95bf6793aa
Fixes an issue where each alternative in choice nodes would get their own arguments. Now cdot function expansion is aware of choice nodes. Also modifies the variable naming so that multi-argument functions like `(· + ·)` expand as `fun x1 x2 => x1 + x2` rather than `fun x x_1 => x + x_1`. Closes #4832
652 lines
35 KiB
Text
652 lines
35 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. \n***\n*import Init.Prelude*",
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"```lean\nTrue.intro : True\n```\n***\n`True` is true, and `True.intro` (or more commonly, `trivial`)\nis the proof. \n***\n*import Init.Prelude*",
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"```lean\nNat.zero : Nat\n```\n***\n`Nat.zero`, is the smallest natural number. This is one of the two\nconstructors of `Nat`. Using `Nat.zero` should usually be avoided in favor of\n`0 : Nat` or simply `0`, in order to remain compatible with the simp normal\nform defined by `Nat.zero_eq`. \n***\n*import Init.Prelude*",
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"```lean\nTrue.intro : True\n```\n***\n`True` is true, and `True.intro` (or more commonly, `trivial`)\nis the proof. \n***\n*import Init.Prelude*",
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"```lean\nLean.Parser.Category.tactic : Lean.Parser.Category\n```\n***\n`tactic` is the builtin syntax category for tactics. These appear after\n`by` in proofs, and they are programs that take in the proof context\n(the hypotheses in scope plus the type of the term to synthesize) and construct\na term of the expected type. For example, `simp` is a tactic, used in:\n```\nexample : 2 + 2 = 4 := by simp\n```\n\n***\n*import Init.Notation*",
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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. \n***\n*import Init.Notation*",
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"kind": "markdown"}}
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"```lean\nLean.Parser.Category.tactic : Lean.Parser.Category\n```\n***\n`tactic` is the builtin syntax category for tactics. These appear after\n`by` in proofs, and they are programs that take in the proof context\n(the hypotheses in scope plus the type of the term to synthesize) and construct\na term of the expected type. For example, `simp` is a tactic, used in:\n```\nexample : 2 + 2 = 4 := by simp\n```\n\n***\n*import Init.Notation*",
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"kind": "markdown"}}
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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. \n***\n*import Init.Notation*",
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"contents": {"value": "My tactic ", "kind": "markdown"}}
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"contents": {"value": "My tactic ", "kind": "markdown"}}
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"contents":
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{"value": "```lean\nmyNota : Lean.ParserDescr\n```\n***\nMy notation ",
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{"value": "```lean\n1 : Nat\n```\n***\nMy notation ", "kind": "markdown"}}
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{"value": "```lean\nNat\n```\n***\nMy notation ", "kind": "markdown"}}
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{"value": "```lean\nNat\n```\n***\nMy ultimate notation ", "kind": "markdown"}}
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"contents":
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{"value": "```lean\nmyInfix : Lean.TrailingParserDescr\n```",
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"kind": "markdown"}}
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"```lean\nNat.add : Nat → Nat → Nat\n```\n***\nAddition of natural numbers.\n\nThis definition is overridden in both the kernel and the compiler to efficiently\nevaluate using the \"bignum\" representation (see `Nat`). The definition provided\nhere is the logical model (and it is soundness-critical that they coincide).\n\n***\n*import Init.Prelude*",
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"```lean\nNat\n```\n***\nAddition of natural numbers.\n\nThis definition is overridden in both the kernel and the compiler to efficiently\nevaluate using the \"bignum\" representation (see `Nat`). The definition provided\nhere is the logical model (and it is soundness-critical that they coincide).\n",
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"kind": "markdown"}}
