clash-prelude-1.4.1: Clash: a functional hardware description language - Prelude library
Copyright(C) 2013-2016 University of Twente
2017-2019 Myrtle Software Ltd
2017 Google Inc.
LicenseBSD2 (see the file LICENSE)
MaintainerChristiaan Baaij <christiaan.baaij@gmail.com>
Safe HaskellSafe
LanguageHaskell2010
Extensions
  • ScopedTypeVariables
  • BangPatterns
  • ViewPatterns
  • DataKinds
  • InstanceSigs
  • StandaloneDeriving
  • DeriveDataTypeable
  • DeriveFunctor
  • DeriveTraversable
  • DeriveFoldable
  • DeriveGeneric
  • DefaultSignatures
  • DeriveLift
  • DerivingStrategies
  • FlexibleContexts
  • MagicHash
  • KindSignatures
  • TupleSections
  • TypeOperators
  • ExplicitNamespaces
  • ExplicitForAll
  • BinaryLiterals
  • TypeApplications

Clash.Prelude.Safe

Description

This is the Safe API only of Clash.Prelude

Clash is a functional hardware description language that borrows both its syntax and semantics from the functional programming language Haskell. The merits of using a functional language to describe hardware comes from the fact that combinational circuits can be directly modeled as mathematical functions and that functional languages lend themselves very well at describing and (de-)composing mathematical functions.

This package provides:

  • Prelude library containing datatypes and functions for circuit design

To use the library:

For now, Clash.Prelude is also the best starting point for exploring the library. A preliminary version of a tutorial can be found in Clash.Tutorial. Some circuit examples can be found in Clash.Examples.

Synopsis

Creating synchronous sequential circuits

mealy Source #

Arguments

:: (HiddenClockResetEnable dom, NFDataX s) 
=> (s -> i -> (s, o))

Transfer function in mealy machine form: state -> input -> (newstate,output)

-> s

Initial state

-> Signal dom i -> Signal dom o

Synchronous sequential function with input and output matching that of the mealy machine

Create a synchronous function from a combinational function describing a mealy machine

macT
  :: Int        -- Current state
  -> (Int,Int)  -- Input
  -> (Int,Int)  -- (Updated state, output)
macT s (x,y) = (s',s)
  where
    s' = x * y + s

mac :: HiddenClockResetEnable dom  => Signal dom (Int, Int) -> Signal dom Int
mac = mealy macT 0
>>> simulate @System mac [(0,0),(1,1),(2,2),(3,3),(4,4)]
[0,0,1,5,14...
...

Synchronous sequential functions can be composed just like their combinational counterpart:

dualMac
  :: HiddenClockResetEnable dom
  => (Signal dom Int, Signal dom Int)
  -> (Signal dom Int, Signal dom Int)
  -> Signal dom Int
dualMac (a,b) (x,y) = s1 + s2
  where
    s1 = mealy mac 0 (bundle (a,x))
    s2 = mealy mac 0 (bundle (b,y))

mealyB Source #

Arguments

:: (HiddenClockResetEnable dom, NFDataX s, Bundle i, Bundle o) 
=> (s -> i -> (s, o))

Transfer function in mealy machine form: state -> input -> (newstate,output)

-> s

Initial state

-> Unbundled dom i -> Unbundled dom o

Synchronous sequential function with input and output matching that of the mealy machine

A version of mealy that does automatic Bundleing

Given a function f of type:

f :: Int -> (Bool, Int) -> (Int, (Int, Bool))

When we want to make compositions of f in g using mealy, we have to write:

g a b c = (b1,b2,i2)
  where
    (i1,b1) = unbundle (mealy f 0 (bundle (a,b)))
    (i2,b2) = unbundle (mealy f 3 (bundle (c,i1)))

Using mealyB however we can write:

g a b c = (b1,b2,i2)
  where
    (i1,b1) = mealyB f 0 (a,b)
    (i2,b2) = mealyB f 3 (c,i1)

(<^>) Source #

Arguments

:: (HiddenClockResetEnable dom, NFDataX s, Bundle i, Bundle o) 
=> (s -> i -> (s, o))

Transfer function in mealy machine form: state -> input -> (newstate,output)

-> s

Initial state

-> Unbundled dom i -> Unbundled dom o

Synchronous sequential function with input and output matching that of the mealy machine

Infix version of mealyB

moore Source #

Arguments

:: (HiddenClockResetEnable dom, NFDataX s) 
=> (s -> i -> s)

Transfer function in moore machine form: state -> input -> newstate

-> (s -> o)

Output function in moore machine form: state -> output

-> s

Initial state

-> Signal dom i -> Signal dom o

Synchronous sequential function with input and output matching that of the moore machine

Create a synchronous function from a combinational function describing a moore machine

macT
  :: Int        -- Current state
  -> (Int,Int)  -- Input
  -> Int        -- Updated state
macT s (x,y) = x * y + s

mac
  :: HiddenClockResetEnable dom
  => Signal dom (Int, Int)
  -> Signal dom Int
mac = moore mac id 0
>>> simulate @System mac [(0,0),(1,1),(2,2),(3,3),(4,4)]
[0,0,1,5,14,30,...
...

