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](./other_commands.md).

Users can dynamically extend the sets of both symbols (via the
commands listed in [Quoted Symbols](#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 ``«»``.

```lean
   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](https://unicode-table.com/en/) 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](#identifiers), but may be interpreted as a field
notation expression by the parser.

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