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"```lean\nNat : Type\n```\n***\nThe type of natural numbers, starting at zero. It is defined as an\ninductive type freely generated by \"zero is a natural number\" and\n\"the successor of a natural number is a natural number\".\n\nYou can prove a theorem `P n` about `n : Nat` by `induction n`, which will\nexpect a proof of the theorem for `P 0`, and a proof of `P (succ i)` assuming\na proof of `P i`. The same method also works to define functions by recursion\non natural numbers: induction and recursion are two expressions of the same\noperation from Lean's point of view.\n\n```\nopen Nat\nexample (n : Nat) : n < succ n := by\n induction n with\n | zero =>\n show 0 < 1\n decide\n | succ i ih => -- ih : i < succ i\n show succ i < succ (succ i)\n exact Nat.succ_lt_succ ih\n```\n\nThis type is special-cased by both the kernel and the compiler:\n* The type of expressions contains \"`Nat` literals\" as a primitive constructor,\n and the kernel knows how to reduce zero/succ expressions to nat literals.\n* If implemented naively, this type would represent a numeral `n` in unary as a\n linked list with `n` links, which is horribly inefficient. Instead, the\n runtime itself has a special representation for `Nat` which stores numbers up\n to 2^63 directly and larger numbers use an arbitrary precision \"bignum\"\n library (usually [GMP](https://gmplib.org/)).\n\n***\n*import Init.Prelude*",
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{"start": {"line": 87, "character": 14}, "end": {"line": 87, "character": 36}},
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"```lean\nLean.Parser.Term.doSeq : Lean.Parser.Parser\n```\n***\nA `doSeq` is a sequence of `doElem`, the main argument after the `do` keyword and other\ndo elements that take blocks. It can either have the form `\"{\" (doElem \";\"?)* \"}\"` or\n`many1Indent (doElem \";\"?)`, where `many1Indent` ensures that all the items are at\nthe same or higher indentation level as the first line. \n***\n*import Lean.Parser.Do*",
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"```lean\nLean.Parser.Term.doSeq : Lean.Parser.Parser\n```\n***\nA `doSeq` is a sequence of `doElem`, the main argument after the `do` keyword and other\ndo elements that take blocks. It can either have the form `\"{\" (doElem \";\"?)* \"}\"` or\n`many1Indent (doElem \";\"?)`, where `many1Indent` ensures that all the items are at\nthe same or higher indentation level as the first line. \n***\n*import Lean.Parser.Do*",
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"kind": "markdown"}}
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"contents": {"value": "My command ", "kind": "markdown"}}
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"contents":
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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. \n***\n*import Lean.Parser.Extra*",
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"kind": "markdown"}}
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{"textDocument": {"uri": "file:///hover.lean"},
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"end": {"line": 102, "character": 31}},
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"```lean\nLean.ParserDescr.sepBy1 (p : Lean.ParserDescr) (sep : String) (psep : Lean.ParserDescr)\n (allowTrailingSep : Bool := false) : Lean.ParserDescr\n```\n***\n`sepBy1` is just like `sepBy`, except it takes 1 or more instead of\n0 or more occurrences of `p`. \n***\n*import Init.Prelude*",
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"kind": "markdown"}}
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{"textDocument": {"uri": "file:///hover.lean"},
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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. \n***\n*import Init.Notation*",
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"kind": "markdown"}}
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{"start": {"line": 111, "character": 0}, "end": {"line": 111, "character": 8}},
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"contents": {"value": "My ultimate command ", "kind": "markdown"}}
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{"textDocument": {"uri": "file:///hover.lean"},
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"end": {"line": 115, "character": 14}},
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"Structure instance. `{ x := e, ... }` assigns `e` to field `x`, which may be\ninherited. If `e` is itself a variable called `x`, it can be elided:\n`fun y => { x := 1, y }`.\nA *structure update* of an existing value can be given via `with`:\n`{ point with x := 1 }`.\nThe structure type can be specified if not inferable:\n`{ x := 1, y := 2 : Point }`.\n",
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"end": {"line": 119, "character": 10}},
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{"value":
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"```lean\nid.{u} {α : Sort u} (a : 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\n***\n*import Init.Prelude*",
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"kind": "markdown"}}
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"contents": {"value": "```lean\nTrue\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nn : Id ℕ\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nfoo : ℕ\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nBar.foo : ℕ\n```", "kind": "markdown"}}
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"end": {"line": 141, "character": 17}},
