Lexical Structure

This section describes the detailed lexical structure of the Lean language.

A Lean program consists of a stream of UTF-8 tokens where each token is one of the following:

   token: symbol | command | ident | string | char | numeral |
        : decimal | doc_comment | mod_doc_comment | field_notation

Tokens can be separated by the whitespace characters space, tab, line feed, and carriage return, as well as comments. Single-line comments start with --, whereas multi-line comments are enclosed by /- and -/ and can be nested.

Symbols and Commands

.. (TODO: list built-in symbols and command tokens?)

Symbols are static tokens that are used in term notations and commands. They can be both keyword-like (e.g. the have <structured_proofs> keyword) or use arbitrary Unicode characters.

Command tokens are static tokens that prefix any top-level declaration or action. They are usually keyword-like, with transitory commands like #print <instructions> prefixed by the # character. The set of built-in commands is listed in Other Commands.

Users can dynamically extend the sets of both symbols (via the commands listed in Quoted Symbols and command tokens (via the [user_command] <attributes> attribute).

.. _identifiers:

Identifiers

An atomic identifier, or atomic name, is (roughly) an alphanumeric string that does not begin with a numeral. A (hierarchical) identifier, or name, consists of one or more atomic names separated by periods.

Parts of atomic names can be escaped by enclosing them in pairs of French double quotes «».

   def Foo.«bar.baz» := 0  -- name parts ["Foo", "bar.baz"]

   ident: atomic_ident | ident "." atomic_ident
   atomic_ident: atomic_ident_start atomic_ident_rest*
   atomic_ident_start: letterlike | "_" | escaped_ident_part
   letterlike: [a-zA-Z] | greek | coptic | letterlike_symbols
   greek: <[α-ωΑ-Ωἀ-῾] except for [λΠΣ]>
   coptic: [ϊ-ϻ]
   letterlike_symbols: [℀-⅏]
   escaped_ident_part: "«" [^«»\r\n\t]* "»"
   atomic_ident_rest: atomic_ident_start | [0-9'ⁿ] | subscript
   subscript: [₀-₉ₐ-ₜᵢ-ᵪ]

String Literals

String literals are enclosed by double quotes ("). They may contain line breaks, which are conserved in the string value. Backslash (\) is a special escape character which can be used to the following special characters:

\\ represents an escaped backslash, so this escape causes one backslash to be included in the string.
\" puts a double quote in the string.
\' puts an apostrophe in the string.
\n puts a new line character in the string.
\t puts a tab character in the string.
\xHH puts the character represented by the 2 digit hexadecimal into the string. For example "this \x26 that" which become "this & that". Values above 0x80 will be interpreted according to the Unicode table so "\xA9 Copyright 2021" is "© Copyright 2021".
\uHHHH puts the character represented by the 4 digit hexadecimal into the string, so the following string "\u65e5\u672c" will become "日本" which means "Japan".

So the complete syntax is:

   string       : '"' string_item '"'
   string_item  : string_char | string_escape
   string_char  : [^\\]
   string_escape: "\" ("\" | '"' | "'" | "n" | "t" | "x" hex_char{2} | "u" hex_char{4} )
   hex_char     : [0-9a-fA-F]

Char Literals

Char literals are enclosed by single quotes (').

   char: "'" string_item "'"

Numeric Literals

Numeric literals can be specified in various bases.

   numeral    : numeral10 | numeral2 | numeral8 | numeral16
   numeral10  : [0-9]+
   numeral2   : "0" [bB] [0-1]+
   numeral8   : "0" [oO] [0-7]+
   numeral16  : "0" [xX] hex_char+

Floating point literals are also possible with optional exponent:

   float    : [0-9]+ "." [0-9]+ [[eE[+-][0-9]+]

For example:

constant w : Int := 55
constant x : Nat := 26085
constant y : Nat := 0x65E5
constant z : Float := 2.548123e-05

Note: that negative numbers are created by applying the "-" negation prefix operator to the number, for example:

constant w : Int := -55

Doc Comments

A special form of comments, doc comments are used to document modules and declarations.

   doc_comment: "/--" ([^-] | "-" [^/])* "-/"
   mod_doc_comment: "/-!" ([^-] | "-" [^/])* "-/"

Field Notation

Trailing field notation tokens are used in expressions such as (1+1).to_string. Note that a.toString is a single Identifier, but may be interpreted as a field notation expression by the parser.

   field_notation: "." ([0-9]+ | atomic_ident)

4.7 KiB Raw Blame History Unescape Escape