Parsing With Haskell (Part 1): Lexing With Alex

This is the first of the two parts of our Parsing with Haskell series. Looking for the second part instead? You can find it here.

This two-part tutorial will look into two tools often used together by Haskellers to parse programs: Alex and Happy. We’ll use them to parse a small programming language from scratch.

Both Alex and Happy are industrial-strength tools powerful enough to parse even Haskell itself. At the bottom of this tutorial, you will find links to GHC’s lexer and parser if you are curious to see how they look.

This tutorial was written using GHC version 9.0.2, Stack resolver LTS-19.8, Alex version, and Happy version 1.20.0.

If you are looking for app development, our Haskell outsourcing services is the solution for your problem. Contact us to discuss your objectives.

Our grammar: MiniML

For this tutorial, we will introduce a small grammar called MiniML (read as “minimal”) that’s based on ML . As the name suggests, it has the minimal syntax needed to get you started with Alex and Happy. Yet we hope to introduce enough concepts for you to be able to create a useful grammar for your programming language and use these tools effectively.

Some of the features that this tutorial series will support are:

  • Variables, constants, function declarations, function applications, local bindings, and operators.
  • Some simple types, as well as arrow types (functions).
  • Conditional expressions: if-then-else and if-then.
  • Block comments.

In addition, exercises will guide you through extending the language with line comments and rational numbers. Later, in the second part, exercises will introduce patterns, list access, and pattern matching.

The snippet below demonstrates a program written in MiniML:

let the_answer : int =
  let a = 20 in
  let b = 1 in
  let c = 2 in
  a * c + b * c

let main (unit : ()) : () =
  print ("The answer is: " + the_answer)

At the end of the parsing process, we will build an abstract syntax tree (AST), which is a data structure representing a program. In contrast to unstructured data (like a string), an AST is much easier to manipulate. You can use it to write an interpreter, transpile into other language, etc.

Here’s how the (simplified and prettified) AST of the snippet above will look at at the end of the second part:

[ Dec _ (Name _ "the_answer") [] (Just (TVar _ (Name _ "int")))
  (ELetIn _ (Dec _ (Name _ "a") [] Nothing (EInt _ 20))
  (ELetIn _ (Dec _ (Name _ "b") [] Nothing (EInt _ 1))
  (ELetIn _ (Dec _ (Name _ "c") [] Nothing (EInt _ 2))
  (EBinOp _ (EBinOp _ (EVar _ (Name _ "a")) (Times _) (EVar _ (Name _ "c"))) (Plus _) (EBinOp _ (EVar _ (Name _ "b")) (Times _) (EVar _ (Name _ "c")))))))
, Dec _ (Name _ "main") [Argument _ (Name _ "unit") (Just (TUnit _))] (Just (TUnit _))
  (EApp _ (EVar _ (Name _ "print")) (EPar _ (EBinOp _ (EString _ "\"The answer is: \"") (Plus _) (EVar _ (Name _ "the_answer")))))

n.b.: The wildcards (_) will contain the ranges of each parsed tree node, omited here for brevitity.

So we transformed unstructured data (a string) into structured data, which is much easier to manipulate. This tree structure is ready to be type-checked, transpiled or interpreted.

Lexing with Alex

Before we can start parsing, we should first write a lexer for the grammar, which is also known as lexical analyzer, scanner, or tokenizer.

According to A. W. Appel in Modern Compiler Implementation in ML (p. 14):

The lexical analyzer takes a stream of characters and produces a stream of names, keywords, and punctuation marks; it discards white space and comments between the tokens. It would unduly complicate the parser to have to account for possible white space and comments at every possible point; this is the main reason for separating lexical analysis from parsing.

We will use Alex as a tool to generate the lexical analyzer for our grammar.

This section aims at giving an introduction to Alex and how you can use it to do useful things in conjunction with Happy.

