Introduction

Speed or simplicity? Why not both?

pest is a library for writing plain-text parsers in Rust.

Parsers that use pest are easy to design and maintain due to the use of Parsing Expression Grammars, or PEGs. And, because of Rust's zero-cost abstractions, pest parsers can be very fast.

Sample

Here is the complete grammar for a simple calculator developed in a (currently unwritten) later chapter:

num = @{ int ~ ("." ~ ASCII_DIGIT*)? ~ (^"e" ~ int)? }
    int = { ("+" | "-")? ~ ASCII_DIGIT+ }

operation = _{ add | subtract | multiply | divide | power }
    add      = { "+" }
    subtract = { "-" }
    multiply = { "*" }
    divide   = { "/" }
    power    = { "^" }

expr = { term ~ (operation ~ term)* }
term = _{ num | "(" ~ expr ~ ")" }

calculation = _{ SOI ~ expr ~ EOI }

WHITESPACE = _{ " " | "\t" }

And here is the function that uses that parser to calculate answers:

#![allow(unused)]
fn main() {
lazy_static! {
    static ref PRATT_PARSER: PrattParser<Rule> = {
        use Rule::*;
        use Assoc::*;

        PrattParser::new()
            .op(Op::infix(add, Left) | Op::infix(subtract, Left))
            .op(Op::infix(multiply, Left) | Op::infix(divide, Left))
            .op(Op::infix(power, Right))
    };
}

fn eval(expression: Pairs<Rule>) -> f64 {
    PRATT_PARSER
        .map_primary(|primary| match primary.as_rule() {
            Rule::num => primary.as_str().parse::<f64>().unwrap(),
            Rule::expr => eval(primary.into_inner()),
            _ => unreachable!(),
        })
        .map_infix(|lhs, op, rhs| match op.as_rule() {
            Rule::add => lhs + rhs,
            Rule::subtract => lhs - rhs,
            Rule::multiply => lhs * rhs,
            Rule::divide => lhs / rhs,
            Rule::power => lhs.powf(rhs),
            _ => unreachable!(),
        })
        .parse(expression)
}
}

About this book

This book provides an overview of pest as well as several example parsers. For more details of pest's API, check the documentation.

Note that pest uses some advanced features of the Rust language. For an introduction to Rust, consult the official Rust book.

Example: CSV

Comma-Separated Values is a very simple text format. CSV files consist of a list of records, each on a separate line. Each record is a list of fields separated by commas.

For example, here is a CSV file with numeric fields:

65279,1179403647,1463895090
3.1415927,2.7182817,1.618034
-40,-273.15
13,42
65537

Let's write a program that computes the sum of these fields and counts the number of records.

Setup

Start by initializing a new project using Cargo:

$ cargo init --bin csv-tool
     Created binary (application) project
$ cd csv-tool

Add the pest and pest_derive crates to the dependencies section in Cargo.toml:

[dependencies]
pest = "2.0"
pest_derive = "2.0"

And finally bring pest and pest_derive into scope in src/main.rs:

#![allow(unused)]
fn main() {
extern crate pest;
#[macro_use]
extern crate pest_derive;
}

The #[macro_use] attribute is necessary to use pest to generate parsing code! This is a very important attribute.

Writing the parser

pest works by compiling a description of a file format, called a grammar, into Rust code. Let's write a grammar for a CSV file that contains numbers. Create a new file named src/csv.pest with a single line:

field = { (ASCII_DIGIT | "." | "-")+ }

This is a description of every number field: each character is either an ASCII digit 0 through 9, a full stop ., or a hyphen–minus -. The plus sign + indicates that the pattern can occur one or more times.

Rust needs to know to compile this file using pest:

#![allow(unused)]
fn main() {
use pest::Parser;

#[derive(Parser)]
#[grammar = "csv.pest"]
pub struct CSVParser;
}

If you run cargo doc, you will see that pest has created the function CSVParser::parse and an enum called Rule with a single variant Rule::field.

Let's test it out! Rewrite main:

fn main() {
    let successful_parse = CSVParser::parse(Rule::field, "-273.15");
    println!("{:?}", successful_parse);

    let unsuccessful_parse = CSVParser::parse(Rule::field, "this is not a number");
    println!("{:?}", unsuccessful_parse);
}

$ cargo run
  [ ... ]
Ok([Pair { rule: field, span: Span { str: "-273.15", start: 0, end: 7 }, inner: [] }])
Err(Error { variant: ParsingError { positives: [field], negatives: [] }, location: Pos(0), path: None, line: "this is not a number", continued_line: None, start: (1, 1), end: None })

Yikes! That's a complicated type! But you can see that the successful parse was Ok, while the failed parse was Err. We'll get into the details later.

For now, let's complete the grammar:

field = { (ASCII_DIGIT | "." | "-")+ }
record = { field ~ ("," ~ field)* }
file = { SOI ~ (record ~ ("\r\n" | "\n"))* ~ EOI }

The tilde ~ means "and then", so that "abc" ~ "def" matches abc followed by def. (For this grammar, "abc" ~ "def" is exactly the same as "abcdef", although this is not true in general; see a later chapter about WHITESPACE.)

In addition to literal strings ("\r\n") and built-ins (ASCII_DIGIT), rules can contain other rules. For instance, a record is a field, and optionally a comma , and then another field repeated as many times as necessary. The asterisk * is just like the plus sign +, except the pattern is optional: it can occur any number of times at all (zero or more).

There are two more rules that we haven't defined: SOI and EOI are two special rules that match, respectively, the start of input and the end of input. Without EOI, the file rule would gladly parse an invalid file! It would just stop as soon as it found the first invalid character and report a successful parse, possibly consisting of nothing at all!

The main program loop

Now we're ready to finish the program. We will use File to read the CSV file into memory. We'll also be messy and use expect everywhere.

use std::fs;

fn main() {
    let unparsed_file = fs::read_to_string("numbers.csv").expect("cannot read file");

    // ...
}

Next we invoke the parser on the file. Don't worry about the specific types for now. Just know that we're producing a pest::iterators::Pair that represents the file rule in our grammar.

fn main() {
    // ...

    let file = CSVParser::parse(Rule::file, &unparsed_file)
        .expect("unsuccessful parse") // unwrap the parse result
        .next().unwrap(); // get and unwrap the `file` rule; never fails

    // ...
}

Finally, we iterate over the records and fields, while keeping track of the count and sum, then print those numbers out.

fn main() {
    // ...

    let mut field_sum: f64 = 0.0;
    let mut record_count: u64 = 0;

    for record in file.into_inner() {
        match record.as_rule() {
            Rule::record => {
                record_count += 1;

                for field in record.into_inner() {
                    field_sum += field.as_str().parse::<f64>().unwrap();
                }
            }
            Rule::EOI => (),
            _ => unreachable!(),
        }
    }

    println!("Sum of fields: {}", field_sum);
    println!("Number of records: {}", record_count);
}

If p is a parse result (a Pair) for a rule in the grammar, then p.into_inner() returns an iterator over the named sub-rules of that rule. For instance, since the file rule in our grammar has record as a sub-rule, file.into_inner() returns an iterator over each parsed record. Similarly, since a record contains field sub-rules, record.into_inner() returns an iterator over each parsed field.

Done

Try it out! Copy the sample CSV at the top of this chapter into a file called numbers.csv, then run the program! You should see something like this:

$ cargo run
  [ ... ]
Sum of fields: 2643429302.327908
Number of records: 5

Parser API

pest provides several ways of accessing the results of a successful parse. The examples below use the following grammar:

number = { ASCII_DIGIT+ }                // one or more decimal digits
enclosed = { "(.." ~ number ~ "..)" }    // for instance, "(..6472..)"
sum = { number ~ " + " ~ number }        // for instance, "1362 + 12"

Tokens

pest represents successful parses using tokens. Whenever a rule matches, two tokens are produced: one at the start of the text that the rule matched, and one at the end. For example, the rule number applied to the string "3130 abc" would match and produce this pair of tokens:

"3130 abc"
 |   ^ end(number)
 ^ start(number)

Note that the rule doesn't match the entire input text. It only matches as much text as possible, then stops if successful.

A token is like a cursor in the input string. It has a character position in the string, as well as a reference to the rule that created it.

Nested rules

If a named rule contains another named rule, tokens will be produced for both rules. For instance, the rule enclosed applied to the string "(..6472..)" would match and produce these four tokens:

"(..6472..)"
 |  |   |  ^ end(enclosed)
 |  |   ^ end(number)
 |  ^ start(number)
 ^ start(enclosed)

Sometimes, tokens might not occur at distinct character positions. For example, when parsing the rule sum, the inner number rules share some start and end positions:

"1773 + 1362"
 |   |  |   ^ end(sum)
 |   |  |   ^ end(number)
 |   |  ^ start(number)
 |   ^ end(number)
 ^ start(number)
 ^ start(sum)

In fact, for a rule that matches empty input, the start and end tokens will be at the same position!

Interface

Tokens are exposed as the Token enum, which has Start and End variants. You can get an iterator of Tokens by calling tokens on a parse result:

#![allow(unused)]
fn main() {
let parse_result = Parser::parse(Rule::sum, "1773 + 1362").unwrap();
let tokens = parse_result.tokens();

for token in tokens {
    println!("{:?}", token);
}
}

After a successful parse, tokens will occur as nested pairs of matching Start and End. Both kinds of tokens have two fields:

• rule, which explains which rule generated them; and
• pos, which indicates their positions.

A start token's position is the first character that the rule matched. An end token's position is the first character that the rule did not match — that is, an end token refers to a position after the match. If a rule matched the entire input string, the end token points to an imaginary position after the string.

Pairs

Tokens are not the most convenient interface, however. Usually you will want to explore the parse tree by considering matching pairs of tokens. For this purpose, pest provides the Pair type.

A Pair represents a matching pair of tokens, or, equivalently, the spanned text that a named rule successfully matched. It is commonly used in several ways:

• Determining which rule produced the Pair
• Using the Pair as a raw &str
• Inspecting the inner named sub-rules that produced the Pair

#![allow(unused)]
fn main() {
let pair = Parser::parse(Rule::enclosed, "(..6472..) and more text")
    .unwrap().next().unwrap();

assert_eq!(pair.as_rule(), Rule::enclosed);
assert_eq!(pair.as_str(), "(..6472..)");

let inner_rules = pair.into_inner();
println!("{}", inner_rules); // --> [number(3, 7)]
}

In general, a Pair might have any number of inner rules: zero, one, or more. For maximum flexibility, Pair::into_inner() returns Pairs, which is an iterator over each pair.

