Remark: Lean commands always start with a upper case letter.
The following symbols are also reserved: `->`, `==`, `Π`, `λ`, `→`, `∀`, `∃`, `_`, `,`, `.`, `:`, `(`, `)`, `{`, `}`
## Identifiers
Lean identifiers are divided in 3 categories.
In the first category, identifiers are of the form `[a-zA-Z_'@][a-zA-Z0-9_'@]*`. Here are examples of valid identifiers in this category: `fact`, `sin`, `move_front`, `f1`, `@cast`, and `A'`.
In Lean, we support hierarchical identifiers. A hierarchical is essentially a sequence of category 1 identifiers separated by `::`. We use hierarchical names to simulate modules in Lean. Here are some examples: `mod::x`, `foo::bla::1`.
In the second category, we have any non empty sequence of the following characters: `=`, `<`, `>`, `^`, `|`, `&`, `~`, `+`, `-`, `*`, `/`, `\\`, `$`, `%`, `?`, `;`, `[`, `]`, `#`. Here are examples of indentifiers in this category: `==`, `++`, `<<==`.
In the third category, we have any non empty sequence of non-ascii characters. Here are some examples: `⊆`, `∨`, and `¬`.
This separation may seem adhoc, the main motivation is to minimize the number of white spaces in Lean files.
For example, we can write `x+y*z` instead of `x + y * z`.
We usually use category 1 identifiers to name variable declarations,
definitions, axioms and theorems. Category 2 and 3 are usually used to
define notation, i.e., symbolic abbreviations denoting terms. For
example, the integer addition is named `Int::add`, and real addition
`Real::add`. The symbol `+` is notation for both of them.
## Numerals
Natural numbers are of the form `[0-9]+`, and decimal numbers are of the form `[0-9]+.[0-9]*`.
Natural numbers have type Nat, and decimal numbers have type Real. Lean automatically introduce coercions when needed.
## Strings
Strings are defined as usual as `"[any sequence of characters excluded "]"`.