In the second part of this tutorial series, we will use Happy to generate a parser that will consume the token stream. Happy will try to match tokens according to specific rules that we will describe and produce a tree structure representing a valid MiniML program.

Although Alex and Happy are frequently used together, they are independent tools. They may be combined with other technologies, so you may, for example, use Alex and Megaparsec together if you prefer.

Making a lexer using parser combinators is pretty doable and manageable. Meanwhile, using Alex is a bit more involved, but it has the advantage that performance will be more predictable. Besides that, it can be easily integrated with Happy to output one token at a time, which may avoid creating a massive list of tokens in the memory in the first place.


Alex is a Haskell tool to generate lexers. It’s similar to the tools lex and flex for C and C++, and it’s the first step of the grammatical analysis for our programming language. It will take an input stream of characters (a String, or in our case, a ByteString) representing the program written by the user and generate a stream of tokens (a list), which will be explained more in-depth shortly.

Note that we’ve mentioned that Alex will generate a lexical analyzer and not that Alex is a lexical analyzer by itself. Alex will read the .x file created by us that specifies how to match lexemes and then create a .hs file, which will be the generated lexer.

Creating the project

We will use Stack to build the project. Alex and Happy use files with extensions .x and .y, respectively, and Stack can automatically detect these file formats and build them.

n.b.: Using Stack is not strictly necessary. You may also use Cabal or plain Alex and Happy files, and it will work as well.

Begin by creating an empty Stack project:

$ stack new mini-ml simple
$ cd mini-ml

You will also need to have Alex and Happy installed on your machine:

$ stack install alex
$ stack install happy

We will create a package.yaml file for our project configuration. Use your favorite text editor to initialize package.yaml with the following:

name: mini-ml


- OverloadedStrings

  source-dirs: src
  - array
  - base
  - bytestring
  - alex
  - happy

n.b.: If you chose to use Stack, you might need to use hpack --force to override the current Cabal file.

You may want to remove src/Main.hs since we won’t need it.

How it works

It will be essential to differentiate between the terms lexeme and token during this section.

A lexeme is a valid atom of the grammar, such as a keyword (in, if, etc.), an operator (+, /, etc.), an integer literal, a string literal, a left or right parenthesis, an identifier, etc. You can think of it as any word, punctuation mark, number, etc. in the input string.

Meanwhile, a token consists of a token name and an optional token value. The token name is the name of the lexical category that the lexeme belongs to, while the token value is implemention-defined.

We can represent tokens as a Haskell sum datatype, where data constructor names correspond to token names and constructor arguments correspond to the token value with optionally the scanned lexeme. For instance, In, If, Plus, Divide, Integer 42, String "\"foo\"", LPar, RPar, and Identifier "my_function" are all tokens generated for their corresponding lexemes.

Note that in some cases the token also carries its lexeme value with it, as it is in the case of Integer, String, and Identifier.

If your goal is to move from lexemes to tokens, how do you discern different lexemes? For that, lexers are often implemented using deterministic finite automata (DFAs), which are state machines.

For example, supposing that our grammar has only the keywords if and in and also identifiers consisting of only lowercase letters, a small automaton for it could look like so:

                 ▼ │ [a-z]
        │       │└─┘│       │       │
        │       └───┘       │       │
        │         ▲         │       │
        │ [a-z]   │ [a-z]   │       │
        │         │         │ [a-z] │
      ┌─┴─┐     ┌─┴─┐     ┌─┴─┐     │
      │   │ i   │┌─┐│ n   │┌─┐│     │
─────►│ 0 ├────►││1│├────►││2││     │
      │   │     │└─┘│     │└─┘│     │
      └───┘     └─┬─┘     └───┘     │
                  │                 │
                  │f                │
                  ▼                 │
                ┌───┐               │
                │┌─┐│ [a-z]         │

To understand how to use the diagram above, imagine that this is a city where each numbered square is a place where you can drive to, and each arrow represents a one-way street. The arrow coming from nowhere to the square with 0 is where you start driving, and squares with another square inside are places where you can park your car. In this case, you are not allowed to park it in the square with 0.

