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

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

  • nil {σ α : Type u} : StateList σ α

    .nil is the empty list.

  • cons {σ α : Type u} : α → σ → StateList σ α → StateList σ α

    If a : α, s : σ and l : List α, then .cons a s l, is the list with first element a with state s and l as the rest of the list.

Instances For
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instance Mathlib.Meta.FunProp.StateList.instAppend {α σ : Type u} :
Append (StateList σ α)
Equations
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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.

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

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

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@[reducible, inline]
abbrev Mathlib.Meta.FunProp.StateListM (σ α : Type u) :
Type u

The combined state and list monad.

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@[always_inline]
instance Mathlib.Meta.FunProp.StateListT.instMonad {σ : Type u} {m : Type u → Type v} [Monad m] :
Monad (StateListT σ m)
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instance Mathlib.Meta.FunProp.StateListT.instAlternative {σ : Type u} {m : Type u → Type v} [Monad m] :
Alternative (StateListT σ m)
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  • One or more equations did not get rendered due to their size.
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@[inline]
def Mathlib.Meta.FunProp.StateListT.get {σ : Type u} {m : Type u → Type v} [Monad m] :
StateListT σ m σ

Return the state from StateListT σ m.

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@[inline]
def Mathlib.Meta.FunProp.StateListT.set {σ : Type u} {m : Type u → Type v} [Monad m] :
σ → StateListT σ m PUnit

Set the state in StateListT σ m.

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

Modify and get the state in StateListT σ m.

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

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

Equations
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instance Mathlib.Meta.FunProp.StateListT.instMonadLift {σ : Type u} {m : Type u → Type v} [Monad m] :
MonadLift m (StateListT σ m)
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@[always_inline]
instance Mathlib.Meta.FunProp.StateListT.instMonadFunctor {σ : Type u} {m : Type u → Type v} :
MonadFunctor m (StateListT σ m)
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@[always_inline]
instance Mathlib.Meta.FunProp.StateListT.instMonadExceptOf {σ : Type u} {m : Type u → Type v} [Monad m] {ε : Type u_1} [MonadExceptOf ε m] :
MonadExceptOf ε (StateListT σ m)
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instance Mathlib.Meta.FunProp.instMonadStateOfStateListT {σ : Type u} {m : Type u → Type v} [Monad m] :
MonadStateOf σ (StateListT σ m)
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@[always_inline]
instance Mathlib.Meta.FunProp.StateListT.monadControl {σ : Type u} {m : Type u → Type v} [Monad m] :
MonadControl m (StateListT σ m)
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  • One or more equations did not get rendered due to their size.