Data.Reflection

reflection-2.1.9: Reifies arbitrary terms into types that can be reflected back into terms

Copyright | 2009-2015 Edward Kmett 2012 Elliott Hird 2004 Oleg Kiselyov and Chung-chieh Shan
License | BSD3
Maintainer | Edward Kmett <ekmett@gmail.com>
Stability | experimental
Portability | non-portable
Safe Haskell | Trustworthy
Language | Haskell98

Data.Reflection

Contents

- Reflection
- Given
- Template Haskell reflection
- Useful compile time naturals
- Reified Monoids
- Reified Applicatives
- Orphan instances

Description

Reifies arbitrary terms at the type level. Based on the Functional Pearl: Implicit Configurations paper by Oleg Kiselyov and Chung-chieh Shan.

http://okmij.org/ftp/Haskell/tr-15-04.pdf

The approach from the paper was modified to work with Data.Proxy and to cheat by using knowledge of GHC's internal representations by Edward Kmett and Elliott Hird.

Usage comes down to two combinators, `reify` and `reflect`.

    >>> reify 6 (\p -> reflect p + reflect p)
    12

The argument passed along by reify is just a `data `Proxy` t = Proxy`, so all of the information needed to reconstruct your value has been moved to the type level. This enables it to be used when constructing instances (see `examples/Monoid.hs`).

In addition, a simpler API is offered for working with singleton values such as a system configuration, etc.

Synopsis

- class Reifies (s :: k) a | s -> a where
  - reflect :: proxy s -> a
- reify :: a -> (forall s. Reifies s a => Proxy s -> r) -> r
- reifyNat :: Integer -> (forall (n :: Nat). KnownNat n => Proxy n -> r) -> r
- reifySymbol :: String -> (forall (n :: Symbol). KnownSymbol n => Proxy n -> r) -> r
- reifyTypeable :: Typeable a => a -> (forall s. (Typeable s, Reifies s a) => Proxy s -> r) -> r
- class Given a where
  - given :: a
- give :: a -> (Given a => r) -> r
- int :: Int -> TypeQ
- nat :: Int -> TypeQ
- data Z
- data D n
- data SD n
- data PD n
- data ReifiedMonoid a = ReifiedMonoid {
  - reifiedMappend :: a -> a -> a
  - reifiedMempty :: a
  }
- newtype ReflectedMonoid a (s :: k) = ReflectedMonoid a
- reifyMonoid :: (a -> a -> a) -> a -> (forall s. Reifies s (ReifiedMonoid a) => t -> ReflectedMonoid a s) -> t -> a
- foldMapBy :: Foldable t => (r -> r -> r) -> r -> (a -> r) -> t a -> r
- foldBy :: Foldable t => (a -> a -> a) -> a -> t a -> a
- data ReifiedApplicative (f :: Type -> Type) = ReifiedApplicative {
  - reifiedPure :: forall a. a -> f a
  - reifiedAp :: forall a b. f (a -> b) -> f a -> f b
  }
- newtype ReflectedApplicative (f :: k -> Type) (s :: k1) (a :: k) = ReflectedApplicative (f a)
- reifyApplicative :: (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (forall s. Reifies s (ReifiedApplicative f) => t -> ReflectedApplicative f s a) -> t -> f a
- traverseBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> t a -> f (t b)
- sequenceBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> t (f a) -> f (t a)

# Reflection

class Reifies (s :: k) a | s -> a where #

Methods

reflect :: proxy s -> a #

Recover a value inside a `reify` context, given a proxy for its reified type.

#### Instances

Instances details

KnownNat n => Reifies (n :: Nat) Integer # |
Instance details Defined in Data.Reflection Methods reflect :: proxy n -> Integer #
KnownSymbol n => Reifies (n :: Symbol) String # |
Instance details Defined in Data.Reflection Methods reflect :: proxy n -> String #
Reifies Z Int # |
Instance details Defined in Data.Reflection Methods reflect :: proxy Z -> Int #
Reifies n Int => Reifies (D n :: Type) Int # |
Instance details Defined in Data.Reflection Methods reflect :: proxy (D n) -> Int #
Reifies n Int => Reifies (PD n :: Type) Int # |
Instance details Defined in Data.Reflection Methods reflect :: proxy (PD n) -> Int #
Reifies n Int => Reifies (SD n :: Type) Int # |
Instance details Defined in Data.Reflection Methods reflect :: proxy (SD n) -> Int #

reify :: a -> (forall s. Reifies s a => Proxy s -> r) -> r #

Reify a value at the type level, to be recovered with `reflect`.

reifyNat :: Integer -> (forall (n :: Nat). KnownNat n => Proxy n -> r) -> r #

This upgraded version of `reify` can be used to generate a `KnownNat` suitable for use with other APIs.

