generics-sop-0.3.2.0: Generic Programming using True Sums of Products

Safe HaskellNone
LanguageHaskell2010

Generics.SOP.Constraint

Contents

Description

Constraints for indexed datatypes.

This module contains code that helps to specify that all elements of an indexed structure must satisfy a particular constraint.

Synopsis

Documentation

class (AllF f xs, SListI xs) => All (f :: k -> Constraint) (xs :: [k]) Source #

Require a constraint for every element of a list.

If you have a datatype that is indexed over a type-level list, then you can use All to indicate that all elements of that type-level list must satisfy a given constraint.

Example: The constraint

All Eq '[ Int, Bool, Char ]

is equivalent to the constraint

(Eq Int, Eq Bool, Eq Char)

Example: A type signature such as

f :: All Eq xs => NP I xs -> ...

means that f can assume that all elements of the n-ary product satisfy Eq.

Instances

(AllF k f xs, SListI k xs) => All k f xs Source # 

type family AllF (c :: k -> Constraint) (xs :: [k]) :: Constraint where ... Source #

Type family used to implement All.

Equations

AllF _c '[] = () 
AllF c (x ': xs) = (c x, All c xs) 

type SListI2 = All SListI Source #

Require a singleton for every inner list in a list of lists.

class (AllF (All f) xss, SListI xss) => All2 f xss Source #

Require a constraint for every element of a list of lists.

If you have a datatype that is indexed over a type-level list of lists, then you can use All2 to indicate that all elements of the innert lists must satisfy a given constraint.

Example: The constraint

All2 Eq '[ '[ Int ], '[ Bool, Char ] ]

is equivalent to the constraint

(Eq Int, Eq Bool, Eq Char)

Example: A type signature such as

f :: All2 Eq xss => SOP I xs -> ...

means that f can assume that all elements of the sum of product satisfy Eq.

Instances

(AllF [k] (All k f) xss, SListI [k] xss) => All2 k f xss Source # 

class (SListI xs, SListI ys, SameShapeAs xs ys, SameShapeAs ys xs, AllZipF c xs ys) => AllZip (c :: a -> b -> Constraint) (xs :: [a]) (ys :: [b]) Source #

Require a constraint for pointwise for every pair of elements from two lists.

Example: The constraint

All (~) '[ Int, Bool, Char ] '[ a, b, c ]

is equivalent to the constraint

(Int ~ a, Bool ~ b, Char ~ c)

Since: 0.3.1.0

Instances

(SListI a xs, SListI b ys, SameShapeAs a b xs ys, SameShapeAs b a ys xs, AllZipF a b c xs ys) => AllZip a b c xs ys Source # 

type family AllZipF (c :: a -> b -> Constraint) (xs :: [a]) (ys :: [b]) :: Constraint where ... Source #

Type family used to implement AllZip.

Since: 0.3.1.0

Equations

AllZipF _c '[] '[] = () 
AllZipF c (x ': xs) (y ': ys) = (c x y, AllZip c xs ys) 

type family SameShapeAs (xs :: [a]) (ys :: [b]) :: Constraint where ... Source #

Type family that forces a type-level list to be of the same shape as the given type-level list.

The main use of this constraint is to help type inference to learn something about otherwise unknown type-level lists.

Since: 0.3.1.0

Equations

SameShapeAs '[] ys = ys ~ '[] 
SameShapeAs (x ': xs) ys = (ys ~ (Head ys ': Tail ys), SameShapeAs xs (Tail ys)) 

type family Head (xs :: [a]) :: a where ... Source #

Utility function to compute the head of a type-level list.

Since: 0.3.1.0

Equations

Head (x ': xs) = x 

type family Tail (xs :: [a]) :: [a] where ... Source #

Utility function to compute the tail of a type-level list.

Since: 0.3.1.0

Equations

Tail (x ': xs) = xs 

class Coercible (f x) (g y) => LiftedCoercible f g x y Source #

The constraint LiftedCoercible f g x y is equivalent to Coercible (f x) (g y).

Since: 0.3.1.0

Instances

Coercible k0 (f x) (g y) => LiftedCoercible k0 k2 k1 f g x y Source # 

class (AllZipF (AllZip f) xss yss, SListI xss, SListI yss, SameShapeAs xss yss, SameShapeAs yss xss) => AllZip2 f xss yss Source #

Require a constraint for pointwise for every pair of elements from two lists of lists.

Instances

(AllZipF [a] [b] (AllZip a b f) xss yss, SListI [a] xss, SListI [b] yss, SameShapeAs [a] [b] xss yss, SameShapeAs [b] [a] yss xss) => AllZip2 a b f xss yss Source # 

class f (g x) => Compose f g x infixr 9 Source #

Composition of constraints.

Note that the result of the composition must be a constraint, and therefore, in f :. g, the kind of f is k -> Constraint. The kind of g, however, is l -> k and can thus be an normal type constructor.

A typical use case is in connection with All on an NP or an NS. For example, in order to denote that all elements on an NP f xs satisfy Show, we can say All (Show :. f) xs.

Since: 0.2

Instances

f (g x) => Compose k2 k1 f g x Source # 

class (f x, g x) => And f g x infixl 7 Source #

Pairing of constraints.

Since: 0.2

Instances

(f x, g x) => And k f g x Source # 

class Top x Source #

A constraint that can always be satisfied.

Since: 0.2

Instances

Top k x Source # 

type family AllN (h :: (k -> *) -> l -> *) (c :: k -> Constraint) :: l -> Constraint Source #

A generalization of All and All2.

The family AllN expands to All or All2 depending on whether the argument is indexed by a list or a list of lists.

Instances

type AllN k [k] (NP k) c Source # 
type AllN k [k] (NP k) c = All k c
type AllN k [[k]] (POP k) c Source # 
type AllN k [[k]] (POP k) c = All2 k c
type AllN k [k] (NS k) c Source # 
type AllN k [k] (NS k) c = All k c
type AllN k [[k]] (SOP k) c Source # 
type AllN k [[k]] (SOP k) c = All2 k c

type family AllZipN (h :: (k -> *) -> l -> *) (c :: k1 -> k2 -> Constraint) :: l1 -> l2 -> Constraint Source #

A generalization of AllZip and AllZip2.

The family AllZipN expands to AllZip or AllZip2 depending on whther the argument is indexed by a list or a list of lists.

Instances

type AllZipN k [k] a b [a] [b] (NP k) c Source # 
type AllZipN k [k] a b [a] [b] (NP k) c = AllZip a b c
type AllZipN k [[k]] a b [[a]] [[b]] (POP k) c Source # 
type AllZipN k [[k]] a b [[a]] [[b]] (POP k) c = AllZip2 a b c

type family SListIN (h :: (k -> *) -> l -> *) :: l -> Constraint Source #

A generalization of SListI.

The family SListIN expands to SListI or SListI2 depending on whether the argument is indexed by a list or a list of lists.

Instances

type SListIN k [k] (NP k) Source # 
type SListIN k [k] (NP k) = SListI k
type SListIN k [[k]] (POP k) Source # 
type SListIN k [[k]] (POP k) = SListI2 k
type SListIN k [k] (NS k) Source # 
type SListIN k [k] (NS k) = SListI k
type SListIN k [[k]] (SOP k) Source # 
type SListIN k [[k]] (SOP k) = SListI2 k

data Constraint :: * #

The kind of constraints, like Show a

Orphan instances

SListI k xs => SingI k xs Source # 

Methods

sing :: Sing xs xs Source #

(All [k] (SListI k) xss, SListI [k] xss) => SingI [k] xss Source # 

Methods

sing :: Sing xss xs Source #