The arrows also have directions in them, guided by your GPS. Your GPS may tell you to drive straight into an i, then turn at an [a-z], and then to stop, for example. However, your GPS may also ask you to take illegal turns, for example, to turn at an @, which will always lead you to a dead end, where you will be stuck.

To refine the terminology, the city is the automaton (plural: automata) represented by a state transition graph, each numbered square is called a state, and each arrow is called a transition. When a transition comes from nowhere and into a state, we say that this state is a start state, which is state 0 in this example. The places were you can park are called accepting states, i.e., 1, 2, 3, and 4.

The GPS represents the input (string) of the automaton. The dead ends represent an implicit error state present in every DFA, which you can think of like a hidden state number 5, with all invalid transitions from every state to it.

To simplify matters, on ambiguous transitions such as i and [a-z], assume that the one with a single letter takes precedence.

For example, to check the expression “int”, we will follow this path: 0 → 1 → 2 → 4.

Now, we need to attribute meanings to each state so that this automaton can be useful, and we will do so like this:

  • 0: Error.
  • 1: Identifier.
  • 2: In.
  • 3: If.
  • 4: Identifier.
  • 5 (implicit): Error.

Since we stopped at 4, the result is that “int” is an identifier, so we get a token that is Identifier "int". The resulting token would be In if we stopped at 2 instead (for the expression “in”).

What if we consumed no input and stopped at state 0, or the input was something like “Foo123” where we’d reach the implicit state 5? In such cases, we halt and indicate a lexical error.

As stated previously, we won’t write our lexical analyzer from scratch. Instead, we will use Alex to generate a lexer that creates a stream of tokens, which the Happy-generated parser will parse.

Regular expressions

Alex uses regular expressions (regexes) to define patterns. We’ll keep it pretty simple and explain some of them which we’ll use.

A syntax like [0-9] means that any digit character between 0 and 9 (inclusive) will be matched. Likewise, [a-zA-Z] means that any lowercase or uppercase character can be matched. Characters may be excluded as well, for example, [^\"] reads as “anything except a double quote mark”.

A * (called Kleene star) means that the expression can be matched zero or more times. Similarly, + means that it can be matched one or more times. For instance, [0-9]+ can match 1234. You may also find ?, which means that an expression may match either zero or one time (i.e., it’s optional).

A dot (.) means “match anything but a newline”. You can also use common escape codes like \n which will match a newline.

A double-quoted string, such as ">=", will match exactly the string inside quotes. An escaped character like \? will match exactly that character.

You can group regexes by concatenating them or by inserting a pipe (|) between them.

When you concatenate regexes, such as in [a-z][A-Za-z0-9]*, it means that Alex should match each set of strings in sequence. One example of a lexeme that can be matched by this regex is myVariable1.

The pipe means that Alex can alternate between choices, such as 0(x[0-9a-fA-F]+ | o[0-7]+), which is a regex that can match hexadecimal or octal numbers.

Parentheses are used to group regexes together, and Alex ignores white space unless they ere escaped. For example, foo bar and foobar can both be matched only by foobar, and you’d write foo\ bar in case you’d like to explicitly require a single space between them.

Our first lexer

Begin by creating a new file: src/Lexer.x. For now, let’s add a “skeleton” for the file, which we will use to get Stack to compile the file. Don’t worry; I will explain everything there soon. :)

-- At the top of the file, we define the module and its imports, similarly to Haskell.
module Lexer
  ( -- * Invoking Alex
  , AlexPosn (..)
  , alexGetInput
  , alexError
  , runAlex
  , alexMonadScan

  , Range (..)
  , RangedToken (..)
  , Token (..)
  ) where
-- In the middle, we insert our definitions for the lexer, which will generate the lexemes for our grammar.
%wrapper "monadUserState-bytestring"

tokens :-

<0> $white+ ;

