doc(doc/lean): lexical conventions

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

doc/lean/lexical.md

@@ -0,0 +1,71 @@
+# Lexical conventions
+
+## Reserved keywords
+
+This is the list of reserved keywords in Lean:
+`Axiom`,
+`Check`,
+`Coercion`,
+`Definition`,
+`Echo`,
+`EndScope`,
+`Environment`,
+`Eval`,
+`Exit`,
+`Help`,
+`Import`,
+`Infix`,
+`Infixr`,
+`Notation`,
+`Options`,
+`Pi`,
+`Pop`,
+`Push`,
+`Scope`,
+`Show`,
+`Theorem`,
+`Type`,
+`Universe`,
+`Variable`,
+`Variables`,
+`by`,
+`exists`,
+`forall`,
+`fun`,
+`in`,
+`let`,
+`show`
+
+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 "]"`.