71 lines
2.2 KiB
Markdown
71 lines
2.2 KiB
Markdown
# Lexical conventions
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## Reserved keywords
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This is the list of reserved keywords in Lean:
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`Axiom`,
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`Check`,
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`Coercion`,
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`Definition`,
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`Echo`,
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`EndScope`,
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`Environment`,
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`Eval`,
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`Exit`,
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`Help`,
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`Import`,
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`Infix`,
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`Infixr`,
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`Notation`,
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`Options`,
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`Pi`,
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`Pop`,
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`Push`,
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`Scope`,
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`Show`,
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`Theorem`,
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`Type`,
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`Universe`,
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`Variable`,
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`Variables`,
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`by`,
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`exists`,
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`forall`,
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`fun`,
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`in`,
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`let`,
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`show`
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Remark: Lean commands always start with a upper case letter.
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The following symbols are also reserved: `->`, `==`, `Π`, `λ`, `→`, `∀`, `∃`, `_`, `,`, `.`, `:`, `(`, `)`, `{`, `}`
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## Identifiers
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Lean identifiers are divided in 3 categories.
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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'`.
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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`.
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In the second category, we have any non empty sequence of the following characters: `=`, `<`, `>`, `^`, `|`, `&`, `~`, `+`, `-`, `*`, `/`, `\\`, `$`, `%`, `?`, `;`, `[`, `]`, `#`. Here are examples of indentifiers in this category: `==`, `++`, `<<==`.
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In the third category, we have any non empty sequence of non-ascii characters. Here are some examples: `⊆`, `∨`, and `¬`.
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This separation may seem adhoc, the main motivation is to minimize the number of white spaces in Lean files.
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For example, we can write `x+y*z` instead of `x + y * z`.
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We usually use category 1 identifiers to name variable declarations,
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definitions, axioms and theorems. Category 2 and 3 are usually used to
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define notation, i.e., symbolic abbreviations denoting terms. For
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example, the integer addition is named `Int::add`, and real addition
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`Real::add`. The symbol `+` is notation for both of them.
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## Numerals
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Natural numbers are of the form `[0-9]+`, and decimal numbers are of the form `[0-9]+.[0-9]*`.
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Natural numbers have type Nat, and decimal numbers have type Real. Lean automatically introduce coercions when needed.
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## Strings
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Strings are defined as usual as `"[any sequence of characters excluded "]"`.
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