Fcf.Alg.List

Fcf.Alg.List

Type-level ListF to be used with Cata, Ana and Hylo.

This module also contains other list-related functions (that might move to other place some day).

Documentation

>>> import           Fcf.Combinators

data ListF a b

Base functor for a list of type [a].

Constructors

ConsF a b

NilF

Instances

type Eval (DedupAlg (ConsF ((,) a2 as) ((,) _fxs past)) :: [a1] -> Type)

Defined in Fcf.Alg.List

type Eval (DedupAlg (ConsF ((,) a2 as) ((,) _fxs past)) :: [a1] -> Type) = Eval (If (Eval (TyEq (Eval (Elem a2 past)) True)) (Pure past) (Pure (a2 ': as)))

type Eval (DedupAlg (NilF :: ListF (a, [a]) (Fix (ListF (a, [a])), [a])) :: [a] -> Type)

Defined in Fcf.Alg.List

type Eval (DedupAlg (NilF :: ListF (a, [a]) (Fix (ListF (a, [a])), [a])) :: [a] -> Type) = ([] :: [a])

type Eval (EvensStrip (ConsF x y) :: [a] -> Type)

Defined in Fcf.Alg.List

type Eval (EvensStrip (ConsF x y) :: [a] -> Type) = x ': Eval (Attr y)

type Eval (EvensStrip (NilF :: ListF a (Ann (ListF a) [a])) :: [a] -> Type)

Defined in Fcf.Alg.List

type Eval (EvensStrip (NilF :: ListF a (Ann (ListF a) [a])) :: [a] -> Type) = ([] :: [a])

type Eval (EvensAlg (ConsF _ rst) :: [a] -> Type)

Defined in Fcf.Alg.List

type Eval (EvensAlg (ConsF _ rst) :: [a] -> Type) = Eval ((EvensStrip :: ListF a (Ann (ListF a) [a]) -> [a] -> Type) =<< Strip rst)

type Eval (EvensAlg (NilF :: ListF a (Ann (ListF a) [a])) :: [a] -> Type)

Defined in Fcf.Alg.List

type Eval (EvensAlg (NilF :: ListF a (Ann (ListF a) [a])) :: [a] -> Type) = ([] :: [a])

type Eval (ListToParaFix (a2 ': as) :: Fix (ListF (a1, [a1])) -> Type)

Defined in Fcf.Alg.List

type Eval (ListToParaFix (a2 ': as) :: Fix (ListF (a1, [a1])) -> Type) = Fix (ConsF ((,) a2 as) (Eval (ListToParaFix as)))

type Eval (ListToParaFix ([] :: [a]) :: Fix (ListF (a, [a])) -> Type)

Defined in Fcf.Alg.List

type Eval (ListToParaFix ([] :: [a]) :: Fix (ListF (a, [a])) -> Type) = Fix (NilF :: ListF (a, [a]) (Fix (ListF (a, [a]))))

type Eval (ListToFix (a2 ': as) :: Fix (ListF a1) -> Type)

Defined in Fcf.Alg.List

type Eval (ListToFix (a2 ': as) :: Fix (ListF a1) -> Type) = Fix (ConsF a2 (Eval (ListToFix as)))

type Eval (ListToFix ([] :: [a]) :: Fix (ListF a) -> Type)

Defined in Fcf.Alg.List

type Eval (ListToFix ([] :: [a]) :: Fix (ListF a) -> Type) = Fix (NilF :: ListF a (Fix (ListF a)))

type Eval (SlidingAlg n (ConsF ((,) a2 as) ((,) _fxs past)) :: [[a1]] -> Type)

Defined in Fcf.Alg.List

type Eval (SlidingAlg n (ConsF ((,) a2 as) ((,) _fxs past)) :: [[a1]] -> Type) = Eval (Take n (a2 ': as)) ': past

type Eval (SlidingAlg _ (NilF :: ListF (a, [a]) (Fix (ListF (a, [a])), [[a]])) :: [[a]] -> Type)

Defined in Fcf.Alg.List

type Eval (SlidingAlg _ (NilF :: ListF (a, [a]) (Fix (ListF (a, [a])), [[a]])) :: [[a]] -> Type) = ([] :: [[a]])

type Eval (FMap f (ConsF a3 b2) :: ListF a2 b1 -> Type)