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"contents": {"value": "```lean\n_root_.foo : ℕ\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nBar.bar : ℕ\n```", "kind": "markdown"}}
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{"textDocument": {"uri": "file:///hover.lean"},
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"position": {"line": 147, "character": 10}}
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"end": {"line": 147, "character": 13}},
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"contents": {"value": "```lean\nBar.Foo : Type\n```", "kind": "markdown"}}
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{"textDocument": {"uri": "file:///hover.lean"},
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"position": {"line": 147, "character": 17}}
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{"start": {"line": 147, "character": 17},
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"end": {"line": 147, "character": 19}},
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"contents":
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{"value": "```lean\nBar.Foo.mk (hi : ℕ) : Foo\n```", "kind": "markdown"}}
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{"value": "```lean\nBar.Foo.hi (self : Foo) : ℕ\n```", "kind": "markdown"}}
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"end": {"line": 153, "character": 13}},
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"contents": {"value": "```lean\nBar.Bar : Type\n```", "kind": "markdown"}}
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"position": {"line": 155, "character": 4}}
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{"range":
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{"start": {"line": 155, "character": 4}, "end": {"line": 155, "character": 6}},
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"contents": {"value": "```lean\nBar.Bar.mk : Bar\n```", "kind": "markdown"}}
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"position": {"line": 158, "character": 2}}
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{"range":
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{"start": {"line": 158, "character": 0}, "end": {"line": 158, "character": 8}},
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"contents":
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{"value": "```lean\nBar.instToStringNat : ToString ℕ\n```",
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"kind": "markdown"}}
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"position": {"line": 160, "character": 9}}
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"contents": {"value": "```lean\nBar.f : ToString ℕ\n```", "kind": "markdown"}}
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{"value": "A type universe. `Type ≡ Type 0`, `Type u ≡ Sort (u + 1)`. ",
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"kind": "markdown"}}
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"contents": {"value": "```lean\nBar.foo.bar : ℕ\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nBar.foo.bar : ℕ\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nx : ℕ\n```", "kind": "markdown"}}
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{"value": "Enables or disables all unused variable linter warnings ",
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"contents": {"value": "```lean\nn : ℕ\n```", "kind": "markdown"}}
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{"value":
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"`declModifiers` is the collection of modifiers on a declaration:\n* a doc comment `/-- ... -/`\n* a list of attributes `@[attr1, attr2]`\n* a visibility specifier, `private` or `protected`\n* `noncomputable`\n* `unsafe`\n* `partial` or `nonrec`\n\nAll modifiers are optional, and have to come in the listed order.\n\n`nestedDeclModifiers` is the same as `declModifiers`, but attributes are printed\non the same line as the declaration. It is used for declarations nested inside other syntax,\nsuch as inductive constructors, structure projections, and `let rec` / `where` definitions. ",
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"kind": "markdown"}}
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"end": {"line": 200, "character": 15}},
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{"value":
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"`· tac` focuses on the main goal and tries to solve it using `tac`, or else fails. ",
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"kind": "markdown"}}
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{"value":
|
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"```lean\nId ℕ\n```\n***\nParentheses, used for grouping expressions (e.g., `a * (b + c)`).\nCan also be used for 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 - also applies to other parentheses-like notations such as `(·, 1)`\n",
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"kind": "markdown"}}
