/- Copyright (c) 2019 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Sebastian Ullrich -/ module prelude public import Lean.Parser.Term public import Lean.Parser.Do public section namespace Lean namespace Parser /-- Syntax quotation for terms. -/ @[builtin_term_parser] def Term.quot := leading_parser "`(" >> withoutPosition (incQuotDepth termParser) >> ")" @[builtin_term_parser] def Term.precheckedQuot := leading_parser "`" >> Term.quot namespace Command /-- Skip input until the next character that satisfies the predicate, then skip whitespace -/ private def skipUntil (pred : Char → Bool) : Parser where fn := andthenFn (takeUntilFn pred) (takeWhileFn Char.isWhitespace) /-- Skip input until the next whitespace character (used for error recovery for certain tokens) -/ private def skipUntilWs : Parser := skipUntil Char.isWhitespace /-- Skip input until the next whitespace character or delimiter (used for error recovery for certain tokens, especially names that occur in signatures) -/ private def skipUntilWsOrDelim : Parser := skipUntil fun c => c.isWhitespace || c == '(' || c == ')' || c == ':' || c == '{' || c == '}' || c == '|' /-- Syntax quotation for (sequences of) commands. The identical syntax for term quotations takes priority, so ambiguous quotations like `` `($x $y) `` will be parsed as an application, not two commands. Use `` `($x:command $y:command) `` instead. Multiple commands will be put in a `` `null `` node, but a single command will not (so that you can directly match against a quotation in a command kind's elaborator). -/ @[builtin_term_parser low] def quot := leading_parser "`(" >> withoutPosition (incQuotDepth (many1Unbox commandParser)) >> ")" /-- `/-! -/` defines a *module docstring* that can be displayed by documentation generation tools. The string is associated with the corresponding position in the file. It can be used multiple times in the same file. -/ @[builtin_command_parser] def moduleDoc := leading_parser ppDedent <| "/-!" >> commentBody >> ppLine def namedPrio := leading_parser atomic (" (" >> nonReservedSymbol "priority") >> " := " >> withoutPosition priorityParser >> ")" def optNamedPrio := optional namedPrio def «private» := leading_parser "private " def «public» := leading_parser "public " def visibility := withAntiquot (mkAntiquot "visibility" decl_name% (isPseudoKind := true)) <| «private» <|> «public» def «protected» := leading_parser "protected " def «meta» := leading_parser "meta " def «noncomputable» := leading_parser "noncomputable " def «unsafe» := leading_parser "unsafe " def «partial» := leading_parser "partial " def «nonrec» := leading_parser "nonrec " /-- `declModifiers` is the collection of modifiers on a declaration: * a doc comment `/-- ... -/` * a list of attributes `@[attr1, attr2]` * a visibility specifier, `private` or `public` * `protected` * `noncomputable` * `unsafe` * `partial` or `nonrec` All modifiers are optional, and have to come in the listed order. `nestedDeclModifiers` is the same as `declModifiers`, but attributes are printed on the same line as the declaration. It is used for declarations nested inside other syntax, such as inductive constructors, structure projections, and `let rec` / `where` definitions. -/ @[builtin_doc] def declModifiers (inline : Bool) := leading_parser optional docComment >> optional (Term.«attributes» >> if inline then skip else ppDedent ppLine) >> optional visibility >> optional «protected» >> optional («meta» <|> «noncomputable») >> optional «unsafe» >> optional («partial» <|> «nonrec») /-- `declId` matches `foo` or `foo.{u,v}`: an identifier possibly followed by a list of universe names -/ -- @[builtin_doc] -- FIXME: suppress the hover def declId := leading_parser ident >> optional (".{" >> sepBy1 (recover ident (skipUntil (fun c => c.isWhitespace || c ∈ [',', '}']))) ", " >> "}") /-- `declSig` matches the signature of a declaration with required type: a list of binders and then `: type` -/ -- @[builtin_doc] -- FIXME: suppress the hover def declSig := leading_parser many (ppSpace >> (Term.binderIdent <|> Term.bracketedBinder)) >> Term.typeSpec /-- `optDeclSig` matches the signature of a declaration with optional type: a list of binders and then possibly `: type` -/ -- @[builtin_doc] -- FIXME: suppress the hover def optDeclSig := leading_parser many (ppSpace >> (Term.binderIdent <|> Term.bracketedBinder)) >> Term.optType /-- Right-hand side of a `:=` in a declaration, a term. -/ def declBody : Parser := /- We want to make sure that bodies starting with `by` in fact create a single `by` node instead of accidentally parsing some remnants after it as well. This can especially happen when starting