-- At the bottom, we may insert more Haskell definitions, such as data structures, auxiliary functions, etc.
data AlexUserState = AlexUserState

alexInitUserState :: AlexUserState
alexInitUserState = AlexUserState

alexEOF :: Alex RangedToken
alexEOF = do
  (pos, _, _, _) <- alexGetInput
  pure $ RangedToken EOF (Range pos pos)

data Range = Range
  { start :: AlexPosn
  , stop :: AlexPosn
  } deriving (Eq, Show)

data RangedToken = RangedToken
  { rtToken :: Token
  , rtRange :: Range
  } deriving (Eq, Show)

data Token
  = EOF
  deriving (Eq, Show)

Running stack build --fast --file-watch will build the project, and Stack will automatically compile the Alex file into a Haskell file.

The top and bottom sections are provided between the { and }, and all Haskell code will be inlined in the generated Stack file.

Curious to see the generated file? There are two ways in which you can access it.

  1. If you run alex src/Lexer.x, it will generate src/Lexer.hs, where all the generated Alex code will be, together with the provided snippets of your code.
  2. Stack automatically generates a file whose path varies between OS and Cabal versions, but on my machine, it’s in .stack-work/dist/x86_64-linux-tinfo6/Cabal- You can also use $(stack path --dist-dir)/build/Lexer.hs to access this file.

For now, at the top of our file, we only declare the module name, but we will soon increase our export list and add more imports.

In the middle section, we first declare our wrapper, which indicates the type of code Alex should generate for us (monadUserState, which allows us to save custom state) and the input type (bytestring, but we could use plain Haskell Strings instead). Consult the Alex User Guide on wrappers if you want to see other wrappers.

Then we have tokens :-, where we will list all the patterns defined by regular expressions to match lexemes in our grammar plus an action on what the lexer should do with the matched lexeme. The first definition we provided is <0> $white+ ;, which simply indicates that all white space should be skipped.

The bottom section contains some boilerplate that Alex requires us to write. These include:

  • A data type that needs to be called AlexUserState.
  • A value with the initial state called alexInitUserState.
  • A value called alexEOF, which instructs Alex how to build the EOF (end-of-file) token. It is reached when Alex has finished lexing the input string.
  • Some additional datatypes: Range, RangedToken, and Token, which we will use throughout the article to describe the tokens that we’ve successfully created, as well as their positions. Saving the ranges is unnecessary, but they are useful when reporting errors.

Finally, for the EOF token, we use the alexGetInput action to retrieve the current position of the scanner and provide it to the token.

We should provide one token name to Token for each lexical category in the grammar. You are free to add new token names as you wish.

For this tutorial, we will have the following: operators, keywords, literals (strings and integers), identifiers, a token representing the end-of-file (EOF), etc.

Our token datatype is thus:

data Token
  -- Identifiers
  = Identifier ByteString
  -- Constants
  | String ByteString
  | Integer Integer
  -- Keywords
  | Let
  | In
  | If
  | Then
  | Else
  -- Arithmetic operators
  | Plus
  | Minus
  | Times
  | Divide
  -- Comparison operators
  | Eq
  | Neq
  | Lt
  | Le
  | Gt
  | Ge
  -- Logical operators
  | And
  | Or
  -- Parenthesis
  | LPar
  | RPar
  -- Lists
  | Comma
  | LBrack
  | RBrack
  -- Types
  | Colon
  | Arrow
  -- EOF
  | EOF
  deriving (Eq, Show)

At the top of the file, make sure to include the appropriate imports:

import Data.ByteString.Lazy.Char8 (ByteString)
import qualified Data.ByteString.Lazy.Char8 as BS

Lexing identifiers

Let’s start with a simple one: identifiers. We are free to choose the specification for identifiers, but let’s use the following:

An identifier is a sequence of alphanumeric characters, primes ('), question marks (?), and underscores (_). The identifier must begin with a letter or an underscore.