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"contents": {"value": "```lean\n?m\n```", "kind": "markdown"}}
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{"textDocument": {"uri": "file:///hover.lean"},
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"contents":
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{"value":
|
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"```lean\n?m x1✝ x2✝\n```\n***\n`a + b` computes the sum of `a` and `b`.\nThe meaning of this notation is type-dependent. ",
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"kind": "markdown"}}
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"contents": {"value": "```lean\nx : α\n```", "kind": "markdown"}}
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{"textDocument": {"uri": "file:///hover.lean"},
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{"range":
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"end": {"line": 217, "character": 29}},
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"contents": {"value": "```lean\nα\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nx : α\n```", "kind": "markdown"}}
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{"range":
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"end": {"line": 222, "character": 32}},
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"contents": {"value": "my_intro tactic ", "kind": "markdown"}}
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{"textDocument": {"uri": "file:///hover.lean"},
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"position": {"line": 222, "character": 31}}
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"contents": {"value": "```lean\nα\n```", "kind": "markdown"}}
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{"range":
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"contents": {"value": "my_intro tactic ", "kind": "markdown"}}
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"contents":
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{"value": "```lean\nmy_intro : ℕ\n```\n***\nmy_intro term ",
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"kind": "markdown"}}
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"position": {"line": 235, "character": 8}}
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{"range":
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"contents": {"value": "```lean\nx : ℕ\n```", "kind": "markdown"}}
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{"textDocument": {"uri": "file:///hover.lean"},
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"position": {"line": 238, "character": 4}}
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{"range":
|
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{"start": {"line": 238, "character": 2}, "end": {"line": 238, "character": 8}},
|
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"contents":
|
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{"value":
|
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"The left hand side of an induction arm, `| foo a b c` or `| @foo a b c`\nwhere `foo` is a constructor of the inductive type and `a b c` are the arguments\nto the constructor.\n",
|
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"kind": "markdown"}}
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{"textDocument": {"uri": "file:///hover.lean"},
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"position": {"line": 241, "character": 4}}
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{"range":
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{"start": {"line": 241, "character": 2},
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"end": {"line": 241, "character": 10}},
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"contents":
|
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{"value":
|
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"The left hand side of an induction arm, `| foo a b c` or `| @foo a b c`\nwhere `foo` is a constructor of the inductive type and `a b c` are the arguments\nto the constructor.\n",
|
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"kind": "markdown"}}
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{"textDocument": {"uri": "file:///hover.lean"},
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"position": {"line": 241, "character": 9}}
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{"range":
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{"start": {"line": 241, "character": 9},
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"end": {"line": 241, "character": 10}},
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"contents": {"value": "```lean\nx : ℕ\n```", "kind": "markdown"}}
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{"textDocument": {"uri": "file:///hover.lean"},
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"position": {"line": 245, "character": 8}}
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{"range":
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{"start": {"line": 245, "character": 8}, "end": {"line": 245, "character": 9}},
