TypeFun.Data.List

Collection of type families on type lists. This module differs from Data.Singletons.Prelude.List because works with [*] and relies on GHC's type equality (~). The rest of required operations like Reverse or (:++:) you could find in singletons

Primitive operations on lists

type family Length (a :: [k]) :: N where ...

Equations

Length '[] = 'Z

Length (a ': as) = 'S (Length as)

type family Drop (c :: N) (s :: [k]) :: [k] where ...

Equations

Drop 'Z s = s

Drop ('S c) '[] = '[]

Drop ('S c) (a ': as) = Drop c as

type family Take (c :: N) (s :: [k]) :: [k] where ...

Equations

Take 'Z s = '[]

Take ('S c) '[] = '[]

Take ('S c) (a ': as) = a ': Take c as

type family Delete (a :: k) (s :: [k]) :: [k] where ...

Remove first argument type from anywhere in a list.

Equations

Delete a '[] = '[]

Delete a (a ': as) = Delete a as

Delete a (b ': as) = b ': Delete a as

type family Remove (i :: N) (a :: [k]) :: [k] where ...

Remove index from the list

Equations

Remove i '[] = '[]

Remove 'Z (a ': as) = as

Remove ('S i) (a ': as) = a ': Remove i as

type family (a :: [k]) :++: (b :: [k]) :: [k] where ...

Equations

'[] :++: b = b

(a ': as) :++: b = a ': (as :++: b)

Elements lookup

type IndexOf a s = FromJust (IndexOfMay a s)

type IndexOfMay a s = IndexOfMay' Z a s

type family IndexOfMay' (acc :: N) (a :: k) (s :: [k]) :: Maybe N where ...

Equations

IndexOfMay' acc a '[] = 'Nothing

IndexOfMay' acc a (a ': as) = 'Just acc

IndexOfMay' acc a (b ': as) = IndexOfMay' (S acc) a as

type family IndicesOfMay (a :: [k]) (b :: [k]) :: [Maybe N] where ...

Equations

IndicesOfMay '[] bs = '[]

IndicesOfMay (a ': as) bs = IndexOfMay a bs ': IndicesOfMay as bs

type family IndicesOf (a :: [k]) (b :: [k]) :: [N] where ...

Equations

IndicesOf '[] bs = '[]

IndicesOf (a ': as) bs = IndexOf a bs ': IndicesOf as bs

type Index idx s = FromJust (IndexMay idx s)

type family IndexMay (idx :: N) (s :: [k]) :: Maybe k where ...

Equations

IndexMay idx '[] = 'Nothing

IndexMay Z (a ': as) = 'Just a

IndexMay (S idx) (a ': as) = IndexMay idx as

type family IndicesMay (idxs :: [N]) (a :: [k]) :: [Maybe k] where ...

Equations

IndicesMay '[] as = '[]

IndicesMay (i ': idxs) as = IndexMay i as ': IndicesMay idxs as

type family Indices (idxs :: [N]) (a :: [k]) :: [k] where ...

Equations

Indices '[] as = '[]

Indices (i ': idxs) as = Index i as ': Indices idxs as

type Elem a s = NothingToConstr (IndexOfMay a s) (ElementNotFoundInList a s)

Generates unresolvable constraint if fists element is not contained inside of second

type NotElem a s = JustToConstr (IndexOfMay a s) (ElementIsInList a s)

Reverse of Elem

type family Count (a :: k) (s :: [k]) :: N where ...

Count elements in a list

Equations

Count a '[] = 'Z

Count a (a ': as) = 'S (Count a as)

Count a (b ': as) = Count a as

Operations with lists

type family SubList (a :: [k]) (b :: [k]) :: Constraint where ...

Constrains that first argument is a sublist of second. Reduces to (Elem a1 b, Elem a2 b, Elem a3 b, ...)

Equations

SubList '[] bs = ()

SubList (a ': as) bs = (Elem a bs, SubList as bs)

type family NotSubList (a :: [k]) (b :: [k]) :: Constraint where ...

Equations

NotSubList '[] bs = ()

NotSubList (a ': as) bs = (NotElem a bs, NotSubList as bs)

type IsPrefixOf a b = (If (IsPrefixOfBool a b) (() :: Constraint) (ListIsNotPrefixOf a b), SubList a b)

type IsNotPrefixOf a b = If (IsPrefixOfBool a b) (ListIsPrefixOf a b) (() :: Constraint)

type family IsPrefixOfBool (a :: [k]) (b :: [k]) :: Bool where ...

First argument is prefix of second

Equations

IsPrefixOfBool '[] b = 'True

IsPrefixOfBool (a ': as) (a ': bs) = IsPrefixOfBool as bs

IsPrefixOfBool as bs = 'False

Set operations

type family Union (a :: [k]) (b :: [k]) :: [k] where ...

Appends elements from first list to second if they are not presented in.

Equations

Union '[] bs = bs

Union (a ': as) bs = Union as (AppendUniq a bs)

type family UnionList (l :: [[k]]) :: [k] where ...

Equations

UnionList '[] = '[]

UnionList (a ': as) = Union a (UnionList as)

type family AppendUniq (a :: k) (s :: [k]) :: [k] where ...

Append element to list if element is not already presented in

Equations

AppendUniq a (a ': bs) = a ': bs

AppendUniq a (b ': bs) = b ': AppendUniq a bs

AppendUniq a '[] = '[a]

type Intersect a b = Indices (CatMaybes (IndicesOfMay a b)) b

Calculates intersection between two lists. Order of elements is taken from first list

type family Substract (a :: [k]) (b :: [k]) :: [k] where ...

Removes from first list all elements occured in second

Equations

Substract '[] b = '[]

Substract a '[] = a

Substract a (b ': bs) = Substract (Delete b a) bs

Uniqueness checking

type ElementIsUniq a s = If (Equal (S Z) (Count a s)) (() :: Constraint) (ElementIsNotUniqInList a s)

Checks that element a occurs in a list just once

type UniqElements a = UniqElements' a a

Checks that all elements in list are unique

type family UniqElements' (a :: [k]) (self :: [k]) :: Constraint where ...

Equations

UniqElements' '[] self = ()

UniqElements' (a ': as) self = (ElementIsUniq a self, UniqElements' as self)

Unsafe helpers

appendId :: forall proxy l r. proxy l -> (l ~ (l :++: '[]) => r) -> r

subListId :: forall proxy l r. proxy l -> (SubList l l => r) -> r