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 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.

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

instance Mathlib.Meta.FunProp.StateList.instAppend {α σ : Type u} :

Append (StateList σ α)

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

Mathlib.Meta.FunProp.StateListT σ m α = (σ → m (Mathlib.Meta.FunProp.StateList σ α))

Instances For

@[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

x.run s = Mathlib.Meta.FunProp.StateList.toList✝ <$> x s

Instances For

@[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.

Equations

x.run' s = Mathlib.Meta.FunProp.StateList.toList'✝ <$> x s

Instances For

@[reducible, inline]

abbrev Mathlib.Meta.FunProp.StateListM (σ α : Type u) :

The combined state and list monad.

Equations

Mathlib.Meta.FunProp.StateListM σ α = Mathlib.Meta.FunProp.StateListT σ Id α

Instances For

@[always_inline]

instance Mathlib.Meta.FunProp.StateListT.instMonad {σ : Type u} {m : Type u → Type v} [Monad m] :

Monad (StateListT σ m)

Equations

Mathlib.Meta.FunProp.StateListT.instMonad = Monad.mk

instance Mathlib.Meta.FunProp.StateListT.instAlternative {σ : Type u} {m : Type u → Type v} [Monad m] :

Alternative (StateListT σ m)

Equations

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

@[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.

Equations

Mathlib.Meta.FunProp.StateListT.get s = pure (Mathlib.Meta.FunProp.StateList.cons s s Mathlib.Meta.FunProp.StateList.nil)

Instances For

@[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

Mathlib.Meta.FunProp.StateListT.set s' x✝ = pure (Mathlib.Meta.FunProp.StateList.cons PUnit.unit s' Mathlib.Meta.FunProp.StateList.nil)

Instances For

@[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.

Equations

Mathlib.Meta.FunProp.StateListT.modifyGet f s = pure (Mathlib.Meta.FunProp.StateList.cons (f s).fst (f s).snd Mathlib.Meta.FunProp.StateList.nil)

Instances For

@[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

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

Instances For

instance Mathlib.Meta.FunProp.StateListT.instMonadLift {σ : Type u} {m : Type u → Type v} [Monad m] :

MonadLift m (StateListT σ m)

Equations

Mathlib.Meta.FunProp.StateListT.instMonadLift = { monadLift := fun {α : Type ?u.26} => Mathlib.Meta.FunProp.StateListT.lift }

@[always_inline]

instance Mathlib.Meta.FunProp.StateListT.instMonadFunctor {σ : Type u} {m : Type u → Type v} :

MonadFunctor m (StateListT σ m)

Equations

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

@[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)

Equations

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

instance Mathlib.Meta.FunProp.instMonadStateOfStateListT {σ : Type u} {m : Type u → Type v} [Monad m] :

MonadStateOf σ (StateListT σ m)

Equations

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

@[always_inline]

instance Mathlib.Meta.FunProp.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.