|
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"contents": {"value": "```lean\nx : ℕ\n```", "kind": "markdown"}}
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{"textDocument": {"uri": "file:///hover.lean"},
|
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"position": {"line": 247, "character": 12}}
|
||
{"range":
|
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{"start": {"line": 247, "character": 12},
|
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"end": {"line": 247, "character": 13}},
|
||
"contents": {"value": "```lean\nx : ℕ\n```", "kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 249, "character": 4}}
|
||
{"range":
|
||
{"start": {"line": 249, "character": 2}, "end": {"line": 249, "character": 8}},
|
||
"contents":
|
||
{"value":
|
||
"The left hand side of an induction arm, `| foo a b c` or `| @foo a b c`\nwhere `foo` is a constructor of the inductive type and `a b c` are the arguments\nto the constructor.\n",
|
||
"kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 252, "character": 9}}
|
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{"range":
|
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{"start": {"line": 252, "character": 9},
|
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"end": {"line": 252, "character": 10}},
|
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"contents":
|
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{"value":
|
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"```lean\nℕ\n```\n***\nA placeholder term, to be synthesized by unification. ",
|
||
"kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
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"position": {"line": 252, "character": 11}}
|
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{"range":
|
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{"start": {"line": 252, "character": 11},
|
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"end": {"line": 252, "character": 13}},
|
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"contents": {"value": "```lean\nih : True\n```", "kind": "markdown"}}
|
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{"textDocument": {"uri": "file:///hover.lean"},
|
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"position": {"line": 257, "character": 6}}
|
||
{"range":
|
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{"start": {"line": 257, "character": 4}, "end": {"line": 257, "character": 9}},
|
||
"contents":
|
||
{"value":
|
||
"```lean\nNat.zero : ℕ\n```\n***\n`Nat.zero`, is the smallest natural number. This is one of the two\nconstructors of `Nat`. Using `Nat.zero` should usually be avoided in favor of\n`0 : Nat` or simply `0`, in order to remain compatible with the simp normal\nform defined by `Nat.zero_eq`. \n***\n*import Init.Prelude*",
|
||
"kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 257, "character": 15}}
|
||
{"range":
|
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{"start": {"line": 257, "character": 13},
|
||
"end": {"line": 257, "character": 18}},
|
||
"contents":
|
||
{"value":
|
||
"```lean\nNat.zero : ℕ\n```\n***\n`Nat.zero`, is the smallest natural number. This is one of the two\nconstructors of `Nat`. Using `Nat.zero` should usually be avoided in favor of\n`0 : Nat` or simply `0`, in order to remain compatible with the simp normal\nform defined by `Nat.zero_eq`. \n***\n*import Init.Prelude*",
|
||
"kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 260, "character": 6}}
|
||
{"range":
|
||
{"start": {"line": 260, "character": 4}, "end": {"line": 260, "character": 9}},
|
||
"contents":
|
||
{"value":
|
||
"```lean\nNat.succ (n : ℕ) : ℕ\n```\n***\nThe successor function on natural numbers, `succ n = n + 1`.\nThis is one of the two constructors of `Nat`. Using `succ n` should usually\nbe avoided in favor of `n + 1`, in order to remain compatible with the simp\nnormal form defined by `Nat.succ_eq_add_one`. \n***\n*import Init.Prelude*",
|
||
"kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 260, "character": 17}}
|
||
{"range":
|
||
{"start": {"line": 260, "character": 15},
|
||
"end": {"line": 260, "character": 20}},
|
||
"contents":
|
||
{"value":
|
||
"```lean\nNat.succ (n : ℕ) : ℕ\n```\n***\nThe successor function on natural numbers, `succ n = n + 1`.\nThis is one of the two constructors of `Nat`. Using `succ n` should usually\nbe avoided in favor of `n + 1`, in order to remain compatible with the simp\nnormal form defined by `Nat.succ_eq_add_one`. \n***\n*import Init.Prelude*",
|
||
"kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 263, "character": 27}}
|
||
{"range":
|
||
{"start": {"line": 263, "character": 27},
|
||
"end": {"line": 263, "character": 37}},
|
||
"contents":
|
||
{"value":
|
||
"```lean\nInhabited.mk.{u} {α : Sort u} (default : α) : Inhabited α\n```\n***\n*import Init.Prelude*",
|
||
"kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 263, "character": 28}}
|
||
{"range":
|
||
{"start": {"line": 263, "character": 28},
|
||