Synchronous sequential functions can be composed just like their combinational counterpart:

dualMac
  :: HiddenClockResetEnable dom
  => (Signal dom Int, Signal dom Int)
  -> (Signal dom Int, Signal dom Int)
  -> Signal dom Int
dualMac (a,b) (x,y) = s1 + s2
  where
    s1 = moore mac id 0 (bundle (a,x))
    s2 = moore mac id 0 (bundle (b,y))

mooreB Source #

Arguments

:: (HiddenClockResetEnable dom, NFDataX s, Bundle i, Bundle o) 
=> (s -> i -> s)

Transfer function in moore machine form: state -> input -> newstate

-> (s -> o)

Output function in moore machine form: state -> output

-> s

Initial state

-> Unbundled dom i -> Unbundled dom o

Synchronous sequential function with input and output matching that of the moore machine

A version of moore that does automatic Bundleing

Given a functions t and o of types:

t :: Int -> (Bool, Int) -> Int
o :: Int -> (Int, Bool)

When we want to make compositions of t and o in g using moore, we have to write:

g a b c = (b1,b2,i2)
  where
    (i1,b1) = unbundle (moore t o 0 (bundle (a,b)))
    (i2,b2) = unbundle (moore t o 3 (bundle (c,i1)))

Using mooreB however we can write:

g a b c = (b1,b2,i2)
  where
    (i1,b1) = mooreB t o 0 (a,b)
    (i2,b2) = mooreB t o 3 (c,i1)

registerB :: (HiddenClockResetEnable dom, NFDataX a, Bundle a) => a -> Unbundled dom a -> Unbundled dom a infixr 3 Source #

Create a register function for product-type like signals (e.g. '(Signal a, Signal b)')

rP :: HiddenClockResetEnable dom
   => (Signal dom Int, Signal dom Int)
   -> (Signal dom Int, Signal dom Int)
rP = registerB (8,8)
>>> simulateB @System rP [(1,1),(2,2),(3,3)] :: [(Int,Int)]
[(8,8),(1,1),(2,2),(3,3)...
...

ROMs

asyncRom Source #

Arguments

:: (KnownNat n, Enum addr) 
=> Vec n a

ROM content

NB: must be a constant

-> addr

Read address rd

-> a

The value of the ROM at address rd

An asynchronous/combinational ROM with space for n elements

Additional helpful information:

asyncRomPow2 Source #

Arguments

:: KnownNat n 
=> Vec (2 ^ n) a

ROM content

NB: must be a constant

-> Unsigned n

Read address rd

-> a

The value of the ROM at address rd

An asynchronous/combinational ROM with space for 2^n elements

Additional helpful information:

rom Source #

Arguments

:: forall dom n m a. (NFDataX a, KnownNat n, KnownNat m, HiddenClock dom, HiddenEnable dom) 
=> Vec n a

ROM content

NB: must be a constant

-> Signal dom (Unsigned m)

Read address rd

-> Signal dom a

The value of the ROM at address rd

A ROM with a synchronous read port, with space for n elements

  • NB: Read value is delayed by 1 cycle
  • NB: Initial output value is undefined

Additional helpful information:

romPow2 Source #

Arguments

:: forall dom n a. (KnownNat n, NFDataX a, HiddenClock dom, HiddenEnable dom) 
=> Vec (2 ^ n) a

ROM content

NB: must be a constant

-> Signal dom (Unsigned n)

Read address rd

-> Signal dom a

The value of the ROM at address rd

A ROM with a synchronous read port, with space for 2^n elements

  • NB: Read value is delayed by 1 cycle
  • NB: Initial output value is undefined

Additional helpful information:

RAM primitives with a combinational read port

asyncRam Source #

Arguments

:: (Enum addr, HiddenClock dom, HiddenEnable dom, HasCallStack) 
=> SNat n

Size n of the RAM

-> Signal dom addr

Read address r

-> Signal dom (Maybe (addr, a))

(write address w, value to write)

-> Signal dom a

Value of the RAM at address r

Create a RAM with space for n elements.

Additional helpful information:

asyncRamPow2 Source #

Arguments

:: (KnownNat n, HiddenClock dom, HiddenEnable dom, HasCallStack) 
=> Signal dom (Unsigned n)

Read address r

-> Signal dom (Maybe (Unsigned n, a))

(write address w, value to write)

-> Signal dom a

Value of the RAM at address r

Create a RAM with space for 2^n elements

Additional helpful information:

BlockRAM primitives

blockRam Source #

Arguments

:: (HasCallStack, HiddenClock dom, HiddenEnable dom, NFDataX a, Enum addr) 
=> Vec n a

Initial content of the BRAM, also determines the size, n, of the BRAM.

NB: MUST be a constant.

-> Signal dom addr

Read address r

-> Signal dom (Maybe (addr, a))

(write address w, value to write)

-> Signal dom a

Value of the blockRAM at address r from the previous clock cycle

Create a blockRAM with space for n elements.

  • NB: Read value is delayed by 1 cycle
  • NB: Initial output value is undefined
bram40
  :: HiddenClock dom
  => Signal dom (Unsigned 6)
  -> Signal dom (Maybe (Unsigned 6, Bit))
  -> Signal dom Bit
bram40 = blockRam (replicate d40 1)

Additional helpful information:

  • See Clash.Prelude.BlockRam for more information on how to use a Block RAM.
  • Use the adapter readNew for obtaining write-before-read semantics like this: readNew (blockRam inits) rd wrM.

blockRamPow2 Source #

Arguments

:: (HasCallStack, HiddenClock dom, HiddenEnable dom, NFDataX a, KnownNat n) 
=> Vec (2 ^ n) a

Initial content of the BRAM, also determines the size, 2^n, of the BRAM.

NB: MUST be a constant.

-> Signal dom (Unsigned n)

Read address r

-> Signal dom (Maybe (Unsigned n, a))

(write address w, value to write)

-> Signal dom a

Value of the blockRAM at address r from the previous clock cycle

Create a blockRAM with space for 2^n elements

  • NB: Read value is delayed by 1 cycle
  • NB: Initial output value is undefined
bram32
  :: HiddenClock dom
  => Signal dom (Unsigned 5)
  -> Signal dom (Maybe (Unsigned 5, Bit))
  -> Signal dom Bit
bram32 = blockRamPow2 (replicate d32 1)

Additional helpful information:

  • See Clash.Prelude.BlockRam for more information on how to use a Block RAM.
  • Use the adapter readNew for obtaining write-before-read semantics like this: readNew (blockRamPow2 inits) rd wrM.

