Copyright	(c) gspia 2020-
License	BSD
Maintainer	gspia
Safe Haskell	Safe
Language	Haskell2010

Fcf.Alg.List

Description

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).

Synopsis

data ListF a b
- = ConsF a b
- | NilF
data ListToFix :: [a] -> Exp (Fix (ListF a))
data LenAlg :: Algebra (ListF a) Nat
data SumAlg :: Algebra (ListF Nat) Nat
data ProdAlg :: Algebra (ListF Nat) Nat
data Sum :: [Nat] -> Exp Nat
data Partition :: (a -> Exp Bool) -> [a] -> Exp ([a], [a])
data PartHelp :: (a -> Exp Bool) -> a -> ([a], [a]) -> Exp ([a], [a])
data All :: [Bool] -> Exp Bool
data Any :: [Bool] -> Exp Bool

Documentation

>>> import           Fcf.Combinators

data ListF a b Source #

Base functor for a list of type [a].

Constructors

ConsF a b
NilF

Instances

type Eval (ListToFix (a2 ': as) :: Fix (ListF a1) -> Type) Source #
Instance details 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) Source #
Instance details Defined in Fcf.Alg.List type Eval (ListToFix ([] :: [a]) :: Fix (ListF a) -> Type) = Fix (NilF :: ListF a (Fix (ListF a)))
type Eval (Map f (ConsF a3 b2) :: ListF a2 b1 -> Type) Source #
Instance details Defined in Fcf.Alg.List type Eval (Map f (ConsF a3 b2) :: ListF a2 b1 -> Type) = ConsF a3 (Eval (f b2))
type Eval (Map f (NilF :: ListF a2 a1) :: ListF a2 b -> Type) Source #
Instance details Defined in Fcf.Alg.List type Eval (Map f (NilF :: ListF a2 a1) :: ListF a2 b -> Type) = (NilF :: ListF a2 b)

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

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.

Instances

type Eval (ListToFix (a2 ': as) :: Fix (ListF a1) -> Type) Source #
Instance details 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) Source #
Instance details 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 Source #

Example algebra to calculate list length.

>>> :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) Source #
Instance details Defined in Fcf.Alg.List type Eval (LenAlg (ConsF a2 b) :: Nat -> Type) = 1 + b
type Eval (LenAlg (NilF :: ListF a Nat) :: Nat -> Type) Source #
Instance details Defined in Fcf.Alg.List type Eval (LenAlg (NilF :: ListF a Nat) :: Nat -> Type) = 0

data SumAlg :: Algebra (ListF Nat) Nat Source #

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

>>> :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) Source #
Instance details Defined in Fcf.Alg.List type Eval (SumAlg (ConsF a b) :: Nat -> Type) = a + b
type Eval (SumAlg (NilF :: ListF Nat Nat)) Source #
Instance details Defined in Fcf.Alg.List type Eval (SumAlg (NilF :: ListF Nat Nat)) = 0

data ProdAlg :: Algebra (ListF Nat) Nat Source #

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

>>> :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) Source #
Instance details Defined in Fcf.Alg.List type Eval (ProdAlg (ConsF a b) :: Nat -> Type) = a * b
type Eval (ProdAlg (NilF :: ListF Nat Nat)) Source #
Instance details Defined in Fcf.Alg.List type Eval (ProdAlg (NilF :: ListF Nat Nat)) = 1

data Sum :: [Nat] -> Exp Nat Source #

Sum a Nat-list.

Example

Expand

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

Instances

type Eval (Sum ns :: Nat -> Type) Source #
Instance details Defined in Fcf.Alg.List type Eval (Sum ns :: Nat -> Type) = Eval (Foldr (+) 0 ns)

data Partition :: (a -> Exp Bool) -> [a] -> Exp ([a], [a]) Source #

Partition

Example

Expand

>>> :kind! Eval (Fcf.Alg.List.Partition ((>=) 35) '[ 20, 30, 40, 50])
Eval (Fcf.Alg.List.Partition ((>=) 35) '[ 20, 30, 40, 50]) :: ([Nat],
                                                               [Nat])
= '( '[20, 30], '[40, 50])

Instances

type Eval (Partition p lst :: ([a], [a]) -> Type) Source #
Instance details Defined in Fcf.Alg.List type Eval (Partition p lst :: ([a], [a]) -> Type) = Eval (Foldr (PartHelp p) ((,) ([] :: [a]) ([] :: [a])) lst)

data PartHelp :: (a -> Exp Bool) -> a -> ([a], [a]) -> Exp ([a], [a]) Source #

Instances

type Eval (PartHelp p a2 ((,) xs ys) :: ([a1], [a1]) -> Type) Source #
Instance details Defined in Fcf.Alg.List type Eval (PartHelp p a2 ((,) xs ys) :: ([a1], [a1]) -> Type) = If (Eval (p a2)) ((,) (a2 ': xs) ys) ((,) xs (a2 ': ys))

data All :: [Bool] -> Exp Bool Source #

Give true if all of the booleans in the list are true.

Example

Expand

>>> :kind! Eval (All '[ 'True, 'True])
Eval (All '[ 'True, 'True]) :: Bool
= 'True

>>> :kind! Eval (All '[ 'True, 'True, 'False])
Eval (All '[ 'True, 'True, 'False]) :: Bool
= 'False

Instances

type Eval (All lst :: Bool -> Type) Source #
Instance details Defined in Fcf.Alg.List type Eval (All lst :: Bool -> Type) = Eval (Foldr (&&) True lst)

data Any :: [Bool] -> Exp Bool Source #

Give true if any of the booleans in the list is true.

Example

Expand

>>> :kind! Eval (Any '[ 'True, 'True])
Eval (Any '[ 'True, 'True]) :: Bool
= 'True

>>> :kind! Eval (Any '[ 'False, 'False])
Eval (Any '[ 'False, 'False]) :: Bool
= 'False

Instances

type Eval (Any lst :: Bool -> Type) Source #
Instance details Defined in Fcf.Alg.List type Eval (Any lst :: Bool -> Type) = Eval (Foldr (\|\|) False lst)