This means that you can use for loops on parse results, as well as iterator methods such as map, filter, and collect.

#![allow(unused)]
fn main() {
let pairs = Parser::parse(Rule::sum, "1773 + 1362")
    .unwrap().next().unwrap()
    .into_inner();

let numbers = pairs
    .clone()
    .map(|pair| str::parse(pair.as_str()).unwrap())
    .collect::<Vec<i32>>();
assert_eq!(vec![1773, 1362], numbers);

for (found, expected) in pairs.zip(vec!["1773", "1362"]) {
    assert_eq!(Rule::number, found.as_rule());
    assert_eq!(expected, found.as_str());
}
}

Pairs iterators are also commonly used via the next method directly. If a rule consists of a known number of sub-rules (for instance, the rule sum has exactly two sub-rules), the sub-matches can be extracted with next and unwrap:

#![allow(unused)]
fn main() {
let parse_result = Parser::parse(Rule::sum, "1773 + 1362")
    .unwrap().next().unwrap();
let mut inner_rules = parse_result.into_inner();

let match1 = inner_rules.next().unwrap();
let match2 = inner_rules.next().unwrap();

assert_eq!(match1.as_str(), "1773");
assert_eq!(match2.as_str(), "1362");
}

Sometimes rules will not have a known number of sub-rules, such as when a sub-rule is repeated with an asterisk *:

list = { number* }

In cases like these it is not possible to call .next().unwrap(), because the number of sub-rules depends on the input string — it cannot be known at compile time.

The parse method

A pest-derived Parser has a single method parse which returns a Result< Pairs, Error >. To access the underlying parse tree, it is necessary to match on or unwrap the result:

#![allow(unused)]
fn main() {
// check whether parse was successful
match Parser::parse(Rule::enclosed, "(..6472..)") {
    Ok(mut pairs) => {
        let enclosed = pairs.next().unwrap();
        // ...
    }
    Err(error) => {
        // ...
    }
}
}

Our examples so far have included the calls Parser::parse(...).unwrap().next().unwrap(). The first unwrap turns the result into a Pairs. If parsing had failed, the program would panic! We only use unwrap in these examples because we already know that they will parse successfully.

In the example above, in order to get to the enclosed rule inside of the Pairs, we use the iterator interface. The next() call returns an Option<Pair>, which we finally unwrap to get the Pair for the enclosed rule.

Using Pair and Pairs with a grammar

While the Result from Parser::parse(...) might very well be an error on invalid input, Pair and Pairs often have more subtle behavior. For instance, with this grammar:

number = { ASCII_DIGIT+ }
sum = { number ~ " + " ~ number }

this function will never panic:

#![allow(unused)]
fn main() {
fn process(pair: Pair<Rule>) -> f64 {
    match pair.as_rule() {
        Rule::number => str::parse(pair.as_str()).unwrap(),
        Rule::sum => {
            let mut pairs = pair.into_inner();

            let num1 = pairs.next().unwrap();
            let num2 = pairs.next().unwrap();

            process(num1) + process(num2)
        }
    }
}
}

str::parse(...).unwrap() is safe because the number rule only ever matches digits, which str::parse(...) can handle. And pairs.next().unwrap() is safe to call twice because a sum match always has two sub-matches, which is guaranteed by the grammar.

Since these sorts of guarantees are awkward to express with Rust types, pest only provides a few high-level types to represent parse trees. Nevertheless, you should rely on the meaning of your grammar for properties such as "contains n sub-rules", "is safe to parse to f32", and "never fails to match". Idiomatic pest code uses unwrap and unreachable!.

Spans and positions

Occasionally, you will want to refer to a matching rule in the context of the raw source text, rather than the interior text alone. For example, you might want to print the entire line that contained the match. For this you can use Span and Position.

A Span is returned from Pair::as_span. Spans have a start position and an end position (which correspond to the start and end tokens of the rule that made the pair).

Spans can be decomposed into their start and end Positions, which provide useful methods for examining the string around that position. For example, Position::line_col() finds out the line and column number of a position.

Essentially, a Position is a Token without a rule. In fact, you can use pattern matching to turn a Token into its component Rule and Position.

Example: INI

INI (short for initialization) files are simple configuration files. Since there is no standard for the format, we'll write a program that is able to parse this example file:

username = noha
password = plain_text
salt = NaCl

[server_1]
interface=eth0
ip=127.0.0.1
document_root=/var/www/example.org

[empty_section]

[second_server]
document_root=/var/www/example.com
ip=
interface=eth1

Each line contains a key and value separated by an equals sign; or contains a section name surrounded by square brackets; or else is blank and has no meaning.

Whenever a section name appears, the following keys and values belong to that section, until the next section name. The key–value pairs at the beginning of the file belong to an implicit "empty" section.

Writing the grammar

Start by initializing a new project using Cargo, adding the dependencies pest = "2.0" and pest_derive = "2.0". Make a new file, src/ini.pest, to hold the grammar.

The text of interest in our file — username, /var/www/example.org, etc. — consists of only a few characters. Let's make a rule to recognize a single character in that set. The built-in rule ASCII_ALPHANUMERIC is a shortcut to represent any uppercase or lowercase ASCII letter, or any digit.

char = { ASCII_ALPHANUMERIC | "." | "_" | "/" }

Section names and property keys must not be empty, but property values may be empty (as in the line ip= above). That is, the former consist of one or more characters, char+; and the latter consist of zero or more characters, char*. We separate the meaning into two rules:

name = { char+ }
value = { char* }

Now it's easy to express the two kinds of input lines.

section = { "[" ~ name ~ "]" }
property = { name ~ "=" ~ value }

Finally, we need a rule to represent an entire input file. The expression (section | property)? matches section, property, or else nothing. Using the built-in rule NEWLINE to match line endings:

file = {
    SOI ~
    ((section | property)? ~ NEWLINE)* ~
    EOI
}

To compile the parser into Rust, we need to add the following to src/main.rs:

#![allow(unused)]
fn main() {
extern crate pest;
#[macro_use]
extern crate pest_derive;

use pest::Parser;

#[derive(Parser)]
#[grammar = "ini.pest"]
pub struct INIParser;
}

Program initialization

Now we can read the file and parse it with pest:

use std::collections::HashMap;
use std::fs;

fn main() {
    let unparsed_file = fs::read_to_string("config.ini").expect("cannot read file");

    let file = INIParser::parse(Rule::file, &unparsed_file)
        .expect("unsuccessful parse") // unwrap the parse result
        .next().unwrap(); // get and unwrap the `file` rule; never fails

    // ...
}

We'll express the properties list using nested HashMaps. The outer hash map will have section names as keys and section contents (inner hash maps) as values. Each inner hash map will have property keys and property values. For example, to access the document_root of server_1, we could write properties["server_1"]["document_root"]. The implicit "empty" section will be represented by a regular section with an empty string "" for the name, so that properties[""]["salt"] is valid.

fn main() {
    // ...

    let mut properties: HashMap<&str, HashMap<&str, &str>> = HashMap::new();

    // ...
}

Note that the hash map keys and values are all &str, borrowed strings. pest parsers do not copy the input they parse; they borrow it. All methods for inspecting a parse result return strings which are borrowed from the original parsed string.

The main loop

Now we interpret the parse result. We loop through each line of the file, which is either a section name or a key–value property pair. If we encounter a section name, we update a variable. If we encounter a property pair, we obtain a reference to the hash map for the current section, then insert the pair into that hash map.

#![allow(unused)]
fn main() {
    // ...

    let mut current_section_name = "";

    for line in file.into_inner() {
        match line.as_rule() {
            Rule::section => {
                let mut inner_rules = line.into_inner(); // { name }
                current_section_name = inner_rules.next().unwrap().as_str();
            }
            Rule::property => {
                let mut inner_rules = line.into_inner(); // { name ~ "=" ~ value }

                let name: &str = inner_rules.next().unwrap().as_str();
                let value: &str = inner_rules.next().unwrap().as_str();

                // Insert an empty inner hash map if the outer hash map hasn't
                // seen this section name before.
                let section = properties.entry(current_section_name).or_default();
                section.insert(name, value);
            }
            Rule::EOI => (),
            _ => unreachable!(),
        }
    }

    // ...
}

For output, let's simply dump the hash map using the pretty-printed Debug format.

fn main() {
    // ...

    println!("{:#?}", properties);
}

Whitespace

If you copy the example INI file at the top of this chapter into a file config.ini and run the program, it will not parse. We have forgotten about the optional spaces around equals signs!

Handling whitespace can be inconvenient for large grammars. Explicitly writing a whitespace rule and manually inserting it makes a grammar difficult to read and modify. pest provides a solution using the special rule WHITESPACE. If defined, it will be implicitly run, as many times as possible, at every tilde ~ and between every repetition (for example, * and +). For our INI parser, only spaces are legal whitespace.

WHITESPACE = _{ " " }

We mark the WHITESPACE rule silent with a leading low line (underscore) _{ ... }. This way, even if it matches, it won't show up inside other rules. If it weren't silent, parsing would be much more complicated, since every call to Pairs::next(...) could potentially return Rule::WHITESPACE instead of the desired next regular rule.

But wait! Spaces shouldn't be allowed in section names, keys, or values! Currently, whitespace is automatically inserted between characters in name = { char+ }. Rules that are whitespace-sensitive need to be marked atomic with a leading at sign @{ ... }. In atomic rules, automatic whitespace handling is disabled, and interior rules are silent.

name = @{ char+ }
value = @{ char* }

Done

Try it out! Make sure that the file config.ini exists, then run the program! You should see something like this:

$ cargo run
  [ ... ]
{
    "": {
        "password": "plain_text",
        "username": "noha",
        "salt": "NaCl"
    },
    "second_server": {
        "ip": "",
        "document_root": "/var/www/example.com",
        "interface": "eth1"
    },
    "server_1": {
        "interface": "eth0",
        "document_root": "/var/www/example.org",
        "ip": "127.0.0.1"
    }
}

Grammars

Like many parsing tools, pest operates using a formal grammar that is distinct from your Rust code. The format that pest uses is called a parsing expression grammar, or PEG. When building a project, pest automatically compiles the PEG, located in a separate file, into a plain Rust function that you can call.

