286 lines
14 KiB
Text
286 lines
14 KiB
Text
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"```lean\nTrue.intro : True\n```\n***\n`True` is true, and `True.intro` (or more commonly, `trivial`)\nis the proof. ",
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"```lean\nTrue.intro : True\n```\n***\n`True` is true, and `True.intro` (or more commonly, `trivial`)\nis the proof. ",
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"```lean\nTrue.intro : True\n```\n***\n`True` is true, and `True.intro` (or more commonly, `trivial`)\nis the proof. ",
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"contents": {"value": "My way better tactic ", "kind": "markdown"}}
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"contents": {"value": "My way better tactic ", "kind": "markdown"}}
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{"value": "```lean\n1 : Nat\n```\n***\nMy notation ", "kind": "markdown"}}
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{"value": "```lean\nNat\n```\n***\nMy way better notation ",
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"contents":
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{"value": "```lean\nNat\n```\n***\nMy ultimate notation ", "kind": "markdown"}}
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"contents": {"value": "My command ", "kind": "markdown"}}
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"contents": {"value": "My way better command ", "kind": "markdown"}}
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{"value":
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"```lean\nLean.Parser.ppSpace : Lean.Parser.Parser\n```\n***\nNo-op parser that advises the pretty printer to emit a space/soft line break. ",
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"```lean\nLean.ParserDescr.sepBy1 : Lean.ParserDescr → String → Lean.ParserDescr → optParam Bool false → Lean.ParserDescr\n```",
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"```lean\nLean.Parser.Category.term : Lean.Parser.Category\n```\n***\n`term` is the builtin syntax category for terms. A term denotes an expression\nin lean's type theory, for example `2 + 2` is a term. The difference between\n`Term` and `Expr` is that the former is a kind of syntax, while the latter is\nthe result of elaboration. For example `by simp` is also a `Term`, but it elaborates\nto different `Expr`s depending on the context. ",
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null
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"```lean\nid.{0} : ∀ {α : Prop}, α → α\n```\n***\nThe identity function. `id` takes an implicit argument `α : Sort u`\n(a type in any universe), and an argument `a : α`, and returns `a`.\n\nAlthough this may look like a useless function, one application of the identity\nfunction is to explicitly put a type on an expression. If `e` has type `T`,\nand `T'` is definitionally equal to `T`, then `@id T' e` typechecks, and lean\nknows that this expression has type `T'` rather than `T`. This can make a\ndifference for typeclass inference, since `T` and `T'` may have different\ntypeclass instances on them. `show T' from e` is sugar for an `@id T' e`\nexpression.\n",
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"contents": {"value": "```lean\nTrue\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nn : Id Nat\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nBar.foo : Nat\n```", "kind": "markdown"}}
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{"value": "```lean\nBar.Foo.mk : Nat → Foo\n```", "kind": "markdown"}}
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{"value": "```lean\nBar.Foo.hi : Foo → Nat\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nBar.Bar.mk : Bar\n```", "kind": "markdown"}}
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"contents":
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{"value": "```lean\nBar.instToStringNat : ToString Nat\n```",
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"contents":
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{"value": "```lean\nBar.f : ToString Nat\n```", "kind": "markdown"}}
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"contents":
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{"value": "A type universe. `Type ≡ Type 0`, `Type u ≡ Sort (u + 1)`. ",
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"`· tac` focuses on the main goal and tries to solve it using `tac`, or else fails. ",
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"```lean\nId Nat\n```\n***\nYou can use parentheses for\n- Grouping expressions, e.g., `a * (b + c)`.\n- Creating tuples, e.g., `(a, b, c)` is notation for `Prod.mk a (Prod.mk b c)`.\n- Performing type ascription, e.g., `(0 : Int)` instructs Lean to process `0` as a value of type `Int`.\n- Creating `Unit.unit`, `()` is just a shorthand for `Unit.unit`.\n- Creating simple functions when combined with `·`. Here are some examples:\n - `(· + 1)` is shorthand for `fun x => x + 1`\n - `(· + ·)` is shorthand for `fun x y => x + y`\n - `(f · a b)` is shorthand for `fun x => f x a b`\n - `(h (· + 1) ·)` is shorthand for `fun x => h (fun y => y + 1) x`\n",
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