Parser Combinators

This document is a primer on Parser Combinators and their use in Flang.


The Fortran language recognizer here can be classified as an LL recursive descent parser. It is composed from a parser combinator library that defines a few fundamental parsers and a few ways to compose them into more powerful parsers.

For our purposes here, a parser is any object that attempts to recognize an instance of some syntax from an input stream. It may succeed or fail. On success, it may return some semantic value to its caller.

In C++ terms, a parser is any instance of a class that

  1. has a constexpr default constructor,
  2. defines a type named resultType, and
  3. provides a function (const member or static) that accepts a reference to a ParseState as its argument and returns a std::optional<resultType> as a result, with the presence or absence of a value in the std::optional<> signifying success or failure, respectively.
std::optional<resultType> Parse(ParseState &) const;

The resultType of a parser is typically the class type of some particular node type in the parse tree.

ParseState is a class that encapsulates a position in the source stream, collects messages, and holds a few state flags that determine tokenization (e.g., are we in a character literal?). Instances of ParseState are independent and complete – they are cheap to duplicate whenever necessary to implement backtracking.

The constexpr default constructor of a parser is important. The functions (below) that operate on instances of parsers are themselves all constexpr. This use of compile-time expressions allows the entirety of a recursive descent parser for a language to be constructed at compilation time through the use of templates.

Fundamental Predefined Parsers

These objects and functions are (or return) the fundamental parsers:

  • ok is a trivial parser that always succeeds without advancing.
  • pure(x) returns a trivial parser that always succeeds without advancing, returning some value x.
  • pure<T>() is pure(T{}) but does not require that T be copy-constructible.
  • fail<T>(msg) denotes a trivial parser that always fails, emitting the given message as a side effect. The template parameter is the type of the value that the parser never returns.
  • nextCh consumes the next character and returns its location, and fails at EOF.
  • "xyz"_ch succeeds if the next character consumed matches any of those in the string and returns its location. Be advised that the source will have been normalized to lower case (miniscule) letters outside character and Hollerith literals and edit descriptors before parsing.


These functions and operators combine existing parsers to generate new parsers. They are constexpr, so they should be viewed as type-safe macros.

  • !p succeeds if p fails, and fails if p succeeds.
  • p >> q fails if p does, otherwise running q and returning its value when it succeeds.
  • p / q fails if p does, otherwise running q and returning p’s value if q succeeds.
  • p || q succeeds if p does, otherwise running q. The two parsers must have the same type, and the value returned by the first succeeding parser is the value of the combination.
  • first(p1, p2, ...) returns the value of the first parser that succeeds. All of the parsers in the list must return the same type. It is essentially the same as p1 || p2 || ... but has a slightly faster implementation and may be easier to format in your code.
  • lookAhead(p) succeeds if p does, but doesn’t modify any state.
  • attempt(p) succeeds if p does, safely preserving state on failure.
  • many(p) recognizes a greedy sequence of zero or more nonempty successes of p, and returns std::list<> of their values. It always succeeds.
  • some(p) recognized a greedy sequence of one or more successes of p. It fails if p immediately fails.
  • skipMany(p) is the same as many(p), but it discards the results.
  • maybe(p) tries to match p, returning an std::optional<T> value. It always succeeds.
  • defaulted(p) matches p, and when p fails it returns a default-constructed instance of p’s resultType. It always succeeds.
  • nonemptySeparated(p, q) repeatedly matches “p q p q p q … p”, returning a std::list<> of only the values of the p’s. It fails if p immediately fails.
  • extension(p) parses p if strict standard compliance is disabled, or with a warning if nonstandard usage warnings are enabled.
  • deprecated(p) parses p if strict standard compliance is disabled, with a warning if deprecated usage warnings are enabled.
  • inContext(msg, p) runs p within an error message context; any message that p generates will be tagged with msg as its context. Contexts may nest.
  • withMessage(msg, p) succeeds if p does, and if it does not, it discards the messages from p and fails with the specified message.
  • recovery(p, q) is equivalent to p || q, except that error messages generated from the first parser are retained, and a flag is set in the ParseState to remember that error recovery was necessary.
  • localRecovery(msg, p, q) is equivalent to recovery(withMessage(msg, p), q >> pure<A>()) where A is the result type of ‘p’. It is useful for targeted error recovery situations within statements.

Note that

a >> b >> c / d / e

matches a sequence of five parsers, but returns only the result that was obtained by matching c.


The following applicative combinators combine parsers and modify or collect the values that they return.

  • construct<T>(p1, p2, ...) matches zero or more parsers in succession, collecting their results and then passing them with move semantics to a constructor for the type T if they all succeed. If there is a single parser as the argument and it returns no usable value but only success or failure (e.g., "IF"_tok), the default nullary constructor of the type T is called.
  • sourced(p) matches p, and fills in its source data member with the locations of the cooked character stream that it consumed
  • applyFunction(f, p1, p2, ...) matches one or more parsers in succession, collecting their results and passing them as rvalue reference arguments to some function, returning its result.
  • applyLambda([](&&x){}, p1, p2, ...) is the same thing, but for lambdas and other function objects.
  • applyMem(mf, p1, p2, ...) is the same thing, but invokes a member function of the result of the first parser for updates in place.

Token Parsers

Last, we have these basic parsers on which the actual grammar of the Fortran is built. All of the following parsers consume characters acquired from nextCh.

  • space always succeeds after consuming any spaces
  • spaceCheck always succeeds after consuming any spaces, and can emit a warning if there was no space in free form code before a character that could continue a name or keyword
  • digit matches one cooked decimal digit (0-9)
  • letter matches one cooked letter (A-Z)
  • "..."_tok match the content of the string, skipping spaces before and after. Internal spaces are optional matches. The _tok suffix is optional when the parser appears before the combinator >> or after the combinator /.
  • "..."_sptok is a string match in which the spaces are required in free form source.
  • "..."_id is a string match for a complete identifier (not a prefix of a longer identifier or keyword).
  • parenthesized(p) is shorthand for "(" >> p / ")".
  • bracketed(p) is shorthand for "[" >> p / "]".
  • nonEmptyList(p) matches a comma-separated list of one or more instances of p.
  • nonEmptyList(errorMessage, p) is equivalent to withMessage(errorMessage, nonemptyList(p)), which allows one to supply a meaningful error message in the event of an empty list.
  • optionalList(p) is the same thing, but can be empty, and always succeeds.

Debugging Parser

Last, a string literal "..."_debug denotes a parser that emits the string to llvm::errs and succeeds. It is useful for tracing while debugging a parser but should obviously not be committed for production code.