s_expression.rs

//! In this example we build an [S-expression](https://en.wikipedia.org/wiki/S-expression)
//! parser and tiny [lisp](https://en.wikipedia.org/wiki/Lisp_(programming_language)) interpreter.
//! Lisp is a simple type of language made up of Atoms and Lists, forming easily parsable trees.

#![cfg(feature = "alloc")]

use nom::{
  branch::alt,
  bytes::complete::tag,
  character::complete::{alpha1, char, digit1, multispace0, multispace1, one_of},
  combinator::{cut, map, map_res, opt},
  error::context,
  multi::many,
  sequence::{delimited, preceded, terminated},
  IResult, Parser,
};
use nom_language::error::VerboseError;

/// We start by defining the types that define the shape of data that we want.
/// In this case, we want something tree-like

/// Starting from the most basic, we define some built-in functions that our lisp has
#[derive(Debug, Eq, PartialEq, Clone, Copy)]
pub enum BuiltIn {
  Plus,
  Minus,
  Times,
  Divide,
  Equal,
  Not,
}

/// We now wrap this type and a few other primitives into our Atom type.
/// Remember from before that Atoms form one half of our language.

#[derive(Debug, Eq, PartialEq, Clone)]
pub enum Atom {
  Num(i32),
  Keyword(String),
  Boolean(bool),
  BuiltIn(BuiltIn),
}

/// The remaining half is Lists. We implement these as recursive Expressions.
/// For a list of numbers, we have `'(1 2 3)`, which we'll parse to:
/// ```
/// Expr::Quote(vec![Expr::Constant(Atom::Num(1)),
///                  Expr::Constant(Atom::Num(2)),
///                  Expr::Constant(Atom::Num(3))])
/// Quote takes an S-expression and prevents evaluation of it, making it a data
/// structure that we can deal with programmatically. Thus any valid expression
/// is also a valid data structure in Lisp itself.

#[derive(Debug, Eq, PartialEq, Clone)]
pub enum Expr {
  Constant(Atom),
  /// (func-name arg1 arg2)
  Application(Box<Expr>, Vec<Expr>),
  /// (if predicate do-this)
  If(Box<Expr>, Box<Expr>),
  /// (if predicate do-this otherwise-do-this)
  IfElse(Box<Expr>, Box<Expr>, Box<Expr>),
  /// '(3 (if (+ 3 3) 4 5) 7)
  Quote(Vec<Expr>),
}

/// Continuing the trend of starting from the simplest piece and building up,
/// we start by creating a parser for the built-in operator functions.
fn parse_builtin_op(i: &str) -> IResult<&str, BuiltIn, VerboseError<&str>> {
  // one_of matches one of the characters we give it
  let (i, t) = one_of("+-*/=")(i)?;

  // because we are matching single character tokens, we can do the matching logic
  // on the returned value
  Ok((
    i,
    match t {
      '+' => BuiltIn::Plus,
      '-' => BuiltIn::Minus,
      '*' => BuiltIn::Times,
      '/' => BuiltIn::Divide,
      '=' => BuiltIn::Equal,
      _ => unreachable!(),
    },
  ))
}

fn parse_builtin(i: &str) -> IResult<&str, BuiltIn, VerboseError<&str>> {
  // alt gives us the result of first parser that succeeds, of the series of
  // parsers we give it
  alt((
    parse_builtin_op,
    // map lets us process the parsed output, in this case we know what we parsed,
    // so we ignore the input and return the BuiltIn directly
    map(tag("not"), |_| BuiltIn::Not),
  ))
  .parse(i)
}

/// Our boolean values are also constant, so we can do it the same way
fn parse_bool(i: &str) -> IResult<&str, Atom, VerboseError<&str>> {
  alt((
    map(tag("#t"), |_| Atom::Boolean(true)),
    map(tag("#f"), |_| Atom::Boolean(false)),
  ))
  .parse(i)
}

/// The next easiest thing to parse are keywords.
/// We introduce some error handling combinators: `context` for human readable errors
/// and `cut` to prevent back-tracking.
///
/// Put plainly: `preceded(tag(":"), cut(alpha1))` means that once we see the `:`
/// character, we have to see one or more alphabetic characters or the input is invalid.
fn parse_keyword(i: &str) -> IResult<&str, Atom, VerboseError<&str>> {
  map(
    context("keyword", preceded(tag(":"), cut(alpha1))),
    |sym_str: &str| Atom::Keyword(sym_str.to_string()),
  )
  .parse(i)
}

