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Mathlib.Tactic.DeriveTraversable

Deriving handler for Traversable instances #

This module gives deriving handlers for Functor, LawfulFunctor, Traversable, and LawfulTraversable. These deriving handlers automatically derive their dependencies, for example deriving LawfulTraversable all by itself gives all four.

nestedMap f α (List (Array (List α))) synthesizes the expression Functor.map (Functor.map (Functor.map f)). nestedMap assumes that α appears in (List (Array (List α))).

(Similar to nestedTraverse but for Functor.)

similar to traverseField but for Functor

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    Get the auxiliary local declaration corresponding to the current declaration. If there are multiple declaraions it will throw.

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      similar to traverseConstructor but for Functor

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        Makes a match expression corresponding to the application of casesOn like:

        match (motive := motive) indices₁, indices₂, .., (val : type.{univs} params₁ params₂ ..) with
        | _, _, .., ctor₁ fields₁₁ fields₁₂ .. => rhss ctor₁ [fields₁₁, fields₁₂, ..]
        | _, _, .., ctor₂ fields₂₁ fields₂₂ .. => rhss ctor₂ [fields₂₁, fields₂₂, ..]
        

        This is convenient to make a definition with equation lemmas.

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          Get FVarIds which is not implementation details in the current context.

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            derive the map definition of a Functor

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              derive the map definition and declare Functor using this.

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                Similar to mkInstanceName, but for a Expr type.

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                  Derive the cls instance for the inductive type constructor n using the tac tactic.

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                    Make the new deriving handler depends on other deriving handlers.

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                      Prove the functor laws and derive LawfulFunctor.

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                        The deriving handler for LawfulFunctor.

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                          nestedTraverse f α (List (Array (List α))) synthesizes the expression traverse (traverse (traverse f)). nestedTraverse assumes that α appears in (List (Array (List α)))

                          For a sum type inductive Foo (α : Type) | foo1 : List α → ℕ → Foo α | ... traverseField `Foo f `α `(x : List α) synthesizes traverse f x as part of traversing foo1.

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                            For a sum type inductive Foo (α : Type) | foo1 : List α → ℕ → Foo α | ... traverseConstructor `foo1 `Foo applInst f `α `β [`(x : List α), `(y : ℕ)] synthesizes foo1 <$> traverse f x <*> pure y.

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                              mkFunCtor ctor [(true, (arg₁ : m type₁)), (false, (arg₂ : type₂)), (true, (arg₃ : m type₃)), (false, (arg₄ : type₄))] makes fun (x₁ : type₁) (x₃ : type₃) => ctor x₁ arg₂ x₃ arg₄.

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                                derive the traverse definition of a Traversable instance

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                                  derive the traverse definition and declare Traversable using this.

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                                    The deriving handler for Traversable.

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                                      def Mathlib.Deriving.Traversable.simpFunctorGoal (m : Lean.MVarId) (s : Lean.Meta.Simp.Context) (simprocs : optParam Lean.Meta.Simp.SimprocsArray ) (discharge? : optParam (Option Lean.Meta.Simp.Discharge) none) (simplifyTarget : optParam Bool true) (fvarIdsToSimp : optParam (Array Lean.FVarId) #[]) (stats : optParam Lean.Meta.Simp.Stats { usedTheorems := { map := { root := Lean.PersistentHashMap.Node.entries Lean.PersistentHashMap.mkEmptyEntriesArray }, size := 0 }, diag := { usedThmCounter := { root := Lean.PersistentHashMap.Node.entries Lean.PersistentHashMap.mkEmptyEntriesArray }, triedThmCounter := { root := Lean.PersistentHashMap.Node.entries Lean.PersistentHashMap.mkEmptyEntriesArray }, congrThmCounter := { root := Lean.PersistentHashMap.Node.entries Lean.PersistentHashMap.mkEmptyEntriesArray }, thmsWithBadKeys := { root := Lean.PersistentArrayNode.node (Array.mkEmpty Lean.PersistentArray.branching.toNat), tail := Array.mkEmpty Lean.PersistentArray.branching.toNat, size := 0, shift := Lean.PersistentArray.initShift, tailOff := 0 } } }) :

                                      Simplify the goal m using functor_norm.

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                                        Run the following tactic:

                                        intros _ .. x
                                        dsimp only [Traversable.traverse, Functor.map]
                                        induction x <;> (the simp tactic corresponding to s) <;> (tac)
                                        
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                                          Prove the traversable laws and derive LawfulTraversable.

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                                            The deriving handler for LawfulTraversable.

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