Loogle!

Result

Found 9 declarations mentioning Turing.Tape.map.

• Turing.Tape.map 📋 Mathlib.Computability.Tape
  {Γ : Type u_1} {Γ' : Type u_2} [Inhabited Γ] [Inhabited Γ'] (f : Turing.PointedMap Γ Γ') (T : Turing.Tape Γ) : Turing.Tape Γ'
• Turing.Tape.map_fst 📋 Mathlib.Computability.Tape
  {Γ : Type u_1} {Γ' : Type u_2} [Inhabited Γ] [Inhabited Γ'] (f : Turing.PointedMap Γ Γ') (T : Turing.Tape Γ) : (Turing.Tape.map f T).head = f.f T.head
• Turing.Tape.map_mk₁ 📋 Mathlib.Computability.Tape
  {Γ : Type u_1} {Γ' : Type u_2} [Inhabited Γ] [Inhabited Γ'] (f : Turing.PointedMap Γ Γ') (l : List Γ) : Turing.Tape.map f (Turing.Tape.mk₁ l) = Turing.Tape.mk₁ (List.map f.f l)
• Turing.Tape.map_move 📋 Mathlib.Computability.Tape
  {Γ : Type u_1} {Γ' : Type u_2} [Inhabited Γ] [Inhabited Γ'] (f : Turing.PointedMap Γ Γ') (T : Turing.Tape Γ) (d : Turing.Dir) : Turing.Tape.map f (Turing.Tape.move d T) = Turing.Tape.move d (Turing.Tape.map f T)
• Turing.Tape.map_write 📋 Mathlib.Computability.Tape
  {Γ : Type u_1} {Γ' : Type u_2} [Inhabited Γ] [Inhabited Γ'] (f : Turing.PointedMap Γ Γ') (b : Γ) (T : Turing.Tape Γ) : Turing.Tape.map f (Turing.Tape.write b T) = Turing.Tape.write (f.f b) (Turing.Tape.map f T)
• Turing.Tape.map_mk' 📋 Mathlib.Computability.Tape
  {Γ : Type u_1} {Γ' : Type u_2} [Inhabited Γ] [Inhabited Γ'] (f : Turing.PointedMap Γ Γ') (L R : Turing.ListBlank Γ) : Turing.Tape.map f (Turing.Tape.mk' L R) = Turing.Tape.mk' (Turing.ListBlank.map f L) (Turing.ListBlank.map f R)
• Turing.Tape.map_mk₂ 📋 Mathlib.Computability.Tape
  {Γ : Type u_1} {Γ' : Type u_2} [Inhabited Γ] [Inhabited Γ'] (f : Turing.PointedMap Γ Γ') (L R : List Γ) : Turing.Tape.map f (Turing.Tape.mk₂ L R) = Turing.Tape.mk₂ (List.map f.f L) (List.map f.f R)
• Turing.Tape.map.eq_1 📋 Mathlib.Computability.Tape
  {Γ : Type u_1} {Γ' : Type u_2} [Inhabited Γ] [Inhabited Γ'] (f : Turing.PointedMap Γ Γ') (T : Turing.Tape Γ) : Turing.Tape.map f T = { head := f.f T.head, left := Turing.ListBlank.map f T.left, right := Turing.ListBlank.map f T.right }
• 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 }

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