How to activate pest

Most projects will have at least two files that use pest: the parser (say, src/parser/mod.rs) and the grammar (src/parser/grammar.pest). Assuming that they are in the same directory:

#![allow(unused)]
fn main() {
use pest::Parser;
use pest_derive::Parser;

#[derive(Parser)]
#[grammar = "parser/grammar.pest"] // relative to project `src`
struct MyParser;
}

Whenever you compile this file, pest will automatically use the grammar file to generate items like this:

#![allow(unused)]
fn main() {
pub enum Rules { /* ... */ }

impl Parser for MyParser {
    pub fn parse(Rules, &str) -> pest::Pairs { /* ... */ }
}
}

You will never see enum Rules or impl Parser as plain text! The code only exists during compilation. However, you can use Rules just like any other enum, and you can use parse(...) through the Pairs interface described in the Parser API chapter.

Inline grammar

If you don't want to have a separate grammar file, you can use the grammar_inline:

#![allow(unused)]
fn main() {
use pest::Parser;
use pest_derive::Parser;

#[derive(Parser)]
#[grammar_inline = r#"
// your grammar here
a = { "a" }
"#]
struct MyParser;
}

Load multiple grammars

If you have multiple grammars, you can load them all at once:

#![allow(unused)]
fn main() {
use pest::Parser;
use pest_derive::Parser;

#[derive(Parser)]
#[grammar = "parser/base.pest"]
#[grammar = "parser/grammar.pest"]
struct MyParser;
}

Then pest will generate a Rules enum that contains all the rules from both. This is useful if you have a base grammar that you want to extend in multiple grammars.

Warning about PEGs!

Parsing expression grammars look quite similar to other parsing tools you might be used to, like regular expressions, BNF grammars, and others (Yacc/Bison, LALR, CFG). However, PEGs behave subtly differently: PEGs are eager, non-backtracking, ordered, and unambiguous.

Don't be scared if you don't recognize any of the above names! You're already a step ahead of people who do — when you use pest's PEGs, you won't be tripped up by comparisons to other tools.

If you have used other parsing tools before, be sure to read the next section carefully. We'll mention some common mistakes regarding PEGs.

Parsing expression grammar

Parsing expression grammars (PEGs) are simply a strict representation of the simple imperative code that you would write if you were writing a parser by hand.

number = {            // To recognize a number...
    ASCII_DIGIT+      //   take as many ASCII digits as possible (at least one).
}
expression = {        // To recognize an expression...
    number            //   first try to take a number...
    | "true"          //   or, if that fails, the string "true".
}

In fact, pest produces code that is quite similar to the pseudo-code in the comments above.

Eagerness

When a repetition PEG expression is run on an input string,

ASCII_DIGIT+      // one or more characters from '0' to '9'

it runs that expression as many times as it can (matching "eagerly", or "greedily"). It either succeeds, consuming whatever it matched and passing the remaining input on to the next step in the parser,

"42 boxes"
 ^ Running ASCII_DIGIT+

"42 boxes"
   ^ Successfully took one or more digits!

" boxes"
 ^ Remaining unparsed input.

or fails, consuming nothing.

"galumphing"
 ^ Running ASCII_DIGIT+
   Failed to take one or more digits!

"galumphing"
 ^ Remaining unparsed input (everything).

If an expression fails to match, the failure propagates upwards, eventually leading to a failed parse, unless the failure is "caught" somewhere in the grammar. The choice operator is one way to "catch" such failures.

Ordered choice

The choice operator, written as a vertical line |, is ordered. The PEG expression first | second means "try first; but if it fails, try second instead".

In many cases, the ordering does not matter. For instance, "true" | "false" will match either the string "true" or the string "false" (and fail if neither occurs).

However, sometimes the ordering does matter. Consider the PEG expression "a" | "ab". You might expect it to match either the string "a" or the string "ab". But it will not — the expression means "try "a"; but if it fails, try "ab" instead". If you are matching on the string "abc", "try "a"" will not fail; it will instead match "a" successfully, leaving "bc" unparsed!

In general, when writing a parser with choices, put the longest or most specific choice first, and the shortest or most general choice last.

Non-backtracking

During parsing, a PEG expression either succeeds or fails. If it succeeds, the next step is performed as usual. But if it fails, the whole expression fails. The engine will not back up and try again.

Consider this grammar, matching on the string "frumious":

word = {     // to recognize a word...
    ANY*     //   take any character, zero or more times...
    ~ ANY    //   followed by any character
}

You might expect this rule to parse any input string that contains at least one character (equivalent to ANY+). But it will not. Instead, the first ANY* will eagerly eat the entire string — it will succeed. Then, the next ANY will have nothing left, so it will fail.

"frumious"
 ^ (word)

"frumious"
         ^ (ANY*) Success! Continue to `ANY` with remaining input "".

""
 ^ (ANY) Failure! Expected one character, but found end of string.

In a system with backtracking (like regular expressions), you would back up one step, "un-eating" a character, and then try again. But PEGs do not do this. In the rule first ~ second, once first parses successfully, it has consumed some characters that will never come back. second can only run on the input that first did not consume.

Unambiguous

These rules form an elegant and simple system. Every PEG rule is run on the remainder of the input string, consuming as much input as necessary. Once a rule is done, the rest of the input is passed on to the rest of the parser.

For instance, the expression ASCII_DIGIT+, "one or more digits", will always match the largest sequence of consecutive digits possible. There is no danger of accidentally having a later rule back up and steal some digits in an unintuitive and nonlocal way.

This contrasts with other parsing tools, such as regular expressions and CFGs, where the results of a rule often depend on code some distance away. Indeed, the famous "shift/reduce conflict" in LR parsers is not a problem in PEGs.

Don't panic

This all might be a bit counterintuitive at first. But as you can see, the basic logic is very easy and straightforward. You can trivially step through the execution of any PEG expression.

• Try this.
• If it succeeds, try the next thing.
• Otherwise, try the other thing.

(this ~ next_thing) | (other_thing)

These rules together make PEGs very pleasant tools for writing a parser.

Syntax of pest grammars

pest grammars are lists of rules. Rules are defined like this:

//! Grammar doc
my_rule = { ... }

/// Rule doc
another_rule = {        // comments are preceded by two slashes
    ...                 // whitespace goes anywhere
}

Since rule names are translated into Rust enum variants, they are not allowed to be Rust keywords.

The left curly bracket { defining a rule can be preceded by symbols that affect its operation:

silent_rule = _{ ... }
atomic_rule = @{ ... }

Expressions

Grammar rules are built from expressions (hence "parsing expression grammar"). These expressions are a terse, formal description of how to parse an input string.

Expressions are composable: they can be built out of other expressions and nested inside of each other to produce arbitrarily complex rules (although you should break very complicated expressions into multiple rules to make them easier to manage).

PEG expressions are suitable for both high-level meaning, like "a function signature, followed by a function body", and low-level meaning, like "a semicolon, followed by a line feed". The combining form "followed by", the sequence operator, is the same in either case.

Terminals

The most basic rule is a literal string in double quotes: "text".

A string can be case-insensitive (for ASCII characters only) if preceded by a caret: ^"text".

A single character in a range is written as two single-quoted characters, separated by two dots: '0'..'9'.

You can match any single character at all with the special rule ANY. This is equivalent to '\u{00}'..'\u{10FFFF}', any single Unicode character.

"a literal string"
^"ASCII case-insensitive string"
'a'..'z'
ANY

Finally, you can refer to other rules by writing their names directly, and even use rules recursively:

my_rule = { "slithy " ~ other_rule }
other_rule = { "toves" }
recursive_rule = { "mimsy " ~ recursive_rule }

Sequence

The sequence operator is written as a tilde ~.

first ~ and_then

("abc") ~ (^"def") ~ ('g'..'z')        // matches "abcDEFr"

When matching a sequence expression, first is attempted. If first matches successfully, and_then is attempted next. However, if first fails, the entire expression fails.

A list of expressions can be chained together with sequences, which indicates that all of the components must occur, in the specified order.

Ordered choice

The choice operator is written as a vertical line |.

first | or_else

("abc") | (^"def") | ('g'..'z')        // matches "DEF"

When matching a choice expression, first is attempted. If first matches successfully, the entire expression succeeds immediately. However, if first fails, or_else is attempted next.

Note that first and or_else are always attempted at the same position, even if first matched some input before it failed. When encountering a parse failure, the engine will try the next ordered choice as though no input had been matched. Failed parses never consume any input.

start = { "Beware " ~ creature }
creature = {
    ("the " ~ "Jabberwock")
    | ("the " ~ "Jubjub bird")
}

"Beware the Jubjub bird"
 ^ (start) Parses via the second choice of `creature`,
           even though the first choice matched "the " successfully.

It is somewhat tempting to borrow terminology and think of this operation as "alternation" or simply "OR", but this is misleading. The word "choice" is used specifically because the operation is not merely logical "OR".

Repetition

There are two repetition operators: the asterisk * and plus sign +. They are placed after an expression. The asterisk * indicates that the preceding expression can occur zero or more times. The plus sign + indicates that the preceding expression can occur one or more times (it must occur at least once).

The question mark operator ? is similar, except it indicates that the expression is optional — it can occur zero or one times.

("zero" ~ "or" ~ "more")*
 ("one" | "or" | "more")+
           (^"optional")?

Note that expr* and expr? will always succeed, because they are allowed to match zero times. For example, "a"* ~ "b"? will succeed even on an empty input string.

Other numbers of repetitions can be indicated using curly brackets:

expr{n}           // exactly n repetitions
expr{m, n}        // between m and n repetitions, inclusive

expr{, n}         // at most n repetitions
expr{m, }         // at least m repetitions

Thus expr* is equivalent to expr{0, }; expr+ is equivalent to expr{1, }; and expr? is equivalent to expr{0, 1}.

