Control.Comonad.Transformerless.Env

newtype Env e a

Constructors

• Env (Tuple e a)

Instances

• Newtype (Env e a) _
• Functor (Env e)
• Extend (Env e)

  Law: extend f <<< extend g = extend (f <<< extend g) Proof: First, rewrite in pointful form: (extend f <<< extend g) x = extend (f <<< extend g) x RHS := extend (f <<< extend g) x = extend (\ y -> f (extend g y)) x = extend (\ (y1, y2) -> f (extend g (y1, y2))) (x1, x2) = extend (\ (y1, y2) -> f (y1, g (y1, y2))) (x1, x2) = (x1, (\ (y1, y2) -> f (y1, g (y1, y2))) (x1, x2)) = (x1, f (x1, g (x1, x2))) LHS := (\ y -> extend f (extend g y)) x = (\ (y1, y2) -> extend f (extend g (y1, y2))) (x1, x2) = (\ (y1, y2) -> extend f (y1, g (y1, y2))) (x1, x2) = (\ (y1, y2) -> (y1, f (y1, g (y1, y2)))) (x1, x2) = (x1, f (x1, g (x1, x2)))

• Comonad (Env e)

  Law: extract <<= xs = xs Proof: LHS := extend extract xs = extend extract (x1, x2) = (x1, extract (x1, x2)) = (x1, x2) RHS := (x1, x2) Law: extract (f <<= xs) = f xs Proof: LHS := extract (extend f xs) = extract (extend f (x1, x2)) = extract (x1, f (x1, x2)) = f (x1, x2) RHS := f (x1, x2)

runEnv :: forall a e. Env e a -> Tuple e a

withEnv :: forall a e2 e1. (e1 -> e2) -> Env e1 a -> Env e2 a

mapEnv :: forall e b a. (a -> b) -> Env e a -> Env e b

env :: forall e a. e -> a -> Env e a

ask :: forall e a. Env e a -> e

asks :: forall e2 e1 a. (e1 -> e2) -> Env e1 a -> e2

local :: forall a e. (e -> e) -> Env e a -> Env e a