Documentation

Lean.Level

def Nat.imax (n : Nat) (m : Nat) :
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  • n.imax m = if m = 0 then 0 else n.max m
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    Cached hash code, cached results, and other data for Level. hash : 32-bits hasMVar : 1-bit hasParam : 1-bit depth : 24-bits

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              def Lean.Level.mkData (h : UInt64) (depth : optParam Nat 0) (hasMVar : optParam Bool false) (hasParam : optParam Bool false) :
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                Universe level metavariable Id

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                  @[reducible, inline]

                  Short for LevelMVarId

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                        instance Lean.instForInLMVarIdMapProdLMVarId {m : Type u_1 → Type u_2} {α : Type} :
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                        • Lean.instInhabitedLMVarIdMap = { default := }
                        @[implemented_by Lean.Level.data._override]
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                          • u.hash = u.data.hash
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                            • u.depth = u.data.depth.toNat
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                              • u.hasMVar = u.data.hasMVar
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                                • u.hasParam = u.data.hasParam
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                                  @[export lean_level_hash]
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                                  • u.hashEx = (hash u).toUInt32
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                                    @[export lean_level_has_mvar]
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                                      @[export lean_level_has_param]
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                                        @[export lean_level_depth]
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                                        • u.depthEx = u.data.depth
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                                                  @[export lean_level_mk_zero]
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                                                    @[export lean_level_mk_succ]
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                                                      @[export lean_level_mk_mvar]
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                                                        @[export lean_level_mk_param]
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                                                          @[export lean_level_mk_max]
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                                                            @[export lean_level_mk_imax]
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                                                                • x.isSucc = match x with | a.succ => true | x => false
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                                                                  • x.isMax = match x with | a.max a_1 => true | x => false
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                                                                    • x.isIMax = match x with | a.imax a_1 => true | x => false
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                                                                      • x.isMaxIMax = match x with | a.max a_1 => true | a.imax a_1 => true | x => false
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                                                                              If result is true, then forall assignments A which assigns all parameters and metavariables occurring in l, l[A] != zero

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                                                                                    • u.succ.getOffsetAux x = u.getOffsetAux (x + 1)
                                                                                    • x✝.getOffsetAux x = x
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                                                                                      • lvl.getOffset = lvl.getOffsetAux 0
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                                                                                        • a.succ.getLevelOffset = a.getLevelOffset
                                                                                        • x.getLevelOffset = x
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                                                                                            @[extern lean_level_eq]

                                                                                            occurs u l return true iff u occurs in l.

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                                                                                            • x.occurs v₁.succ = (x == v₁.succ || x.occurs v₁)
                                                                                            • x.occurs (v₁.max v₂) = (x == v₁.max v₂ || x.occurs v₁ || x.occurs v₂)
                                                                                            • x.occurs (v₁.imax v₂) = (x == v₁.imax v₂ || x.occurs v₁ || x.occurs v₂)
                                                                                            • x✝.occurs x = (x✝ == x)
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                                                                                                @[irreducible]
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                                                                                                  A total order on level expressions that has the following properties

                                                                                                  • succ l is an immediate successor of l.
                                                                                                  • zero is the minimal element. This total order is used in the normalization procedure.
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                                                                                                  • l₁.normLt l₂ = l₁.normLtAux 0 l₂ 0
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                                                                                                    Return true if u and v denote the same level. Check is currently incomplete.

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                                                                                                    • u.isEquiv v = (u == v || u.normalize == v.normalize)
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                                                                                                      Reduce (if possible) universe level by 1

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                                                                                                                    The update functions try to avoid allocating new values using pointer equality. Note that if the update*! functions are used under a match-expression, the compiler will eliminate the double-match.

                                                                                                                    @[implemented_by _private.Lean.Level.0.Lean.Level.updateSucc!Impl]
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                                                                                                                      @[implemented_by _private.Lean.Level.0.Lean.Level.updateMax!Impl]
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                                                                                                                        @[implemented_by _private.Lean.Level.0.Lean.Level.updateIMax!Impl]
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                                                                                                                          @[specialize #[]]
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                                                                                                                                  @[irreducible]
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                                                                                                                                    @[reducible, inline]
                                                                                                                                    abbrev Lean.LevelMap (α : Type) :
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                                                                                                                                              • v.succ.collectMVars s = v.collectMVars s
                                                                                                                                              • (u_2.max v).collectMVars s = u_2.collectMVars (v.collectMVars s)
                                                                                                                                              • (u_2.imax v).collectMVars s = u_2.collectMVars (v.collectMVars s)
                                                                                                                                              • (Lean.Level.mvar n).collectMVars s = Lean.RBTree.insert s n
                                                                                                                                              • u.collectMVars s = s
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                                                                                                                                                    • u.any p = (u.find? p).isSome
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                                                                                                                                                      @[reducible, inline]
                                                                                                                                                      abbrev Nat.toLevel (n : Nat) :
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