The combined state and list monad transformer.

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. v

inductive StateList (σ : Type u) (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.

instance StateList.instAppendStateList {α : Type u} {σ : Type u} : Append (StateList σ α)

Equations

• StateList.instAppendStateList = { append := StateList.append }

def StateListT (σ : Type u) (m : Type u → Type v) (α : Type u) : Type (max u v)

The combined state and list monad transformer.

Equations

• StateListT σ m α = (σ → m (StateList σ α))

@[inline]

def StateListT.run {α : Type u} {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

• StateListT.run x s = StateList.toList <$> x s

@[inline]

def StateListT.run' {α : Type u} {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.

Equations

• StateListT.run' x s = StateList.toList' <$> x s

@[reducible]

def StateListM (σ : Type u) (α : Type u) : Type u

The combined state and list monad.

Equations

• StateListM σ α = StateListT σ Id α

@[always_inline]

instance StateListT.instMonadStateListT {σ : Type u} {m : Type u → Type v} [Monad m] : Monad (StateListT σ m)

Equations

• StateListT.instMonadStateListT = Monad.mk

instance StateListT.instAlternativeStateListT {σ : Type u} {m : Type u → Type v} [Monad m] : Alternative (StateListT σ m)

Equations

• StateListT.instAlternativeStateListT = Alternative.mk (fun {α : Type u} => StateListT.failure) fun {α : Type u} => StateListT.orElse

@[inline]

def StateListT.get {σ : Type u} {m : Type u → Type v} [Monad m] : StateListT σ m σ

Return the state from StateListT σ m.

Equations

• StateListT.get s = pure (StateList.cons s s StateList.nil)

@[inline]

def 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

• StateListT.set s' x = pure (StateList.cons PUnit.unit s' StateList.nil)

@[inline]

def StateListT.modifyGet {α : Type u} {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.

Equations

• StateListT.modifyGet f s = let a := f s; pure (StateList.cons a.fst a.snd StateList.nil)

@[inline]

def StateListT.lift {α : Type u} {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

• StateListT.lift t s = do let a ← t pure (StateList.cons a s StateList.nil)

instance StateListT.instMonadLiftStateListT {σ : Type u} {m : Type u → Type v} [Monad m] : MonadLift m (StateListT σ m)

Equations

• StateListT.instMonadLiftStateListT = { monadLift := fun {α : Type u} => StateListT.lift }

@[always_inline]

instance StateListT.instMonadFunctorStateListT {σ : Type u} {m : Type u → Type v} : MonadFunctor m (StateListT σ m)

Equations

• StateListT.instMonadFunctorStateListT = { monadMap := fun {α : Type u} (f : {β : Type u} → m β → m β) (x : StateListT σ m α) (s : σ) => f (x s) }

@[always_inline]

instance StateListT.instMonadExceptOfStateListT {σ : Type u} {m : Type u → Type v} [Monad m] {ε : Type w} [MonadExceptOf ε m] : MonadExceptOf ε (StateListT σ m)

Equations

• One or more equations did not get rendered due to their size.

instance instMonadStateOfStateListT {σ : Type u} {m : Type u → Type v} [Monad m] : MonadStateOf σ (StateListT σ m)

Equations

• instMonadStateOfStateListT = { get := StateListT.get, set := StateListT.set, modifyGet := fun {α : Type u} => StateListT.modifyGet }

@[always_inline]

instance StateListT.monadControl {σ : Type u} {m : Type u → Type v} [Monad m] : MonadControl m (StateListT σ m)

Equations

• One or more equations did not get rendered due to their size.