Structures · Lean core
Inhabited
Inhabited α is a typeclass that says that α has a designated element,
called (default : α). This is sometimes referred to as a "pointed type".
This class is used by functions that need to return a value of the type
when called "out of domain". For example, Array.get! arr i : α returns
a value of type α when arr : Array α, but if i is not in range of
the array, it reports a panic message, but this does not halt the program,
so it must still return a value of type α (and in fact this is required
for logical consistency), so in this case it returns default.
- Defined in
- Init.Prelude
- Shape
- One type argument · adds default
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by2
Forgetful instances
Concrete types that are instances100
- Int
- Nat
- Real
- Rat
- Bool
- Quiver.Hom
- Complex
- SeparationQuotient
- NNReal
- BitVec
- ContinuousLinearMap
- ZMod
- ENNReal
- Polynomial
- Filter.Germ
- BoundedContinuousFunction
- Padic
- CStarMatrix
- CategoryTheory.Functor
- RatFunc
- UniformSpace.Completion
- UInt64
- NNRat
- TensorProduct
- UInt8
- UInt16
- UInt32
- Quaternion
- Unitization
- Matrix
- WithVal
- HahnSeries
- NumberField.InfinitePlace.Completion
- NonemptyInterval
- LocallyConstant
- USize
- ENat
- PadicInt
- CategoryTheory.Over
- QuadraticAlgebra
- Units
- MeasureTheory.SimpleFunc
- FreeAbelianGroup
- EReal
- MonoidAlgebra
- TrivSqZeroExt
- Hyperreal
- AddMonoidAlgebra
- Finsupp
- DirectSum
- IsLocalRing.ResidueField
- Polynomial.SplittingField
- RatFunc.CompletionAtInfty
- RestrictScalars
- DoubleCentralizer
- Zsqrtd
- GaloisField
- CategoryTheory.Discrete
- ZNum
- SymAlg
- SkewMonoidAlgebra
- ModuleCat
- Interval
- AddUnits
- CauSeq.Completion.Cauchy
- AlgebraicClosure
- PerfectClosure
- ContMDiffMap
- AdjoinRoot
- OreLocalization
- CyclotomicField
- Polynomial.SplittingFieldAux
- PiTensorProduct
- CategoryTheory.Grp
- QuaternionAlgebra
- ZeroAtInftyContinuousMap
- Int32
- Int8
- Int64
- ContinuousAlternatingMap
- Int16
- DFinsupp
- WittVector
- SetSemiring
- PNat
- NumberField.InfiniteAdeleRing
- TopologicalSpace.NonemptyCompacts
- CauSeq
- TruncatedWittVector
- LucasLehmer.X
- CategoryTheory.End
- NumberField.AdeleRing
- HomologicalComplex
- WithCStarModule
- Tropical
- MvPowerSeries
- FreeRing
- CompareReals.Q
- Action
- Ordinal
How is a type an instance?
Loading the hierarchy index…
Assumed by528
- Turing.ListBlank
- List.headI
- Turing.ListBlank.cons
- Turing.ListBlank.head
- Turing.ListBlank.tail
- Turing.Tape.mk'
- Turing.Tape.move
- Turing.PointedMap.f
- Turing.ListBlank.map
- Turing.ListBlank.head_cons
- List.getI
- Turing.Tape.head
- Turing.ListBlank.tail_cons
- Turing.ListBlank.nth
- Turing.Tape.write
- SymbolicDynamics.FullShift.Pattern.support
- Turing.ListBlank.cons_head_tail
- Turing.TM1.stepAux
- Directed.sequence
- Turing.TM1.step
- Turing.proj
- SymbolicDynamics.FullShift.Pattern.config
- Turing.Tape.nth
- Turing.TM1to1.trTape'
- PFunctor.M.iselect
- Turing.ListBlank.append
- Turing.Tape.map
- Turing.Tape.right₀
- ManyOneDegree.of
- SymbolicDynamics.FullShift.Pattern.occursInAt
- Turing.Tape.left
- SymbolicDynamics.FullShift.Pattern.mulOccursInAt
- List.head!_mem_self
- Turing.ListBlank.flatMap
- Turing.Tape.right
- PFunctor.M.isubtree
- List.cons_head!_tail
- toNat
- Turing.ListBlank.modifyNth
- Turing.TM0.step
- Turing.BlankExtends
- Option.iget
- Turing.ListBlank.induction_on
- Turing.TM1.Supports
- Turing.TM0.Machine
- Turing.ListBlank.nth_succ
- Turing.BlankRel
- List.takeI
- SymbolicDynamics.FullShift.Pattern.shift
- Turing.ListBlank.nth_map