Haskus.Utils.Types.List

Utils for type lists

Construction

type family Snoc (xs :: [k]) (x :: k) :: [k] where ...

Snoc

Equations

Snoc '[] x = '[x]

Snoc (y ': ys) x = y ': Snoc ys x

type family Concat (xs :: [k]) (ys :: [k]) :: [k] where ...

Concat two type lists

Equations

Concat '[] '[] = '[]

Concat '[] ys = ys

Concat (x ': xs) ys = x ': Concat xs ys

type family Replicate (n :: Nat) (s :: k) :: [k] where ...

Replicate

Equations

Replicate n s = Replicate' s n '[]

type family Zip (l :: [*]) (l2 :: [*]) where ...

Zip two lists

Equations

Zip '[] xs = '[]

Zip xs '[] = '[]

Zip (x ': xs) (y ': ys) = (x, y) ': Zip xs ys

Removal

type family RemoveAt (n :: Nat) (l :: [k]) :: [k] where ...

Remove a type at index

Equations

RemoveAt 0 (x ': xs) = xs

RemoveAt n (x ': xs) = x ': RemoveAt (n - 1) xs

type family RemoveAt1 (n :: Nat) (l :: [k]) :: [k] where ...

Remove a type at index (0 == don't remove)

Equations

RemoveAt1 0 xs = xs

RemoveAt1 1 (x ': xs) = xs

RemoveAt1 n (x ': xs) = x ': RemoveAt1 (n - 1) xs

type family RemoveAtN (ns :: [Nat]) (l :: [k]) :: [k] where ...

Remove types at several indexes

Equations

RemoveAtN '[] xs = xs

RemoveAtN (i ': is) xs = RemoveAtN is (RemoveAt i xs)

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

Remove a in l

Equations

Remove a '[] = '[]

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

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

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

Keep only a single value of each type

Equations

Nub xs = Reverse (Nub' xs '[])

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

Keep only a single value of the head type

Equations

NubHead '[] = '[]

NubHead (x ': xs) = x ': Remove x xs

Sublist

type family Head (xs :: [k]) :: k where ...

Head of a list

Equations

Head (x ': xs) = x

type family Tail (xs :: [k]) :: [k] where ...

Tail of a list

Equations

Tail (x ': xs) = xs

type family Init (xs :: [k]) :: [k] where ...

Init of a list

Equations

Init '[x] = '[]

Init (x ': xs) = x ': Init xs

type family Take (n :: Nat) (xs :: [k]) :: [k] where ...

Take elements in a list

Equations

Take 0 xs = '[]

Take n (x ': xs) = x ': Take (n - 1) xs

type family Drop (n :: Nat) (xs :: [k]) :: [k] where ...

Drop elements in a list

Equations

Drop 0 xs = xs

Drop n (x ': xs) = Drop (n - 1) xs

Insert/replace

type family InsertAt (n :: Nat) (l :: [k]) (l2 :: [k]) :: [k] where ...

Insert a list at n

Equations

InsertAt 0 xs ys = Concat ys xs

InsertAt n (x ': xs) ys = x ': InsertAt (n - 1) xs ys

type family ReplaceAt (n :: Nat) (l :: [k]) (l2 :: [k]) :: [k] where ...

replace l[n] with l2 (folded)

Equations

ReplaceAt 0 (x ': xs) ys = Concat ys xs

ReplaceAt n (x ': xs) ys = x ': ReplaceAt (n - 1) xs ys

type family Replace (t1 :: k) (t2 :: k) (l :: [k]) :: [k] where ...

replace a type by another in l

Equations

Replace t1 t2 '[] = '[]

Replace t1 t2 (t1 ': xs) = t2 ': Replace t1 t2 xs

Replace t1 t2 (x ': xs) = x ': Replace t1 t2 xs

type family ReplaceN (n :: Nat) (t :: k) (l :: [k]) :: [k] where ...

replace a type at offset n in l

Equations

ReplaceN 0 t (x ': xs) = t ': xs

ReplaceN n t (x ': xs) = x ': ReplaceN (n - 1) t xs

type family ReplaceNS (ns :: [Nat]) (t :: k) (l :: [k]) :: [k] where ...

replace types at offsets ns in l

Equations

ReplaceNS '[] t l = l

ReplaceNS (i ': is) t l = ReplaceNS is t (ReplaceN i t l)

Set operations

type family Subset (t :: b) (f :: b) (xs :: [a]) (ys :: [a]) :: b where ...

