Control.Comonad.Transformerless.Env

newtype Env e a

Constructors

• Env (Tuple e a)

Instances

• Newtype (Env e a) _
• Functor (Env e)
• Extend (Env e)
  1. Law: extend f <<< extend g = extend (f <<< extend g)
  2. Proof:
  3. First, rewrite in pointful form:
  4. (extend f <<< extend g) x = extend (f <<< extend g) x
  5. RHS := extend (f <<< extend g) x =
  6. extend (\ y -> f (extend g y)) x =
  7. extend (\ (y1, y2) -> f (extend g (y1, y2))) (x1, x2) =
  8. extend (\ (y1, y2) -> f (y1, g (y1, y2))) (x1, x2) =
  9. (x1, (\ (y1, y2) -> f (y1, g (y1, y2))) (x1, x2)) =
  10. (x1, f (x1, g (x1, x2)))
  11. LHS := (\ y -> extend f (extend g y)) x =
  12. (\ (y1, y2) -> extend f (extend g (y1, y2))) (x1, x2) =
  13. (\ (y1, y2) -> extend f (y1, g (y1, y2))) (x1, x2) =
  14. (\ (y1, y2) -> (y1, f (y1, g (y1, y2)))) (x1, x2) =
  15. (x1, f (x1, g (x1, x2)))
• Comonad (Env e)
  1. Law: extract <<= xs = xs
  2. Proof:
  3. LHS := extend extract xs =
  4. extend extract (x1, x2) =
  5. (x1, extract (x1, x2)) =
  6. (x1, x2)
  7. RHS := (x1, x2)
  8. Law: extract (f <<= xs) = f xs
  9. Proof:
  10. LHS := extract (extend f xs) =
  11. extract (extend f (x1, x2)) =
  12. extract (x1, f (x1, x2)) =
  13. f (x1, x2)
  14. 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