/// Next up is number parsing. We're keeping it simple here by accepting any number (> 1)
/// of digits but ending the program if it doesn't fit into an i32.
fn parse_num(i: &str) -> IResult<&str, Atom, VerboseError<&str>> {
  alt((
    map_res(digit1, |digit_str: &str| {
      digit_str.parse::<i32>().map(Atom::Num)
    }),
    map(preceded(tag("-"), digit1), |digit_str: &str| {
      Atom::Num(-digit_str.parse::<i32>().unwrap())
    }),
  ))
  .parse(i)
}

/// Now we take all these simple parsers and connect them.
/// We can now parse half of our language!
fn parse_atom(i: &str) -> IResult<&str, Atom, VerboseError<&str>> {
  alt((
    parse_num,
    parse_bool,
    map(parse_builtin, Atom::BuiltIn),
    parse_keyword,
  ))
  .parse(i)
}

/// We then add the Expr layer on top
fn parse_constant(i: &str) -> IResult<&str, Expr, VerboseError<&str>> {
  map(parse_atom, Expr::Constant).parse(i)
}

/// Before continuing, we need a helper function to parse lists.
/// A list starts with `(` and ends with a matching `)`.
/// By putting whitespace and newline parsing here, we can avoid having to worry about it
/// in much of the rest of the parser.
///
/// Unlike the previous functions, this function doesn't take or consume input, instead it
/// takes a parsing function and returns a new parsing function.
fn s_exp<'a, O1, F>(inner: F) -> impl Parser<&'a str, Output = O1, Error = VerboseError<&'a str>>
where
  F: Parser<&'a str, Output = O1, Error = VerboseError<&'a str>>,
{
  delimited(
    char('('),
    preceded(multispace0, inner),
    context("closing paren", cut(preceded(multispace0, char(')')))),
  )
}

/// We can now use our new combinator to define the rest of the `Expr`s.
///
/// Starting with function application, we can see how the parser mirrors our data
/// definitions: our definition is `Application(Box<Expr>, Vec<Expr>)`, so we know
/// that we need to parse an expression and then parse 0 or more expressions, all
/// wrapped in an S-expression.
///
/// We can sequence parsers together by grouping them in a tuple, forming a new
/// parser returning a tuple containing the result of each parser in the same order,
/// and then map over it to transform the output into an `Expr::Application`
fn parse_application(i: &str) -> IResult<&str, Expr, VerboseError<&str>> {
  let application_inner = map((parse_expr, many(0.., parse_expr)), |(head, tail)| {
    Expr::Application(Box::new(head), tail)
  });
  // finally, we wrap it in an s-expression
  s_exp(application_inner).parse(i)
}

/// Because `Expr::If` and `Expr::IfElse` are so similar (we easily could have
/// defined `Expr::If` to have an `Option` for the else block), we parse both
/// in a single function.
///
/// In fact, we define our parser as if `Expr::If` was defined with an Option in it,
/// we have the `opt` combinator which fits very nicely here.
fn parse_if(i: &str) -> IResult<&str, Expr, VerboseError<&str>> {
  let if_inner = context(
    "if expression",
    map(
      preceded(
        // here to avoid ambiguity with other names starting with `if`, if we added
        // variables to our language, we say that if must be terminated by at least
        // one whitespace character
        terminated(tag("if"), multispace1),
        cut((parse_expr, parse_expr, opt(parse_expr))),
      ),
      |(pred, true_branch, maybe_false_branch)| {
        if let Some(false_branch) = maybe_false_branch {
          Expr::IfElse(
            Box::new(pred),
            Box::new(true_branch),
            Box::new(false_branch),
          )
        } else {
          Expr::If(Box::new(pred), Box::new(true_branch))
        }
      },
    ),
  );
  s_exp(if_inner).parse(i)
}

/// A quoted S-expression is list data structure.
///
/// This example doesn't have the symbol atom, but by adding variables and changing
/// the definition of quote to not always be around an S-expression, we'd get them
/// naturally.
fn parse_quote(i: &str) -> IResult<&str, Expr, VerboseError<&str>> {
  // this should look very straight-forward after all we've done:
  // we find the `'` (quote) character, use cut to say that we're unambiguously
  // looking for an s-expression of 0 or more expressions, and then parse them
  map(
    context(
      "quote",
      preceded(tag("'"), cut(s_exp(many(0.., parse_expr)))),
    ),
    Expr::Quote,
  )
  .parse(i)
}

/// We tie them all together again, making a top-level expression parser!