Predicates

Preceding an expression with an ampersand & or exclamation mark ! turns it into a predicate that never consumes any input. You might know these operators as "lookahead" or "non-progressing".

The positive predicate, written as an ampersand &, attempts to match its inner expression. If the inner expression succeeds, parsing continues, but at the same position as the predicate — &foo ~ bar is thus a kind of "AND" statement: "the input string must match foo AND bar". If the inner expression fails, the whole expression fails too.

The negative predicate, written as an exclamation mark !, attempts to match its inner expression. If the inner expression fails, the predicate succeeds and parsing continues at the same position as the predicate. If the inner expression succeeds, the predicate fails — !foo ~ bar is thus a kind of "NOT" statement: "the input string must match bar but NOT foo".

This leads to the common idiom meaning "any character but":

not_space_or_tab = {
    !(                // if the following text is not
        " "           //     a space
        | "\t"        //     or a tab
    )
    ~ ANY             // then consume one character
}

triple_quoted_string = {
    "'''"
    ~ triple_quoted_character*
    ~ "'''"
}
triple_quoted_character = {
    !"'''"        // if the following text is not three apostrophes
    ~ ANY         // then consume one character
}

Operator precedence and grouping (WIP)

The repetition operators asterisk *, plus sign +, and question mark ? apply to the immediately preceding expression.

"One " ~ "or " ~ "more. "+
"One " ~ "or " ~ ("more. "+)
    are equivalent and match
"One or more. more. more. more. "

Larger expressions can be repeated by surrounding them with parentheses.

("One " ~ "or " ~ "more. ")+
    matches
"One or more. One or more. "

Repetition operators have the highest precedence, followed by predicate operators, the sequence operator, and finally ordered choice.

my_rule = {
    "a"* ~ "b"?
    | &"b"+ ~ "a"
}

// equivalent to

my_rule = {
      ( ("a"*) ~ ("b"?) )
    | ( (&("b"+)) ~ "a" )
}

Start and end of input

The rules SOI and EOI match the start and end of the input string, respectively. Neither consumes any text. They only indicate whether the parser is currently at one edge of the input.

For example, to ensure that a rule matches the entire input, where any syntax error results in a failed parse (rather than a successful but incomplete parse):

main = {
    SOI
    ~ (...)
    ~ EOI
}

Implicit whitespace

Many languages and text formats allow arbitrary whitespace and comments between logical tokens. For instance, Rust considers 4+5 equivalent to 4 + 5 and 4 /* comment */ + 5.

The optional rules WHITESPACE and COMMENT implement this behaviour. If either (or both) are defined, they will be implicitly inserted at every sequence and between every repetition (except in atomic rules).

expression = { "4" ~ "+" ~ "5" }
WHITESPACE = _{ " " }
COMMENT = _{ "/*" ~ (!"*/" ~ ANY)* ~ "*/" }

"4+5"
"4 + 5"
"4  +     5"
"4 /* comment */ + 5"

As you can see, WHITESPACE and COMMENT are run repeatedly, so they need only match a single whitespace character or a single comment. The grammar above is equivalent to:

expression = {
    "4"   ~ (ws | com)*
    ~ "+" ~ (ws | com)*
    ~ "5"
}
ws = _{ " " }
com = _{ "/*" ~ (!"*/" ~ ANY)* ~ "*/" }

Note that Implicit whitespace is not inserted at the beginning or end of rules — for instance, expression does not match " 4+5 ". If you want to include Implicit whitespace at the beginning and end of a rule, you will need to sandwich it between two empty rules (often SOI and EOI as above):

WHITESPACE = _{ " " }
expression = { "4" ~ "+" ~ "5" }
main = { SOI ~ expression ~ EOI }

"4+5"
"  4 + 5   "

(Be sure to mark the WHITESPACE and COMMENT rules as silent unless you want to see them included inside other rules!)

Silent and atomic rules

Silent

Silent rules are just like normal rules — when run, they function the same way — except they do not produce pairs or tokens. If a rule is silent, it will never appear in a parse result.

To make a silent rule, precede the left curly bracket { with a low line (underscore) _.

silent = _{ ... }

Rules called from a silent rule are not treated as silent unless they are declared to be silent. These rules may produce pairs or tokens and can appear in a parse result.

Atomic

Pest has two kinds of atomic rules: atomic and compound atomic. To make one, write the sigil before the left curly bracket {.

/// Atomic rule start with `@`
atomic = @{ ... }

/// Compound Atomic start with `$`
compound_atomic = ${ ... }

Both kinds of atomic rule prevent implicit whitespace:

1. Inside an atomic rule, the tilde ~ means "immediately followed by".
2. Repetition operators (asterisk * and plus sign +) have no implicit separation.

In addition, all other rules called from an atomic rule are also treated as atomic.

The difference between the two is how they produce tokens for inner rules:

• atomic - In an Atomic rule, interior matching rules are silent.
• compound atomic - By contrast, compound atomic rules produce inner tokens as normal.

Atomic rules are useful when the text you are parsing ignores whitespace except in a few cases, such as literal strings. In this instance, you can write WHITESPACE or COMMENT rules, then make your string-matching rule be atomic.

Non-atomic

Sometimes, you'll want to cancel the effects of atomic parsing. For instance, you might want to have string interpolation with an expression inside, where the inside expression can still have whitespace like normal.

#!/bin/env python3
print(f"The answer is {2 + 4}.")

This is where you use a non-atomic rule. Write an exclamation mark ! in front of the defining curly bracket. The rule will run as non-atomic, whether it is called from an atomic rule or not.

fstring = @{ "\"" ~ ... }
expr = !{ ... }

The stack (WIP)

pest maintains a stack that can be manipulated directly from the grammar. An expression can be matched and pushed onto the stack with the keyword PUSH, then later matched exactly with the keywords PEEK and POP.

Using the stack allows the exact same text to be matched multiple times, rather than the same pattern.

For example,

same_text = {
    PUSH( "a" | "b" | "c" )
    ~ POP
}
same_pattern = {
    ("a" | "b" | "c")
    ~ ("a" | "b" | "c")
}

In this case, same_pattern will match "ab", while same_text will not.

One practical use is in parsing Rust "raw string literals", which look like this:

#![allow(unused)]
fn main() {
const raw_str: &str = r###"
    Some number of number signs # followed by a quotation mark ".

    Quotation marks can be used anywhere inside: """"""""",
    as long as one is not followed by a matching number of number signs,
    which ends the string: "###;
}

When parsing a raw string, we have to keep track of how many number signs # occurred before the quotation mark. We can do this using the stack:

raw_string = {
    "r" ~ PUSH("#"*) ~ "\""    // push the number signs onto the stack
    ~ raw_string_interior
    ~ "\"" ~ POP               // match a quotation mark and the number signs
}
raw_string_interior = {
    (
        !("\"" ~ PEEK)    // unless the next character is a quotation mark
                          // followed by the correct amount of number signs,
        ~ ANY             // consume one character
    )*
}

Indentation-Sensitive Languages

In conjunction with some extra helpers, the stack can be used to allow parsing indentation-sensitive languages, such as Python.

The general idea is that you store the leading whitespace on the stack with PUSH and then use PEEK_ALL to match all of the whitespace on subsequent lines.

When exiting an indented block, use DROP to remove the stack entry without needing to match it.

An example grammar demonstrating this concept is given here:

Grammar = { SOI ~ NEWLINE* ~ BlockContent* ~ NEWLINE* ~ EOI }

NewBlock = _{
    // The first line in the block
    PEEK_ALL ~ PUSH("  "+ | "\t"+) ~ BlockContent ~
    // Subsequent lines in the block
    (PEEK_ALL ~ BlockContent)* ~
    // Remove the last layer of indentation from the stack when exiting the block
    DROP
}

BlockName = { ASCII_ALPHA+ }

BlockContent = {
    BlockName ~ (NEWLINE | EOI) ~ NewBlock*
}

This matches texts such as the following, whilst preserving indentation structure:

Hello
  This
    Is
    An
  Indentation
    Sensitive
      Language
Demonstration

Cheat sheet

Comments

Non-doc comments

Comments follow the general Rust style of line (//) and block (/* ... */) comment forms. Non-doc comments are interpreted as a form of whitespace.

/* 
  Block comment
 */
another_rule = {        // line comment
    ...                 // whitespace goes anywhere
}

Doc comments

Line doc comments begin with exactly three slashes /// and //! is used to document the entire grammar file.

//! A parser for JSON file.

json = { ... }

/// Matches object, e.g.: `{ "foo": "bar" }`
object = { ... }

Then will get

#![allow(unused)]
fn main() {
/// A parser for JSON file.
enum Rule {
    json,
    /// Matches object, e.g.: `{ "foo": "bar" }`
    object,
}
}

Built-in rules

Besides ANY, matching any single Unicode character, pest provides several rules to make parsing text more convenient.

ASCII rules

Among the printable ASCII characters, it is often useful to match alphabetic characters and numbers. For numbers, pest provides digits in common radixes (bases):

For alphabetic characters, distinguishing between uppercase and lowercase:

And for miscellaneous use:

Unicode rules

To make it easier to correctly parse arbitrary Unicode text, pest includes a large number of rules corresponding to Unicode character properties. These rules are divided into general category and binary property rules.

Unicode characters are partitioned into categories based on their general purpose. Every character belongs to a single category, in the same way that every ASCII character is a control character, a digit, a letter, a symbol, or a space.

In addition, every Unicode character has a list of binary properties (true or false) that it does or does not satisfy. Characters can belong to any number of these properties, depending on their meaning.

For example, the character "A", "Latin capital letter A", is in the general category "Uppercase Letter" because its general purpose is being a letter. It has the binary property "Uppercase" but not "Emoji". By contrast, the character "🅰", "negative squared Latin capital letter A", is in the general category "Other Symbol" because it does not generally occur as a letter in text. It has both the binary properties "Uppercase" and "Emoji".

For more details, consult Chapter 4 of The Unicode Standard.

General categories

Formally, categories are non-overlapping: each Unicode character belongs to exactly one category, and no category contains another. However, since certain groups of categories are often useful together, pest exposes the hierarchy of categories below. For example, the rule CASED_LETTER is not technically a Unicode general category; it instead matches characters that are UPPERCASE_LETTER or LOWERCASE_LETTER, which are general categories.