To make it easier to write the regex pattern for identifiers, we can use character set macros and regex macros.

Character set and regex macros

Character set macros are shortcuts that you can use to avoid duplicating character sets. We use $NAME = CHARACTER_SET to define a character set macro.

%wrapper "monadUserState-bytestring"

$digit = [0-9]
$alpha = [a-zA-Z]

tokens :-

We may also combine multiple regex macros into one, which will be appropriately expanded in its equivalent regular expression. For example, here’s how we can match an identifier:

$digit = [0-9]
$alpha = [a-zA-Z]

@id = ($alpha | \_) ($alpha | $digit | \_ | \' | \?)*

tokens :-

We use @NAME = REGEX to define a regular expression macro. Note that macros may not be recursive.

Let’s define our first lexeme based on our identifier:

tokens :-

<0> $white+ ;

<0> @id     { tokId }

The syntax <START_CODE> REGEX { CODE } means that if Alex has managed to match a pattern REGEX and it’s starting from the START_CODE state, it should execute the code CODE.

The idea of start codes is quite valuable. Alex works as a state machine, and 0 indicates the initial state in which the machine starts. In this case, we can match white space and identifiers when we start in state 0. We will later create other start codes.

CODE may contain any Haskell expression, as it will be included verbatim in the generated code. For white space, we can use ; instead of giving it an explicit action, which simply means that Alex should do nothing interesting with it. This is the same as writing { skip }.

Alex expects that the expression will have the type AlexAction RangedToken. Here’s the automatically-genereated definition for AlexAction when using monadUserState-bytestring:

type AlexAction result = AlexInput -> Int64 -> Alex result

Where result will be RangedToken in our case and the Int64 corresponds to the length of the input. It will be useful to know how AlexInput looks like as well:

type AlexInput = (AlexPosn,    -- current position,
                  Char,        -- previous char
                  ByteString,  -- current input string
                  Int64)       -- bytes consumed so far

Let’s create our tokId function. We do so by inserting this definition at the bottom part of the file. Here I placed Token as an anchor as a suggestion where you can put the new functions.

data Token  -- anchor: don't copy and paste this
  | EOF
  deriving (Eq, Show)

mkRange :: AlexInput -> Int64 -> Range
mkRange (start, _, str, _) len = Range{start = start, stop = stop}
    stop = BS.foldl' alexMove start $ BS.take len str

tokId :: AlexAction RangedToken
tokId inp@(_, _, str, _) len =
  pure RangedToken
    { rtToken = Identifier $ BS.take len str
    , rtRange = mkRange inp len

tokId will extract the lexeme from the input string, which will be the first len characters of str. The range will then be handled by mkRange, a function that advances the position accordingly to each seen character in the input string using alexMove. Alex automatically generates this function, and you don’t need to include it with your code.

We should check whether our code works. Here’s a small function that we can use for testing. Don’t forget to export it!

tokId = ...  -- anchor, don't copy and paste this

scanMany :: ByteString -> Either String [RangedToken]
scanMany input = runAlex input go
    go = do
      output <- alexMonadScan
      if rtToken output == EOF
        then pure [output]
        else (output :) <$> go

Start GHCi (run stack ghci) and let’s check whether this works. It should result in something like this (slightly prettified for ease of visualization):

>>> runAlex "my_identifier" alexMonadScan
Right (RangedToken {rtToken = Identifier "my_identifier", rtRange = Range {start = AlexPn 0 1 1, stop = AlexPn 13 1 14}})
>>> scanMany "my_identifier other'identifier ALL_CAPS"
  [ RangedToken {rtToken = Identifier "my_identifier", rtRange = Range {start = AlexPn 0 1 1, stop = AlexPn 13 1 14}}
  , RangedToken {rtToken = Identifier "other'identifier", rtRange = Range {start = AlexPn 14 1 15, stop = AlexPn 30 1 31}}
  , RangedToken {rtToken = Identifier "ALL_CAPS", rtRange = Range {start = AlexPn 31 1 32, stop = AlexPn 39 1 40}}
  , RangedToken {rtToken = EOF, rtRange = Range {start = AlexPn 39 1 40, stop = AlexPn 39 1 40}}

The AlexPn values mean the following, respectively: the number of characters before the token, the line number, and the line column.