Defined in Fcf.Alg.List

type Eval (FMap f (ConsF a3 b2) :: ListF a2 b1 -> Type) = ConsF a3 (Eval (f b2))

type Eval (FMap f (NilF :: ListF a2 a1) :: ListF a2 b -> Type)

Defined in Fcf.Alg.List

type Eval (FMap f (NilF :: ListF a2 a1) :: ListF a2 b -> Type) = (NilF :: ListF a2 b)

data ListToFix :: [a] -> Exp (Fix (ListF a))

ListToFix can be used to turn a norma type-level list into the base functor type ListF, to be used with e.g. Cata. For examples in use, see LenAlg and SumAlg.

Ideally, we would have one ToFix type-level function for which we could give type instances for different type-level types, like lists, trees etc. See TODO.md.

Example

>>> :kind! Eval (ListToFix '[1,2,3])
Eval (ListToFix '[1,2,3]) :: Fix (ListF Nat)
= 'Fix ('ConsF 1 ('Fix ('ConsF 2 ('Fix ('ConsF 3 ('Fix 'NilF))))))

Instances

type Eval (ListToFix (a2 ': as) :: Fix (ListF a1) -> Type)

Defined in Fcf.Alg.List

type Eval (ListToFix (a2 ': as) :: Fix (ListF a1) -> Type) = Fix (ConsF a2 (Eval (ListToFix as)))

type Eval (ListToFix ([] :: [a]) :: Fix (ListF a) -> Type)

Defined in Fcf.Alg.List

type Eval (ListToFix ([] :: [a]) :: Fix (ListF a) -> Type) = Fix (NilF :: ListF a (Fix (ListF a)))

data LenAlg :: Algebra (ListF a) Nat

Example algebra to calculate list length.

Example

>>> :kind! Eval (Cata LenAlg =<< ListToFix '[1,2,3])
Eval (Cata LenAlg =<< ListToFix '[1,2,3]) :: Nat
= 3

Instances

type Eval (LenAlg (ConsF a2 b) :: Nat -> Type)

Defined in Fcf.Alg.List

type Eval (LenAlg (ConsF a2 b) :: Nat -> Type) = 1 + b

type Eval (LenAlg (NilF :: ListF a Nat) :: Nat -> Type)

Defined in Fcf.Alg.List

type Eval (LenAlg (NilF :: ListF a Nat) :: Nat -> Type) = 0

data SumAlg :: Algebra (ListF Nat) Nat

Example algebra to calculate the sum of Nats in a list.

Example

>>> :kind! Eval (Cata SumAlg =<< ListToFix '[1,2,3,4])
Eval (Cata SumAlg =<< ListToFix '[1,2,3,4]) :: Nat
= 10

Instances

type Eval (SumAlg (ConsF a b) :: Nat -> Type)

Defined in Fcf.Alg.List

type Eval (SumAlg (ConsF a b) :: Nat -> Type) = a + b

type Eval (SumAlg (NilF :: ListF Nat Nat))

Defined in Fcf.Alg.List

type Eval (SumAlg (NilF :: ListF Nat Nat)) = 0

data ProdAlg :: Algebra (ListF Nat) Nat

Example algebra to calculate the prod of Nats in a list.

Example

>>> :kind! Eval (Cata ProdAlg =<< ListToFix '[1,2,3,4])
Eval (Cata ProdAlg =<< ListToFix '[1,2,3,4]) :: Nat
= 24

Instances

type Eval (ProdAlg (ConsF a b) :: Nat -> Type)

Defined in Fcf.Alg.List

type Eval (ProdAlg (ConsF a b) :: Nat -> Type) = a * b

type Eval (ProdAlg (NilF :: ListF Nat Nat))

Defined in Fcf.Alg.List

type Eval (ProdAlg (NilF :: ListF Nat Nat)) = 1

data ListToParaFix :: [a] -> Exp (Fix (ListF (a, [a])))

Form a Fix-structure that can be used with Para.