• LETTER
  • CASED_LETTER
    • UPPERCASE_LETTER
    • LOWERCASE_LETTER
  • TITLECASE_LETTER
  • MODIFIER_LETTER
  • OTHER_LETTER
• MARK
  • NONSPACING_MARK
  • SPACING_MARK
  • ENCLOSING_MARK
• NUMBER
  • DECIMAL_NUMBER
  • LETTER_NUMBER
  • OTHER_NUMBER
• PUNCTUATION
  • CONNECTOR_PUNCTUATION
  • DASH_PUNCTUATION
  • OPEN_PUNCTUATION
  • CLOSE_PUNCTUATION
  • INITIAL_PUNCTUATION
  • FINAL_PUNCTUATION
  • OTHER_PUNCTUATION
• SYMBOL
  • MATH_SYMBOL
  • CURRENCY_SYMBOL
  • MODIFIER_SYMBOL
  • OTHER_SYMBOL
• SEPARATOR
  • SPACE_SEPARATOR
  • LINE_SEPARATOR
  • PARAGRAPH_SEPARATOR
• OTHER
  • CONTROL
  • FORMAT
  • SURROGATE
  • PRIVATE_USE
  • UNASSIGNED

Binary properties

Many of these properties are used to define Unicode text algorithms, such as the bidirectional algorithm and the text segmentation algorithm. Such properties are not likely to be useful for most parsers.

However, the properties XID_START and XID_CONTINUE are particularly notable because they are defined "to assist in the standard treatment of identifiers", "such as programming language variables". See Technical Report 31 for more details.

• ALPHABETIC
• BIDI_CONTROL
• BIDI_MIRRORED
• CASE_IGNORABLE
• CASED
• CHANGES_WHEN_CASEFOLDED
• CHANGES_WHEN_CASEMAPPED
• CHANGES_WHEN_LOWERCASED
• CHANGES_WHEN_TITLECASED
• CHANGES_WHEN_UPPERCASED
• DASH
• DEFAULT_IGNORABLE_CODE_POINT
• DEPRECATED
• DIACRITIC
• EMOJI
• EMOJI_COMPONENT
• EMOJI_MODIFIER
• EMOJI_MODIFIER_BASE
• EMOJI_PRESENTATION
• EXTENDED_PICTOGRAPHIC
• EXTENDER
• GRAPHEME_BASE
• GRAPHEME_EXTEND
• GRAPHEME_LINK
• HEX_DIGIT
• HYPHEN
• IDS_BINARY_OPERATOR
• IDS_TRINARY_OPERATOR
• ID_CONTINUE
• ID_START
• IDEOGRAPHIC
• JOIN_CONTROL
• LOGICAL_ORDER_EXCEPTION
• LOWERCASE
• MATH
• NONCHARACTER_CODE_POINT
• OTHER_ALPHABETIC
• OTHER_DEFAULT_IGNORABLE_CODE_POINT
• OTHER_GRAPHEME_EXTEND
• OTHER_ID_CONTINUE
• OTHER_ID_START
• OTHER_LOWERCASE
• OTHER_MATH
• OTHER_UPPERCASE
• PATTERN_SYNTAX
• PATTERN_WHITE_SPACE
• PREPENDED_CONCATENATION_MARK
• QUOTATION_MARK
• RADICAL
• REGIONAL_INDICATOR
• SENTENCE_TERMINAL
• SOFT_DOTTED
• TERMINAL_PUNCTUATION
• UNIFIED_IDEOGRAPH
• UPPERCASE
• VARIATION_SELECTOR
• WHITE_SPACE
• XID_CONTINUE
• XID_START

Script properties

The Unicode script property has included built-in rules for matching characters in particular languages.

For example:

We want match a string that contains any CJK (regexp: \p{CJK}) characters such as 你好世界 or こんにちは世界 or 안녕하세요 세계.

• HAN: representing Chinese characters, including Simplified Chinese, Traditional Chinese, Japanese kanji, and Korean hanja.
• HIRAGANA: representing the Japanese hiragana syllabary.
• KATAKANA: representing the Japanese katakana syllabary.
• HANGUL: representing Korean alphabetical characters.
• BOPOMOFO: representing Chinese phonetic symbols.

So we define a rule named CJK like this:

CJK = { HAN | HIRAGANA | KATAKANA | HANGUL | BOPOMOFO }

All available rules:

• ADLAM
• AHOM
• ANATOLIAN_HIEROGLYPHS
• ARABIC
• ARMENIAN
• AVESTAN
• BALINESE
• BAMUM
• BASSA_VAH
• BATAK
• BENGALI
• BHAIKSUKI
• BOPOMOFO
• BRAHMI
• BRAILLE
• BUGINESE
• BUHID
• CANADIAN_ABORIGINAL
• CARIAN
• CAUCASIAN_ALBANIAN
• CHAKMA
• CHAM
• CHEROKEE
• CHORASMIAN
• COMMON
• COPTIC
• CUNEIFORM
• CYPRIOT
• CYPRO_MINOAN
• CYRILLIC
• DESERET
• DEVANAGARI
• DIVES_AKURU
• DOGRA
• DUPLOYAN
• EGYPTIAN_HIEROGLYPHS
• ELBASAN
• ELYMAIC
• ETHIOPIC
• GEORGIAN
• GLAGOLITIC
• GOTHIC
• GRANTHA
• GREEK
• GUJARATI
• GUNJALA_GONDI
• GURMUKHI
• HAN
• HANGUL
• HANIFI_ROHINGYA
• HANUNOO
• HATRAN
• HEBREW
• HIRAGANA
• IMPERIAL_ARAMAIC
• INHERITED
• INSCRIPTIONAL_PAHLAVI
• INSCRIPTIONAL_PARTHIAN
• JAVANESE
• KAITHI
• KANNADA
• KATAKANA
• KAWI
• KAYAH_LI
• KHAROSHTHI
• KHITAN_SMALL_SCRIPT
• KHMER
• KHOJKI
• KHUDAWADI
• LAO
• LATIN
• LEPCHA
• LIMBU
• LINEAR_A
• LINEAR_B
• LISU
• LYCIAN
• LYDIAN
• MAHAJANI
• MAKASAR
• MALAYALAM
• MANDAIC
• MANICHAEAN
• MARCHEN
• MASARAM_GONDI
• MEDEFAIDRIN
• MEETEI_MAYEK
• MENDE_KIKAKUI
• MEROITIC_CURSIVE
• MEROITIC_HIEROGLYPHS
• MIAO
• MODI
• MONGOLIAN
• MRO
• MULTANI
• MYANMAR
• NABATAEAN
• NAG_MUNDARI
• NANDINAGARI
• NEW_TAI_LUE
• NEWA
• NKO
• NUSHU
• NYIAKENG_PUACHUE_HMONG
• OGHAM
• OL_CHIKI
• OLD_HUNGARIAN
• OLD_ITALIC
• OLD_NORTH_ARABIAN
• OLD_PERMIC
• OLD_PERSIAN
• OLD_SOGDIAN
• OLD_SOUTH_ARABIAN
• OLD_TURKIC
• OLD_UYGHUR
• ORIYA
• OSAGE
• OSMANYA
• PAHAWH_HMONG
• PALMYRENE
• PAU_CIN_HAU
• PHAGS_PA
• PHOENICIAN
• PSALTER_PAHLAVI
• REJANG
• RUNIC
• SAMARITAN
• SAURASHTRA
• SHARADA
• SHAVIAN
• SIDDHAM
• SIGNWRITING
• SINHALA
• SOGDIAN
• SORA_SOMPENG
• SOYOMBO
• SUNDANESE
• SYLOTI_NAGRI
• SYRIAC
• TAGALOG
• TAGBANWA
• TAI_LE
• TAI_THAM
• TAI_VIET
• TAKRI
• TAMIL
• TANGSA
• TANGUT
• TELUGU
• THAANA
• THAI
• TIBETAN
• TIFINAGH
• TIRHUTA
• TOTO
• UGARITIC
• VAI
• VITHKUQI
• WANCHO
• WARANG_CITI
• YEZIDI
• YI
• ZANABAZAR_SQUARE

Example: JSON

JSON is a popular format for data serialization that is derived from the syntax of JavaScript. JSON documents are tree-like and potentially recursive — two data types, objects and arrays, can contain other values, including other objects and arrays.

Here is an example JSON document:

{
    "nesting": { "inner object": {} },
    "an array": [1.5, true, null, 1e-6],
    "string with escaped double quotes" : "\"quick brown foxes\""
}

Let's write a program that parses the JSON to an Rust object, known as an abstract syntax tree, then serializes the AST back to JSON.

Setup

We'll start by defining the AST in Rust. Each JSON data type is represented by an enum variant.

#![allow(unused)]
fn main() {
enum JSONValue<'a> {
    Object(Vec<(&'a str, JSONValue<'a>)>),
    Array(Vec<JSONValue<'a>>),
    String(&'a str),
    Number(f64),
    Boolean(bool),
    Null,
}
}

To avoid copying when deserializing strings, JSONValue borrows strings from the original unparsed JSON. In order for this to work, we cannot interpret string escape sequences: the input string "\n" will be represented by JSONValue::String("\\n"), a Rust string with two characters, even though it represents a JSON string with just one character.

Let's move on to the serializer. For the sake of clarity, it uses allocated Strings instead of providing an implementation of std::fmt::Display, which would be more idiomatic.

#![allow(unused)]
fn main() {
fn serialize_jsonvalue(val: &JSONValue) -> String {
    use JSONValue::*;

    match val {
        Object(o) => {
            let contents: Vec<_> = o
                .iter()
                .map(|(name, value)|
                     format!("\"{}\":{}", name, serialize_jsonvalue(value)))
                .collect();
            format!("{{{}}}", contents.join(","))
        }
        Array(a) => {
            let contents: Vec<_> = a.iter().map(serialize_jsonvalue).collect();
            format!("[{}]", contents.join(","))
        }
        String(s) => format!("\"{}\"", s),
        Number(n) => format!("{}", n),
        Boolean(b) => format!("{}", b),
        Null => format!("null"),
    }
}
}

Note that the function invokes itself recursively in the Object and Array cases. This pattern appears throughout the parser. The AST creation function iterates recursively through the parse result, and the grammar has rules which include themselves.

