(Symbol "val", Pair(Symbol name, Pair(exp, Nil))) ->
            let (expval, _) = eval_sexp exp env in
            let env' = bind (name, expval, env) in
            (expval, env')
    [...]

It evaluates the expression, binds the name to that value, and then returns the value and modified environment.

Binding a name to the value is all well and good, but not much use if we can’t access the value. So let’s return to our evaluation of Symbols — there’s some work to be done. Currently it looks like this:

let rec eval_sexp sexp env =
    match sexp with
    [...]
    | Symbol(v) -> (Symbol(v), env)
    [...]

We probably want to, instead of just returning the Symbol unmodified, look up the corresponding value to that name. So let’s use that function that we defined:

let rec eval_sexp sexp env =
    match sexp with
    [...]
    | Symbol(name) -> (lookup (name, env), env)
    [...]

And there we have it! Let’s give it a go:

$ ocaml 06_prim1.ml
> (val x 5)
5
> x
5
> (val x 7)
7
> x
7
> Exception: End_of_file.
$

Neat. But the code is still pretty clunky and could definitely be improved. Since we know that all primitive calls (for now just if and val) will be lists (Pairs ending with Nil), why not just convert and save the pattern matching headache?

If it’s not a list, it’s some pair (we still don’t have a way of generating those), and should just be returned as-is. If it’s not a function call we recognize, just return it as-is for now.

let rec eval_sexp sexp env =
    [...]
    match sexp with
    [...]
    | Pair(_, _) when is_list sexp ->
            (match pair_to_list sexp with
                 | [Symbol "if"; cond; iftrue; iffalse] ->
                         eval_sexp (eval_if cond iftrue iffalse) env
                 | [Symbol "env"] -> (env, env)
                 | [Symbol "val"; Symbol name; exp] ->
                         let (expval, _) = eval_sexp exp env in
                         let env' = bind (name, expval, env) in
                         (expval, env')
                 | _ -> (sexp, env)
            )
    | _ -> (sexp, env)

Note that this requires pulling is_list out of print_sexp for use in eval_sexp.

Also note that I’ve added in a neat little primitive, env, that shows the current environment. This will be helpful with debugging, and is also useful in demonstrating that our functions work as we expect. For example:

$ ocaml 06_prim1.ml
> (env)
nil
> (val x 5)
5
> (env)
((x . 5))
> (val x 7)
7
> (env)
((x . 7) (x . 5))
> Exception: End_of_file.
$

How about we finally get around to making some pairs? I think that could be fun — and another one-liner!

let rec eval_sexp sexp env =
    [...]
    | Pair(_, _) when is_list sexp ->
            (match pair_to_list sexp with
                 | [Symbol "if"; cond; iftrue; iffalse] ->
                         eval_sexp (eval_if cond iftrue iffalse) env
                 | [Symbol "env"] -> (env, env)
                 | [Symbol "pair"; car; cdr] ->  (* new! *)
                         (Pair(car, cdr), env)   (* new! *)
                 | [Symbol "val"; Symbol name; exp] ->
                         let (expval, _) = eval_sexp exp env in
                         let env' = bind (name, expval, env) in
                         (expval, env')
                 | _ -> (sexp, env)
            )
    | _ -> (sexp, env)

Well, two lines, if (like me) you are loathe to break the column boundary. And let’s see it in action:

$ ocaml 06_prim1.ml
> (pair 3 4)
(3 . 4)
> (val x (pair 3 4))
(3 . 4)
> (env)
((x . (3 . 4)))
> Exception: End_of_file.
$

Download the code here if you want to mess with it.

Next up, primitives II.