Documentation

Mathlib.Tactic.FunProp.StateList

The combined state and list monad transformer. StateListT σ α is equivalent to StateT σ (ListT α) but more efficient.

WARNING: StateListT σ α m is only a monad if m is a commutative monad. For example,

def problem : StateListT Unit (StateM (Array Nat)) Unit := do
  Alternative.orElse (pure ()) (fun _ => pure ())
  StateListT.lift $ modify (·.push 0)
  StateListT.lift $ modify (·.push 1)

#eval ((problem.run' ()).run #[]).2

will yield either #[0,1,0,1], or #[0,0,1,1], depending on the order in which the actions in the do block are combined.

StateList

inductive Mathlib.Meta.FunProp.StateList (σ : Type u) (α : Type u) :

StateList is a List with a state associated to each element. This is used instead of List (α × σ) as it is more efficient.

Instances For
    Equations
    • Mathlib.Meta.FunProp.StateList.instAppend = { append := Mathlib.Meta.FunProp.StateList.append }
    def Mathlib.Meta.FunProp.StateListT (σ : Type u) (m : Type u → Type v) (α : Type u) :
    Type (max u v)

    The combined state and list monad transformer.

    Equations
    Instances For
      @[inline]
      def Mathlib.Meta.FunProp.StateListT.run {α : Type u} {σ : Type u} {m : Type u → Type v} [Functor m] (x : Mathlib.Meta.FunProp.StateListT σ m α) (s : σ) :
      m (List (α × σ))

      Run x on a given state s, returning the list of values with corresponding states.

      Equations
      • x.run s = Mathlib.Meta.FunProp.StateList.toList <$> x s
      Instances For
        @[inline]
        def Mathlib.Meta.FunProp.StateListT.run' {α : Type u} {σ : Type u} {m : Type u → Type v} [Functor m] (x : Mathlib.Meta.FunProp.StateListT σ m α) (s : σ) :
        m (List α)

        Run x on a given state s, returning the list of values.

        Equations
        • x.run' s = Mathlib.Meta.FunProp.StateList.toList' <$> x s
        Instances For
          @[reducible, inline]
          abbrev Mathlib.Meta.FunProp.StateListM (σ : Type u) (α : Type u) :

          The combined state and list monad.

          Equations
          Instances For
            @[always_inline]
            Equations
            • Mathlib.Meta.FunProp.StateListT.instMonad = Monad.mk
            Equations
            • Mathlib.Meta.FunProp.StateListT.instAlternative = Alternative.mk (fun {α : Type ?u.27} => Mathlib.Meta.FunProp.StateListT.failure) fun {α : Type ?u.27} => Mathlib.Meta.FunProp.StateListT.orElse
            @[inline]

            Return the state from StateListT σ m.

            Equations
            Instances For
              @[inline]

              Set the state in StateListT σ m.

              Equations
              Instances For
                @[inline]
                def Mathlib.Meta.FunProp.StateListT.modifyGet {α : Type u} {σ : Type u} {m : Type u → Type v} [Monad m] (f : σα × σ) :

                Modify and get the state in StateListT σ m.

                Equations
                Instances For
                  @[inline]
                  def Mathlib.Meta.FunProp.StateListT.lift {α : Type u} {σ : Type u} {m : Type u → Type v} [Monad m] (t : m α) :

                  Lift an action from m α to StateListT σ m α.

                  Equations
                  Instances For
                    Equations
                    • Mathlib.Meta.FunProp.StateListT.instMonadLift = { monadLift := fun {α : Type ?u.26} => Mathlib.Meta.FunProp.StateListT.lift }
                    @[always_inline]
                    Equations
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                    @[always_inline]
                    Equations
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                    Equations
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                    @[always_inline]
                    Equations
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