Writing the grammar

Let's begin with whitespace. JSON whitespace can appear anywhere, except inside strings (where it must be parsed separately) and between digits in numbers (where it is not allowed). This makes it a good fit for pest's implicit whitespace. In src/json.pest:

WHITESPACE = _{ " " | "\t" | "\r" | "\n" }

The JSON specification includes diagrams for parsing JSON strings. We can write the grammar directly from that page. Let's write object as a sequence of pairs separated by commas ,.

object = {
    "{" ~ "}" |
    "{" ~ pair ~ ("," ~ pair)* ~ "}"
}
pair = { string ~ ":" ~ value }

array = {
    "[" ~ "]" |
    "[" ~ value ~ ("," ~ value)* ~ "]"
}

The object and array rules show how to parse a potentially empty list with separators. There are two cases: one for an empty list, and one for a list with at least one element. This is necessary because a trailing comma in an array, such as in [0, 1,], is illegal in JSON.

Now we can write value, which represents any single data type. We'll mimic our AST by writing boolean and null as separate rules.

value = _{ object | array | string | number | boolean | null }

boolean = { "true" | "false" }

null = { "null" }

Let's separate the logic for strings into three parts. char is a rule matching any logical character in the string, including any backslash escape sequence. inner represents the contents of the string, without the surrounding double quotes. string matches the inner contents of the string, including the surrounding double quotes.

The char rule uses the idiom !(...) ~ ANY, which matches any character except the ones given in parentheses. In this case, any character is legal inside a string, except for double quote " and backslash \, which require separate parsing logic.

string = ${ "\"" ~ inner ~ "\"" }
inner = @{ char* }
char = {
    !("\"" | "\\") ~ ANY
    | "\\" ~ ("\"" | "\\" | "/" | "b" | "f" | "n" | "r" | "t")
    | "\\" ~ ("u" ~ ASCII_HEX_DIGIT{4})
}

Because string is marked compound atomic, string token pairs will also contain a single inner pair. Because inner is marked atomic, no char pairs will appear inside inner. Since these rules are atomic, no whitespace is permitted between separate tokens.

Numbers have four logical parts: an optional sign, an integer part, an optional fractional part, and an optional exponent. We'll mark number atomic so that whitespace cannot appear between its parts.

number = @{
    "-"?
    ~ ("0" | ASCII_NONZERO_DIGIT ~ ASCII_DIGIT*)
    ~ ("." ~ ASCII_DIGIT*)?
    ~ (^"e" ~ ("+" | "-")? ~ ASCII_DIGIT+)?
}

We need a final rule to represent an entire JSON file. The only legal contents of a JSON file is a single object or array. We'll mark this rule silent, so that a parsed JSON file contains only two token pairs: the parsed value itself, and the EOI rule.

json = _{ SOI ~ (object | array) ~ EOI }

AST generation

Let's compile the grammar into Rust.

#![allow(unused)]
fn main() {
extern crate pest;
#[macro_use]
extern crate pest_derive;

use pest::Parser;

#[derive(Parser)]
#[grammar = "json.pest"]
struct JSONParser;
}

We'll write a function that handles both parsing and AST generation. Users of the function can call it on an input string, then use the result returned as either a JSONValue or a parse error.

#![allow(unused)]
fn main() {
use pest::error::Error;

fn parse_json_file(file: &str) -> Result<JSONValue, Error<Rule>> {
    let json = JSONParser::parse(Rule::json, file)?.next().unwrap();

    // ...
}
}

Now we need to handle Pairs recursively, depending on the rule. We know that json is either an object or an array, but these values might contain an object or an array themselves! The most logical way to handle this is to write an auxiliary recursive function that parses a Pair into a JSONValue directly.

#![allow(unused)]
fn main() {
fn parse_json_file(file: &str) -> Result<JSONValue, Error<Rule>> {
    // ...

    use pest::iterators::Pair;

    fn parse_value(pair: Pair<Rule>) -> JSONValue {
        match pair.as_rule() {
            Rule::object => JSONValue::Object(
                pair.into_inner()
                    .map(|pair| {
                        let mut inner_rules = pair.into_inner();
                        let name = inner_rules
                            .next()
                            .unwrap()
                            .into_inner()
                            .next()
                            .unwrap()
                            .as_str();
                        let value = parse_value(inner_rules.next().unwrap());
                        (name, value)
                    })
                    .collect(),
            ),
            Rule::array => JSONValue::Array(pair.into_inner().map(parse_value).collect()),
            Rule::string => JSONValue::String(pair.into_inner().next().unwrap().as_str()),
            Rule::number => JSONValue::Number(pair.as_str().parse().unwrap()),
            Rule::boolean => JSONValue::Boolean(pair.as_str().parse().unwrap()),
            Rule::null => JSONValue::Null,
            Rule::json
            | Rule::EOI
            | Rule::pair
            | Rule::value
            | Rule::inner
            | Rule::char
            | Rule::WHITESPACE => unreachable!(),
        }
    }

    // ...
}
}

The object and array cases deserve special attention. The contents of an array token pair is just a sequence of values. Since we're working with a Rust iterator, we can simply map each value to its parsed AST node recursively, then collect them into a Vec. For objects, the process is similar, except the iterator is over pairs, from which we need to extract names and values separately.

The number and boolean cases use Rust's str::parse method to convert the parsed string to the appropriate Rust type. Every legal JSON number can be parsed directly into a Rust floating point number!

We run parse_value on the parse result to finish the conversion.

#![allow(unused)]
fn main() {
fn parse_json_file(file: &str) -> Result<JSONValue, Error<Rule>> {
    // ...

    Ok(parse_value(json))
}
}

Finishing

Our main function is now very simple. First, we read the JSON data from a file named data.json. Next, we parse the file contents into a JSON AST. Finally, we serialize the AST back into a string and print it.

use std::fs;

fn main() {
    let unparsed_file = fs::read_to_string("data.json").expect("cannot read file");

    let json: JSONValue = parse_json_file(&unparsed_file).expect("unsuccessful parse");

    println!("{}", serialize_jsonvalue(&json));
}

Try it out! Copy the example document at the top of this chapter into data.json, then run the program! You should see something like this:

$ cargo run
  [ ... ]
{"nesting":{"inner object":{}},"an array":[1.5,true,null,0.000001],"string with escaped double quotes":"\"quick brown foxes\""}

Example: The J language

The J language is an array programming language influenced by APL. In J, operations on individual numbers (2 * 3) can just as easily be applied to entire lists of numbers (2 * 3 4 5, returning 6 8 10).

Operators in J are referred to as verbs. Verbs are either monadic (taking a single argument, such as *: 3, "3 squared") or dyadic (taking two arguments, one on either side, such as 5 - 4, "5 minus 4").

Here's an example of a J program:

'A string'

*: 1 2 3 4

matrix =: 2 3 $ 5 + 2 3 4 5 6 7
10 * matrix

1 + 10 20 30
1 2 3 + 10

residues =: 2 | 0 1 2 3 4 5 6 7
residues

Using J's interpreter to run the above program yields the following on standard out:

A string

1 4 9 16

 70  80  90
100 110 120

11 21 31
11 12 13

0 1 0 1 0 1 0 1

In this section we'll write a grammar for a subset of J. We'll then walk through a parser that builds an AST by iterating over the rules that pest gives us. You can find the full source code within this book's repository.

The grammar

We'll build up a grammar section by section, starting with the program rule:

program = _{ SOI ~ "\n"* ~ (stmt ~ "\n"+) * ~ stmt? ~ EOI }

Each J program contains statements delimited by one or more newlines. Notice the leading underscore, which tells pest to silence the program rule — we don't want program to appear as a token in the parse stream, we want the underlying statements instead.

A statement is simply an expression, and since there's only one such possibility, we also silence this stmt rule as well, and thus our parser will receive an iterator of underlying exprs:

stmt = _{ expr }

An expression can be an assignment to a variable identifier, a monadic expression, a dyadic expression, a single string, or an array of terms:

expr = {
      assgmtExpr
    | monadicExpr
    | dyadicExpr
    | string
    | terms
}

A monadic expression consists of a verb with its sole operand on the right; a dyadic expression has operands on either side of the verb. Assignment expressions associate identifiers with expressions.

In J, there is no operator precedence — evaluation is right-associative (proceeding from right to left), with parenthesized expressions evaluated first.

monadicExpr = { verb ~ expr }

dyadicExpr = { (monadicExpr | terms) ~ verb ~ expr }

assgmtExpr = { ident ~ "=:" ~ expr }

A list of terms should contain at least one decimal, integer, identifier, or parenthesized expression; we care only about those underlying values, so we make the term rule silent with a leading underscore:

terms = { term+ }

term = _{ decimal | integer | ident | "(" ~ expr ~ ")" }

A few of J's verbs are defined in this grammar; J's full vocabulary is much more extensive.

verb = {
    ">:" | "*:" | "-"  | "%" | "#" | ">."
  | "+"  | "*"  | "<"  | "=" | "^" | "|"
  | ">"  | "$"
}

Now we can get into lexing rules. Numbers in J are represented as usual, with the exception that negatives are represented using a leading _ underscore (because - is a verb that performs negation as a monad and subtraction as a dyad). Identifiers in J must start with a letter, but can contain numbers thereafter. Strings are surrounded by single quotes; quotes themselves can be embedded by escaping them with an additional quote.

Notice how we use pest's @ modifier to make each of these rules atomic, meaning implicit whitespace is forbidden, and that interior rules (i.e., ASCII_ALPHA in ident) become silent — when our parser receives any of these tokens, they will be terminal:

integer = @{ "_"? ~ ASCII_DIGIT+ }

decimal = @{ "_"? ~ ASCII_DIGIT+ ~ "." ~ ASCII_DIGIT* }

ident = @{ ASCII_ALPHA ~ (ASCII_ALPHANUMERIC | "_")* }

string = @{ "'" ~ ( "''" | (!"'" ~ ANY) )* ~ "'" }

Whitespace in J consists solely of spaces and tabs. Newlines are significant because they delimit statements, so they are excluded from this rule:

WHITESPACE = _{ " " | "\t" }

Finally, we must handle comments. Comments in J start with NB. and continue to the end of the line on which they are found. Critically, we must not consume the newline at the end of the comment line; this is needed to separate any statement that might precede the comment from the statement on the succeeding line.