"end": {"line": 263, "character": 36}},
|
||
"contents":
|
||
{"value":
|
||
"```lean\nNat.zero : ℕ\n```\n***\n`Nat.zero`, is the smallest natural number. This is one of the two\nconstructors of `Nat`. Using `Nat.zero` should usually be avoided in favor of\n`0 : Nat` or simply `0`, in order to remain compatible with the simp normal\nform defined by `Nat.zero_eq`. \n***\n*import Init.Prelude*",
|
||
"kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 269, "character": 2}}
|
||
{"range":
|
||
{"start": {"line": 269, "character": 2}, "end": {"line": 269, "character": 3}},
|
||
"contents":
|
||
{"value":
|
||
"```lean\nlet x :=\n match 0 with\n | x => 0;\nℕ\n```\n***\nA placeholder term, to be synthesized by unification. ",
|
||
"kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 272, "character": 4}}
|
||
{"range":
|
||
{"start": {"line": 272, "character": 4}, "end": {"line": 272, "character": 8}},
|
||
"contents":
|
||
{"value": "```lean\nauto (o : ℕ := by exact 1) : ℕ\n```", "kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 277, "character": 22}}
|
||
{"range":
|
||
{"start": {"line": 277, "character": 22},
|
||
"end": {"line": 277, "character": 23}},
|
||
"contents": {"value": "```lean\nx : ℕ\n```", "kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 277, "character": 13}}
|
||
{"range":
|
||
{"start": {"line": 277, "character": 13},
|
||
"end": {"line": 277, "character": 15}},
|
||
"contents": {"value": "```lean\n_e : 1 = x\n```", "kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 282, "character": 8}}
|
||
{"range":
|
||
{"start": {"line": 282, "character": 8},
|
||
"end": {"line": 282, "character": 10}},
|
||
"contents": {"value": "```lean\n_e : 1 = 0\n```", "kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 285, "character": 9}}
|
||
{"range":
|
||
{"start": {"line": 285, "character": 9},
|
||
"end": {"line": 285, "character": 10}},
|
||
"contents": {"value": "```lean\nx : ℕ\n```", "kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 290, "character": 13}}
|
||
{"range":
|
||
{"start": {"line": 290, "character": 13},
|
||
"end": {"line": 290, "character": 16}},
|
||
"contents":
|
||
{"value":
|
||
"```lean\nList.nil.{u} {α : Type u} : List α\n```\n***\n`[]` is the empty list. \n***\n*import Init.Prelude*",
|
||
"kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 292, "character": 13}}
|
||
{"range":
|
||
{"start": {"line": 292, "character": 11},
|
||
"end": {"line": 292, "character": 15}},
|
||
"contents":
|
||
{"value":
|
||
"```lean\nList.cons.{u} {α : Type u} (head : α) (tail : List α) : List α\n```\n***\nIf `a : α` and `l : List α`, then `cons a l`, or `a :: l`, is the\nlist whose first element is `a` and with `l` as the rest of the list. \n***\n*import Init.Prelude*",
|
||
"kind": "markdown"}}
|
||
{"textDocument": {"uri": "file:///hover.lean"},
|
||
"position": {"line": 294, "character": 18}}
|
||
{"range":
|
||
{"start": {"line": 294, "character": 17},
|
||
"end": {"line": 294, "character": 20}},
|
||
"contents":
|
||
{"value":
|
||
"```lean\nList.map.{u, v} {α : Type u} {β : Type v} (f : α → β) : List α → List β\n```\n***\n`O(|l|)`. `map f l` applies `f` to each element of the list.\n* `map f [a, b, c] = [f a, f b, f c]`\n\n***\n*import Init.Data.List.Basic*",
|
||
"kind": "markdown"}}
|
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{"textDocument": {"uri": "file:///hover.lean"},
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"position": {"line": 297, "character": 26}}
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"end": {"line": 297, "character": 29}},
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"contents":
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{"value":
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"```lean\nList.zip.{u, v} {α : Type u} {β : Type v} : List α → List β → List (α × β)\n```\n***\n`O(min |xs| |ys|)`. Combines the two lists into a list of pairs, with one element from each list.\nThe longer list is truncated to match the shorter list.\n* `zip [x₁, x₂, x₃] [y₁, y₂, y₃, y₄] = [(x₁, y₁), (x₂, y₂), (x₃, y₃)]`\n\n***\n*import Init.Data.List.Basic*",
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"kind": "markdown"}}
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{"textDocument": {"uri": "file:///hover.lean"},
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"position": {"line": 297, "character": 19}}
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"end": {"line": 297, "character": 22}},
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"contents":
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{"value":
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"```lean\nList.zip.{u, v} {α : Type u} {β : Type v} : List α → List β → List (α × β)\n```\n***\n`O(min |xs| |ys|)`. Combines the two lists into a list of pairs, with one element from each list.\nThe longer list is truncated to match the shorter list.\n* `zip [x₁, x₂, x₃] [y₁, y₂, y₃, y₄] = [(x₁, y₁), (x₂, y₂), (x₃, y₃)]`\n\n***\n*import Init.Data.List.Basic*",
|
||
"kind": "markdown"}}
|