Functor Laws, applicative laws, and monad Laws

def StateT.mk {σ : Type u} {m : Type u → Type v} {α : Type u} (f : σ → m (α × σ)) : StateT σ m α

Equations

• StateT.mk f = f

@[simp]

theorem StateT.run_mk {σ : Type u} {m : Type u → Type v} {α : Type u} (f : σ → m (α × σ)) (st : σ) : (StateT.mk f).run st = f st

@[simp]

theorem ExceptT.run_monadLift {α ε : Type u} {m : Type u → Type v} {n : Type u → Type u_1} [Monad m] [MonadLiftT n m] (x : n α) : (monadLift x).run = Except.ok <$> monadLift x

@[simp]

theorem ExceptT.run_monadMap {α ε : Type u} {m : Type u → Type v} (x : ExceptT ε m α) {n : Type u → Type u_1} [MonadFunctorT n m] (f : {α : Type u} → n α → n α) : (monadMap f x).run = monadMap f x.run

def ReaderT.mk {m : Type u → Type v} {α σ : Type u} (f : σ → m α) : ReaderT σ m α

Equations

• ReaderT.mk f = f

@[simp]

theorem ReaderT.run_mk {m : Type u → Type v} {α σ : Type u} (f : σ → m α) (r : σ) : (ReaderT.mk f).run r = f r