to type comments inside tactic blocks where ``` by sleep 2000 unfold f -starting comment here ``` is parsed as ``` (by sleep 2000 unfold f ) - (starting comment here) ``` where the new nesting will discard incrementality data. By using `byTactic`'s precedence, the stray `-` will be flagged as an unexpected token and will not disturb the syntax tree up to it. We do not call `byTactic` directly to avoid differences in pretty printing or behavior or error reporting between the two branches. -/ lookahead (setExpected [] "by") >> termParser leadPrec <|> termParser -- As the pretty printer ignores `lookahead`, we need a custom parenthesizer to choose the correct -- precedence open PrettyPrinter in @[combinator_parenthesizer declBody, expose] def declBody.parenthesizer : Parenthesizer := Parenthesizer.categoryParser.parenthesizer `term 0 def declValSimple := leading_parser " :=" >> ppHardLineUnlessUngrouped >> declBody >> Termination.suffix >> optional Term.whereDecls def declValEqns := leading_parser Term.matchAltsWhereDecls def whereStructInst := leading_parser ppIndent ppSpace >> "where" >> Term.structInstFields (sepByIndent Term.structInstField "; " (allowTrailingSep := true)) >> optional Term.whereDecls /-- `declVal` matches the right-hand side of a declaration, one of: * `:= expr` (a "simple declaration") * a sequence of `| pat => expr` (a declaration by equations), shorthand for a `match` * `where` and then a sequence of `field := value` initializers, shorthand for a structure constructor -/ @[builtin_doc] def declVal := -- Remark: we should not use `Term.whereDecls` at `declVal` -- because `Term.whereDecls` is defined using `Term.letRecDecl` which may contain attributes. -- Issue #753 shows an example that fails to be parsed when we used `Term.whereDecls`. withAntiquot (mkAntiquot "declVal" decl_name% (isPseudoKind := true)) <| declValSimple <|> declValEqns <|> whereStructInst def «abbrev» := leading_parser "abbrev " >> declId >> ppIndent optDeclSig >> declVal def derivingClass := leading_parser optional ("@[" >> nonReservedSymbol "expose" >> "]") >> withForbidden "for" termParser def derivingClasses := sepBy1 derivingClass ", " def optDefDeriving := optional (ppDedent ppLine >> atomic ("deriving " >> notSymbol "instance") >> derivingClasses) def definition := leading_parser "def " >> recover declId skipUntilWsOrDelim >> ppIndent optDeclSig >> declVal >> optDefDeriving def «theorem» := leading_parser "theorem " >> recover declId skipUntilWsOrDelim >> ppIndent declSig >> declVal def «opaque» := leading_parser "opaque " >> recover declId skipUntilWsOrDelim >> ppIndent declSig >> optional declValSimple /- As `declSig` starts with a space, "instance" does not need a trailing space if we put `ppSpace` in the optional fragments. -/ def «instance» := leading_parser Term.attrKind >> "instance" >> optNamedPrio >> optional (ppSpace >> declId) >> ppIndent declSig >> declVal def «axiom» := leading_parser "axiom " >> recover declId skipUntilWsOrDelim >> ppIndent declSig /- As `declSig` starts with a space, "example" does not need a trailing space. -/ def «example» := leading_parser "example" >> ppIndent optDeclSig >> declVal def ctor := leading_parser atomic (optional docComment >> "\n| ") >> ppGroup (declModifiers true >> rawIdent >> optDeclSig) def optDeriving := leading_parser optional (ppLine >> atomic ("deriving " >> notSymbol "instance") >> derivingClasses) def computedField := leading_parser declModifiers true >> ident >> " : " >> termParser >> Term.matchAlts def computedFields := leading_parser "with" >> manyIndent (ppLine >> ppGroup computedField) /-- In Lean, every concrete type other than the universes and every type constructor other than dependent arrows is an instance of a general family of type constructions known as inductive types. It is remarkable that it is possible to construct a substantial edifice of mathematics based on nothing more than the type universes, dependent arrow types, and inductive types; everything else follows from those. Intuitively, an inductive type is built up from a specified list of constructors. For example, `List α` is the list of elements of type `α`, and is defined as follows: ``` inductive List (α : Type u) where | nil | cons (head : α) (tail : List α) ``` A list of elements of type `α` is either the empty list, `nil`, or an element `head : α` followed by a list `tail : List α`. See [Inductive types](https://lean-lang.org/theorem_proving_in_lean4/inductive_types.html) for more information. -/ @[builtin_doc] def «inductive» := leading_parser "inductive " >> recover declId skipUntilWsOrDelim >> ppIndent optDeclSig >> optional (symbol " :=" <|> " where") >> many