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Parser and AST Generator

The syn subcommand of mi is used to generate a parser and language fragments for a language defined in a .syn file.

mi syn input.syn


This .syn file describes a small language with integers, addition, subtraction, and multiplication.

language Example

type File
start File

type Expr {
grouping = "(" ")",

-- Basic tokens
token Integer {
repr = UIntRepr {},
constructor = UIntTok,
fragment = UIntTokenParser,

-- Tokens used only through literals
token {fragment = OperatorTokenParser,}

-- Whitespace and comments
token {fragment = LineCommentParser,}
token {fragment = MultilineCommentParser,}
token {fragment = WhitespaceParser,}

-- Productions
prod SingleExpr: File = e:Expr

prod Int: Expr = v:Integer
infix left Add: Expr = "+"
infix left Sub: Expr = "-"
infix left Mul: Expr = "*"

precedence {
Add Sub;

The Contents of a .syn File

A language defined by a .syn file has a name, a number of syntactic types, tokens, and productions, as well as precedence rules. Each of the relevant declarations are described below.


The syntax of a .syn file is itself defined in a .syn file.


Example Usage
language Example

The first declaration in a .syn file must be the language declaration, which names the language. This name is later used to name language fragments (<name>BaseAst and <name>Ast primarily) as well as the parse functions (parse<name> and parse<name>Exn).


Example Usage
type File
type Expr {
grouping = "(" ")",

The type declaration introduces a type in the AST as well as a syntactic type in the concrete grammar. The optional grouping property enables explitic grouping in the syntax, e.g., grouping parentheses, which are not present in the final AST.


A syntactic type is mostly equivalent with a non-terminal in a context-free grammar, and can typically be thought of as such. It also defines a type in the generated AST language fragments.


Example Usage
start File

The start declaration designates the syntactic type at which parsing starts, as well as the return-type of the generated parsing functions.


Example Usage
include "path/to/"

A language can use certain definitions from MCore code (typically in lexing related declaration), which must then be included in the grammar with an include declaration, which functions exactly the same as the MCore equivalent declaration.


Example Usage
token LIdent {
repr = LIdentRepr {},
constructor = LIdentTok,
fragment = LIdentTokenParser,
ty = String,
token {fragment = OperatorTokenParser,}
token {fragment = LineCommentParser,}
token LName {
base = LIdent,
wrap = nameNoSym,
ty = Name,

A token declaration extends the generated lexer with tokens and how to lex them. Each token is declared in its own language fragment in an .mc file, which can be included via an include declaration.

For examples of lexing language fragments, see parser/ in the Miking standard library. All language fragments in parser/ are available in a .syn without an explicit include, though they still require token declarations to be usable in the grammar.

Each token declaration can have a number of properties:

  • An optional name, given between token and the { before the other properties.
  • fragment: the name of a language fragment to include in the lexer.
  • repr: an expression of type TokenRepr, representing the token in a grammar.
  • constructor: the name of the constructor of the token when it is parsed.
  • ty: the type of the value carried by the token, e.g., String or Int. Only valid if a name is set.
  • base: the name of another token to wrap with some processing, often to change the type.
  • wrap: only valid with base. An expression representing a function to call on the value carried by the base token.

A token that does not have a name cannot be explicitly used in the grammar, but can serve one of two purposes:

  • Adding lexical syntax for whitespace and/or comments.
  • Adding lexical syntax that is only used for literals (e.g., "(" and ")" from BracketTokenParser).

Each literal (e.g., "(", ")", or "let") must presently be lexed as exactly one token by one of the included lexing language fragments. For example, if the lexer would lex as an LIdent, Dot, and a LIdent, then the literal "" is not valid; it doesn't lex as exactly one token.

This restriction is very likely to be lifted in the future.

prod, prefix, infix, and postfix

Example Usage
prod Record: Expr =
"{" fields:{name:LIdent "=" val:Expr ","}* "}"

A prod declaration introduces a production in the syntax and a constructor in the AST. Each prod has a name, a syntactic type, and a syntax description.


The AST constructor is typically named using both the production name and syntactic type, e.g., RecordExpr. However, if the name already ends with the syntactic type it's kept as is, e.g., prod RecordExpr: Expr has the constructor RecordExpr, not RecordExprExpr.

Syntax Descriptions

The right-hand side of a prod is a mixed description of its syntax and the data carried in its constructor. The language is mostly based on regular expressions:

  • X Y means X followed by Y.
  • X | Y means X or Y.
  • X* means zero or more Xs in sequence. X+ means one or more, and X? means zero or one.
  • empty is an empty sequence. For example, X empty is the same as just X, and X | empty is the same as X?.
  • Parentheses can be used for grouping, e.g., X (Y Z)*.