Pretty cool stuff.

If you are stuck or want to check that we’re on the same page, the code for the lexer up to this section may be found here.

Lexing keywords and operators

We can now lex identifiers, but a programming language typically consists of much more than just this. Let’s now scan other keywords that we defined. Thankfully, they are pretty simple:

tokens :-

<0> $white+ ;

-- Keywords
<0> let     { tok Let }
<0> in      { tok In }
<0> if      { tok If }
<0> then    { tok Then }
<0> else    { tok Else }

-- Arithmetic operators
<0> "+"     { tok Plus }
<0> "-"     { tok Minus }
<0> "*"     { tok Times }
<0> "/"     { tok Divide }

-- Comparison operators
<0> "="     { tok Eq }
<0> "<>"    { tok Neq }
<0> "<"     { tok Lt }
<0> "<="    { tok Le }
<0> ">"     { tok Gt }
<0> ">="    { tok Ge }

-- Logical operators
<0> "&"     { tok And }
<0> "|"     { tok Or }

-- Parenthesis
<0> "("     { tok LPar }
<0> ")"     { tok RPar }

-- Lists
<0> "["     { tok LBrack }
<0> "]"     { tok RBrack }
<0> ","     { tok Comma }

-- Types
<0> ":"     { tok Colon }
<0> "->"    { tok Arrow }

-- Identifiers
<0> @id     { tokId }

We also need to define tok:

tokId = ...  -- anchor

tok :: Token -> AlexAction RangedToken
tok ctor inp len =
  pure RangedToken
    { rtToken = ctor
    , rtRange = mkRange inp len

There should be no mystery to this function. It simply inserts the provided Token and creates a range for it.

We can now check it out in GHCi:

>>> scanMany "if true then foo else (bar baz)"
  [ RangedToken {rtToken = If, rtRange = Range {start = AlexPn 0 1 1, stop = AlexPn 2 1 3}}
  , RangedToken {rtToken = Identifier "true", rtRange = Range {start = AlexPn 3 1 4, stop = AlexPn 7 1 8}}
  , RangedToken {rtToken = Then, rtRange = Range {start = AlexPn 8 1 9, stop = AlexPn 12 1 13}}
  , RangedToken {rtToken = Identifier "foo", rtRange = Range {start = AlexPn 13 1 14, stop = AlexPn 16 1 17}}
  , RangedToken {rtToken = Else, rtRange = Range {start = AlexPn 17 1 18, stop = AlexPn 21 1 22}}
  , RangedToken {rtToken = LPar, rtRange = Range {start = AlexPn 22 1 23, stop = AlexPn 23 1 24}}
  , RangedToken {rtToken = Identifier "bar", rtRange = Range {start = AlexPn 23 1 24, stop = AlexPn 26 1 27}}
  , RangedToken {rtToken = Identifier "baz", rtRange = Range {start = AlexPn 27 1 28, stop = AlexPn 30 1 31}}
  , RangedToken {rtToken = RPar, rtRange = Range {start = AlexPn 30 1 31, stop = AlexPn 31 1 32}}
  , RangedToken {rtToken = EOF, rtRange = Range {start = AlexPn 31 1 32, stop = AlexPn 31 1 32}}

Lexing integers

Lexing integers is pretty straightforward. We can just use a sequence of one or more digits.

