Documentation

Init.Meta

@[extern lean_get_githash]
@[extern lean_version_get_is_release]
@[extern lean_version_get_special_desc]

Additional version description like "nightly-2018-03-11"

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        @[extern lean_internal_is_stage0]
        @[extern lean_internal_has_llvm_backend]

        This function can be used to detect whether the compiler has support for generating LLVM instead of C. It is used by lake instead of the --features flag in order to avoid having to run a compiler for this every time on startup. See #2572.

        Valid identifier names

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                          @[export lean_is_inaccessible_user_name]
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                          • (pre.str s).isInaccessibleUserName = (s.contains '✝' || s == "_inaccessible")
                          • (p.num i).isInaccessibleUserName = p.isInaccessibleUserName
                          • x.isInaccessibleUserName = false
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                                      • x.capitalize = match x with | p.str s => p.str s.capitalize | n => n
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                                          eraseSuffix? n s return n' if n is of the form n == n' ++ s.

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                                          • x.eraseSuffix? Lean.Name.anonymous = some x
                                          • (p.str s).eraseSuffix? (p'.str s') = if (s == s') = true then p.eraseSuffix? p' else none
                                          • (p.num s).eraseSuffix? (p'.num s') = if (s == s') = true then p.eraseSuffix? p' else none
                                          • x✝.eraseSuffix? x = none
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                                            @[inline]

                                            Remove macros scopes, apply f, and put them back

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                                              @[export lean_name_append_after]
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                                              • n.appendAfter suffix = n.modifyBase fun (x : Lake.Name) => match x with | p.str s => p.mkStr (s ++ suffix) | n => n.mkStr suffix
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                                                @[export lean_name_append_index_after]
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                                                  @[export lean_name_append_before]
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                                                    theorem Lean.Name.beq_iff_eq {m : Lake.Name} {n : Lake.Name} :
                                                    (m == n) = true m = n
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                                                    • g.curr = g.namePrefix.mkNum g.idx
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                                                      • g.next = { namePrefix := g.namePrefix, idx := g.idx + 1 }
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                                                        • g.mkChild = ({ namePrefix := g.namePrefix.mkNum g.idx, idx := 1 }, { namePrefix := g.namePrefix, idx := g.idx + 1 })
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                                                              • Lean.Syntax.instReprTSyntax = { reprPrec := Lean.Syntax.reprTSyntax✝ }
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                                                                                      • Lean.TSyntax.instCoeConsSyntaxNodeKindNil = { coe := fun (stx : Lean.TSyntax k) => { raw := stx.raw } }
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                                                                                      • Lean.TSyntax.instCoeConsSyntaxNodeKind = { coe := fun (stx : Lean.TSyntax ks) => { raw := stx.raw } }
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                                                                                      • Lean.TSyntax.instCoeDepTermMkIdentIdent = { coe := { raw := Lean.Syntax.ident info ss n res } }
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                                                                                      • Lean.TSyntax.Compat.instCoeTailSyntax = { coe := fun (s : Lean.Syntax) => { raw := s } }
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                                                                                        • Lean.TSyntax.Compat.instCoeTailArraySyntaxTSyntaxArray = { coe := Lean.TSyntaxArray.mk }
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                                                                                          Compare syntax structures modulo source info.

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                                                                                          • Lean.Syntax.instBEqTSyntax = { beq := fun (x x_1 : Lean.TSyntax k) => x.raw == x_1.raw }
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                                                                                              Return substring of original input covering stx. Result is meaningful only if all involved SourceInfo.originals refer to the same string (as is the case after parsing).

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                                                                                                  Replaces the trailing whitespace in stx, if any, with an empty substring.

                                                                                                  The trailing substring's startPos and str are preserved in order to ensure that the result could have been produced by the parser, in case any syntax consumers rely on such an assumption.

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                                                                                                        Return the first atom/identifier that has position information

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                                                                                                        • target.copyHeadTailInfoFrom source = (target.setHeadInfo source.getHeadInfo).setTailInfo source.getTailInfo
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                                                                                                          Ensure head position is synthetic. The server regards syntax as "original" only if both head and tail info are original.