The data carried in the constructor is captured by naming parts of the syntax description. The carried data is always a record, and each named part adds a field to it. Four kinds of things can be named:

  • A token (e.g., name:LIdent) carries the location it was parsed from (type Info) as well as some data (e.g., LIdent carries a String). The field contains both of these (e.g., name : {v:String, i:Info}).
  • A literal (e.g., foo:"foo") carries only the location, no additional data (e.g., the field becomes foo : Info rather than foo : {v:(), i:Info}.
  • A syntactic type (defined with type) carries a value of its corresponding AST type, e.g., val:Expr adds a field val : Expr.
  • Multiple fields can be grouped into a nested record by surrounding the corresponding syntax description with {}. For example, foo:{a:LIdent "in" b:Expr} adds a field foo : {a : {v:String, i:Info}, b : Expr}.

Finally, a field can occur multiple times, which might further change the type of the field:

  • If it must appear exactly once the type is unchanged (e.g., name:LIdent produces name : {v:String, i:Info}).
  • If it can appear once or not at all it's wrapped in Option (e.g., name:Ident? produces name : Option {v:String, i:Info}).
  • Otherwise it's wrapped in a sequence (e.g., name:Ident+ produces name : [{v:String, i:Info}]).

A name can occur multiple times via * or +, but also by being named multiple times:

prod Foo: Bar = "(" x:Bar "," x:Bar ")"

This produces a field x : [Bar].

Operators and Associativity

prefix, infix, and postfix can be used to declare operators. These are syntactic sugar for prod declarations:

prefix Negate: Expr = "-"
-- is exactly the same as
prod Negate: Expr = "-" right:Expr

infix Plus: Expr = "+"
-- is exactly the same as
prod Plus: Expr = left:Expr "-" right:Expr

postfix Factorial: Expr = "!"
-- is exactly the same as
prod Factorial: Expr = left:Expr "!"

The operator syntactic sugar will use the names left and right, but this is not essential for a production being an operator. For example, prod Plus: Expr = a:Expr "+" b:Expr is also an infix operator, what matters is that it begins and ends with self-recursion (in this case Expr).

Prefix operators are right-associative, postfix operators are left-associative, and infix operators default to no associativity. To declare associativity for an infix operator, add left or right before the name:

prod left Plus: Expr = left:Expr "+" right:Expr
infix right Exponentiation: Expr = "^"


Example Usage
precedence {
Mul Div;
Add Sub Mod;
Equal NotEqual;
~And Or;
} except {
Mod ? Add Sub Mul Div;

A precedence declaration defines relative precedence between some set of operators in the form of a precedence table. Each precedence level ends with a semi-colon, and levels earlier/higher in the list have higher precedence.

If a precedence level is preceeded by ~ that means that the operators on that level have precedence relative to all other levels, but not relative to the other operators on that level.

A precedence declaration can optionally end with an except list, to remove pairs of relative precedence that would otherwise be defined by the precedence declaration. Each entry in an except list has the form A B ... ? C D ...;, and removes all possible pairs between operators before and after ? (e.g., A and C, A and D, B and C, etc.).


~ in a precedence list is syntactic sugar for an entry in an except list, e.g.,

precedence {
Equal NotEqual;
~And Or;

is the same as

precedence {
Equal NotEqual;
And Or;
} except {
And Or ? And Or;

The API of a Generated .mc File

A generated .mc file is used like any other .mc file (i.e., included) and provides the API below.

Base AST Language Fragment

The first language fragment is named based on the language name (see language) and has the form <lang-name>BaseAst. It defines a syn type (but no constructors) for each syntactic type (see type), along with type signatures and default implementations for a number of convenience functions.

  • Tree traversal functions, in the form of shallow mappings for all pairs of syntactic types (referred to below as T1 and T2).
    • sem smap_T1_T2 : (T2 -> T2) -> T1 -> T1
    • sem sfold_T1_T2 : all a. (a -> T2 -> a) -> a -> T1 -> a
    • sem smapAccumL_T1_T2 : all a. (a -> T2 -> (a, T2)) -> a -> T1 -> (a, T1)
  • Accessor functions for the info : Info field of each syntactic type (referred to below as T).
    • get_T_info : T -> Info
    • set_T_info : Info -> T -> Info
    • map_T_info : (Info -> Info) -> T -> T
    • mapAccum_T_info : all a. (a -> Info -> (a, Info)) -> a -> T -> (a, T)

prod Language Fragments

Each prod declaration gives rise to a language fragment defining its constructor and appropriate implementations for the convenience functions defined in the base AST fragment. For example, given a prod Foo: Bar = ... definition:

lang FooBarAst = -- ...
type FooBarRecord = { info : Info, /- ... -/ }
syn Bar =
| FooBar FooBarRecord

-- ... elided ...

See Syntax Descriptions to see how the type of the record in <prod-name>Record is computed.

Composed AST Language Fragment

The generated file contains a language fragment that composes all of the prod language fragments, with a name of the form <lang-name>Ast.

Parsing Functions

There are one primary parsing function generated, along with one simple wrapper. Given the declarations lang Example and start Foo:

-- Takes a filename and the contents of that file, then parse
-- it. In case of error, return `Left [...errors...]`, otherwise
-- `Right result`
parseExample : String -> String -> Either [(Info, String)] Foo

-- Same arguments as `parseExample`. In case of error, print them,
-- then exit the program with code 1, otherwise return the result.
parseExampleExn : String -> String -> Foo