BlockRAM read/write conflict resolution

readNew Source #

Arguments

:: (HiddenClockResetEnable dom, NFDataX a, Eq addr) 
=> (Signal dom addr -> Signal dom (Maybe (addr, a)) -> Signal dom a)

The ram component

-> Signal dom addr

Read address r

-> Signal dom (Maybe (addr, a))

(Write address w, value to write)

-> Signal dom a

Value of the ram at address r from the previous clock cycle

Create read-after-write blockRAM from a read-before-write one (synchronized to system clock)

>>> import Clash.Prelude
>>> :t readNew (blockRam (0 :> 1 :> Nil))
readNew (blockRam (0 :> 1 :> Nil))
  :: ...
     ...
     ...
     ...
     ... =>
     Signal dom addr -> Signal dom (Maybe (addr, a)) -> Signal dom a

Utility functions

isRising Source #

Arguments

:: (HiddenClockResetEnable dom, NFDataX a, Bounded a, Eq a) 
=> a

Starting value

-> Signal dom a 
-> Signal dom Bool 

Give a pulse when the Signal goes from minBound to maxBound

isFalling Source #

Arguments

:: (HiddenClockResetEnable dom, NFDataX a, Bounded a, Eq a) 
=> a

Starting value

-> Signal dom a 
-> Signal dom Bool 

Give a pulse when the Signal goes from maxBound to minBound

riseEvery :: HiddenClockResetEnable dom => SNat n -> Signal dom Bool Source #

Give a pulse every n clock cycles. This is a useful helper function when combined with functions like regEn or mux, in order to delay a register by a known amount.

To be precise: the given signal will be False for the next n-1 cycles, followed by a single True value:

>>> Prelude.last (sampleN @System 1025 (riseEvery d1024)) == True
True
>>> Prelude.or (sampleN @System 1024 (riseEvery d1024)) == False
True

For example, to update a counter once every 10 million cycles:

counter = regEn 0 (riseEvery (SNat :: SNat 10000000)) (counter + 1)

oscillate :: HiddenClockResetEnable dom => Bool -> SNat n -> Signal dom Bool Source #

Oscillate a Bool for a given number of cycles. This is a convenient function when combined with something like regEn, as it allows you to easily hold a register value for a given number of cycles. The input Bool determines what the initial value is.

To oscillate on an interval of 5 cycles:

>>> sampleN @System 11 (oscillate False d5)
[False,False,False,False,False,False,True,True,True,True,True]

To oscillate between True and False:

>>> sampleN @System 11 (oscillate False d1)
[False,False,True,False,True,False,True,False,True,False,True]

An alternative definition for the above could be:

>>> let osc' = register False (not <$> osc')
>>> sampleN @System 200 (oscillate False d1) == sampleN @System 200 osc'
True

Exported modules

Synchronous signals

Datatypes

Bit vectors

Arbitrary-width numbers

Fixed point numbers

Fixed size vectors

data Vec :: Nat -> Type -> Type where Source #

Fixed size vectors.

  • Lists with their length encoded in their type
  • Vector elements have an ASCENDING subscript starting from 0 and ending at length - 1.

Constructors

Nil :: Vec 0 a 
Cons :: a -> Vec n a -> Vec (n + 1) a infixr 5 

Bundled Patterns

pattern (:<) :: Vec n a -> a -> Vec (n + 1) a infixl 5

Add an element to the tail of a vector.

>>> (3:>4:>5:>Nil) :< 1
<3,4,5,1>
>>> let x = (3:>4:>5:>Nil) :< 1
>>> :t x
x :: Num a => Vec 4 a

Can be used as a pattern:

>>> let f (_ :< y :< x) = y + x
>>> :t f
f :: Num a => Vec ((n + 1) + 1) a -> a
>>> f (3:>4:>5:>6:>7:>Nil)
13

Also in conjunctions with (:>):

>>> let g (a :> b :> (_ :< y :< x)) = a + b +  x + y
>>> :t g
g :: Num a => Vec ((((n + 1) + 1) + 1) + 1) a -> a
>>> g (1:>2:>3:>4:>5:>Nil)
12
pattern (:>) :: a -> Vec n a -> Vec (n + 1) a infixr 5

Add an element to the head of a vector.

>>> 3:>4:>5:>Nil
<3,4,5>
>>> let x = 3:>4:>5:>Nil
>>> :t x
x :: Num a => Vec 3 a

Can be used as a pattern:

>>> let f (x :> y :> _) = x + y
>>> :t f
f :: Num a => Vec ((n + 1) + 1) a -> a
>>> f (3:>4:>5:>6:>7:>Nil)
7

Also in conjunctions with (:<):

>>> let g (a :> b :> (_ :< y :< x)) = a + b +  x + y
>>> :t g
g :: Num a => Vec ((((n + 1) + 1) + 1) + 1) a -> a
>>> g (1:>2:>3:>4:>5:>Nil)
12

Instances

Instances details
Lift a => Lift (Vec n a :: Type) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

lift :: Vec n a -> Q Exp #

liftTyped :: Vec n a -> Q (TExp (Vec n a)) #

Functor (Vec n) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

fmap :: (a -> b) -> Vec n a -> Vec n b #

(<$) :: a -> Vec n b -> Vec n a #

KnownNat n => Applicative (Vec n) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

pure :: a -> Vec n a #

(<*>) :: Vec n (a -> b) -> Vec n a -> Vec n b #

liftA2 :: (a -> b -> c) -> Vec n a -> Vec n b -> Vec n c #

(*>) :: Vec n a -> Vec n b -> Vec n b #

(<*) :: Vec n a -> Vec n b -> Vec n a #

(KnownNat n, 1 <= n) => Foldable (Vec n) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

