<|im_start|>system
You are a helpful AI assistant.<|im_end|>
<|im_start|>user
What is combinator parsing? Give an explanation of the concept, but do not explain about it's history or information which is irrelevant to developing or using a combinator parsing library.<|im_end|>
<|im_start|>assistant
Combinator parsing is a technique used in computer science to build parsers for formal languages. It involves combining small parsing functions, called combinators, to create more complex parsers that can handle a wide range of input patterns.

In combinator parsing, a parser is essentially a function that takes an input string and produces a parse tree or some other form of structured representation of the input. Combinators are higher-order functions that take parsers as input and return a new parser as output. They allow parsers to be combined and composed in a modular and flexible way.

There are different types of combinators used in combinator parsing, including:

1. Sequence Combinators: These combinators allow parsers to be executed sequentially. For example, a sequence combinator might take two parsers as input and return a new parser that matches the first parser, followed by the second parser.

2. Choice Combinators: Choice combinators allow parsers to match one of several alternatives. For example, a choice combinator might take two parsers as input and return a new parser that matches either the first parser or the second parser.

3. Transformation Combinators: Transformation combinators modify the output of a parser. They can be used to convert the parsed input into a different representation or perform other transformations on the parsed data.

By combining these basic combinators, complex parsers can be built that can handle a variety of input patterns and grammars. Combinator parsing libraries provide a set of predefined combinators along with mechanisms for creating custom combinators.

The advantage of combinator parsing is its simplicity and modularity. Combinator parsers are often easy to understand and maintain because they are built from small, reusable components. Combinator parsing also allows for incremental development, as parsers can be built step by step by combining and refining smaller parsers.

Combinator parsing is widely used in the development of programming language compilers, interpreters, and other systems that require parsing and analyzing input languages. It provides a flexible and expressive approach to parsing that can accommodate a wide range of language grammars and input patterns.<|im_end|>
<|im_start|>user
Could you provide some examples of how parser combinators are used in practice to parse different types of inputs?<|im_end|>
<|im_start|>assistant
Sure, I'm happy to help you with some examples of parser combinators. Parser combinators are a way of building complex parsers from simpler ones, using functions that combine parsers together. They are often used to parse structured text, such as JSON, XML, HTML, or programming languages.

For example, suppose we have the following parsers:

- `char(c)` is a parser that matches a single character `c`.
- `digit` is a parser that matches a single digit from `0` to `9`.
- `letter` is a parser that matches a single letter from `A` to `Z` or `a` to `z`.

We can use parser combinators to create more complex parsers from these basic ones. For example:

- `char('+') >> digit >> digit` is a parser that matches a plus sign followed by two digits, such as `+31`.
- `digit.repeat(3)` is a parser that matches three digits in a row, such as `105`.
- `(letter | digit).repeat(1)` is a parser that matches one or more letters or digits, such as `abc`, `42`, or `a1b2`.

These are just some examples of how parser combinators can be used to combine parsers and create new parsers. There are many more possible combinations and variations, depending on the syntax and semantics of the language or format we want to parse. 

One real-world example of a parser combinator library in Python is [parsy](https://github.com/python-parsy/parsy), which allows you to create parsers using operators like `+` for concatenation, `|` for alternation, and `>>` for transformation. For instance, here is a simple parser that parses a __JSON string__:

```python
from parsy import string, regex

# A JSON string is a double-quoted sequence of characters
json_string = string('"') >> regex(r'[^"]*') << string('"')

# Test the parser on some inputs
print(json_string.parse('"hello"')) # hello
print(json_string.parse('"world"')) # world
print(json_string.parse('""')) # (empty string)
print(json_string.parse('"foo"bar"')) # raises ParseError
```

Here is a simple parser that parses a list of __comma-separated integers__:

```python
from parsy import string, regex

# An integer is an optional sign followed by one or more digits
integer = regex(r'[-+]?\d+').parsecmap(int)

# A list of integers is zero or more integers separated by commas
integer_list = integer.sep_by(string(','))

# Test the parser on some inputs
print(integer_list.parse('1,2,3')) # [1, 2, 3]
print(integer_list.parse('-42')) # [-42]
print(integer_list.parse('')) # []
print(integer_list.parse('1,2,x')) # raises ParseError
```

I hope these examples give you some idea of how parser combinators work.<|im_end|>