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                                                                                                            def Lean.withHeadRefOnly {m : TypeType} [Monad m] [Lean.MonadRef m] {α : Type} (x : m α) :
                                                                                                            m α

                                                                                                            Use the head atom/identifier of the current ref as the ref

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                                                                                                              partial def Lean.expandMacros (stx : Lean.Syntax) (p : optParam (Lean.SyntaxNodeKindBool) fun (k : Lean.SyntaxNodeKind) => k != `Lean.Parser.Term.byTactic) :

                                                                                                              Expand macros in the given syntax. A node with kind k is visited only if p k is true.

                                                                                                              Note that the default value for p returns false for by ... nodes. This is a "hack". The tactic framework abuses the macro system to implement extensible tactics. For example, one can define

                                                                                                              syntax "my_trivial" : tactic -- extensible tactic
                                                                                                              
                                                                                                              macro_rules | `(tactic| my_trivial) => `(tactic| decide)
                                                                                                              macro_rules | `(tactic| my_trivial) => `(tactic| assumption)
                                                                                                              

                                                                                                              When the tactic evaluator finds the tactic my_trivial, it tries to evaluate the macro_rule expansions until one "works", i.e., the macro expansion is evaluated without producing an exception. We say this solution is a bit hackish because the term elaborator may invoke expandMacros with (p := fun _ => true), and expand the tactic macros as just macros. In the example above, my_trivial would be replaced with assumption, decide would not be tried if assumption fails at tactic evaluation time.

                                                                                                              We are considering two possible solutions for this issue: 1- A proper extensible tactic feature that does not rely on the macro system.

                                                                                                              2- Typed macros that know the syntax categories they're working in. Then, we would be able to select which syntactic categories are expanded by expandMacros.

                                                                                                              Helper functions for processing Syntax programmatically #

                                                                                                              Create an identifier copying the position from src. To refer to a specific constant, use mkCIdentFrom instead.

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                                                                                                                def Lean.mkIdentFromRef {m : TypeType} [Monad m] [Lean.MonadRef m] (val : Lake.Name) (canonical : optParam Bool false) :
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                                                                                                                  Create an identifier referring to a constant c copying the position from src. This variant of mkIdentFrom makes sure that the identifier cannot accidentally be captured.

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                                                                                                                      @[export lean_mk_syntax_ident]
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                                                                                                                                    • Lean.Syntax.instCoeArraySepArray = { coe := Lean.Syntax.SepArray.ofElems }

                                                                                                                                    Constructs a typed separated array from elements. The given array does not include the separators.

                                                                                                                                    Like Syntax.SepArray.ofElems but for typed syntax.

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                                                                                                                                      • Lean.Syntax.instCoeTSyntaxArrayTSepArray = { coe := Lean.Syntax.TSepArray.ofElems }

                                                                                                                                      Create syntax representing a Lean term application, but avoid degenerate empty applications.

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                                                                                                                                            Recall that we don't have special Syntax constructors for storing numeric and string atoms. The idea is to have an extensible approach where embedded DSLs may have new kind of atoms and/or different ways of representing them. So, our atoms contain just the parsed string. The main Lean parser uses the kind numLitKind for storing natural numbers that can be encoded in binary, octal, decimal and hexadecimal format. isNatLit implements a "decoder" for Syntax objects representing these numerals.

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                                                                                                                                                Decodes a 'scientific number' string which is consumed by the OfScientific class. Takes as input a string such as 123, 123.456e7 and returns a triple (n, sign, e) with value given by n * 10^-e if sign else n * 10^e.

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                                                                                                                                                  partial def Lean.Syntax.decodeScientificLitVal?.decodeAfterExp (s : String) (i : String.Pos) (val : Nat) (e : Nat) (sign : Bool) (exp : Nat) :
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                                                                                                                                                        • stx.toNat = match stx.isNatLit? with | some val => val | none => 0
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                                                                                                                                                            Decodes a valid string gap after the \. Note that this function matches "\" whitespace+ rather than the more restrictive "\" newline whitespace* since this simplifies the implementation. Justification: this does not overlap with any other sequences beginning with \.

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                                                                                                                                                              partial def Lean.Syntax.decodeRawStrLitAux (s : String) (i : String.Pos) (num : Nat) :

                                                                                                                                                              Takes a raw string literal, counts the number of #'s after the r, and interprets it as a string. The position i should start at 1, which is the character after the leading r. The algorithm is simple: we are given r##...#"...string..."##...# with zero or more #s. By counting the number of leading #'s, we can extract the ...string....

