---
title: Monadic Parsing with User State
date: August 26, 2016
---

> {-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-}
> module StatefulParsing where
> import Control.Monad.State.Class
> import Control.Applicative

In this post I propose an extension to the monadic parser framework
introduced in a previous post, _[You could have invented
Parsec](/posts/2016-08-17.html)_, that extends
the parser to also support embedded user state in your parsing.

This could be used, for example, for parsing a language with
user-extensible operators: The precedences and fixidities of operators
would be kept in a hashmap threaded along the bind chain.

Instead of posing these changes as diffs, we will rewrite the parser
framework from scratch with the updated type.

---

Parser `newtype`{.haskell}
=========================

Our new parser is polymorphic in both the return type and the user state
that, so we have to update the `newtype`{.haskell} declaration to match.

> newtype Parser state result
>    = Parser { runParser :: String
>                         -> state
>                         -> Either String (result, state, String) }

Our tuple now contains the result of the parsing operation and the new
user state, along with the stream. We still need to supply a stream to
parse, and now also supply the initial state. This will be reflected in
our functions.

For convenience, we also make a `Parser' a`{.haskell} type alias for
parsers with no user state.

< type Parser' a = Parser () a

Seeing as type constructors are also curried, we can apply η-reduction
to get the following, which is what we'll go
with.

> type Parser' = Parser ()

`Functor`{.haskell} instance
============================

> instance Functor (Parser st) where

The functor instance remains mostly the same, except now we have to
thread the user state around, too.

The instance head also changes to fit the kind signature of the
`Functor`{.haskell} typeclass. Since user state can not change from
fmapping, this is fine.

>   fn `fmap` (Parser p) = Parser go where
>      go st us = case p st us of
>           Left e -> Left e
>           Right (r, us', st') -> Right (fn r, us', st')

As you can see, the new user state (`us'`) is just returned as is.

`Applicative`{.haskell} instance
================================

> instance Applicative (Parser st) where

The new implementations of `pure`{.haskell} and `<*>`{.haskell} need to
correctly manipulate the user state. In the case of `pure`, it's just passed
as-is to the `Right`{.haskell} constructor.

>   pure ret = Parser go where
>     go st us = Right (ret, us, st)

Since `(<*>)` needs to evaluate both sides before applying the function, we need
to pass the right-hand side's generated user state to the right-hand side for
evaluation.

>   (Parser f) <*> (Parser v) = Parser go where
>     go st us = case f st us of
>       Left e -> Left e
>       Right (fn, us', st') -> case v st' us' of
>         Left e -> Left e
>         Right (vl, us'', st'') -> Right (fn vl, us'', st'')


`Monad`{.haskell} instance
==========================

> instance Monad (Parser st) where

Since we already have an implementation of `pure`{.haskell} from the Applicative
instance, we don't need to worry about an implementation of `return`.

>   return = pure

The monad instance is much like the existing monad instance, except now we have
to give the updated parser state to the new computation.

>   (Parser p) >>= f = Parser go where
>     go s u = case p s u of
>         Left e -> Left e
>         Right (x, u', s') -> runParser (f x) s' u'

`MonadState`{.haskell} instance
===============================

> instance MonadState st (Parser st) where

Since we now have a state transformer in the parser, we can make it an instance
of the MTL's `MonadState` class.

The implementation of `put`{.haskell} must return `()` (the unit value), and
needs to replace the existing state with the supplied one. This operation can
not fail.

Since this is a parsing framework, we also need to define how the stream is
going to be affected: In this case, it isn't.

>   put us' = Parser go where
>     go st _ = Right ((), us', st)

The `get`{.haskell} function returns the current user state, and leaves it
untouched. This operation also does not fail.

>   get = Parser go where
>     go st us = Right (us, us, st)

Since we're an instance of `MonadState`{.haskell}, we needn't an implementation
of `modify` and friends - They're given by the MTL.

`Alternative`{.haskell} instance
================================

> instance Alternative (Parser st) where

The `Alternative`{.haskell} instance uses the same state as it was given for
trying the next parse.

The `empty`{.haskell} parser just fails unconditionally.

>   empty = Parser go where
>     go _ _ = Left "empty parser"

`(<|>)` will try both parsers in order, reusing both the state and the stream.

>   (Parser p) <|> (Parser q) = Parser go where
>     go st us = case p st us of
>       Left e -> q st us
>       Right v -> Right v

Conclusion
==========

This was a relatively short post. This is because many of the convenience
functions defined in the previous post also work with this parser framework, if
you replace `Parser` with `Parser'`. You can now use `get`, `put` and `modify`
to work on the parser's user state. As a closing note, a convenience function
for running parsers with no state is given.

> parse :: Parser' a -> String -> Either String a
> parse str = case runParser str () of
>   Left e -> Left e
>   Right (x, _, _) -> x