ctor >> optional (ppDedent ppLine >> computedFields) >> optDeriving def classInductive := leading_parser atomic (group (symbol "class " >> "inductive ")) >> recover declId skipUntilWsOrDelim >> ppIndent optDeclSig >> optional (symbol " :=" <|> " where") >> many ctor >> optDeriving def structExplicitBinder := leading_parser atomic (declModifiers true >> "(") >> withoutPosition (many1 ident >> ppIndent optDeclSig >> optional (Term.binderTactic <|> Term.binderDefault)) >> ")" def structImplicitBinder := leading_parser atomic (declModifiers true >> "{") >> withoutPosition (many1 ident >> declSig) >> "}" def structInstBinder := leading_parser atomic (declModifiers true >> "[") >> withoutPosition (many1 ident >> declSig) >> "]" def structSimpleBinder := leading_parser atomic (declModifiers true >> ident) >> optDeclSig >> optional (Term.binderTactic <|> Term.binderDefault) def structFields := leading_parser manyIndent <| ppLine >> checkColGe >> ppGroup ( structExplicitBinder <|> structImplicitBinder <|> structInstBinder <|> structSimpleBinder) def structCtor := leading_parser atomic (ppIndent (declModifiers true >> ident >> many (ppSpace >> Term.bracketedBinder) >> " :: ")) def structureTk := leading_parser "structure " def classTk := leading_parser "class " def structParent := leading_parser optional (atomic (ident >> " : ")) >> termParser def «extends» := leading_parser -- The optType is to catch code that uses the old order for optType and extends. " extends " >> sepBy1 structParent ", " >> Term.optType def «structure» := leading_parser (structureTk <|> classTk) >> -- Note: no error recovery here due to clashing with the `class abbrev` syntax declId >> ppIndent (optDeclSig >> optional «extends») >> optional ((symbol " := " <|> " where ") >> optional structCtor >> structFields) >> optDeriving @[builtin_command_parser] def declaration := leading_parser declModifiers false >> («abbrev» <|> definition <|> «theorem» <|> «opaque» <|> «instance» <|> «axiom» <|> «example» <|> «inductive» <|> classInductive <|> «structure») @[builtin_command_parser] def «deriving» := leading_parser "deriving " >> "instance " >> derivingClasses >> " for " >> sepBy1 (recover termParser skip) ", " def sectionHeader := leading_parser optional ("@[" >> nonReservedSymbol "expose" >> "] ") >> optional ("public ") >> optional ("noncomputable ") /-- A `section`/`end` pair delimits the scope of `variable`, `include`, `open`, `set_option`, and `local` commands. Sections can be nested. `section ` provides a label to the section that has to appear with the matching `end`. In either case, the `end` can be omitted, in which case the section is closed at the end of the file. -/ @[builtin_command_parser] def «section» := leading_parser sectionHeader >> "section" >> optional (ppSpace >> checkColGt >> ident) /-- `namespace ` opens a section with label `` that influences naming and name resolution inside the section: * Declarations names are prefixed: `def seventeen : ℕ := 17` inside a namespace `Nat` is given the full name `Nat.seventeen`. * Names introduced by `export` declarations are also prefixed by the identifier. * All names starting with `.` become available in the namespace without the prefix. These names are preferred over names introduced by outer namespaces or `open`. * Within a namespace, declarations can be `protected`, which excludes them from the effects of opening the namespace. As with `section`, namespaces can be nested and the scope of a namespace is terminated by a corresponding `end ` or the end of the file. `namespace` also acts like `section` in delimiting the scope of `variable`, `open`, and other scoped commands. -/ @[builtin_command_parser] def «namespace» := leading_parser "namespace " >> checkColGt >> ident /-- `end` closes a `section` or `namespace` scope. If the scope is named ``, it has to be closed with `end `. The `end` command is optional at the end of a file. -/ @[builtin_command_parser] def «end» := leading_parser "end" >> optional (ppSpace >> checkColGt >> ident) /-- Declares one or more typed variables, or modifies whether already-declared variables are implicit. Introduces variables that can be used in definitions within the same `namespace` or `section` block. When a definition mentions a variable, Lean will add it as an argument of the definition. This is useful in particular when writing many definitions that have parameters in common (see below for an example). Variable declarations have the same flexibility as regular function parameters. In particular they can be [explicit, implicit][binder docs], or [instance implicit][tpil classes] (in which case they can be anonymous). This