fn parse_expr(i: &str) -> IResult<&str, Expr, VerboseError<&str>> {
  preceded(
    multispace0,
    alt((parse_constant, parse_application, parse_if, parse_quote)),
  )
  .parse(i)
}

/// And that's it!
/// We can now parse our entire lisp language.
///
/// But in order to make it a little more interesting, we can hack together
/// a little interpreter to take an Expr, which is really an
/// [Abstract Syntax Tree](https://en.wikipedia.org/wiki/Abstract_syntax_tree) (AST),
/// and give us something back

/// To start we define a couple of helper functions
fn get_num_from_expr(e: Expr) -> Option<i32> {
  if let Expr::Constant(Atom::Num(n)) = e {
    Some(n)
  } else {
    None
  }
}

fn get_bool_from_expr(e: Expr) -> Option<bool> {
  if let Expr::Constant(Atom::Boolean(b)) = e {
    Some(b)
  } else {
    None
  }
}

/// This function tries to reduce the AST.
/// This has to return an Expression rather than an Atom because quoted s_expressions
/// can't be reduced
fn eval_expression(e: Expr) -> Option<Expr> {
  match e {
    // Constants and quoted s-expressions are our base-case
    Expr::Constant(_) | Expr::Quote(_) => Some(e),
    // we then recursively `eval_expression` in the context of our special forms
    // and built-in operators
    Expr::If(pred, true_branch) => {
      let reduce_pred = eval_expression(*pred)?;
      if get_bool_from_expr(reduce_pred)? {
        eval_expression(*true_branch)
      } else {
        None
      }
    }
    Expr::IfElse(pred, true_branch, false_branch) => {
      let reduce_pred = eval_expression(*pred)?;
      if get_bool_from_expr(reduce_pred)? {
        eval_expression(*true_branch)
      } else {
        eval_expression(*false_branch)
      }
    }
    Expr::Application(head, tail) => {
      let reduced_head = eval_expression(*head)?;
      let reduced_tail = tail
        .into_iter()
        .map(eval_expression)
        .collect::<Option<Vec<Expr>>>()?;
      if let Expr::Constant(Atom::BuiltIn(bi)) = reduced_head {
        Some(Expr::Constant(match bi {
          BuiltIn::Plus => Atom::Num(
            reduced_tail
              .into_iter()
              .map(get_num_from_expr)
              .collect::<Option<Vec<i32>>>()?
              .into_iter()
              .sum(),
          ),
          BuiltIn::Times => Atom::Num(
            reduced_tail
              .into_iter()
              .map(get_num_from_expr)
              .collect::<Option<Vec<i32>>>()?
              .into_iter()
              .product(),
          ),
          BuiltIn::Equal => Atom::Boolean(
            reduced_tail
              .iter()
              .zip(reduced_tail.iter().skip(1))
              .all(|(a, b)| a == b),
          ),
          BuiltIn::Not => {
            if reduced_tail.len() != 1 {
              return None;
            } else {
              Atom::Boolean(!get_bool_from_expr(reduced_tail.first().cloned().unwrap())?)
            }
          }
          BuiltIn::Minus => Atom::Num(if let Some(first_elem) = reduced_tail.first().cloned() {
            let fe = get_num_from_expr(first_elem)?;
            reduced_tail
              .into_iter()
              .map(get_num_from_expr)
              .collect::<Option<Vec<i32>>>()?
              .into_iter()
              .skip(1)
              .fold(fe, |a, b| a - b)
          } else {
            Default::default()
          }),
          BuiltIn::Divide => Atom::Num(if let Some(first_elem) = reduced_tail.first().cloned() {
            let fe = get_num_from_expr(first_elem)?;
            reduced_tail
              .into_iter()
              .map(get_num_from_expr)
              .collect::<Option<Vec<i32>>>()?
              .into_iter()
              .skip(1)
              .fold(fe, |a, b| a / b)
          } else {
            Default::default()
          }),
        }))
      } else {
        None
      }
    }
  }
}

/// And we add one more top-level function to tie everything together, letting
/// us call eval on a string directly
fn eval_from_str(src: &str) -> Result<Expr, String> {
  parse_expr(src)
    .map_err(|e: nom::Err<VerboseError<&str>>| format!("{:#?}", e))
    .and_then(|(_, exp)| eval_expression(exp).ok_or_else(|| "Eval failed".to_string()))
}

fn main() {
  let expression_1 = "((if (= (+ 3 (/ 9 3))
         (* 2 3))
     *
     /)
  456 123)";
  println!(
    "\"{}\"\nevaled gives us: {:?}",
    expression_1,
    eval_from_str(expression_1)
  );
}