fold :: Monoid m => Vec n m -> m #

foldMap :: Monoid m => (a -> m) -> Vec n a -> m #

foldMap' :: Monoid m => (a -> m) -> Vec n a -> m #

foldr :: (a -> b -> b) -> b -> Vec n a -> b #

foldr' :: (a -> b -> b) -> b -> Vec n a -> b #

foldl :: (b -> a -> b) -> b -> Vec n a -> b #

foldl' :: (b -> a -> b) -> b -> Vec n a -> b #

foldr1 :: (a -> a -> a) -> Vec n a -> a #

foldl1 :: (a -> a -> a) -> Vec n a -> a #

toList :: Vec n a -> [a] #

null :: Vec n a -> Bool #

length :: Vec n a -> Int #

elem :: Eq a => a -> Vec n a -> Bool #

maximum :: Ord a => Vec n a -> a #

minimum :: Ord a => Vec n a -> a #

sum :: Num a => Vec n a -> a #

product :: Num a => Vec n a -> a #

(KnownNat n, 1 <= n) => Traversable (Vec n) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

traverse :: Applicative f => (a -> f b) -> Vec n a -> f (Vec n b) #

sequenceA :: Applicative f => Vec n (f a) -> f (Vec n a) #

mapM :: Monad m => (a -> m b) -> Vec n a -> m (Vec n b) #

sequence :: Monad m => Vec n (m a) -> m (Vec n a) #

(KnownNat n, Eq a) => Eq (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

(==) :: Vec n a -> Vec n a -> Bool #

(/=) :: Vec n a -> Vec n a -> Bool #

(KnownNat n, Typeable a, Data a) => Data (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Vec n a -> c (Vec n a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Vec n a) #

toConstr :: Vec n a -> Constr #

dataTypeOf :: Vec n a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Vec n a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Vec n a)) #

gmapT :: (forall b. Data b => b -> b) -> Vec n a -> Vec n a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Vec n a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Vec n a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Vec n a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Vec n a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Vec n a -> m (Vec n a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Vec n a -> m (Vec n a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Vec n a -> m (Vec n a) #

(KnownNat n, Ord a) => Ord (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

compare :: Vec n a -> Vec n a -> Ordering #

(<) :: Vec n a -> Vec n a -> Bool #

(<=) :: Vec n a -> Vec n a -> Bool #

(>) :: Vec n a -> Vec n a -> Bool #

(>=) :: Vec n a -> Vec n a -> Bool #

max :: Vec n a -> Vec n a -> Vec n a #

min :: Vec n a -> Vec n a -> Vec n a #

Show a => Show (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

showsPrec :: Int -> Vec n a -> ShowS #

show :: Vec n a -> String #

showList :: [Vec n a] -> ShowS #

KnownNat n => Generic (Vec n a) Source #

In many cases, this Generic instance only allows generic functions/instances over vectors of at least size 1, due to the n-1 in the Rep (Vec n a) definition.

We'll have to wait for things like https://ryanglscott.github.io/2018/02/11/how-to-derive-generic-for-some-gadts/ before we can work around this limitation

Instance details

Defined in Clash.Sized.Vector

Associated Types

type Rep (Vec n a) :: Type -> Type #

Methods

from :: Vec n a -> Rep (Vec n a) x #

to :: Rep (Vec n a) x -> Vec n a #

(KnownNat n, Semigroup a) => Semigroup (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

(<>) :: Vec n a -> Vec n a -> Vec n a #

sconcat :: NonEmpty (Vec n a) -> Vec n a #

stimes :: Integral b => b -> Vec n a -> Vec n a #

(KnownNat n, Monoid a) => Monoid (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

mempty :: Vec n a #

mappend :: Vec n a -> Vec n a -> Vec n a #

mconcat :: [Vec n a] -> Vec n a #

(KnownNat n, Arbitrary a) => Arbitrary (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

arbitrary :: Gen (Vec n a) #

shrink :: Vec n a -> [Vec n a] #

CoArbitrary a => CoArbitrary (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

coarbitrary :: Vec n a -> Gen b -> Gen b #

(Default a, KnownNat n) => Default (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

def :: Vec n a #

NFData a => NFData (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

rnf :: Vec n a -> () #

KnownNat n => Ixed (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

ix :: Index (Vec n a) -> Traversal' (Vec n a) (IxValue (Vec n a)) #

(NFDataX a, KnownNat n) => NFDataX (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

deepErrorX :: String -> Vec n a Source #

hasUndefined :: Vec n a -> Bool Source #

ensureSpine :: Vec n a -> Vec n a Source #

rnfX :: Vec n a -> () Source #

ShowX a => ShowX (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

Methods

showsPrecX :: Int -> Vec n a -> ShowS Source #

showX :: Vec n a -> String Source #

showListX :: [Vec n a] -> ShowS Source #

(KnownNat n, BitPack a) => BitPack (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

Associated Types

type BitSize (Vec n a) :: Nat Source #

Methods

pack :: Vec n a -> BitVector (BitSize (Vec n a)) Source #

unpack :: BitVector (BitSize (Vec n a)) -> Vec n a Source #

KnownNat n => Bundle (Vec n a) Source # 
Instance details

Defined in Clash.Signal.Bundle

Associated Types

type Unbundled dom (Vec n a) = (res :: Type) Source #

Methods

bundle :: forall (dom :: Domain). Unbundled dom (Vec n a) -> Signal dom (Vec n a) Source #

unbundle :: forall (dom :: Domain). Signal dom (Vec n a) -> Unbundled dom (Vec n a) Source #

KnownNat n => Bundle (Vec n a) Source # 
Instance details

Defined in Clash.Signal.Delayed.Bundle

Associated Types

type Unbundled dom d (Vec n a) = (res :: Type) Source #

Methods

bundle :: forall (dom :: Domain) (d :: Nat). Unbundled dom d (Vec n a) -> DSignal dom d (Vec n a) Source #

unbundle :: forall (dom :: Domain) (d :: Nat). DSignal dom d (Vec n a) -> Unbundled dom d (Vec n a) Source #

(KnownNat n, AutoReg a) => AutoReg (Vec n a) Source # 
Instance details

Defined in Clash.Class.AutoReg.Internal

Methods

autoReg :: forall (dom :: Domain). (HasCallStack, KnownDomain dom) => Clock dom -> Reset dom -> Enable dom -> Vec n a -> Signal dom (Vec n a) -> Signal dom (Vec n a) Source #

