Data.SOP.Sing

sop-core-0.5.0.2: True Sums of Products

Safe Haskell | None
Language | Haskell2010

Data.SOP.Sing

Contents

- Singletons
  - Shape of type-level lists

Description

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.

Synopsis

- data SList (a :: [k]) where
  - SNil :: forall {k}. SList ('[] :: [k])
  - SCons :: forall {k} (xs :: [k]) (x :: k). SListI xs => SList (x ': xs)
- type SListI = All (Top :: k -> Constraint)
- sList :: forall {k} (xs :: [k]). SListI xs => SList xs
- para_SList :: forall {a} (xs :: [a]) r. SListI xs => r ('[] :: [a]) -> (forall (y :: a) (ys :: [a]). SListI ys => r ys -> r (y ': ys)) -> r xs
- case_SList :: forall {a} (xs :: [a]) r. SListI xs => r ('[] :: [a]) -> (forall (y :: a) (ys :: [a]). SListI ys => r (y ': ys)) -> r xs
- data Shape (a :: [k]) where
  - ShapeNil :: forall {k}. Shape ('[] :: [k])
  - ShapeCons :: forall {k} (xs :: [k]) (x :: k). SListI xs => Shape xs -> Shape (x ': xs)
- shape :: forall k (xs :: [k]). SListI xs => Shape xs
- lengthSList :: forall k (xs :: [k]) proxy. SListI xs => proxy xs -> Int

# Singletons

data SList (a :: [k]) 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 :: forall {k}. SList ('[] :: [k]) |
SCons :: forall {k} (xs :: [k]) (x :: k). SListI xs => SList (x ': xs) |

#### Instances

Instances details

Show (SList xs) # |
Instance details Defined in Data.SOP.Sing Methods showsPrec :: Int -> SList xs -> ShowS # show :: SList xs -> String # showList :: [SList xs] -> ShowS #
Eq (SList xs) # |
Instance details Defined in Data.SOP.Sing Methods (==) :: SList xs -> SList xs -> Bool # (/=) :: SList xs -> SList xs -> Bool #
Ord (SList xs) # |
Instance details 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 #

type SListI = All (Top :: k -> Constraint) #

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 :: forall {k} (xs :: [k]). SListI xs => SList xs #

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

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

Paramorphism for a type-level list.

Since: 0.4.0.0

case_SList :: forall {a} (xs :: [a]) r. SListI xs => r ('[] :: [a]) -> (forall (y :: a) (ys :: [a]). 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 (a :: [k]) where #

Occasionally 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 :: forall {k}. Shape ('[] :: [k]) |
ShapeCons :: forall {k} (xs :: [k]) (x :: k). SListI xs => Shape xs -> Shape (x ': xs) |

#### Instances

Instances details

Show (Shape xs) # |
Instance details Defined in Data.SOP.Sing Methods showsPrec :: Int -> Shape xs -> ShowS # show :: Shape xs -> String # showList :: [Shape xs] -> ShowS #
Eq (Shape xs) # |
Instance details Defined in Data.SOP.Sing Methods (==) :: Shape xs -> Shape xs -> Bool # (/=) :: Shape xs -> Shape xs -> Bool #
Ord (Shape xs) # |
Instance details 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 #

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

The shape of a type-level list.

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

The length of a type-level list.

Since: 0.2