COMMENT = _{ "NB." ~ (!"\n" ~ ANY)* }

Parsing and AST generation

This section will walk through a parser that uses the grammar above. Library includes and self-explanatory code are omitted here; you can find the parser in its entirety within this book's repository.

First we'll enumerate the verbs defined in our grammar, distinguishing between monadic and dyadic verbs. These enumerations will be be used as labels in our AST:

#![allow(unused)]
fn main() {
pub enum MonadicVerb {
    Increment,
    Square,
    Negate,
    Reciprocal,
    Tally,
    Ceiling,
    ShapeOf,
}

pub enum DyadicVerb {
    Plus,
    Times,
    LessThan,
    LargerThan,
    Equal,
    Minus,
    Divide,
    Power,
    Residue,
    Copy,
    LargerOf,
    LargerOrEqual,
    Shape,
}
}

Then we'll enumerate the various kinds of AST nodes:

#![allow(unused)]
fn main() {
pub enum AstNode {
    Print(Box<AstNode>),
    Integer(i32),
    DoublePrecisionFloat(f64),
    MonadicOp {
        verb: MonadicVerb,
        expr: Box<AstNode>,
    },
    DyadicOp {
        verb: DyadicVerb,
        lhs: Box<AstNode>,
        rhs: Box<AstNode>,
    },
    Terms(Vec<AstNode>),
    IsGlobal {
        ident: String,
        expr: Box<AstNode>,
    },
    Ident(String),
    Str(CString),
}
}

To parse top-level statements in a J program, we have the following parse function that accepts a J program in string form and passes it to pest for parsing. We get back a sequence of Pairs. As specified in the grammar, a statement can only consist of an expression, so the match below parses each of those top-level expressions and wraps them in a Print AST node in keeping with the J interpreter's REPL behavior:

#![allow(unused)]
fn main() {
pub fn parse(source: &str) -> Result<Vec<AstNode>, Error<Rule>> {
    let mut ast = vec![];

    let pairs = JParser::parse(Rule::program, source)?;
    for pair in pairs {
        match pair.as_rule() {
            Rule::expr => {
                ast.push(Print(Box::new(build_ast_from_expr(pair))));
            }
            _ => {}
        }
    }

    Ok(ast)
}
}

AST nodes are built from expressions by walking the Pair iterator in lockstep with the expectations set out in our grammar file. Common behaviors are abstracted out into separate functions, such as parse_monadic_verb and parse_dyadic_verb, and Pairs representing expressions themselves are passed in recursive calls to build_ast_from_expr:

#![allow(unused)]
fn main() {
fn build_ast_from_expr(pair: pest::iterators::Pair<Rule>) -> AstNode {
    match pair.as_rule() {
        Rule::expr => build_ast_from_expr(pair.into_inner().next().unwrap()),
        Rule::monadicExpr => {
            let mut pair = pair.into_inner();
            let verb = pair.next().unwrap();
            let expr = pair.next().unwrap();
            let expr = build_ast_from_expr(expr);
            parse_monadic_verb(verb, expr)
        }
        // ... other cases elided here ...
    }
}
}

Dyadic verbs are mapped from their string representations to AST nodes in a straightforward way:

#![allow(unused)]
fn main() {
fn parse_dyadic_verb(pair: pest::iterators::Pair<Rule>, lhs: AstNode, rhs: AstNode) -> AstNode {
    AstNode::DyadicOp {
        lhs: Box::new(lhs),
        rhs: Box::new(rhs),
        verb: match pair.as_str() {
            "+" => DyadicVerb::Plus,
            "*" => DyadicVerb::Times,
            "-" => DyadicVerb::Minus,
            "<" => DyadicVerb::LessThan,
            "=" => DyadicVerb::Equal,
            ">" => DyadicVerb::LargerThan,
            "%" => DyadicVerb::Divide,
            "^" => DyadicVerb::Power,
            "|" => DyadicVerb::Residue,
            "#" => DyadicVerb::Copy,
            ">." => DyadicVerb::LargerOf,
            ">:" => DyadicVerb::LargerOrEqual,
            "$" => DyadicVerb::Shape,
            _ => panic!("Unexpected dyadic verb: {}", pair.as_str()),
        },
    }
}
}

As are monadic verbs:

#![allow(unused)]
fn main() {
fn parse_monadic_verb(pair: pest::iterators::Pair<Rule>, expr: AstNode) -> AstNode {
    AstNode::MonadicOp {
        verb: match pair.as_str() {
            ">:" => MonadicVerb::Increment,
            "*:" => MonadicVerb::Square,
            "-" => MonadicVerb::Negate,
            "%" => MonadicVerb::Reciprocal,
            "#" => MonadicVerb::Tally,
            ">." => MonadicVerb::Ceiling,
            "$" => MonadicVerb::ShapeOf,
            _ => panic!("Unsupported monadic verb: {}", pair.as_str()),
        },
        expr: Box::new(expr),
    }
}
}

Finally, we define a function to process terms such as numbers and strings. Numbers require some manuevering to handle J's leading underscores representing negation, but other than that the process is typical:

#![allow(unused)]
fn main() {
fn build_ast_from_term(pair: pest::iterators::Pair<Rule>) -> AstNode {
    match pair.as_rule() {
        Rule::integer => {
            let istr = pair.as_str();
            let (sign, istr) = match &istr[..1] {
                "_" => (-1, &istr[1..]),
                _ => (1, &istr[..]),
            };
            let integer: i32 = istr.parse().unwrap();
            AstNode::Integer(sign * integer)
        }
        Rule::decimal => {
            let dstr = pair.as_str();
            let (sign, dstr) = match &dstr[..1] {
                "_" => (-1.0, &dstr[1..]),
                _ => (1.0, &dstr[..]),
            };
            let mut flt: f64 = dstr.parse().unwrap();
            if flt != 0.0 {
                // Avoid negative zeroes; only multiply sign by nonzeroes.
                flt *= sign;
            }
            AstNode::DoublePrecisionFloat(flt)
        }
        Rule::expr => build_ast_from_expr(pair),
        Rule::ident => AstNode::Ident(String::from(pair.as_str())),
        unknown_term => panic!("Unexpected term: {:?}", unknown_term),
    }
}
}

Running the Parser

We can now define a main function to pass J programs to our pest-enabled parser:

fn main() {
    let unparsed_file = std::fs::read_to_string("example.ijs")
      .expect("cannot read ijs file");
    let astnode = parse(&unparsed_file).expect("unsuccessful parse");
    println!("{:?}", &astnode);
}

Using this code in example.ijs:

_2.5 ^ 3
*: 4.8
title =: 'Spinning at the Boundary'
*: _1 2 _3 4
1 2 3 + 10 20 30
1 + 10 20 30
1 2 3 + 10
2 | 0 1 2 3 4 5 6 7
another =: 'It''s Escaped'
3 | 0 1 2 3 4 5 6 7
(2+1)*(2+2)
3 * 2 + 1
1 + 3 % 4
x =: 100
x - 1
y =: x - 1
y

We'll get the following abstract syntax tree on stdout when we run the parser:

$ cargo run
  [ ... ]
[Print(DyadicOp { verb: Power, lhs: DoublePrecisionFloat(-2.5),
    rhs: Integer(3) }),
Print(MonadicOp { verb: Square, expr: DoublePrecisionFloat(4.8) }),
Print(IsGlobal { ident: "title", expr: Str("Spinning at the Boundary") }),
Print(MonadicOp { verb: Square, expr: Terms([Integer(-1), Integer(2),
    Integer(-3), Integer(4)]) }),
Print(DyadicOp { verb: Plus, lhs: Terms([Integer(1), Integer(2), Integer(3)]),
    rhs: Terms([Integer(10), Integer(20), Integer(30)]) }),
Print(DyadicOp { verb: Plus, lhs: Integer(1), rhs: Terms([Integer(10),
    Integer(20), Integer(30)]) }),
Print(DyadicOp { verb: Plus, lhs: Terms([Integer(1), Integer(2), Integer(3)]),
    rhs: Integer(10) }),
Print(DyadicOp { verb: Residue, lhs: Integer(2),
    rhs: Terms([Integer(0), Integer(1), Integer(2), Integer(3), Integer(4),
    Integer(5), Integer(6), Integer(7)]) }),
Print(IsGlobal { ident: "another", expr: Str("It\'s Escaped") }),
Print(DyadicOp { verb: Residue, lhs: Integer(3), rhs: Terms([Integer(0),
    Integer(1), Integer(2), Integer(3), Integer(4), Integer(5),
    Integer(6), Integer(7)]) }),
Print(DyadicOp { verb: Times, lhs: DyadicOp { verb: Plus, lhs: Integer(2),
    rhs: Integer(1) }, rhs: DyadicOp { verb: Plus, lhs: Integer(2),
        rhs: Integer(2) } }),
Print(DyadicOp { verb: Times, lhs: Integer(3), rhs: DyadicOp { verb: Plus,
    lhs: Integer(2), rhs: Integer(1) } }),
Print(DyadicOp { verb: Plus, lhs: Integer(1), rhs: DyadicOp { verb: Divide,
    lhs: Integer(3), rhs: Integer(4) } }),
Print(IsGlobal { ident: "x", expr: Integer(100) }),
Print(DyadicOp { verb: Minus, lhs: Ident("x"), rhs: Integer(1) }),
Print(IsGlobal { ident: "y", expr: DyadicOp { verb: Minus, lhs: Ident("x"),
    rhs: Integer(1) } }),
Print(Ident("y"))]

Operator precedence

There are several methods for dealing with operator precedence in pest:

1. directly in the PEG grammar;
2. using a PrecClimber (deprecated);
3. using a PrattParser.

Given PrattParser is the most general available method that supports unary prefix and suffix operators, we provide more details on its usage.

Pratt Parser

The following pest grammar defines a calculator which can be used for Pratt parsing.