can be changed, for instance one can turn explicit variable `x` into an implicit one with `variable {x}`. Note that currently, you should avoid changing how variables are bound and declare new variables at the same time; see [issue 2789] for more on this topic. In *theorem bodies* (i.e. proofs), variables are not included based on usage in order to ensure that changes to the proof cannot change the statement of the overall theorem. Instead, variables are only available to the proof if they have been mentioned in the theorem header or in an `include` command or are instance implicit and depend only on such variables. See [*Variables and Sections* from Theorem Proving in Lean][tpil vars] for a more detailed discussion. [tpil vars]: https://lean-lang.org/theorem_proving_in_lean4/dependent_type_theory.html#variables-and-sections (Variables and Sections on Theorem Proving in Lean) [tpil classes]: https://lean-lang.org/theorem_proving_in_lean4/type_classes.html (Type classes on Theorem Proving in Lean) [binder docs]: https://leanprover-community.github.io/mathlib4_docs/Lean/Expr.html#Lean.BinderInfo (Documentation for the BinderInfo type) [issue 2789]: https://github.com/leanprover/lean4/issues/2789 (Issue 2789 on github) ## Examples ```lean section variable {α : Type u} -- implicit (a : α) -- explicit [instBEq : BEq α] -- instance implicit, named [Hashable α] -- instance implicit, anonymous def isEqual (b : α) : Bool := a == b #check isEqual -- isEqual.{u} {α : Type u} (a : α) [instBEq : BEq α] (b : α) : Bool variable {a} -- `a` is implicit now def eqComm {b : α} := a == b ↔ b == a #check eqComm -- eqComm.{u} {α : Type u} {a : α} [instBEq : BEq α] {b : α} : Prop end ``` The following shows a typical use of `variable` to factor out definition arguments: ```lean variable (Src : Type) structure Logger where trace : List (Src × String) #check Logger -- Logger (Src : Type) : Type namespace Logger -- switch `Src : Type` to be implicit until the `end Logger` variable {Src} def empty : Logger Src where trace := [] #check empty -- Logger.empty {Src : Type} : Logger Src variable (log : Logger Src) def len := log.trace.length #check len -- Logger.len {Src : Type} (log : Logger Src) : Nat variable (src : Src) [BEq Src] -- at this point all of `log`, `src`, `Src` and the `BEq` instance can all become arguments def filterSrc := log.trace.filterMap fun (src', str') => if src' == src then some str' else none #check filterSrc -- Logger.filterSrc {Src : Type} (log : Logger Src) (src : Src) [inst✝ : BEq Src] : List String def lenSrc := log.filterSrc src |>.length #check lenSrc -- Logger.lenSrc {Src : Type} (log : Logger Src) (src : Src) [inst✝ : BEq Src] : Nat end Logger ``` The following example demonstrates availability of variables in proofs: ```lean variable {α : Type} -- available in the proof as indirectly mentioned through `a` [ToString α] -- available in the proof as `α` is included (a : α) -- available in the proof as mentioned in the header {β : Type} -- not available in the proof [ToString β] -- not available in the proof theorem ex : a = a := rfl ``` After elaboration of the proof, the following warning will be generated to highlight the unused hypothesis: ``` included section variable '[ToString α]' is not used in 'ex', consider excluding it ``` In such cases, the offending variable declaration should be moved down or into a section so that only theorems that do depend on it follow it until the end of the section. -/ @[builtin_command_parser] def «variable» := leading_parser "variable" >> many1 (ppSpace >> checkColGt >> Term.bracketedBinder) /-- Declares one or more universe variables. `universe u v` `Prop`, `Type`, `Type u` and `Sort u` are types that classify other types, also known as *universes*. In `Type u` and `Sort u`, the variable `u` stands for the universe's *level*, and a universe at level `u` can only classify universes that are at levels lower than `u`. For more details on type universes, please refer to [the relevant chapter of Theorem Proving in Lean][tpil universes]. Just as type arguments allow polymorphic definitions to be used at many different types, universe parameters, represented by universe variables, allow a definition to be used at any required level. While Lean mostly handles universe levels automatically, declaring them explicitly can provide more control when writing signatures. The `universe` keyword allows the declared universe variables to be used in a collection of definitions, and Lean will ensure that these definitions use them consistently. [tpil universes]: https://lean-lang.org/theorem_proving_in_lean4/dependent_type_theory.html#types-as-objects (Type universes on Theorem Proving in Lean) ```lean /- Explicit type-universe parameter. -/ def id₁.