(LockStep en a, KnownNat n) => LockStep (Vec n en) (Vec n a) Source # 
Instance details

Defined in Clash.Prelude.DataFlow

Methods

lockStep :: forall (dom :: Domain). DataFlow dom (Vec n en) Bool (Vec n a) (Vec n a) Source #

stepLock :: forall (dom :: Domain). DataFlow dom Bool (Vec n en) (Vec n a) (Vec n a) Source #

type Unbundled t d (Vec n a) Source # 
Instance details

Defined in Clash.Signal.Delayed.Bundle

type Unbundled t d (Vec n a) = Vec n (DSignal t d a)
type HasDomain dom (Vec n a) Source # 
Instance details

Defined in Clash.Class.HasDomain.HasSpecificDomain

type HasDomain dom (Vec n a) = HasDomain dom a
type TryDomain t (Vec n a) Source # 
Instance details

Defined in Clash.Class.HasDomain.HasSingleDomain

type TryDomain t (Vec n a) = TryDomain t a
type Unbundled t (Vec n a) Source # 
Instance details

Defined in Clash.Signal.Bundle

type Unbundled t (Vec n a) = Vec n (Signal t a)
type Rep (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

type Rep (Vec n a) = D1 ('MetaData "Vec" "Clash.Data.Vector" "clash-prelude" 'False) (C1 ('MetaCons "Nil" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Cons" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Vec (n - 1) a))))
type Index (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

type Index (Vec n a) = Index n
type IxValue (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

type IxValue (Vec n a) = a
type BitSize (Vec n a) Source # 
Instance details

Defined in Clash.Sized.Vector

type BitSize (Vec n a) = n * BitSize a

foldl :: (b -> a -> b) -> b -> Vec n a -> b Source #

foldl, applied to a binary operator, a starting value (typically the left-identity of the operator), and a vector, reduces the vector using the binary operator, from left to right:

foldl f z (x1 :> x2 :> ... :> xn :> Nil) == (...((z `f` x1) `f` x2) `f`...) `f` xn
foldl f z Nil                            == z
>>> foldl (/) 1 (5 :> 4 :> 3 :> 2 :> Nil)
8.333333333333333e-3

"foldl f z xs" corresponds to the following circuit layout:

NB: "foldl f z xs" produces a linear structure, which has a depth, or delay, of O(length xs). Use fold if your binary operator f is associative, as "fold f xs" produces a structure with a depth of O(log_2(length xs)).

foldr :: (a -> b -> b) -> b -> Vec n a -> b Source #

foldr, applied to a binary operator, a starting value (typically the right-identity of the operator), and a vector, reduces the vector using the binary operator, from right to left:

foldr f z (x1 :> ... :> xn1 :> xn :> Nil) == x1 `f` (... (xn1 `f` (xn `f` z))...)
foldr r z Nil                             == z
>>> foldr (/) 1 (5 :> 4 :> 3 :> 2 :> Nil)
1.875

"foldr f z xs" corresponds to the following circuit layout:

NB: "foldr f z xs" produces a linear structure, which has a depth, or delay, of O(length xs). Use fold if your binary operator f is associative, as "fold f xs" produces a structure with a depth of O(log_2(length xs)).

map :: (a -> b) -> Vec n a -> Vec n b Source #

"map f xs" is the vector obtained by applying f to each element of xs, i.e.,

map f (x1 :> x2 :>  ... :> xn :> Nil) == (f x1 :> f x2 :> ... :> f xn :> Nil)

and corresponds to the following circuit layout:

bv2v :: KnownNat n => BitVector n -> Vec n Bit Source #

Convert a BitVector to a Vec of Bits.

>>> let x = 6 :: BitVector 8
>>> x
0000_0110
>>> bv2v x
<0,0,0,0,0,1,1,0>

data VCons (a :: Type) (f :: TyFun Nat Type) :: Type Source #

To be used as the motive p for dfold, when the f in "dfold p f" is a variation on (:>), e.g.:

map' :: forall n a b . KnownNat n => (a -> b) -> Vec n a -> Vec n b
map' f = dfold (Proxy @(VCons b)) (_ x xs -> f x :> xs)

Instances

Instances details
type Apply (VCons a :: TyFun Nat Type -> Type) (l :: Nat) Source # 
Instance details

Defined in Clash.Sized.Vector

type Apply (VCons a :: TyFun Nat Type -> Type) (l :: Nat) = Vec l a

traverse# :: forall a f b n. Applicative f => (a -> f b) -> Vec n a -> f (Vec n b) Source #

singleton :: a -> Vec 1 a Source #

Create a vector of one element

>>> singleton 5
<5>

head :: Vec (n + 1) a -> a Source #

Extract the first element of a vector

>>> head (1:>2:>3:>Nil)
1

# 421 "srcClashSized/Vector.hs" >>> head Nil BLANKLINE interactive:... • Couldn't match type ‘1’ with ‘0’ Expected type: Vec (0 + 1) a Actual type: Vec 0 a • In the first argument of ‘head’, namely ‘Nil’ In the expression: head Nil In an equation for ‘it’: it = head Nil

tail :: Vec (n + 1) a -> Vec n a Source #

Extract the elements after the head of a vector

>>> tail (1:>2:>3:>Nil)
<2,3>

# 454 "srcClashSized/Vector.hs" >>> tail Nil BLANKLINE interactive:... • Couldn't match type ‘1’ with ‘0’ Expected type: Vec (0 + 1) a Actual type: Vec 0 a • In the first argument of ‘tail’, namely ‘Nil’ In the expression: tail Nil In an equation for ‘it’: it = tail Nil

last :: Vec (n + 1) a -> a Source #

Extract the last element of a vector

>>> last (1:>2:>3:>Nil)
3

# 487 "srcClashSized/Vector.hs" >>> last Nil BLANKLINE interactive:... • Couldn't match type ‘1’ with ‘0’ Expected type: Vec (0 + 1) a Actual type: Vec 0 a • In the first argument of ‘last’, namely ‘Nil’ In the expression: last Nil In an equation for ‘it’: it = last Nil

init :: Vec (n + 1) a -> Vec n a Source #

Extract all the elements of a vector except the last element

>>> init (1:>2:>3:>Nil)
<1,2>

# 521 "srcClashSized/Vector.hs" >>> init Nil BLANKLINE interactive:... • Couldn't match type ‘1’ with ‘0’ Expected type: Vec (0 + 1) a Actual type: Vec 0 a • In the first argument of ‘init’, namely ‘Nil’ In the expression: init Nil In an equation for ‘it’: it = init Nil

shiftInAt0 Source #

Arguments

:: KnownNat n 
=> Vec n a

The old vector

-> Vec m a

The elements to shift in at the head

-> (Vec n a, Vec m a)

