Data.SOP.Sing

Singleton types corresponding to type-level data structures.

The implementation is similar, but subtly different to that of the singletons package. See the "True Sums of Products" paper for details.

Singletons

data SList :: [k] -> Type where

Explicit singleton list.

A singleton list can be used to reveal the structure of a type-level list argument that the function is quantified over. For every type-level list xs, there is one non-bottom value of type SList xs.

Note that these singleton lists are polymorphic in the list elements; we do not require a singleton representation for them.

Since: 0.2

Constructors

SNil :: SList '[]

SCons :: SListI xs => SList (x ': xs)

Instances

Eq (SList xs)

Defined in Data.SOP.Sing

Methods

(==) :: SList xs -> SList xs -> Bool

(/=) :: SList xs -> SList xs -> Bool

Ord (SList xs)

Defined in Data.SOP.Sing

Methods

compare :: SList xs -> SList xs -> Ordering

(<) :: SList xs -> SList xs -> Bool

(<=) :: SList xs -> SList xs -> Bool

(>) :: SList xs -> SList xs -> Bool

(>=) :: SList xs -> SList xs -> Bool

max :: SList xs -> SList xs -> SList xs

min :: SList xs -> SList xs -> SList xs

Show (SList xs)

Defined in Data.SOP.Sing

Methods

showsPrec :: Int -> SList xs -> ShowS

show :: SList xs -> String

showList :: [SList xs] -> ShowS

type SListI = All Top

Implicit singleton list.

A singleton list can be used to reveal the structure of a type-level list argument that the function is quantified over.

Since 0.4.0.0, this is now defined in terms of All. A singleton list provides a witness for a type-level list where the elements need not satisfy any additional constraints.

Since: 0.4.0.0

sList :: SListI xs => SList xs

Get hold of an explicit singleton (that one can then pattern match on) for a type-level list

para_SList :: SListI xs => r '[] -> (forall y ys. SListI ys => r ys -> r (y ': ys)) -> r xs

Paramorphism for a type-level list.

Since: 0.4.0.0

case_SList :: SListI xs => r '[] -> (forall y ys. SListI ys => r (y ': ys)) -> r xs

Case distinction on a type-level list.

Since: 0.4.0.0

Shape of type-level lists

data Shape :: [k] -> Type where

Occassionally it is useful to have an explicit, term-level, representation of type-level lists (esp because of https://ghc.haskell.org/trac/ghc/ticket/9108 )

Constructors

ShapeNil :: Shape '[]

ShapeCons :: SListI xs => Shape xs -> Shape (x ': xs)

Instances

Eq (Shape xs)

Defined in Data.SOP.Sing

Methods

(==) :: Shape xs -> Shape xs -> Bool

(/=) :: Shape xs -> Shape xs -> Bool

Ord (Shape xs)

Defined in Data.SOP.Sing

Methods

compare :: Shape xs -> Shape xs -> Ordering

(<) :: Shape xs -> Shape xs -> Bool

(<=) :: Shape xs -> Shape xs -> Bool

(>) :: Shape xs -> Shape xs -> Bool

(>=) :: Shape xs -> Shape xs -> Bool

max :: Shape xs -> Shape xs -> Shape xs

min :: Shape xs -> Shape xs -> Shape xs

Show (Shape xs)

Defined in Data.SOP.Sing

Methods

showsPrec :: Int -> Shape xs -> ShowS

show :: Shape xs -> String

showList :: [Shape xs] -> ShowS

shape :: forall (xs :: [k]). SListI xs => Shape xs

The shape of a type-level list.

lengthSList :: forall (xs :: [k]) proxy. SListI xs => proxy xs -> Int

The length of a type-level list.

Since: 0.2