Loogle!

Result

Found 5 declarations mentioning Turing.TM0.Cfg.map.

• Turing.TM0.Cfg.map 📋 Mathlib.Computability.PostTuringMachine
  {Γ : Type u_1} [Inhabited Γ] {Γ' : Type u_2} [Inhabited Γ'] {Λ : Type u_3} {Λ' : Type u_4} (f : Turing.PointedMap Γ Γ') (g : Λ → Λ') : Turing.TM0.Cfg Γ Λ → Turing.TM0.Cfg Γ' Λ'
• Turing.TM0.Cfg.map.eq_1 📋 Mathlib.Computability.PostTuringMachine
  {Γ : Type u_1} [Inhabited Γ] {Γ' : Type u_2} [Inhabited Γ'] {Λ : Type u_3} {Λ' : Type u_4} (f : Turing.PointedMap Γ Γ') (g : Λ → Λ') (q : Λ) (T : Turing.Tape Γ) : Turing.TM0.Cfg.map f g { q := q, Tape := T } = { q := g q, Tape := Turing.Tape.map f T }
• Turing.TM0.map_init 📋 Mathlib.Computability.PostTuringMachine
  {Γ : Type u_1} [Inhabited Γ] {Γ' : Type u_2} [Inhabited Γ'] {Λ : Type u_3} [Inhabited Λ] {Λ' : Type u_4} [Inhabited Λ'] (f₁ : Turing.PointedMap Γ Γ') (g₁ : Turing.PointedMap Λ Λ') (l : List Γ) : Turing.TM0.Cfg.map f₁ g₁.f (Turing.TM0.init l) = Turing.TM0.init (List.map f₁.f l)
• Turing.TM0.Machine.map_step 📋 Mathlib.Computability.PostTuringMachine
  {Γ : Type u_1} [Inhabited Γ] {Γ' : Type u_2} [Inhabited Γ'] {Λ : Type u_3} [Inhabited Λ] {Λ' : Type u_4} [Inhabited Λ'] (M : Turing.TM0.Machine Γ Λ) (f₁ : Turing.PointedMap Γ Γ') (f₂ : Turing.PointedMap Γ' Γ) (g₁ : Λ → Λ') (g₂ : Λ' → Λ) {S : Set Λ} (f₂₁ : Function.RightInverse f₁.f f₂.f) (g₂₁ : ∀ q ∈ S, g₂ (g₁ q) = q) (c : Turing.TM0.Cfg Γ Λ) : c.q ∈ S → Option.map (Turing.TM0.Cfg.map f₁ g₁) (Turing.TM0.step M c) = Turing.TM0.step (M.map f₁ f₂ g₁ g₂) (Turing.TM0.Cfg.map f₁ g₁ c)
• Turing.TM0.Machine.map_respects 📋 Mathlib.Computability.PostTuringMachine
  {Γ : Type u_1} [Inhabited Γ] {Γ' : Type u_2} [Inhabited Γ'] {Λ : Type u_3} [Inhabited Λ] {Λ' : Type u_4} [Inhabited Λ'] (M : Turing.TM0.Machine Γ Λ) (f₁ : Turing.PointedMap Γ Γ') (f₂ : Turing.PointedMap Γ' Γ) (g₁ : Turing.PointedMap Λ Λ') (g₂ : Λ' → Λ) {S : Set Λ} (ss : Turing.TM0.Supports M S) (f₂₁ : Function.RightInverse f₁.f f₂.f) (g₂₁ : ∀ q ∈ S, g₂ (g₁.f q) = q) : Turing.Respects (Turing.TM0.step M) (Turing.TM0.step (M.map f₁ f₂ g₁.f g₂)) fun a b => a.q ∈ S ∧ Turing.TM0.Cfg.map f₁ g₁.f a = b

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using (by default) Ctrl-K Ctrl-S. You can also try the #loogle command from LeanSearchClient, the CLI version, the Loogle VS Code extension, the lean.nvim integration or the Zulip bot.

Usage

Loogle finds definitions and lemmas in various ways:

1. By constant:
   🔍 Real.sin
   finds all lemmas whose statement somehow mentions the sine function.

2. By lemma name substring:
   🔍 "differ"
   finds all lemmas that have "differ" somewhere in their lemma name.

3. By subexpression:
   🔍 _ * (_ ^ _)
   finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.

   The pattern can also be non-linear, as in
   🔍 Real.sqrt ?a * Real.sqrt ?a

   If the pattern has parameters, they are matched in any order. Both of these will find List.map:
   🔍 (?a -> ?b) -> List ?a -> List ?b
   🔍 List ?a -> (?a -> ?b) -> List ?b

4. By main conclusion:
   🔍 |- tsum _ = _ * tsum _
   finds all lemmas where the conclusion (the subexpression to the right of all → and ∀) has the given shape.

   As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example,
   🔍 |- _ < _ → tsum _ < tsum _
   will find tsum_lt_tsum even though the hypothesis f i < g i is not the last.

If you pass more than one such search filter, separated by commas Loogle will return lemmas which match all of them. The search
🔍 Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _
would find all lemmas which mention the constants Real.sin and tsum, have "two" as a substring of the lemma name, include a product and a power somewhere in the type, and have a hypothesis of the form _ < _ (if there were any such lemmas). Metavariables (?a) are assigned independently in each filter.

The #lucky button will directly send you to the documentation of the first hit.

Source code

You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is provided by the Lean FRO.

This is Loogle revision 19971e9 serving mathlib revision bce1d65