{u} (α : Type u) (a : α) := a /- Implicit type-universe parameter, equivalent to `id₁`. Requires option `autoImplicit true`, which is the default. -/ def id₂ (α : Type u) (a : α) := a /- Explicit standalone universe variable declaration, equivalent to `id₁` and `id₂`. -/ universe u def id₃ (α : Type u) (a : α) := a ``` On a more technical note, using a universe variable only in the right-hand side of a definition causes an error if the universe has not been declared previously. ```lean def L₁.{u} := List (Type u) -- def L₂ := List (Type u) -- error: `unknown universe level 'u'` universe u def L₃ := List (Type u) ``` ## Examples ```lean universe u v w structure Pair (α : Type u) (β : Type v) : Type (max u v) where a : α b : β #check Pair.{v, w} -- Pair : Type v → Type w → Type (max v w) ``` -/ @[builtin_command_parser] def «universe» := leading_parser "universe" >> many1 (ppSpace >> checkColGt >> ident) @[builtin_command_parser] def check := leading_parser "#check " >> termParser @[builtin_command_parser] def check_failure := leading_parser "#check_failure " >> termParser -- Like `#check`, but succeeds only if term does not type check /-- `#eval e` evaluates the expression `e` by compiling and evaluating it. * The command attempts to use `ToExpr`, `Repr`, or `ToString` instances to print the result. * If `e` is a monadic value of type `m ty`, then the command tries to adapt the monad `m` to one of the monads that `#eval` supports, which include `IO`, `CoreM`, `MetaM`, `TermElabM`, and `CommandElabM`. Users can define `MonadEval` instances to extend the list of supported monads. The `#eval` command gracefully degrades in capability depending on what is imported. Importing the `Lean.Elab.Command` module provides full capabilities. Due to unsoundness, `#eval` refuses to evaluate expressions that depend on `sorry`, even indirectly, since the presence of `sorry` can lead to runtime instability and crashes. This check can be overridden with the `#eval! e` command. Options: * If `eval.pp` is true (default: true) then tries to use `ToExpr` instances to make use of the usual pretty printer. Otherwise, only tries using `Repr` and `ToString` instances. * If `eval.type` is true (default: false) then pretty prints the type of the evaluated value. * If `eval.derive.repr` is true (default: true) then attempts to auto-derive a `Repr` instance when there is no other way to print the result. See also: `#reduce e` for evaluation by term reduction. -/ @[builtin_command_parser, builtin_doc] def eval := leading_parser "#eval " >> termParser @[builtin_command_parser, inherit_doc eval] def evalBang := leading_parser "#eval! " >> termParser @[builtin_command_parser] def synth := leading_parser "#synth " >> termParser @[builtin_command_parser] def exit := leading_parser "#exit" @[builtin_command_parser] def print := leading_parser "#print " >> (ident <|> strLit) @[builtin_command_parser] def printSig := leading_parser "#print " >> nonReservedSymbol "sig " >> ident @[builtin_command_parser] def printAxioms := leading_parser "#print " >> nonReservedSymbol "axioms " >> ident @[builtin_command_parser] def printEqns := leading_parser "#print " >> (nonReservedSymbol "equations " <|> nonReservedSymbol "eqns ") >> ident /-- Displays all available tactic tags, with documentation. -/ @[builtin_command_parser] def printTacTags := leading_parser "#print " >> nonReservedSymbol "tactic " >> nonReservedSymbol "tags" /-- `#where` gives a description of the state of the current scope scope. This includes the current namespace, `open` namespaces, `universe` and `variable` commands, and options set with `set_option`. -/ @[builtin_command_parser] def «where» := leading_parser "#where" /-- Shows the current Lean version. Prints `Lean.versionString`. -/ @[builtin_command_parser] def version := leading_parser "#version" /-- Debugging command. Runs the following command in an exported context just like elaboration of declaration signatures. -/ @[builtin_command_parser] def withExporting := leading_parser "#with_exporting " >> commandParser /-- Debugging command: Prints the result of `Environment.dumpAsyncEnvState`. -/ @[builtin_command_parser] def dumpAsyncEnvState := leading_parser "#dump_async_env_state" @[builtin_command_parser] def «init_quot» := leading_parser "init_quot" def optionValue := nonReservedSymbol "true" <|> nonReservedSymbol "false" <|> strLit <|> numLit /-- `set_option ` sets the option `` to ``. Depending on the type of the option, the value can be `true`, `false`, a string, or a numeral. Options are used to configure behavior of Lean