MythLang 2
Lexing & Parsing

# Disclaimer

Myth's lexer is built with ocamllex, since that was the first meaningful result that came up when I searched "lexing with OCaml". It's nice enough to use. Either way, the code I've written is pure garbage. The way newlines, INDENTs, and DEDENTs are handled is annoying, and the parser & lexer are way to tightly coupled. But, it's the code that's currently running so, whatever.

# A Whitespace-Sensitive Lexer

Myth's syntax is heavily inspired by Python. I wanted something that was whitespace-sensitive and used indentation to specify code blocks. So I decided to look at the Python 3.7 Grammar to see how they handled whitespace-sensitivity. I saw that a lot of the rules depended on INDENT and DEDENT tokens. So I'd have to make my lexer figure out when to emit those. However, it's often the case that after reading a single \n character followed by a non-whitespace character, we will want to emit multiple DEDENT tokens. For example,

if True:
if True:
if True:
pass
print()

when the lexer sees the \n followed by the p in print, three DEDENT tokens need to be emitted, one for each if block. So I had to find a way to handle this multiple DEDENT nonsense.

## The Lexer Code

This isn't really the place for an ocamllex tutorial, so we'll just look at the code immediately. The meat of the lexer (ignoring the non-interesting rules) looks something like

rule token = parse
| ['\n'] {
if !paren_count = 0 then begin
state := RECENT_NEWLINE;
NEWLINE
end else
token lexbuf
}
| ['('] {
incr paren_count;
LPAREN
}
| [')'] {
decr paren_count;
RPAREN
}
| ['a'-'z' '_']+ ['a'-'z' 'A'-'Z' '0'-'9' '_']* as id {
check_keyword id
}
(*... other rules ... *)

Some important points to notice:

1. We have some special logic in when handling \n.
2. We track parenthesis usage, in order to ignore indents within parenthesized pieces of code across multiple lines.
3. Keywords are checked in a function, not in the lexer rules.

We have a special state variable that has the following type and initial value:

type state =
| CODE
| RECENT_NEWLINE

let state = ref CODE

We'll see why these is useful soon. We also have a variable paren_count that is initialized to ref 0. This just keeps track of whether or not we are inside a parenthesized expression. If we are, then indents and newlines are ignored. Lastly, keywords are checked in a special function check_keyword, this is because, as per ocamllex documentation, this should be done to keep the generated transition table small. The definition is something like

let check_keyword = function
| "if" -> IF
| "else" -> ELSE
| "while" -> WHILE
| "def" -> DEF
| "return" -> RETURN
| "and" -> OPERATOR "and"
| "or" -> OPERATOR "or"
| id -> NAME id

In addition to the rule token, we also have the rule newline, which is defined as follows:

and newline = parse
| [' ']* as spaces {
state := CODE;
match count_indent (String.length spaces) with
| Skip -> token lexbuf
| Token t -> t
}

This counts the spaces immediately after a newline, in order to determine what indent block we are currently on. Specifically, we want to determine if we should emit an INDENT token, or several DEDENT tokens followed by a newline. Here's the definition of count_indent

let space_stack = Stack.create ()
let _ = Stack.push 0 space_stack

(* outputs INDENT, DEDENT, or DEDENTMANY tokens *)
let count_indent count =
if Stack.top space_stack = count then
Skip
else if Stack.top space_stack < count then begin
Stack.push count space_stack;
Token INDENT
end else
(* Pop from the stack until we get an equal indent *)
let dedent_count = ref 0 in
try
while true do
if Stack.top space_stack = count then
raise Exit
else
incr dedent_count;
ignore (Stack.pop space_stack);
done;
raise SyntaxError
with Exit -> `Token (DEDENTMANY !dedent_count)

This is some awful code... What it essentially does is, we have a stack of integers, space_stack, that keeps the counts for the number of spaces used to indent blocks. For example, if the lexer is given this piece of code:

if True:
if True:
if True:
if True:
pass

when it reaches pass, the space stack will have the contents [0, 2, 6, 7, 8]. These numbers are the number of spaces used in each indent block. So, when we dedent, we need to return to a preexisting number of spaces. The space stack ensures that we do this. Furthermore, when deindenting, count_indent counts how many DEDENTS needs to be output, and reports this using a DEDENTMANY token, which contains an int (the number of DEDENTs to output).