Subset test

Equations

Subset t f '[] '[] = t

Subset t f xs ys = AndMany t f (MapElem t f xs ys)

type family SetEq (t :: b) (f :: b) (xs :: [a]) (ys :: [a]) :: b where ...

Set equality

Equations

SetEq t f xs ys = And t f (Subset t f xs ys) (Subset t f ys xs)

type family CheckMember (a :: k) (l :: [k]) :: Constraint where ...

Check that a type is member of a type list

Equations

CheckMember a l = CheckMember' l a l

type family CheckMembers (l1 :: [k]) (l2 :: [k]) :: Constraint where ...

Check that a list is a subset of another

Equations

CheckMembers l1 l1 = ()

CheckMembers l1 l2 = CheckMembers' l2 '[] l1 l2

type family Union (xs :: [k]) (ys :: [k]) :: [k] where ...

Union two lists

Equations

Union xs ys = Nub (Concat xs ys)

type family Complement (xs :: [k]) (ys :: [k]) :: [k] where ...

Complement xs ys

Equations

Complement xs '[] = xs

Complement xs (y ': ys) = Complement (Remove y xs) ys

type family Product (xs :: [*]) (ys :: [*]) :: [*] where ...

Product of two lists

Equations

Product '[] ys = '[]

Product xy '[] = '[]

Product (x ': xs) ys = Concat (Product' x ys) (Product xs ys)

type Member x xs = (x ~ Index (IndexOf x xs) xs, KnownNat (IndexOf x xs))

Constraint: x member of xs

type family Members xs ys :: Constraint where ...

Constraint: all the xs are members of ys

Equations

Members '[] ys = ()

Members (x ': xs) ys = (Member x ys, Members xs ys)

type CheckNub (l :: [k]) = CheckNubEx l (Nub l) ~ True

Check that a list only contain a value of each type

Index operations

type family IndexOf (a :: k) (l :: [k]) :: Nat where ...

Get the first index of a type

Equations

IndexOf x xs = IndexOf' x xs xs

type family IndexesOf (a :: k) (l :: [k]) :: [Nat] where ...

Get all the indexes of a type

Equations

IndexesOf x xs = IndexesOf' 0 x xs

type family MaybeIndexOf (a :: k) (l :: [k]) where ...

Get the first index (starting from 1) of a type or 0 if none

Equations

MaybeIndexOf x xs = MaybeIndexOf' 0 x xs

type family Index (n :: Nat) (l :: [k]) :: k where ...

Indexed access into the list

Equations

Index 0 (x ': xs) = x

Index n (x ': xs) = Index (n - 1) xs

type family Elem (t :: b) (f :: b) (x :: k) (xs :: [k]) :: b where ...

List membership test

Equations

Elem t f x '[] = f

Elem t f x (x ': xs) = t

Elem t f x (y ': xs) = Elem t f x xs

type family MapElem (t :: b) (f :: b) (xs :: [a]) (ys :: [a]) :: [b] where ...

MapElem t f xs ys = Map (x -> Elem t f x ys) xs

Equations

MapElem t f '[] ys = '[]

MapElem t f (x ': xs) ys = Elem t f x ys ': MapElem t f xs ys

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

Reverse a list

Equations

Reverse l = Reverse' l '[]

Nat list

type family Generate (n :: Nat) (m :: Nat) :: [Nat] where ...

Generate a list of Nat [n..m-1]

Equations

Generate n n = '[]

Generate n m = n ': Generate (n + 1) m

Others

type family Map (f :: a -> k) (xs :: [a]) :: [k] where ...

Map a type function

Equations

Map f '[] = '[]

Map f (x ': xs) = f x ': Map f xs

type family ListMax (xs :: [Nat]) where ...

Get the max of a list of Nats

Equations

ListMax (x ': xs) = Max' x xs

type family ListMin (xs :: [Nat]) where ...

Get the min of a list of Nats

Equations

ListMin (x ': xs) = Min' x xs

type family Length (xs :: [k]) :: Nat where ...

Get list length

Equations

Length xs = Length' 0 xs

type family Indexes (l :: [k]) :: [Nat] where ...

Get list indexes

Equations

Indexes xs = IndexesFrom 0 xs

type family MapTest (a :: k) (l :: [k]) :: [Nat] where ...

Map to 1 if type equality, 0 otherwise

Equations

MapTest a '[] = '[]

MapTest a (a ': xs) = 1 ': MapTest a xs

MapTest a (x ': xs) = 0 ': MapTest a xs