as well as user-defined extensions. The setting is active until the end of the current `section` or `namespace` or the end of the file. Auto-completion is available for `` to list available options. `set_option in ` sets the option for just a single command: ``` set_option pp.all true in #check 1 + 1 ``` Similarly, `set_option in` can also be used inside terms and tactics to set an option only in a single term or tactic. -/ @[builtin_command_parser] def «set_option» := leading_parser "set_option " >> identWithPartialTrailingDot >> ppSpace >> optionValue def eraseAttr := leading_parser "-" >> rawIdent @[builtin_command_parser] def «attribute» := leading_parser "attribute " >> "[" >> withoutPosition (sepBy1 (eraseAttr <|> Term.attrInstance) ", ") >> "]" >> many1 (ppSpace >> ident) /-- Adds names from other namespaces to the current namespace. The command `export Some.Namespace (name₁ name₂)` makes `name₁` and `name₂`: - visible in the current namespace without prefix `Some.Namespace`, like `open`, and - visible from outside the current namespace `N` as `N.name₁` and `N.name₂`. ## Examples ```lean namespace Morning.Sky def star := "venus" end Morning.Sky namespace Evening.Sky export Morning.Sky (star) -- `star` is now in scope #check star end Evening.Sky -- `star` is visible in `Evening.Sky` #check Evening.Sky.star ``` -/ @[builtin_command_parser] def «export» := leading_parser "export " >> ident >> " (" >> many1 ident >> ")" @[builtin_command_parser] def «import» := leading_parser "import" -- not a real command, only for error messages def openHiding := leading_parser ppSpace >> atomic (ident >> " hiding") >> many1 (ppSpace >> checkColGt >> ident) def openRenamingItem := leading_parser ident >> unicodeSymbol " → " " -> " >> checkColGt >> ident def openRenaming := leading_parser ppSpace >> atomic (ident >> " renaming ") >> sepBy1 openRenamingItem ", " def openOnly := leading_parser ppSpace >> atomic (ident >> " (") >> many1 ident >> ")" def openSimple := leading_parser many1 (ppSpace >> checkColGt >> ident) def openScoped := leading_parser " scoped" >> many1 (ppSpace >> checkColGt >> ident) /-- `openDecl` is the body of an `open` declaration (see `open`) -/ @[builtin_doc] def openDecl := withAntiquot (mkAntiquot "openDecl" `Lean.Parser.Command.openDecl (isPseudoKind := true)) <| openHiding <|> openRenaming <|> openOnly <|> openSimple <|> openScoped /-- Makes names from other namespaces visible without writing the namespace prefix. Names that are made available with `open` are visible within the current `section` or `namespace` block. This makes referring to (type) definitions and theorems easier, but note that it can also make [scoped instances], notations, and attributes from a different namespace available. The `open` command can be used in a few different ways: * `open Some.Namespace.Path1 Some.Namespace.Path2` makes all non-protected names in `Some.Namespace.Path1` and `Some.Namespace.Path2` available without the prefix, so that `Some.Namespace.Path1.x` and `Some.Namespace.Path2.y` can be referred to by writing only `x` and `y`. * `open Some.Namespace.Path hiding def1 def2` opens all non-protected names in `Some.Namespace.Path` except `def1` and `def2`. * `open Some.Namespace.Path (def1 def2)` only makes `Some.Namespace.Path.def1` and `Some.Namespace.Path.def2` available without the full prefix, so `Some.Namespace.Path.def3` would be unaffected. This works even if `def1` and `def2` are `protected`. * `open Some.Namespace.Path renaming def1 → def1', def2 → def2'` same as `open Some.Namespace.Path (def1 def2)` but `def1`/`def2`'s names are changed to `def1'`/`def2'`. This works even if `def1` and `def2` are `protected`. * `open scoped Some.Namespace.Path1 Some.Namespace.Path2` **only** opens [scoped instances], notations, and attributes from `Namespace1` and `Namespace2`; it does **not** make any other name available. * `open in` makes the names `open`-ed visible only in the next command or expression. [scoped instance]: https://lean-lang.org/theorem_proving_in_lean4/type_classes.html#scoped-instances (Scoped instances in Theorem Proving in Lean) ## Examples ```lean /-- SKI combinators https://en.wikipedia.org/wiki/SKI_combinator_calculus -/ namespace Combinator.Calculus def I (a : α) : α := a def K (a : α) : β → α := fun _ => a def S (x : α → β → γ) (y : α → β) (z : α) : γ := x z (y z) end Combinator.Calculus section -- open everything under `Combinator.Calculus`, *i.e.