(The new vector, shifted out elements)

Shift in elements to the head of a vector, bumping out elements at the tail. The result is a tuple containing:

  • The new vector
  • The shifted out elements
>>> shiftInAt0 (1 :> 2 :> 3 :> 4 :> Nil) ((-1) :> 0 :> Nil)
(<-1,0,1,2>,<3,4>)
>>> shiftInAt0 (1 :> Nil) ((-1) :> 0 :> Nil)
(<-1>,<0,1>)

shiftInAtN Source #

Arguments

:: KnownNat m 
=> Vec n a

The old vector

-> Vec m a

The elements to shift in at the tail

-> (Vec n a, Vec m a)

(The new vector, shifted out elements)

Shift in element to the tail of a vector, bumping out elements at the head. The result is a tuple containing:

  • The new vector
  • The shifted out elements
>>> shiftInAtN (1 :> 2 :> 3 :> 4 :> Nil) (5 :> 6 :> Nil)
(<3,4,5,6>,<1,2>)
>>> shiftInAtN (1 :> Nil) (2 :> 3 :> Nil)
(<3>,<1,2>)

(+>>) :: KnownNat n => a -> Vec n a -> Vec n a infixr 4 Source #

Add an element to the head of a vector, and extract all but the last element.

>>> 1 +>> (3:>4:>5:>Nil)
<1,3,4>
>>> 1 +>> Nil
<>

(<<+) :: Vec n a -> a -> Vec n a infixl 4 Source #

Add an element to the tail of a vector, and extract all but the first element.

>>> (3:>4:>5:>Nil) <<+ 1
<4,5,1>
>>> Nil <<+ 1
<>

shiftOutFrom0 Source #

Arguments

:: (Default a, KnownNat m) 
=> SNat m

m, the number of elements to shift out

-> Vec (m + n) a

The old vector

-> (Vec (m + n) a, Vec m a)

(The new vector, shifted out elements)

Shift m elements out from the head of a vector, filling up the tail with Default values. The result is a tuple containing:

  • The new vector
  • The shifted out values
>>> shiftOutFrom0 d2 ((1 :> 2 :> 3 :> 4 :> 5 :> Nil) :: Vec 5 Integer)
(<3,4,5,0,0>,<1,2>)

shiftOutFromN Source #

Arguments

:: (Default a, KnownNat n) 
=> SNat m

m, the number of elements to shift out

-> Vec (m + n) a

The old vector

-> (Vec (m + n) a, Vec m a)

(The new vector, shifted out elements)

Shift m elements out from the tail of a vector, filling up the head with Default values. The result is a tuple containing:

  • The new vector
  • The shifted out values
>>> shiftOutFromN d2 ((1 :> 2 :> 3 :> 4 :> 5 :> Nil) :: Vec 5 Integer)
(<0,0,1,2,3>,<4,5>)

(++) :: Vec n a -> Vec m a -> Vec (n + m) a infixr 5 Source #

Append two vectors.

>>> (1:>2:>3:>Nil) ++ (7:>8:>Nil)
<1,2,3,7,8>

splitAt :: SNat m -> Vec (m + n) a -> (Vec m a, Vec n a) Source #

Split a vector into two vectors at the given point.

>>> splitAt (SNat :: SNat 3) (1:>2:>3:>7:>8:>Nil)
(<1,2,3>,<7,8>)
>>> splitAt d3 (1:>2:>3:>7:>8:>Nil)
(<1,2,3>,<7,8>)

splitAtI :: KnownNat m => Vec (m + n) a -> (Vec m a, Vec n a) Source #

Split a vector into two vectors where the length of the two is determined by the context.

>>> splitAtI (1:>2:>3:>7:>8:>Nil) :: (Vec 2 Int, Vec 3 Int)
(<1,2>,<3,7,8>)

concat :: Vec n (Vec m a) -> Vec (n * m) a Source #

Concatenate a vector of vectors.

>>> concat ((1:>2:>3:>Nil) :> (4:>5:>6:>Nil) :> (7:>8:>9:>Nil) :> (10:>11:>12:>Nil) :> Nil)
<1,2,3,4,5,6,7,8,9,10,11,12>

concatMap :: (a -> Vec m b) -> Vec n a -> Vec (n * m) b Source #

Map a function over all the elements of a vector and concatentate the resulting vectors.

>>> concatMap (replicate d3) (1:>2:>3:>Nil)
<1,1,1,2,2,2,3,3,3>

unconcat :: KnownNat n => SNat m -> Vec (n * m) a -> Vec n (Vec m a) Source #

Split a vector of (n * m) elements into a vector of "vectors of length m", where the length m is given.

>>> unconcat d4 (1:>2:>3:>4:>5:>6:>7:>8:>9:>10:>11:>12:>Nil)
<<1,2,3,4>,<5,6,7,8>,<9,10,11,12>>

unconcatI :: (KnownNat n, KnownNat m) => Vec (n * m) a -> Vec n (Vec m a) Source #

Split a vector of (n * m) elements into a vector of "vectors of length m", where the length m is determined by the context.

