Parser Combinators: Part 1

Episode #62 • Jun 24, 2019 • Subscriber-Only

Even though map, flatMap and zip pack a punch, there are still many parsing operations that can’t be done using them alone. This is where “parser combinators” come into play. Let’s look at a few common parsing problems and solve them using parser combinators!

Previous episode
Parser Combinators: Part 1
More forgiving parsing
Extracting common parsers
Next time: parsing multiple values

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In the last three episodes of Point-Free we explored the compositional properties of parsers by defining map, flatMap and zip operations on them. Each operation carried with it precise semantic meaning, and that meaning is shared with many other types such as arrays, optionals, results, promises and more, and each one was a little more powerful than the last.

With those three operations we were able to cook up complex parsers by piecing together lots of tiny, easy-to-understand parsers. The example we developed was that of a latitude/longitude coordinate parser, which was built from many small parsers. But even though these three operations pack a punch, there are still some things that they cannot accomplish. For example, we cannot currently parse any number of values from some input string, like say a string that has a bunch of coordinates that are separated by newlines. Nor can we attempt to run a bunch of parsers against an input string till one succeeds, say if we support more than one format for a data type. Doing so with map, flatMap, and zip alone is just not possible, so we need to figure out a way to take our parsers to the next level.

The key to this leveling up is none other than functions. Just plain functions. It’s an idea we’ve seen time and time again on Point-Free. By using functions that return parsers as output, or even better, take parsers as input and return parsers as output, we will unlock a whole new world of possibilities with our parsers. These functions are called “parser combinators”, but they could maybe even be called “higher-order parsers” to draw an analogy with “higher-order functions”.

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  1. We defined prefix(while:) to parse off a substring while characters matched a predicate. It can be just as useful to skip characters. Define a drop(while:) parser that skips characters that match a given predicate. What type of parser should drop(while:) return?

  2. Define a parser combinator, zeroOrMore, that takes a parser of As as input and produces a parser of Array<A>s by running the existing parser as many times as it can.

  3. Define a parser combinator, oneOrMore, that takes a parser of As as input and produces a parser of Array<A>s that must include at least one value.

  4. Because oneOrMore guarantees at least one value, let’s enforce it in the type system! Update oneOrMore to return Parser<NonEmptyArray<A>> instead of Parser<[A]>.

  5. Enhance the zeroOrMore and oneOrMore parsers to take a separatedBy argument in order to parse a comma-separated list. Ensure that only separators between parsed values are consumed.

  6. Redefine the zeroOrMoreSpaces and oneOrMoreSpaces parsers in terms of zeroOrMore and oneOrMore.



Daniel Steinberg • Friday Sep 14, 2018

Daniel gives a wonderful overview of how the idea of “combinators” infiltrates many common programming tasks.

Just as with OO, one of the keys to a functional style of programming is to write very small bits of functionality that can be combined to create powerful results. The glue that combines the small bits are called Combinators. In this talk we’ll motivate the topic with a look at Swift Sets before moving on to infinite sets, random number generators, parser combinators, and Peter Henderson’s Picture Language. Combinators allow you to provide APIs that are friendly to non-functional programmers.

Parser Combinators in Swift

Yasuhiro Inami • Monday May 2, 2016

In the first ever try! Swift conference, Yasuhiro Inami gives a broad overview of parsers and parser combinators, and shows how they can accomplish very complex parsing.

Parser combinators are one of the most awesome functional techniques for parsing strings into trees, like constructing JSON. In this talk from try! Swift, Yasuhiro Inami describes how they work by combining small parsers together to form more complex and practical ones.


Alexander Grebenyuk • Saturday Aug 10, 2019

This library for parsing regular expression strings into a Swift data type uses many of the ideas developed in our series of episodes on parsers. It’s a great example of how to break a very large, complex problem into many tiny parsers that glue back together.

Regexes vs Combinatorial Parsing

Soroush Khanlou • Tuesday Dec 3, 2019

In this article, Soroush Khanlou applies parser combinators to a real world problem: parsing notation for a music app. He found that parser combinators improved on regular expressions not only in readability, but in performance!

Learning Parser Combinators With Rust

Bodil Stokke • Thursday Apr 18, 2019

A wonderful article that explains parser combinators from start to finish. The article assumes you are already familiar with Rust, but it is possible to look past the syntax and see that there are many shapes in the code that are similar to what we have covered in our episodes on parsers.


John Patrick Morgan • Thursday Jan 12, 2017

A parser library built in Swift that uses many of the concepts we cover in our series of episodes on parsers.

Sparse is a simple parser-combinator library written in Swift.


Daan Leijen, Paolo Martini, Antoine Latter

Parsec is one of the first and most widely used parsing libraries, built in Haskell. It’s built on many of the same ideas we have covered in our series of episodes on parsers, but using some of Haskell’s most powerful type-level features.

Parse, don’t validate

Alexis King • Tuesday Nov 5, 2019

This article demonstrates that parsing can be a great alternative to validating. When validating you often check for certain requirements of your values, but don’t have any record of that check in your types. Whereas parsing allows you to upgrade the types to something more restrictive so that you cannot misuse the value later on.

Ledger Mac App: Parsing Techniques

Chris Eidhof & Florian Kugler • Friday Aug 26, 2016

In this free episode of Swift talk, Chris and Florian discuss various techniques for parsing strings as a means to process a ledger file. It contains a good overview of various parsing techniques, including parser grammars.