* `I`, `K` and `S`, -- until the section ends open Combinator.Calculus theorem SKx_eq_K : S K x = I := rfl end -- open everything under `Combinator.Calculus` only for the next command (the next `theorem`, here) open Combinator.Calculus in theorem SKx_eq_K' : S K x = I := rfl section -- open only `S` and `K` under `Combinator.Calculus` open Combinator.Calculus (S K) theorem SKxy_eq_y : S K x y = y := rfl -- `I` is not in scope, we have to use its full path theorem SKxy_eq_Iy : S K x y = Combinator.Calculus.I y := rfl end section open Combinator.Calculus renaming I → identity, K → konstant #check identity #check konstant end section open Combinator.Calculus hiding S #check I #check K end section namespace Demo inductive MyType | val namespace N1 scoped infix:68 " ≋ " => BEq.beq scoped instance : BEq MyType where beq _ _ := true def Alias := MyType end N1 end Demo -- bring `≋` and the instance in scope, but not `Alias` open scoped Demo.N1 #check Demo.MyType.val == Demo.MyType.val #check Demo.MyType.val ≋ Demo.MyType.val -- #check Alias -- unknown identifier 'Alias' end ``` -/ @[builtin_command_parser] def «open» := leading_parser withPosition ("open" >> openDecl) @[builtin_command_parser] def «mutual» := leading_parser "mutual" >> many1 (ppLine >> notSymbol "end" >> commandParser) >> ppDedent (ppLine >> "end") def initializeKeyword := leading_parser "initialize " <|> "builtin_initialize " @[builtin_command_parser] def «initialize» := leading_parser declModifiers false >> initializeKeyword >> optional (atomic (ident >> Term.typeSpec >> ppSpace >> Term.leftArrow)) >> Term.doSeq @[builtin_command_parser] def «in» := trailing_parser withOpen (ppDedent (" in " >> commandParser)) /-- Adds a docstring to an existing declaration, replacing any existing docstring. The provided docstring should be written as a docstring for the `add_decl_doc` command, as in ``` /-- My new docstring -/ add_decl_doc oldDeclaration ``` This is useful for auto-generated declarations for which there is no place to write a docstring in the source code. Parent projections in structures are an example of this: ``` structure Triple (α β γ : Type) extends Prod α β where thrd : γ /-- Extracts the first two projections of a triple. -/ add_decl_doc Triple.toProd ``` Documentation can only be added to declarations in the same module. -/ @[builtin_command_parser] def addDocString := leading_parser docComment >> "add_decl_doc " >> ident /-- Registers a tactic tag, saving its user-facing name and docstring. Tactic tags can be used by documentation generation tools to classify related tactics. -/ @[builtin_command_parser] def «register_tactic_tag» := leading_parser optional (docComment >> ppLine) >> "register_tactic_tag " >> ident >> strLit /-- Adds more documentation as an extension of the documentation for a given tactic. The extended documentation is placed in the command's docstring. It is shown as part of a bulleted list, so it should be brief. -/ @[builtin_command_parser] def «tactic_extension» := leading_parser optional (docComment >> ppLine) >> "tactic_extension " >> ident /-- Documents a recommended spelling for a notation in identifiers. Theorems should generally be systematically named after their statement, rather than creatively. Non-identifier notations should be referred to consistently by their recommended spelling. ``` /-- some additional info -/ recommended_spelling "and" for "∧" in [And, «term_∧_»] ``` will do the following: * Adds the sentence "The recommended spelling of `∧` in identifiers is `and` (some additional info)." to the end of the docstring for `And` and for `∧`. If the additional info is more than a single line, it will be placed below the sentence instead of in parentheses. * Registers this information in an environment extension, so that it will later be possible to generate a table with all recommended spellings. You can add attach the recommended spelling to as many declarations as you want. It is recommended to attach the recommended spelling to all relevant parsers as well as the declaration the parsers refer to (if such a declaration exists). Note that the `inherit_doc` attribute does *not* copy recommended spellings, so even though the parser for `∧` uses `@[inherit_doc And]`, we have to attach the recommended spelling to both `And` and `«term_∧_»`. The `syntax`, `macro`, `elab` and `notation` commands accept a `(name := parserName)` option to assign a name to the created parser so that you do not have to guess the automatically generated name. The `syntax`, `macro` and `elab` commands can be hovered to see the name of the parser. For complex notations which enclose identifiers, the convention is to use example identifiers rather than other placeholders. This is an example following the convention: ``` recommended_spelling "singleton" for "[a]" in [List.cons, «term[_]»] ``` Using `[·]` or `[⋯]` or `[…]` instead