Attemping to pass a negative `Integer` as an argument will result in an `Underflow` exception.

Available only on GHC 7.8+

    >>> import GHC.TypeLits

    >>> reifyNat 4 natVal
    4

    >>> reifyNat 4 reflect
    4

reifySymbol :: String -> (forall (n :: Symbol). KnownSymbol n => Proxy n -> r) -> r #

This upgraded version of `reify` can be used to generate a `KnownSymbol` suitable for use with other APIs.

Available only on GHC 7.8+

    >>> import GHC.TypeLits

    >>> reifySymbol "hello" symbolVal
    "hello"

    >>> reifySymbol "hello" reflect
    "hello"

reifyTypeable :: Typeable a => a -> (forall s. (Typeable s, Reifies s a) => Proxy s -> r) -> r #

Reify a value at the type level in a `Typeable`-compatible fashion, to be recovered with `reflect`.

This can be necessary to work around the changes to `Data.Typeable` in GHC HEAD.

# Given

class Given a where #

This is a version of `Reifies` that allows for only a single value.

This is easier to work with than `Reifies` and permits extended defaulting, but it only offers a single reflected value of a given type at a time.

Methods

given :: a #

Recover the value of a given type previously encoded with `give`.

give :: a -> (Given a => r) -> r #

Reify a value into an instance to be recovered with `given`.

You should only `give` a single value for each type. If multiple instances are in scope, then the behavior is implementation defined.

# Template Haskell reflection

int :: Int -> TypeQ #

This can be used to generate a template haskell splice for a type level version of a given `int`.

This does not use GHC TypeLits, instead it generates a numeric type by hand similar to the ones used in the "Functional Pearl: Implicit Configurations" paper by Oleg Kiselyov and Chung-Chieh Shan.

`instance Num (Q Exp)` provided in this package allows writing `$(3)` instead of `$(int 3)`.

nat :: Int -> TypeQ #

This is a restricted version of `int` that can only generate natural numbers. Attempting to generate a negative number results in a compile time error. Also the resulting sequence will consist entirely of Z, D, and SD constructors representing the number in zeroless binary.

# Useful compile time naturals

data Z #

0

#### Instances

Instances details

Reifies Z Int # |
Instance details Defined in Data.Reflection Methods reflect :: proxy Z -> Int #

data D n #

2n

#### Instances

Instances details

Reifies n Int => Reifies (D n :: Type) Int # |
Instance details Defined in Data.Reflection Methods reflect :: proxy (D n) -> Int #

data SD n #

2n + 1

#### Instances

Instances details

Reifies n Int => Reifies (SD n :: Type) Int # |
Instance details Defined in Data.Reflection Methods reflect :: proxy (SD n) -> Int #

data PD n #

2n - 1

#### Instances

Instances details

Reifies n Int => Reifies (PD n :: Type) Int # |
Instance details Defined in Data.Reflection Methods reflect :: proxy (PD n) -> Int #

# Reified Monoids

data ReifiedMonoid a #

Constructors

ReifiedMonoid |
Fields reifiedMappend :: a -> a -> a reifiedMempty :: a

newtype ReflectedMonoid a (s :: k) #

Constructors

ReflectedMonoid a |

#### Instances

Instances details

Reifies s (ReifiedMonoid a) => Monoid (ReflectedMonoid a s) # |
Instance details Defined in Data.Reflection Methods mempty :: ReflectedMonoid a s # mappend :: ReflectedMonoid a s -> ReflectedMonoid a s -> ReflectedMonoid a s # mconcat :: [ReflectedMonoid a s] -> ReflectedMonoid a s #
Reifies s (ReifiedMonoid a) => Semigroup (ReflectedMonoid a s) # |
Instance details Defined in Data.Reflection Methods (<>) :: ReflectedMonoid a s -> ReflectedMonoid a s -> ReflectedMonoid a s # sconcat :: NonEmpty (ReflectedMonoid a s) -> ReflectedMonoid a s # stimes :: Integral b => b -> ReflectedMonoid a s -> ReflectedMonoid a s #

reifyMonoid :: (a -> a -> a) -> a -> (forall s. Reifies s (ReifiedMonoid a) => t -> ReflectedMonoid a s) -> t -> a #

foldMapBy :: Foldable t => (r -> r -> r) -> r -> (a -> r) -> t a -> r #

Fold a value using its `Foldable` instance using explicitly provided `Monoid` operations. This is like `foldMap` where the `Monoid` instance can be manually specified.