                                                                                                                                                              Takes the string literal lexical syntax parsed by the parser and interprets it as a string. This is where escape sequences are processed for example. The string s is is either a plain string literal or a raw string literal.

                                                                                                                                                              If it returns none then the string literal is ill-formed, which indicates a bug in the parser. The function is not required to return none if the string literal is ill-formed.

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                                                                                                                                                                If the provided Syntax is a string literal, returns the string it represents.

                                                                                                                                                                Even if the Syntax is a str node, the function may return none if its internally ill-formed. The parser should always create well-formed str nodes.

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                                                                                                                                                                      Split a name literal (without the backtick) into its dot-separated components. For example, foo.bla.«bo.o»["foo", "bla", "«bo.o»"]. If the literal cannot be parsed, return [].

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                                                                                                                                                                          Converts a String to a hierarchical Name after splitting it at the dots.

                                                                                                                                                                          "a.b".toName is the name a.b, not «a.b». For the latter, use Name.mkSimple.

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                                                                                                                                                                          • s.toName = s.toSubstring.toName
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                                                                                                                                                                                        • stx.getOptionalIdent? = match stx.getOptional? with | some stx => some stx.getId | none => none
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                                                                                                                                                                                                            class Lean.Quote (α : Type) (k : optParam Lean.SyntaxNodeKind `term) :

                                                                                                                                                                                                            Reflect a runtime datum back to surface syntax (best-effort).

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                                                                                                                                                                                                                instance Lean.instQuoteProdMkStr1 {α : Type} {β : Type} [Lean.Quote α] [Lean.Quote β] :
                                                                                                                                                                                                                Lean.Quote (α × β)
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                                                                                                                                                                                                                Evaluator for prec DSL

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                                                                                                                                                                                                                  Evaluator for prio DSL

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                                                                                                                                                                                                                      @[reducible, inline]
                                                                                                                                                                                                                      abbrev Array.getSepElems {α : Type u_1} (as : Array α) :
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                                                                                                                                                                                                                          • a.filterSepElems p = (a.filterSepElemsM p).run
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                                                                                                                                                                                                                              • a.mapSepElems f = (a.mapSepElemsM f).run
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                                                                                                                                                                                                                                • sa.getElems = sa.elemsAndSeps.getSepElems
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                                                                                                                                                                                                                                    • sa.push e = if sa.elemsAndSeps.isEmpty = true then { elemsAndSeps := #[e.raw] } else { elemsAndSeps := (sa.elemsAndSeps.push (Lean.mkAtom sep)).push e.raw }
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                                                                                                                                                                                                                                      • Lean.Syntax.instEmptyCollectionSepArray = { emptyCollection := { elemsAndSeps := } }
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                                                                                                                                                                                                                                      • Lean.Syntax.instEmptyCollectionTSepArray = { emptyCollection := { elemsAndSeps := } }
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                                                                                                                                                                                                                                      • Lean.Syntax.instCoeOutSepArrayArray = { coe := Lean.Syntax.SepArray.getElems }
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                                                                                                                                                                                                                                      • Lean.Syntax.instCoeOutTSepArrayTSyntaxArray = { coe := Lean.Syntax.TSepArray.getElems }
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                                                                                                                                                                                                                                      • Lean.Syntax.instCoeOutTSyntaxArrayArray = { coe := fun (a : Lean.TSyntaxArray k) => a.raw }
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                                                                                                                                                                                                                                      Helper functions for manipulating interpolated strings #

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                                                                                                                                                                                                                                        • stx.getSepArgs = stx.getArgs.getSepElems
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                                                                                                                                                                                                                                              def Lean.TSyntax.getDocString (stx : Lean.TSyntax `Lean.Parser.Command.docComment) :
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                                                                                                                                                                                                                                              • stx.getDocString = match stx.raw[1] with | Lean.Syntax.atom info val => val.extract 0 (val.endPos - { byteIdx := 2 }) | x => ""
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                                                                                                                                                                                                                                                    Controls which new mvars are turned in to goals by the apply tactic.