Finally, the last part of the lexer is the part that handles outputting multiple DEDENT tokens. It works like this: inside the lexer, there is a function called token_cache that has the following definition:

let token_cache =
let cache = ref [] in
fun lexbuf ->
match !cache with
| x::xs -> cache := xs; x
| [] ->
match !Lexer.state with
| Lexer.CODE -> Lexer.token lexbuf
| Lexer.RECENT_NEWLINE -> begin
match Lexer.newline lexbuf with
| DEDENTMANY n -> begin
cache := (replicate (- 1) DEDENT);
DEDENT
end
| token -> token
end

It essentially keeps a reference to a list (cache) that gets filled with DEDENT tokens once a DEDENTMANY token is output by the lexer. Notice that the parser never expects a DEDENTMANY token, that is only used internally by the lexer.

## Using The Lexer

When looking at ocamllex tutorials, you'll usually see the main lexing rule defined as token. Then, in the main program, or wherever the lexer needs to be used, you'll see a call to Lexer.token. In order to use this whitespace sensitive lexer, you'll instead use Lexer.token_cache, as your "rule" instead of token.

# The Parser (parser.mly)

I'm using Menhir for parsing, since it supports incremental parsing reasonably nicely. This is so I can parse multiline code inside a REPL, which will hopefully be touched on in a later blog post. The parser isn't anything too fancy. The most interesting thing is how operator precedence is handled, which I'll detail here. If you're only interested in the whitespace-sensitivity bit, skip this part I guess.

Somewhere deep in my parser, I have the following bit of BNF grammar:

expr:
| non_op_expr                  { $1 } | non_op_expr op_list { resolve_op_list$1 $2 } op_list: | OPERATOR non_op_expr { [($1, $2)] } | OPERATOR non_op_expr op_list { ($1, $2) ::$3 }

Basically, it's meant to match expressions of the following nature

1 + 2 ^ 3 * 4

And the resolve_op_list call on this expression would look something like

resolve_op_list
(Ast.Num 1)
[("+", Ast.Num 2), ("^", Ast.Num 3), ("*", Ast.Num 4)]

The Ast.Num stuff is just how my language internally represents its abstract syntax tree.

The resolve_op_list code is a bit too long to post here I think, so check it out on the repo The way it works isn't too complicated though. I defined some precedences for each operator. It's a function that takes in an operator and outputs and associativity

let assoc_f i (_, op) = match op with
| "or" -> (0, -i)
| "and" -> (1, -i)
| "<" | "<=" | ">" | ">=" | "!=" | "==" -> (2, -i)
| "+" | "-" -> (3, -i)
| "*" | "/" -> (4, -i)
| "^" -> (5, i)
| _ -> failwith "Unknown operator."

You'll notice it also takes in an integer i. This is the index of the operator in a list of operators. The index is passed in so we can also take into account associativity. Namely, if I search for the minimum precedence element in a list, I will find the left-most, or the right-most operator of minimum precedence, depending on the associativity.

The rest of the resolve_op_list just finds the minimum precedence operator and splits the lists of operators and expressions at that minimum precedence operator. Then it recurses on those two smaller left and right lists.

The ability to handle operators like this is super useful for two reasons:

1. Custom operators are easily added by the user.
2. I don't need to write BNF rules for specific operators.

# Conclusion

My code is garbage. That's the end of the lexing/parsing bit. The rest of the lexer and parser is just standard stuff that is specific to Myth, and not that generalizable. The next post will probably be on the type system, or my serious issues with mutability, or Hindley-Milner, or idk.