Example

>>> :kind! Eval (ListToParaFix '[1,2,3])
Eval (ListToParaFix '[1,2,3]) :: Fix (ListF (Nat, [Nat]))
= 'Fix
    ('ConsF
       '(1, '[2, 3])
       ('Fix ('ConsF '(2, '[3]) ('Fix ('ConsF '(3, '[]) ('Fix 'NilF))))))

Instances

type Eval (ListToParaFix (a2 ': as) :: Fix (ListF (a1, [a1])) -> Type)

Defined in Fcf.Alg.List

type Eval (ListToParaFix (a2 ': as) :: Fix (ListF (a1, [a1])) -> Type) = Fix (ConsF ((,) a2 as) (Eval (ListToParaFix as)))

type Eval (ListToParaFix ([] :: [a]) :: Fix (ListF (a, [a])) -> Type)

Defined in Fcf.Alg.List

type Eval (ListToParaFix ([] :: [a]) :: Fix (ListF (a, [a])) -> Type) = Fix (NilF :: ListF (a, [a]) (Fix (ListF (a, [a]))))

data DedupAlg :: RAlgebra (ListF (a, [a])) [a]

Example from recursion-package by Vanessa McHale.

This removes duplicates from a list (by keeping the right-most one).

Example

>>> :kind! Eval (Para DedupAlg =<< ListToParaFix '[1,1,3,2,5,1,3,2])
Eval (Para DedupAlg =<< ListToParaFix '[1,1,3,2,5,1,3,2]) :: [Nat]
= '[5, 1, 3, 2]

Instances

type Eval (DedupAlg (ConsF ((,) a2 as) ((,) _fxs past)) :: [a1] -> Type)

Defined in Fcf.Alg.List

type Eval (DedupAlg (ConsF ((,) a2 as) ((,) _fxs past)) :: [a1] -> Type) = Eval (If (Eval (TyEq (Eval (Elem a2 past)) True)) (Pure past) (Pure (a2 ': as)))

type Eval (DedupAlg (NilF :: ListF (a, [a]) (Fix (ListF (a, [a])), [a])) :: [a] -> Type)

Defined in Fcf.Alg.List

type Eval (DedupAlg (NilF :: ListF (a, [a]) (Fix (ListF (a, [a])), [a])) :: [a] -> Type) = ([] :: [a])

data Sliding :: Nat -> [a] -> Exp [[a]]

Example from Recursion Schemes by example by Tim Williams.

Example

>>> :kind! Eval (Sliding 3 '[1,2,3,4,5,6])
Eval (Sliding 3 '[1,2,3,4,5,6]) :: [[Nat]]
= '[ '[1, 2, 3], '[2, 3, 4], '[3, 4, 5], '[4, 5, 6], '[5, 6], '[6]]

Instances

type Eval (Sliding n lst :: [[a]] -> Type)

Defined in Fcf.Alg.List

type Eval (Sliding n lst :: [[a]] -> Type) = Eval (Para (SlidingAlg n :: ListF (a, [a]) (Fix (ListF (a, [a])), [[a]]) -> [[a]] -> Type) =<< ListToParaFix lst)

data SlidingAlg :: Nat -> RAlgebra (ListF (a, [a])) [[a]]

Tim Williams, Recursion Schemes by example, example for Para. See Sliding-function.

Instances

type Eval (SlidingAlg n (ConsF ((,) a2 as) ((,) _fxs past)) :: [[a1]] -> Type)

Defined in Fcf.Alg.List

type Eval (SlidingAlg n (ConsF ((,) a2 as) ((,) _fxs past)) :: [[a1]] -> Type) = Eval (Take n (a2 ': as)) ': past

type Eval (SlidingAlg _ (NilF :: ListF (a, [a]) (Fix (ListF (a, [a])), [[a]])) :: [[a]] -> Type)

Defined in Fcf.Alg.List

type Eval (SlidingAlg _ (NilF :: ListF (a, [a]) (Fix (ListF (a, [a])), [[a]])) :: [[a]] -> Type) = ([] :: [[a]])

data EvensStrip :: ListF a (Ann (ListF a) [a]) -> Exp [a]

Tim Williams, Recursion Schemes by example, example for Histo.

Instances

type Eval (EvensStrip (ConsF x y) :: [a] -> Type)

Defined in Fcf.Alg.List

type Eval (EvensStrip (ConsF x y) :: [a] -> Type) = x ': Eval (Attr y)

type Eval (EvensStrip (NilF :: ListF a (Ann (ListF a) [a])) :: [a] -> Type)

Defined in Fcf.Alg.List

type Eval (EvensStrip (NilF :: ListF a (Ann (ListF a) [a])) :: [a] -> Type) = ([] :: [a])

data EvensAlg :: ListF a (Ann (ListF a) [a]) -> Exp [a]

Tim Williams, Recursion Schemes by example, example for Histo.