>>> unconcatI (1:>2:>3:>4:>5:>6:>7:>8:>9:>10:>11:>12:>Nil) :: Vec 2 (Vec 6 Int)
<<1,2,3,4,5,6>,<7,8,9,10,11,12>>

merge :: KnownNat n => Vec n a -> Vec n a -> Vec (2 * n) a Source #

Merge two vectors, alternating their elements, i.e.,

>>> merge (1 :> 2 :> 3 :> 4 :> Nil) (5 :> 6 :> 7 :> 8 :> Nil)
<1,5,2,6,3,7,4,8>

reverse :: Vec n a -> Vec n a Source #

The elements in a vector in reverse order.

>>> reverse (1:>2:>3:>4:>Nil)
<4,3,2,1>

imap :: forall n a b. KnownNat n => (Index n -> a -> b) -> Vec n a -> Vec n b Source #

Apply a function of every element of a vector and its index.

>>> :t imap (+) (2 :> 2 :> 2 :> 2 :> Nil)
imap (+) (2 :> 2 :> 2 :> 2 :> Nil) :: Vec 4 (Index 4)
>>> imap (+) (2 :> 2 :> 2 :> 2 :> Nil)
<2,3,*** Exception: X: Clash.Sized.Index: result 4 is out of bounds: [0..3]
...
>>> imap (\i a -> fromIntegral i + a) (2 :> 2 :> 2 :> 2 :> Nil) :: Vec 4 (Unsigned 8)
<2,3,4,5>

"imap f xs" corresponds to the following circuit layout:

izipWith :: KnownNat n => (Index n -> a -> b -> c) -> Vec n a -> Vec n b -> Vec n c Source #

Zip two vectors with a functions that also takes the elements' indices.

>>> izipWith (\i a b -> i + a + b) (2 :> 2 :> Nil)  (3 :> 3:> Nil)
<*** Exception: X: Clash.Sized.Index: result 3 is out of bounds: [0..1]
...
>>> izipWith (\i a b -> fromIntegral i + a + b) (2 :> 2 :> Nil) (3 :> 3 :> Nil) :: Vec 2 (Unsigned 8)
<5,6>

"imap f xs" corresponds to the following circuit layout:

NB: izipWith is strict in its second argument, and lazy in its third. This matters when izipWith is used in a recursive setting. See lazyV for more information.

ifoldr :: KnownNat n => (Index n -> a -> b -> b) -> b -> Vec n a -> b Source #

Right fold (function applied to each element and its index)

>>> let findLeftmost x xs = ifoldr (\i a b -> if a == x then Just i else b) Nothing xs
>>> findLeftmost 3 (1:>3:>2:>4:>3:>5:>6:>Nil)
Just 1
>>> findLeftmost 8 (1:>3:>2:>4:>3:>5:>6:>Nil)
Nothing

"ifoldr f z xs" corresponds to the following circuit layout:

ifoldl :: KnownNat n => (a -> Index n -> b -> a) -> a -> Vec n b -> a Source #

Left fold (function applied to each element and its index)

>>> let findRightmost x xs = ifoldl (\a i b -> if b == x then Just i else a) Nothing xs
>>> findRightmost 3 (1:>3:>2:>4:>3:>5:>6:>Nil)
Just 4
>>> findRightmost 8 (1:>3:>2:>4:>3:>5:>6:>Nil)
Nothing

"ifoldl f z xs" corresponds to the following circuit layout:

indices :: KnownNat n => SNat n -> Vec n (Index n) Source #

Generate a vector of indices.

>>> indices d4
<0,1,2,3>

indicesI :: KnownNat n => Vec n (Index n) Source #

Generate a vector of indices, where the length of the vector is determined by the context.

>>> indicesI :: Vec 4 (Index 4)
<0,1,2,3>

findIndex :: KnownNat n => (a -> Bool) -> Vec n a -> Maybe (Index n) Source #

"findIndex p xs" returns the index of the first element of xs satisfying the predicate p, or Nothing if there is no such element.

>>> findIndex (> 3) (1:>3:>2:>4:>3:>5:>6:>Nil)
Just 3
>>> findIndex (> 8) (1:>3:>2:>4:>3:>5:>6:>Nil)
Nothing

elemIndex :: (KnownNat n, Eq a) => a -> Vec n a -> Maybe (Index n) Source #

"elemIndex a xs" returns the index of the first element which is equal (by ==) to the query element a, or Nothing if there is no such element.

>>> elemIndex 3 (1:>3:>2:>4:>3:>5:>6:>Nil)
Just 1
>>> elemIndex 8 (1:>3:>2:>4:>3:>5:>6:>Nil)
Nothing

zipWith :: (a -> b -> c) -> Vec n a -> Vec n b -> Vec n c Source #

zipWith generalizes zip by zipping with the function given as the first argument, instead of a tupling function. For example, "zipWith (+)" applied to two vectors produces the vector of corresponding sums.

zipWith f (x1 :> x2 :> ... xn :> Nil) (y1 :> y2 :> ... :> yn :> Nil) == (f x1 y1 :> f x2 y2 :> ... :> f xn yn :> Nil)

"zipWith f xs ys" corresponds to the following circuit layout:

NB: zipWith is strict in its second argument, and lazy in its third. This matters when zipWith is used in a recursive setting. See lazyV for more information.

zipWith3 :: (a -> b -> c -> d) -> Vec n a -> Vec n b -> Vec n c -> Vec n d Source #

zipWith3 generalizes zip3 by zipping with the function given as the first argument, instead of a tupling function.

zipWith3 f (x1 :> x2 :> ... xn :> Nil) (y1 :> y2 :> ... :> yn :> Nil) (z1 :> z2 :> ... :> zn :> Nil) == (f x1 y1 z1 :> f x2 y2 z2 :> ... :> f xn yn zn :> Nil)

"zipWith3 f xs ys zs" corresponds to the following circuit layout:

NB: zipWith3 is strict in its second argument, and lazy in its third and fourth. This matters when zipWith3 is used in a recursive setting. See lazyV for more information.