of `[a]` would be against the convention. When attaching a recommended spelling to a notation whose docstring already has an example, try to reuse the identifier names chosen in the docstring for consistency. -/ @[builtin_command_parser] def «recommended_spelling» := leading_parser optional (docComment >> ppLine) >> "recommended_spelling " >> strLit >> " for " >> strLit >> " in " >> "[" >> sepBy1 ident ", " >> "]" /-- This is an auxiliary command for generation constructor injectivity theorems for inductive types defined at `Prelude.lean`. It is meant for bootstrapping purposes only. -/ @[builtin_command_parser] def genInjectiveTheorems := leading_parser "gen_injective_theorems% " >> ident /-- `include eeny meeny` instructs Lean to include the section `variable`s `eeny` and `meeny` in all theorems in the remainder of the current section, differing from the default behavior of conditionally including variables based on use in the theorem header. Other commands are not affected. `include` is usually followed by `in theorem ...` to limit the inclusion to the subsequent declaration. -/ @[builtin_command_parser] def «include» := leading_parser "include" >> many1 (ppSpace >> checkColGt >> ident) /-- `omit` instructs Lean to not include a variable previously `include`d. Apart from variable names, it can also refer to typeclass instance variables by type using the syntax `omit [TypeOfInst]`, in which case all instance variables that unify with the given type are omitted. `omit` should usually only be used in conjunction with `in` in order to keep the section structure simple. -/ @[builtin_command_parser] def «omit» := leading_parser "omit" >> many1 (ppSpace >> checkColGt >> (ident <|> Term.instBinder)) /-- No-op parser used as syntax kind for attaching remaining whitespace at the end of the input. -/ @[run_builtin_parser_attribute_hooks] def eoi : Parser := leading_parser "" builtin_initialize registerBuiltinNodeKind ``eoi @[run_builtin_parser_attribute_hooks, inherit_doc declModifiers] abbrev declModifiersF := declModifiers false @[run_builtin_parser_attribute_hooks, inherit_doc declModifiers] abbrev declModifiersT := declModifiers true builtin_initialize register_parser_alias (kind := ``declModifiers) "declModifiers" declModifiersF register_parser_alias (kind := ``declModifiers) "nestedDeclModifiers" declModifiersT register_parser_alias declId register_parser_alias declSig register_parser_alias declVal register_parser_alias optDeclSig register_parser_alias openDecl register_parser_alias docComment register_parser_alias visibility /-- Registers an error explanation. Note that the error name is not relativized to the current namespace. -/ @[builtin_command_parser] def registerErrorExplanationStx := leading_parser docComment >> "register_error_explanation " >> ident >> termParser /-- Returns syntax for `private` or `public` visibility depending on `isPublic`. This function should be used to generate visibility syntax for declarations that is independent of the presence of `public section`s. -/ def visibility.ofBool (isPublic : Bool) : TSyntax ``visibility := Unhygienic.run <| if isPublic then `(visibility| public) else `(visibility| private) /-- Returns syntax for `private` if `attrKind` is `local` and `public` otherwise. -/ def visibility.ofAttrKind (attrKind : TSyntax ``Term.attrKind) : TSyntax ``visibility := visibility.ofBool <| !attrKind matches `(attrKind| local) end Command namespace Term /-- `open Foo in e` is like `open Foo` but scoped to a single term. It makes the given namespaces available in the term `e`. -/ @[builtin_term_parser] def «open» := leading_parser:leadPrec "open" >> Command.openDecl >> withOpenDecl (" in " >> termParser) /-- `set_option opt val in e` is like `set_option opt val` but scoped to a single term. It sets the option `opt` to the value `val` in the term `e`. -/ @[builtin_term_parser] def «set_option» := leading_parser:leadPrec "set_option " >> identWithPartialTrailingDot >> ppSpace >> Command.optionValue >> " in " >> termParser end Term namespace Tactic /-- `open Foo in tacs` (the tactic) acts like `open Foo` at command level, but it opens a namespace only within the tactics `tacs`. -/ @[builtin_tactic_parser] def «open» := leading_parser:leadPrec "open " >> Command.openDecl >> withOpenDecl (" in " >> tacticSeq) /-- `set_option opt val in tacs` (the tactic) acts like `set_option opt val` at the command level, but it sets the option only within the tactics `tacs`. -/ @[builtin_tactic_parser] def «set_option» := leading_parser:leadPrec "set_option " >> identWithPartialTrailingDot >> ppSpace >> Command.optionValue >> " in " >> tacticSeq end Tactic end Parser end Lean