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Theorems · Definition · logic and foundations

Turing.TM0.Machine.map

{Γ : Type u_1} →
  [inst : Inhabited Γ] →
    {Γ' : Type u_2} →
      [inst_1 : Inhabited Γ'] →
        {Λ : Type u_3} →
          [inst_2 : Inhabited Λ] →
            {Λ' : Type u_4} →
              [inst_3 : Inhabited Λ'] →
                Turing.TM0.Machine Γ Λ →
                  Turing.PointedMap Γ Γ' → Turing.PointedMap Γ' Γ → (Λ → Λ') → (Λ' → Λ) → Turing.TM0.Machine Γ' Λ'

Because the state transition function uses the alphabet and machine states in both the input and output, to map a machine from one alphabet and machine state space to another we need functions in both directions, essentially an Equiv without the laws.

Defined in
Mathlib.Computability.TuringMachine.PostTuringMachine
Cited by
2 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
InhabitedInhabitedInhabitedInhabited
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Turing.TM0.Machine.map_step · cited by 1Machine.map_stepTuring.TM0.Machine.map_respects · cited by 0Machine.map_respectsTuring.PointedMap.f · cited by 24PointedMap.fTuring.PointedMap · cited by 24Turing.PointedMapTuring.TM0.Stmt · cited by 16TM0.StmtTuring.TM0.Machine · cited by 5TM0.MachineTuring.TM0.Stmt.map · cited by 1Stmt.mapMachine.mapCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.