-- Identifiers
<0> @id     { tokId }

-- Constants
<0> $digit+ { tokInteger }

And of course, we need to define tokInteger:

tok = ...  -- anchor

tokInteger :: AlexAction RangedToken
tokInteger inp@(_, _, str, _) len =
  pure RangedToken
    { rtToken = Integer $ read $ BS.unpack $ BS.take len str
    , rtRange = mkRange inp len

Check that it works:

>>> scanMany "42"
  [ RangedToken {rtToken = Integer 42, rtRange = Range {start = AlexPn 0 1 1, stop = AlexPn 2 1 3}}
  , RangedToken {rtToken = EOF, rtRange = Range {start = AlexPn 2 1 3, stop = AlexPn 2 1 3}}

Lexing comments

Lexing comments will require us to use an extra start code besides just 0. Surely, we could make something as simple as the following:

<0> $white+ ;

<0> "(*" (. | \n)* "*)" ;

-- Keywords

But this will lead to some problems. For instance, what if the comment is unclosed?

>>> scanMany "(* my comment"
  [ RangedToken {rtToken = LPar, rtRange = Range {start = AlexPn 0 1 1, stop = AlexPn 1 1 2}}
  , RangedToken {rtToken = Times, rtRange = Range {start = AlexPn 1 1 2, stop = AlexPn 2 1 3}}
  , RangedToken {rtToken = Identifier "my", rtRange = Range {start = AlexPn 3 1 4, stop = AlexPn 5 1 6}}
  , RangedToken {rtToken = Identifier "comment", rtRange = Range {start = AlexPn 6 1 7, stop = AlexPn 13 1 14}}
  , RangedToken {rtToken = EOF, rtRange = Range {start = AlexPn 13 1 14, stop = AlexPn 13 1 14}}

We would like to detect such cases and also support nested comments. We will create two helper functions, nestComment and unnestComment, which will keep track of how many layers of comments we have and allow us to detect whether we have reached the end of the file with an unclosed comment. But before we implement those two functions, let’s first write the Alex code to deal with recognizing comments as well as some utilities.

In addition, Alex provides the andBegin combinator that will execute an expression and change the current start code.

<0> $white+ ;

<0>       "(*" { nestComment `andBegin` comment }
<0>       "*)" { \_ _ -> alexError "Error: unexpected closing comment" }
<comment> "(*" { nestComment }
<comment> "*)" { unnestComment }
<comment> .    ;
<comment> \n   ;

-- Keywords

The critical thing to notice is that we can start a comment anywhere, as it has start code 0, but we can only match a closing comment pair if we begin to match a comment in the first place, thanks to the comment start code.

Note that checking for the *) lexeme at the start code 0 is unnecessary. Without it, it would be emitted as a multiplication followed by a closing parenthesis, but the parser would catch it later. Like Haskell, MiniML will support passing operators as first-class functions, like let add = (+). However, this has the same deficiency as OCaml: (*) is recognized as a comment. OCaml accepts ( *), but emits a message saying, “Warning : this is not the end of a comment.”. Because of this, we will emit an error using alexError to the user and expect that ( * ) will be used to reference the multiplication operator instead. Alternatively, you can change comments’ syntax to something else here, such as /* */, and avoid this ambiguity, but that wouldn’t feel too ML-like.

Next, we will change AlexUserState so it remembers the nesting level of our comments. We will initialize it with 0. We also define some helper functions for dealing with our state.

tokInteger = ...  -- anchor

data AlexUserState = AlexUserState
  { nestLevel :: Int

alexInitUserState :: AlexUserState
alexInitUserState = AlexUserState
  { nestLevel = 0

get :: Alex AlexUserState
get = Alex $ \s -> Right (s, alex_ust s)

put :: AlexUserState -> Alex ()
put s' = Alex $ \s -> Right (s{alex_ust = s'}, ())

modify :: (AlexUserState -> AlexUserState) -> Alex ()
modify f = Alex $ \s -> Right (s{alex_ust = f (alex_ust s)}, ())

n.b.: If you’re familiar with the mtl library, you might prefer to define instance MonadState Alex.