WHITESPACE   =  _{ " " | "\t" | NEWLINE }
  
program      =   { SOI ~ expr ~ EOI }
  expr       =   { prefix* ~ primary ~ postfix* ~ (infix ~ prefix* ~ primary ~ postfix* )* }
    infix    =  _{ add | sub | mul | div | pow }
      add    =   { "+" } // Addition
      sub    =   { "-" } // Subtraction
      mul    =   { "*" } // Multiplication
      div    =   { "/" } // Division
      pow    =   { "^" } // Exponentiation
    prefix   =  _{ neg }
      neg    =   { "-" } // Negation
    postfix  =  _{ fac }
      fac    =   { "!" } // Factorial
    primary  =  _{ int | "(" ~ expr ~ ")" }
      int    =  @{ (ASCII_NONZERO_DIGIT ~ ASCII_DIGIT+ | ASCII_DIGIT) }

Below is a PrattParser that is able to parse an expr in the above grammar. The order of precedence corresponds to the order in which op is called. Thus, mul will have higher precedence than add. Operators can also be chained with | to give them equal precedence.

#![allow(unused)]
fn main() {
let pratt =
    PrattParser::new()
        .op(Op::infix(Rule::add, Assoc::Left) | Op::infix(Rule::sub, Assoc::Left))
        .op(Op::infix(Rule::mul, Assoc::Left) | Op::infix(Rule::div, Assoc::Left))
        .op(Op::infix(Rule::pow, Assoc::Right))
        .op(Op::postfix(Rule::fac))
        .op(Op::prefix(Rule::neg));
}

To parse an expression, call the map_primary, map_prefix, map_postfix, map_infix and parse methods as follows:

#![allow(unused)]
fn main() {
fn parse_expr(pairs: Pairs<Rule>, pratt: &PrattParser<Rule>) -> i32 {
    pratt
        .map_primary(|primary| match primary.as_rule() {
            Rule::int  => primary.as_str().parse().unwrap(),
            Rule::expr => parse_expr(primary.into_inner(), pratt), // from "(" ~ expr ~ ")"
            _          => unreachable!(),
        })
        .map_prefix(|op, rhs| match op.as_rule() {
            Rule::neg  => -rhs,
            _          => unreachable!(),
        })
        .map_postfix(|lhs, op| match op.as_rule() {
            Rule::fac  => (1..lhs+1).product(),
            _          => unreachable!(),
        })
        .map_infix(|lhs, op, rhs| match op.as_rule() {
            Rule::add  => lhs + rhs,
            Rule::sub  => lhs - rhs,
            Rule::mul  => lhs * rhs,
            Rule::div  => lhs / rhs,
            Rule::pow  => (1..rhs+1).map(|_| lhs).product(),
            _          => unreachable!(),
        })
        .parse(pairs)
}
}

Note that map_prefix, map_postfix and map_infix only need to be specified if the grammar contains the corresponding operators.

Example: Calculator

This example focuses on the practical aspect of using a Pratt parser to parse expressions using pest. To illustrate this, we build a parser for simple equations, and construct an abstract syntax tree.

Precedence and associativity

In a simple equation multiplication and division are evaluated first, which means they have a higher precedence. e.g. 1 + 2 * 3 is evaluated as 1 + (2 * 3), if the precedence was equal it would be (1 + 2) * 3. For our system we have the following operands:

• highest precedence: multiplication & division
• lowest precedence: addition & subtraction

In the expression 1 + 2 - 3, no operator is inherently more important than the other. Addition, subtraction, multiplication and division are evaluated from left to right, e.g. 1 - 2 + 3 is evaluated as (1 - 2) + 3. We call this property left associativity. Operators can also be right associative. For example, we usually evaluate the statement x = y = 1 by first assigning y = 1 and x = 1 (or x = y) afterwards.

Associativity only matters if two operators have the same precedence, as is the case with addition and subtraction for example. This means that if we have an expression with only additions and subtractions, we can just evaluate it from left to right. 1 + 2 - 3 is equal to (1 + 2) - 3. And 1 - 2 + 3 is equal to (1 - 2) + 3.

To go from a flat list of operands separated by operators, it suffices to define a precedence and associativity for each operator. With these definitions an algorithm such as Pratt parsing is able to construct a corresponding expression tree.

If you are curious to know more about how Pratt parsing is implemented, Aleksey Kladov has a great tutorial on implementing it from scratch using Rust.

Calculator example

We want our calculator to be able to parse simple equations that consist of integers and simple binary operators. Additionally, we want to support parenthesis and unary minus. For example:

1 + 2 * 3
-(2 + 5) * 16

Grammar

We start by defining our atoms, bits of self-contained syntax that cannot be split up into smaller parts. For our calculator we start with just simple integers:

// No whitespace allowed between digits
integer = @{ ASCII_DIGIT+ }

atom = _{ integer }

Next, our binary operators:

bin_op = _{ add | subtract | multiply | divide }
	add = { "+" }
	subtract = { "-" }
	multiply = { "*" }
	divide = { "/" }

These two rules will be the input to the PrattParser. It expects to receive atoms separated by operators, like so: atom, bin_op, atom, bin_op, atom, ....

Corresponding to this format, we define our rule for expressions:

expr = { atom ~ (bin_op ~ atom)* }

This defines the grammar which generates the required input for the Pratt parser.

Abstract Syntax Tree

We want to convert our input into an abstract syntax tree. For this we define the following types:

#![allow(unused)]
fn main() {
#[derive(Debug)]
pub enum Expr {
    Integer(i32),
    BinOp {
        lhs: Box<Expr>,
        op: Op,
        rhs: Box<Expr>,
    },
}

#[derive(Debug)]
pub enum Op {
    Add,
    Subtract,
    Multiply,
    Divide,
}
}

Note the Box<Expr> required because Rust does not allow unboxed recursive types.

There is no separate atom type, any atom is also a valid expression.

Pratt parser

The precedence of operations is defined in the Pratt parser.

An easy approach is to define the PrattParser as global using lazy_static.

Adhering to standard rules of arithmetic, we will define addition and subtraction to have lower priority than multiplication and division, and make all operators left associative.

#![allow(unused)]
fn main() {
lazy_static::lazy_static! {
    static ref PRATT_PARSER: PrattParser<Rule> = {
        use pest::pratt_parser::{Assoc::*, Op};
        use Rule::*;

        // Precedence is defined lowest to highest
        PrattParser::new()
            // Addition and subtract have equal precedence
            .op(Op::infix(add, Left) | Op::infix(subtract, Left))
            .op(Op::infix(multiply, Left) | Op::infix(divide, Left))
    };
}
}

We are almost there, the only thing that's left is to use our Pratt parser. For this the map_primary, map_infix, and parse functions are used, the first two take functions and the third one takes an iterator over pairs. map_primary is executed for every primary (atom), and map_infix is executed for every binop with its new left-hand and right-hand side according to the precedence rules defined earlier. In this example, we create an AST in the Pratt parser.

#![allow(unused)]
fn main() {
pub fn parse_expr(pairs: Pairs<Rule>) -> Expr {
    PRATT_PARSER
        .map_primary(|primary| match primary.as_rule() {
            Rule::integer => Expr::Integer(primary.as_str().parse::<i32>().unwrap()),
            rule => unreachable!("Expr::parse expected atom, found {:?}", rule)
        })
        .map_infix(|lhs, op, rhs| {
            let op = match op.as_rule() {
                Rule::add => Op::Add,
                Rule::subtract => Op::Subtract,
                Rule::multiply => Op::Multiply,
                Rule::divide => Op::Divide,
                rule => unreachable!("Expr::parse expected infix operation, found {:?}", rule),
            };
            Expr::BinOp {
                lhs: Box::new(lhs),
                op,
                rhs: Box::new(rhs),
            }
        })
        .parse(pairs)

}
}

Here's an example of how to use the parser.

fn main() -> io::Result<()> {
    for line in io::stdin().lock().lines() {
        match CalculatorParser::parse(Rule::equation, &line?) {
            Ok(mut pairs) => {
                println!(
                    "Parsed: {:#?}",
                    parse_expr(
                        // inner of expr
                        pairs.next().unwrap().into_inner()
                    )
                );
            }
            Err(e) => {
                eprintln!("Parse failed: {:?}", e);
            }
        }
    }
    Ok(())
}

With this, we can parse the following simple equation:

> 1 * 2 + 3 / 4
Parsed: BinOp {
    lhs: BinOp {
        lhs: Integer( 1 ),
        op: Multiply,
        rhs: Integer( 2 ),
    },
    op: Add,
    rhs: BinOp {
        lhs: Integer( 3 ),
        op: Divide,
        rhs: Integer( 4 ),
    },
}

Unary minus and parenthesis

So far, our calculator can parse fairly complicated expressions, but it will fail if it encounters explicit parentheses or a unary minus sign. Let's fix that.

Parentheses

Consider the expression (1 + 2) * 3. Clearly removing the parentheses would give a different result, so we must support parsing such expressions. Luckily, this can be a simple addition to our atom rule:

- atom = _{ integer }
+ atom = _{ integer | "(" ~ expr ~ ")" }

Earlier we said that atoms should be simple token sequences that cannot be split up further, but now an atom can contain arbitrary expressions! The reason we are okay with this is that the parentheses mark clear boundaries for the expression, it will not make ambiguous what operators belong to the inner expression and which to the outer one.

Unary minus

We can currently only parse positive integers, eg 16 or 2342. But we also want to do calculations with negative intergers. To do this, we introduce the unary minus, so we can make -4 and -(8 + 15). We need the following change to grammar:

+ unary_minus = { "-" }
+ primary = _{ integer | "(" ~ expr ~ ")" }
- atom = _{ integer | "(" ~ expr ~ ")" }
+ atom = _{ unary_minus? ~ primary }

For these last changes we've omitted the small changes to the AST and parsing logic (using map_prefix).

You can find all these details in the repository: github.com/pest-parser/book/tree/master/examples/pest-calculator.

Final project: Awk clone (WIP)

This chapter will walk through the creation of a simple variant of Awk (only loosely following the POSIX specification). It will probably have several sections. It will provide an example of a full project based on pest with a manageable grammar, a straightforward AST, and a fairly simple interpreter.

This Awk clone will support regex patterns, string and numeric variables, most of the POSIX operators, and some functions. It will not support user-defined functions in the interest of avoiding variable scoping.