                                                                                                                                                                                                                                                    • nonDependentFirst mvars that don't depend on other goals appear first in the goal list.
                                                                                                                                                                                                                                                    • nonDependentOnly only mvars that don't depend on other goals are added to goal list.
                                                                                                                                                                                                                                                    • all all unassigned mvars are added to the goal list.
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                                                                                                                                                                                                                                                      Configures the behaviour of the apply tactic.

                                                                                                                                                                                                                                                      • synthAssignedInstances : Bool

                                                                                                                                                                                                                                                        If synthAssignedInstances is true, then apply will synthesize instance implicit arguments even if they have assigned by isDefEq, and then check whether the synthesized value matches the one inferred. The congr tactic sets this flag to false.

                                                                                                                                                                                                                                                      • allowSynthFailures : Bool

                                                                                                                                                                                                                                                        If allowSynthFailures is true, then apply will return instance implicit arguments for which typeclass search failed as new goals.

                                                                                                                                                                                                                                                      • approx : Bool

                                                                                                                                                                                                                                                        If approx := true, then we turn on isDefEq approximations. That is, we use the approxDefEq combinator.

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                                                                                                                                                                                                                                                        Configures the behaviour of the omega tactic.

                                                                                                                                                                                                                                                        • splitDisjunctions : Bool

                                                                                                                                                                                                                                                          Split disjunctions in the context.

                                                                                                                                                                                                                                                          Note that with splitDisjunctions := false omega will not be able to solve x = y goals as these are usually handled by introducing ¬ x = y as a hypothesis, then replacing this with x < y ∨ x > y.

                                                                                                                                                                                                                                                          On the other hand, omega does not currently detect disjunctions which, when split, introduce no new useful information, so the presence of irrelevant disjunctions in the context can significantly increase run time.

                                                                                                                                                                                                                                                        • splitNatSub : Bool

                                                                                                                                                                                                                                                          Whenever ((a - b : Nat) : Int) is found, register the disjunction b ≤ a ∧ ((a - b : Nat) : Int) = a - b ∨ a < b ∧ ((a - b : Nat) : Int) = 0 for later splitting.

                                                                                                                                                                                                                                                        • splitNatAbs : Bool

                                                                                                                                                                                                                                                          Whenever Int.natAbs a is found, register the disjunction 0 ≤ a ∧ Int.natAbs a = a ∨ a < 0 ∧ Int.natAbs a = - a for later splitting.

                                                                                                                                                                                                                                                        • splitMinMax : Bool

                                                                                                                                                                                                                                                          Whenever min a b or max a b is found, rewrite in terms of the definition if a ≤ b ..., for later case splitting.

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                                                                                                                                                                                                                                                          inductive Lean.Meta.CheckTactic.CheckGoalType {α : Sort u} (val : α) :

                                                                                                                                                                                                                                                          Type used to lift an arbitrary value into a type parameter so it can appear in a proof goal.

                                                                                                                                                                                                                                                          It is used by the #check_tactic command.

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                                                                                                                                                                                                                                                            erw [rules] is a shorthand for rw (config := { transparency := .default }) [rules]. This does rewriting up to unfolding of regular definitions (by comparison to regular rw which only unfolds @[reducible] definitions).

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                                                                                                                                                                                                                                                                    simp! is shorthand for simp with autoUnfold := true. This will rewrite with all equation lemmas, which can be used to partially evaluate many definitions.

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                                                                                                                                                                                                                                                                      simp_arith is shorthand for simp with arith := true and decide := true. This enables the use of normalization by linear arithmetic.

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                                                                                                                                                                                                                                                                        simp_arith! is shorthand for simp_arith with autoUnfold := true. This will rewrite with all equation lemmas, which can be used to partially evaluate many definitions.

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                                                                                                                                                                                                                                                                          simp_all! is shorthand for simp_all with autoUnfold := true. This will rewrite with all equation lemmas, which can be used to partially evaluate many definitions.

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                                                                                                                                                                                                                                                                            simp_all_arith combines the effects of simp_all and simp_arith.

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                                                                                                                                                                                                                                                                              simp_all_arith! combines the effects of simp_all, simp_arith and simp!.

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                                                                                                                                                                                                                                                                                dsimp! is shorthand for dsimp with autoUnfold := true. This will rewrite with all equation lemmas, which can be used to partially evaluate many definitions.

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