We simply increase the nesting value and skip the consumed input to nest a comment. Note that skip input len is simply alexMonadScan, which asks to scan the next token. Unnesting is similar, except that we decrease the level, and if we reach level 0, we must return to our initial start code (0) as it means we exited the comment. Don’t forget to import when from Control.Monad.

tokInteger = ...  -- anchor

nestComment, unnestComment :: AlexAction RangedToken
nestComment input len = do
  modify $ \s -> s{nestLevel = nestLevel s + 1}
  skip input len
unnestComment input len = do
  state <- get
  let level = nestLevel state - 1
  put state{nestLevel = level}
  when (level == 0) $
    alexSetStartCode 0
  skip input len

Finally, let’s change alexEOF to emit an error if we end up with an unclosed comment by checking whether we were parsing a comment when we reached EOF.

alexEOF :: Alex RangedToken
alexEOF = do
  startCode <- alexGetStartCode
  when (startCode == comment) $
    alexError "Error: unclosed comment"
  (pos, _, _, _) <- alexGetInput
  pure $ RangedToken EOF (Range pos pos)

Trying it out in GHCi yields the expected results.

>>> scanMany "(* my comment"
Left "Error: unclosed comment"
>>> scanMany "if (* my (* nested *) \n comment *) x"
  [ RangedToken {rtToken = If, rtRange = Range {start = AlexPn 0 1 1, stop = AlexPn 2 1 3}}
  , RangedToken {rtToken = Identifier "x", rtRange = Range {start = AlexPn 35 2 13, stop = AlexPn 36 2 14}}
  , RangedToken {rtToken = EOF, rtRange = Range {start = AlexPn 36 2 14, stop = AlexPn 36 2 14}}

Lexing strings

Lexing strings should have no surprises. Just stick this in your lexer:

-- Constants
<0> $digit+ { tokInteger }
<0> \"[^\"]*\" { tokString }

And we use this definition for tokString:

tokInteger = ...  -- anchor

tokString :: AlexAction RangedToken
tokString inp@(_, _, str, _) len =
  pure RangedToken
    { rtToken = String $ BS.take len str
    , rtRange = mkRange inp len

This is a pretty basic string lexer. It does not accept escaped characters or nested quote marks. We invite the reader to extend the string lexer to be more useful in the exercise below.

You can find the complete code for the lexer until now here.


  1. We support block comments with (* *). Change the scanner to accept line comments, such as # foo, which end when they find a newline or EOF.

  2. Change the string lexer to accept the following escaped characters: \\, \n, and \t. Feel free to add any other escape codes that you can think about.

Hint Create a buffer in AlexUserState that adds characters as they are seen and two auxiliary enterString and exitString functions. Entering the string, save the current position in the state, add \" to the buffer, and begin a new start code. For a escape character matched with \\n, \\t or \\\\, add \n, \t, or \\ to the buffer with a new emit function. For an ordinary character matched with a ., add it to the current buffer with a new emitCurrent function. Don't forget to match \\\" as an escaped quote mark and add it with emit. Emit the string as a new token when you exit the string state, reseting the string state, and don't forget to add the closing quote mark. Make sure that the end position is also advanced by one character. Don't forget to check if there is an unclosed string like we did for the block comments.

For inspiration on doing this, you can use Alex’s Tiger example as a guide.

You can find the solutions to both exercises here.

Conclusions and further reading

In this part of the tutorial, we demonstrated how to build a lexer using Alex to turn lexemes into tokens, using start codes and a user state adequate for MiniML.

Your next step in this journey is to use the tokens generated by Alex to create a parser. You can continue reading the second part of this series where you will be introduced to Happy to create the parser of the grammar.

If you liked this article, you might also enjoy these resources:

  • Alex User Guide.
  • GHC’s Alex and Happy files.
  • APPEL, A. W. (1998). Modern Compiler Implementation in ML, Cambridge University Press.

For more Haskell tutorials, you can check out our Haskell articles or follow us on Twitter or Dev.

Found a typo in the article or a bug in the code? You can open an issue or a pull request in our GitHub.

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