Data.Diverse.TypeLevel

Documentation

type UniqueMember x xs = (Unique x xs, KnownNat (IndexOf x xs))

Ensures that x is a unique member of xs, and that natVal can be used.

type UniqueMemberAt n x xs = (Unique x xs, KnownNat n, n ~ IndexOf x xs)

Ensures that x is a unique member of xs, and that natVal can be used.

type UniqueLabelMember l xs = (UniqueLabel l xs, KnownNat (IndexOf (KindAtLabel l xs) xs))

Ensures that x is a unique member of xs, and that natVal can be used.

type MaybeUniqueMemberAt n x xs = (Unique x xs, KnownNat n, n ~ PositionOf x xs)

Ensures that x is a unique member of xs if it exists, and that natVal can be used.

type MemberAt n x xs = (KnownNat n, x ~ KindAtIndex n xs)

Ensures that x is a member of xs at n, and that natVal can be used.

type MaybeMemberAt n x xs = (KnownNat n, KindAtPositionIs n x xs)

Ensures that x is a member of xs at n if it exists, and that natVal can be used.

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

Snoc x to end of xs if x doesn't already exist in xs

Equations

SnocUnique '[] x = '[x]

SnocUnique (x ': xs) x = x ': xs

SnocUnique (y ': xs) x = y ': SnocUnique xs x

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

For each y in ys, snocs them to end of xs if y doesn't already exist in xs

Equations

AppendUnique xs '[] = xs

AppendUnique xs (y ': ys) = AppendUnique (SnocUnique xs y) ys

type family UniqueIfExists ys x xs :: Constraint where ...

Ensures x is a unique member in xs iff it exists in ys

Equations

UniqueIfExists '[] x xs = ()

UniqueIfExists (y ': ys) y xs = Unique y xs

UniqueIfExists (y ': ys) x xs = UniqueIfExists ys x xs

type IsDistinct xs = IsDistinctImpl xs xs

Ensures that the type list contain unique types

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

Return the list of distinct types in a typelist

Equations

Nub '[] = '[]

Nub (x ': xs) = NubImpl xs x xs

type Unique x xs = UniqueImpl xs x xs

Ensures that x only ever appears once in xs

type UniqueLabel l xs = UniqueLabelImpl xs l xs

Ensures that the label in tagged label v only ever appears once in xs.

type family UniqueLabels (ls :: [k1]) (xs :: [k]) :: Constraint where ...

Ensures that the label list all UniqueLabels

Equations

UniqueLabels '[] xs = ()

UniqueLabels (l ': ls) xs = (UniqueLabel l xs, UniqueLabels ls xs)

type IndexOf x xs = IndexOfImpl xs x xs

Get the first index of a type (Indexed by 0) Will result in type error if x doesn't exist in xs.

type PositionOf x xs = PositionOfImpl 0 x xs

Get the first index of a type (Indexed by 1) Will return 0 if x doesn't exists in xs.

type KindAtIndex n xs = KindAtIndexImpl n xs n xs

Get the type at an index

type KindAtLabel l xs = KindAtLabelImpl l xs xs

Get the type at a label

type family KindAtPositionIs (n :: Nat) (x :: k) (xs :: [k]) :: Constraint where ...

It's actually ok for the position to be zero, but if it's not zero then the types must match

Equations

KindAtPositionIs 0 x xs = ()

KindAtPositionIs n x xs = x ~ KindAtIndexImpl (n - 1) xs (n - 1) xs

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

Get the types at an list of index

Equations

KindsAtIndices '[] xs = '[]

KindsAtIndices (n ': ns) xs = KindAtIndex n xs ': KindsAtIndices ns xs

type family KindsAtLabels (ls :: [k1]) (xs :: [k]) :: [k] where ...

Get the types with labels ls from xs

Equations

KindsAtLabels '[] xs = '[]

KindsAtLabels (l ': ls) xs = KindAtLabel l xs ': KindsAtLabels ls xs

type family Without (x :: k) (xs :: [k]) :: [k] where ...

The typelist xs without first x. It is okay for x not to exist in xs

Equations

Without x '[] = '[]

Without x (x ': xs) = xs

Without x (y ': xs) = y ': Without x xs

type Replace x y xs = ReplaceImpl x y xs

The typelist xs with the first x replaced by y. It is okay for x not to exist in xs

type Replaces xs ys zs = ReplacesImpl xs ys xs ys zs

The typelist zs with the first xs replaced by ys. xs must be the same size as ys

type WithoutIndex n xs = WithoutIndexImpl n xs n xs

The typelist xs without the type at Nat n. n must be within bounds of xs

type ReplaceIndex n y xs = ReplaceIndexImpl n xs n y xs

The typelist xs without the type at Nat n replaced by y. n must be within bounds of xs

type ReplacesIndex ns ys xs = ReplacesIndexImpl 0 ns ys xs

The typelist xs replaced by ys at the indices ns. ns and ys must be the same length. ns must be within bounds of xs

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

Get the typelist without the Head type

Equations

Tail '[] = TypeError (Text "Tail error: empty type list")

Tail (x ': xs) = xs

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

Get the first type in a typelist

Equations

Head '[] = TypeError (Text "Head error: empty type list")

Head (x ': xs) = x

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

Get the last type in a typelist

Equations

Last '[] = TypeError (Text "Last error: empty type list")

Last (x ': (x' ': xs)) = Last (x' ': xs)

Last '[x] = x

type SameLength xs ys = SameLengthImpl xs ys xs ys

Ensures two typelists are the same length

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

Set complement. Returns the set of things in xs that are not in ys.

Equations

Complement xs '[] = xs

Complement xs (y ': ys) = Complement (Without y xs) ys

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

Returns a xs appended with ys

Equations

Append '[] ys = ys

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

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

Returns the typelist without the Last type

Equations

Init '[] = TypeError (Text "Init error: empty type list")

Init '[x] = '[]

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

type Zip xs ys = ZipImpl xs ys xs ys

Takes two lists which must be the same length and returns a list of corresponding pairs.