Instances

type Eval (EvensAlg (ConsF _ rst) :: [a] -> Type)

Defined in Fcf.Alg.List

type Eval (EvensAlg (ConsF _ rst) :: [a] -> Type) = Eval ((EvensStrip :: ListF a (Ann (ListF a) [a]) -> [a] -> Type) =<< Strip rst)

type Eval (EvensAlg (NilF :: ListF a (Ann (ListF a) [a])) :: [a] -> Type)

Defined in Fcf.Alg.List

type Eval (EvensAlg (NilF :: ListF a (Ann (ListF a) [a])) :: [a] -> Type) = ([] :: [a])

data Evens :: [a] -> Exp [a]

This picks up the elements on even positions on a list and is an example on how to use Histo. This example is from Tim Williams, Recursion Schemes by example.

Example

>>> :kind! Eval (Evens =<< RunInc 8)
Eval (Evens =<< RunInc 8) :: [Nat]
= '[2, 4, 6, 8]

Instances

type Eval (Evens lst :: [a] -> Type)

Defined in Fcf.Alg.List

type Eval (Evens lst :: [a] -> Type) = Eval (Histo (EvensAlg :: ListF a (Ann (ListF a) [a]) -> [a] -> Type) =<< ListToFix lst)

data NumIter :: a -> Nat -> Exp (Maybe (a, Nat))

For the ListRunAlg

Instances

type Eval (NumIter a s :: Maybe (k, Nat) -> Type)

Defined in Fcf.Alg.List

type Eval (NumIter a s :: Maybe (k, Nat) -> Type) = If (Eval (s > 0)) (Just ((,) a (s - 1))) (Nothing :: Maybe (k, Nat))

data ListRunAlg :: Nat -> Exp (Maybe (Nat, Nat))

For the RunInc

Instances

type Eval (ListRunAlg s :: Maybe (Nat, Nat) -> Type)

Defined in Fcf.Alg.List

type Eval (ListRunAlg s :: Maybe (Nat, Nat) -> Type) = Eval (NumIter s s)

data RunInc :: Nat -> Exp [Nat]

Construct a run (that is, a natuaral number sequence from 1 to arg).

Example

>>> :kind! Eval (RunInc 8)
Eval (RunInc 8) :: [Nat]
= '[1, 2, 3, 4, 5, 6, 7, 8]

Instances

type Eval (RunInc n :: [Nat] -> Type)

Defined in Fcf.Alg.List

type Eval (RunInc n :: [Nat] -> Type) = Eval ((Reverse :: [Nat] -> [Nat] -> Type) =<< Unfoldr ListRunAlg n)

data Sum :: [Nat] -> Exp Nat

Sum a Nat-list.

Example

>>> :kind! Eval (Sum '[1,2,3])
Eval (Sum '[1,2,3]) :: Nat
= 6

Instances

type Eval (Sum ns :: Nat -> Type)

Defined in Fcf.Alg.List

type Eval (Sum ns :: Nat -> Type) = Eval (Foldr (+) 0 ns)

data ToList :: a -> Exp [a]

ToList for type-level lists.

Example

>>> :kind! Eval (ToList 1)
Eval (ToList 1) :: [Nat]
= '[1]

Instances

type Eval (ToList a :: [k] -> Type)

Defined in Fcf.Alg.List

type Eval (ToList a :: [k] -> Type) = a ': ([] :: [k])

data Equal :: [a] -> [a] -> Exp Bool

Equal tests for list equality. We may change the name to (==).

Example

>>> :kind! Eval (Equal '[1,2,3] '[1,2,3])
Eval (Equal '[1,2,3] '[1,2,3]) :: Bool
= 'True

>>> :kind! Eval (Equal '[1,2,3] '[1,3,2])
Eval (Equal '[1,2,3] '[1,3,2]) :: Bool
= 'False

Instances

type Eval (Equal as bs :: Bool -> Type)

Defined in Fcf.Alg.List

type Eval (Equal as bs :: Bool -> Type) = Eval ((And :: [Bool] -> Bool -> Type) =<< ZipWith (TyEq :: b -> b -> Bool -> Type) as bs)