    foldMapBy mappend mempty ≡ foldMap

    >>> foldMapBy (+) 0 length ["hello","world"]
    10

foldBy :: Foldable t => (a -> a -> a) -> a -> t a -> a #

Fold a value using its `Foldable` instance using explicitly provided `Monoid` operations. This is like `fold` where the `Monoid` instance can be manually specified.

    foldBy mappend mempty ≡ fold

    >>> foldBy (++) [] ["hello","world"]
    "helloworld"

# Reified Applicatives

data ReifiedApplicative (f :: Type -> Type) #

Constructors

ReifiedApplicative |
Fields reifiedPure :: forall a. a -> f a reifiedAp :: forall a b. f (a -> b) -> f a -> f b

newtype ReflectedApplicative (f :: k -> Type) (s :: k1) (a :: k) #

Constructors

ReflectedApplicative (f a) |

#### Instances

Instances details

Reifies s (ReifiedApplicative f) => Applicative (ReflectedApplicative f s) # |
Instance details Defined in Data.Reflection Methods pure :: a -> ReflectedApplicative f s a # (<*>) :: ReflectedApplicative f s (a -> b) -> ReflectedApplicative f s a -> ReflectedApplicative f s b # liftA2 :: (a -> b -> c) -> ReflectedApplicative f s a -> ReflectedApplicative f s b -> ReflectedApplicative f s c # (*>) :: ReflectedApplicative f s a -> ReflectedApplicative f s b -> ReflectedApplicative f s b # (<*) :: ReflectedApplicative f s a -> ReflectedApplicative f s b -> ReflectedApplicative f s a #
Reifies s (ReifiedApplicative f) => Functor (ReflectedApplicative f s) # |
Instance details Defined in Data.Reflection Methods fmap :: (a -> b) -> ReflectedApplicative f s a -> ReflectedApplicative f s b # (<$) :: a -> ReflectedApplicative f s b -> ReflectedApplicative f s a #

reifyApplicative :: (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (forall s. Reifies s (ReifiedApplicative f) => t -> ReflectedApplicative f s a) -> t -> f a #

traverseBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> t a -> f (t b) #

Traverse a container using its `Traversable` instance using explicitly provided `Applicative` operations. This is like `traverse` where the `Applicative` instance can be manually specified.

sequenceBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> t (f a) -> f (t a) #

Sequence a container using its `Traversable` instance using explicitly provided `Applicative` operations. This is like `sequence` where the `Applicative` instance can be manually specified.

# Orphan instances

Num Exp # | This permits the use of $(5) as an expression splice, which stands for `Proxy :: Proxy $(5)`
Instance details Methods (+) :: Exp -> Exp -> Exp # (-) :: Exp -> Exp -> Exp # (*) :: Exp -> Exp -> Exp # negate :: Exp -> Exp # abs :: Exp -> Exp # signum :: Exp -> Exp # fromInteger :: Integer -> Exp #
Num Type # | This permits the use of $(5) as a type splice.
Instance details Methods (+) :: Type -> Type -> Type # (-) :: Type -> Type -> Type # (*) :: Type -> Type -> Type # negate :: Type -> Type # abs :: Type -> Type # signum :: Type -> Type # fromInteger :: Integer -> Type #
Num a => Num (Q a) # |
Instance details Methods (+) :: Q a -> Q a -> Q a # (-) :: Q a -> Q a -> Q a # (*) :: Q a -> Q a -> Q a # negate :: Q a -> Q a # abs :: Q a -> Q a # signum :: Q a -> Q a # fromInteger :: Integer -> Q a #
Fractional a => Fractional (Q a) # |
Instance details Methods (/) :: Q a -> Q a -> Q a # recip :: Q a -> Q a # fromRational :: Rational -> Q a #