AST generation

parol can be instructed to generate all types your grammar implies automatically. It therefore analyzes all productions in your grammar.

Grammar transformation

The first step is to canonicalize your grammar into a standard format applying the following transformations.

  • All EBNF constructs, i.e. optional elements, repetitions and groupings are substituted by equivalent representations.
    • A: [B]; => A: BOpt; BOpt: B; BOpt: ;
    • A: {B}; => A: BList; BList: B BList; BList: ;
    • A: (B); => A: BGroup; BGroup: B;
  • Alternations are propagated to multiple productions.
    • A: B | C; => A: B; A: C;

These transformations are applied iteratively until all EBNF constructs are replaced.

Note that the transformations applied on LR grammars are slightly different, but the principle is the same.

Sanity checks

Then parol checks this pre-transformed input grammar for several properties that prevent a successful processing. Those unwanted properties are

  • Left-recursions
  • Non-productive non-terminals
  • Unreachable non-terminals

If the grammar does not have such properties the next step is to left-factor this grammar form. This step is crucial for decreasing the number of necessary lookahead symbols.

The Expanded grammar

This finally transformed grammar is the basis for the parser generation and is typically written to file for later reference. By convention this 'expanded' grammar is stored to files named <original-name>-exp.par.

This expanded grammar is the basis for parser generation.

Type inference

Having such a transformed grammar all productions have the form \[v: s*; \] where \(v \epsilon V, s \epsilon (V \cup \Sigma)\), \(V\) is the set of non-terminals, \(\Sigma\) is the set of terminals.

The relation of the generated productions to their original EBNF constructs is actually lost at this point.

But because we need the information if a set of productions was originated from, e.g. an optional construct ([...]) parolconveys these relationship during the whole transformation process to be able to infer it into a Rust Option<T> eventually.

To explain it using the form of transformation shown above we could write this:

A: [B]; => A: BOpt; BOpt: B; BOpt: ; => typeof A = Option<typeof B>

This step leads directly to a solution if non-terminal A has only one production.

In this case the the type of A is

fn main() {
struct A {
    b: Option<B>

We must use a struct here because this patterns should work for productions with \(n\) elements on its right-hand side. For each such element we then introduce a separate member into the struct.

If non-terminal A has more than one productions the resulting type of A will be a Rust enum type with \(n\) enum variants for \(n\) productions, e.g.:

A: B | C; => A: B; A: C; =>

fn main() {
struct B {
    // ...
struct C {
    // ...
// Type of non-terminal A
enum A {

When finally all types for all non-terminals are inferred parol generates an overall AST type. This is also a Rust enum. It comprises all non-terminal types of the grammar and provides exactly one enum variant for each of them. This type is mainly used by the parser itself to be able to instantiate a typed parse stack. The user rarely have to deal with this AST enum.

Recursive structure of a grammar

A context free grammar is typically defined using recursive constructs. But you can't define types in Rust that are directly recursive because this would lead to an infinitive type size.

To cope with this limitation parol generates boxed types for non-terminals when introducing elements to structs, e.g.:

fn main() {
struct A {
    b: Box<B>

This results in finite type sizes.

Note that parol has a way to minimize the use of boxed types in the generated parser. The parol tool supports a new command line switch (-b, --min_boxes) that enables the minimization of used boxes in generated data structures. The parol::build::Builder also provides a new method minimize_boxed_types() that you can call in your build scripts.

parol then determines where no recursions can occur by applying extra calculations on the structure of the grammar.

Manage Type generation

Omission of elements

You can suffix grammar symbols (terminals and non-terminals) with a cut operator (^). This instructs parol to not propagate them to the AST type, e.g.:

Group: '('^ Alternations ')'^;

The AST type for the symbol Group will then only contain a member for the non-terminal Alternations. The parentheses are suppressed because they have no special purpose for the grammar processing itself.

Assigning user types

You can specify a user type to be inserted into the AST structure at the place where the symbol would otherwise had the originally generated type. Add after a grammar symbol a colon followed by a user type name to instruct parol to use this type instead. In your language implementation you have to provide fallible conversions from references of the original generated types (&T) to your types (U) by implementing the trait TryFrom<&T> for U. An examples can be found in the list_auto example. You can also define aliases for the user type names by inserting as many %user_type directives as you want. Then use these aliases behind the colons.

You may have look at example list_auto that demonstrates the handling of user types.

%start List
%title "A possibly empty comma separated list of integers"
%comment "A trailing comma is allowed."
%user_type Number = crate::list_grammar::Number
%user_type Numbers = crate::list_grammar::Numbers


List: [Items: Numbers] TrailingComma^;
Items: Num {","^ Num};
Num: "0|[1-9][0-9]*": Number;
TrailingComma: [","^];

In this example grammar the terminal in the production Num is assigned to the user type Number which in turn is a shorthand for crate::list_grammar::Number. Also the non-terminal Items is assigned to the user type Numbers which in turn is a shorthand for crate::list_grammar::Numbers.

The parser generator substitutes the automatically inferred type in the type of the production by the user provided one and the parser calls the conversion form the original type to the user type at parse time.

The original type is the one of the source item in the grammar - terminal or non-terminal. Please have a look at the generated semantic action of the internal wrapper for production 1 of the expanded grammar list-exp.par which can be found in also generated traits file examples\list_auto\

fn main() {
    /// Semantic action for production 1:
    /// ListOpt /* Option<T>::Some */: Items : Numbers;
    fn list_opt_0(&mut self, _items: &ParseTreeType<'t>) -> Result<()> {
        let context = function_name!();
        trace!("{}", self.trace_item_stack(context));
        let items = pop_item!(self, items, Items, context);
        let list_opt_0_built = ListOpt {
            items: (&items)
        self.push(ASTType::ListOpt(Some(Box::new(list_opt_0_built))), context);

At the line after the trace the original item is popped from the parse stack. It has the Rust type Items:

fn main() {
/// Type derived for non-terminal Items
pub struct Items {
    pub num: Box<Num>,
    pub items_list: Vec<ItemsList>,

Then later at the construction of the ListOpt structure the conversion to the user's type is called: .items((&items).try_into().

The TryFrom trait is provided by the user. Please see examples\list_auto\ for that:

fn main() {
impl TryFrom<&Items> for Numbers {
    type Error = anyhow::Error;

    fn try_from(items: &Items) -> std::result::Result<Self, Self::Error> {
            |mut acc, e| {

This is an example how non-terminal types are converted into user types.

The easier variant is the conversion of a terminal type (i.e. a Token) into a user type. You can find an example also in examples\list_auto\

fn main() {
impl<'t> TryFrom<&Token<'t>> for Number {
    type Error = anyhow::Error;

    fn try_from(number: &Token<'t>) -> std::result::Result<Self, Self::Error> {

Here the scanned text of the token is accessed using the method text of the Token type that was imported from the parol_runtimecrate. This text is then parsed into an u32 type and finally wrapped into a Numbertype which is a newtype for u32.

By implementing TryFrom traits for your user type you can integrate them easily into the parse process.

There exist some examples that can help to become familiar with this concept. Maybe you would like to have a look at my rudimentary basic interpreter example.