zipWith4 :: (a -> b -> c -> d -> e) -> Vec n a -> Vec n b -> Vec n c -> Vec n d -> Vec n e Source #

zipWith5 :: (a -> b -> c -> d -> e -> f) -> Vec n a -> Vec n b -> Vec n c -> Vec n d -> Vec n e -> Vec n f Source #

zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> Vec n a -> Vec n b -> Vec n c -> Vec n d -> Vec n e -> Vec n f -> Vec n g Source #

zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> Vec n a -> Vec n b -> Vec n c -> Vec n d -> Vec n e -> Vec n f -> Vec n g -> Vec n h Source #

foldr1 :: (a -> a -> a) -> Vec (n + 1) a -> a Source #

foldr1 is a variant of foldr that has no starting value argument, and thus must be applied to non-empty vectors.

foldr1 f (x1 :> ... :> xn2 :> xn1 :> xn :> Nil) == x1 `f` (... (xn2 `f` (xn1 `f` xn))...)
foldr1 f (x1 :> Nil)                            == x1
foldr1 f Nil                                    == TYPE ERROR
>>> foldr1 (/) (5 :> 4 :> 3 :> 2 :> 1 :> Nil)
1.875

"foldr1 f xs" corresponds to the following circuit layout:

NB: "foldr1 f z xs" produces a linear structure, which has a depth, or delay, of O(length xs). Use fold if your binary operator f is associative, as "fold f xs" produces a structure with a depth of O(log_2(length xs)).

foldl1 :: (a -> a -> a) -> Vec (n + 1) a -> a Source #

foldl1 is a variant of foldl that has no starting value argument, and thus must be applied to non-empty vectors.

foldl1 f (x1 :> x2 :> x3 :> ... :> xn :> Nil) == (...((x1 `f` x2) `f` x3) `f`...) `f` xn
foldl1 f (x1 :> Nil)                          == x1
foldl1 f Nil                                  == TYPE ERROR
>>> foldl1 (/) (1 :> 5 :> 4 :> 3 :> 2 :> Nil)
8.333333333333333e-3

"foldl1 f xs" corresponds to the following circuit layout:

NB: "foldl1 f z xs" produces a linear structure, which has a depth, or delay, of O(length xs). Use fold if your binary operator f is associative, as "fold f xs" produces a structure with a depth of O(log_2(length xs)).

fold :: forall n a. (a -> a -> a) -> Vec (n + 1) a -> a Source #

fold is a variant of foldr1 and foldl1, but instead of reducing from right to left, or left to right, it reduces a vector using a tree-like structure. The depth, or delay, of the structure produced by "fold f xs", is hence O(log_2(length xs)), and not O(length xs).

NB: The binary operator "f" in "fold f xs" must be associative.

fold f (x1 :> x2 :> ... :> xn1 :> xn :> Nil) == ((x1 `f` x2) `f` ...) `f` (... `f` (xn1 `f` xn))
fold f (x1 :> Nil)                           == x1
fold f Nil                                   == TYPE ERROR
>>> fold (+) (5 :> 4 :> 3 :> 2 :> 1 :> Nil)
15

"fold f xs" corresponds to the following circuit layout:

scanl :: (b -> a -> b) -> b -> Vec n a -> Vec (n + 1) b Source #

scanl is similar to foldl, but returns a vector of successive reduced values from the left:

scanl f z (x1 :> x2 :> ... :> Nil) == z :> (z `f` x1) :> ((z `f` x1) `f` x2) :> ... :> Nil
>>> scanl (+) 0 (5 :> 4 :> 3 :> 2 :> Nil)
<0,5,9,12,14>

"scanl f z xs" corresponds to the following circuit layout:

NB:

last (scanl f z xs) == foldl f z xs

postscanl :: (b -> a -> b) -> b -> Vec n a -> Vec n b Source #

postscanl is a variant of scanl where the first result is dropped:

postscanl f z (x1 :> x2 :> ... :> Nil) == (z `f` x1) :> ((z `f` x1) `f` x2) :> ... :> Nil
>>> postscanl (+) 0 (5 :> 4 :> 3 :> 2 :> Nil)
<5,9,12,14>

"postscanl f z xs" corresponds to the following circuit layout:

scanr :: (a -> b -> b) -> b -> Vec n a -> Vec (n + 1) b Source #

scanr is similar to foldr, but returns a vector of successive reduced values from the right:

scanr f z (... :> xn1 :> xn :> Nil) == ... :> (xn1 `f` (xn `f` z)) :> (xn `f` z) :> z :> Nil
>>> scanr (+) 0 (5 :> 4 :> 3 :> 2 :> Nil)
<14,9,5,2,0>

"scanr f z xs" corresponds to the following circuit layout:

NB:

head (scanr f z xs) == foldr f z xs

postscanr :: (a -> b -> b) -> b -> Vec n a -> Vec n b Source #

postscanr is a variant of scanr that where the last result is dropped:

postscanr f z (... :> xn1 :> xn :> Nil) == ... :> (xn1 `f` (xn `f` z)) :> (xn `f` z) :> Nil
>>> postscanr (+) 0 (5 :> 4 :> 3 :> 2 :> Nil)
<14,9,5,2>

"postscanr f z xs" corresponds to the following circuit layout:

mapAccumL :: (acc -> x -> (acc, y)) -> acc -> Vec n x -> (acc, Vec n y) Source #

The mapAccumL function behaves like a combination of map and foldl; it applies a function to each element of a vector, passing an accumulating parameter from left to right, and returning a final value of this accumulator together with the new vector.

>>> mapAccumL (\acc x -> (acc + x,acc + 1)) 0 (1 :> 2 :> 3 :> 4 :> Nil)
(10,<1,2,4,7>)

"mapAccumL f acc xs" corresponds to the following circuit layout:

mapAccumR :: (acc -> x -> (acc, y)) -> acc -> Vec n x -> (acc, Vec n y) Source #

The mapAccumR function behaves like a combination of map and foldr; it applies a function to each element of a vector, passing an accumulating parameter from right to left, and returning a final value of this accumulator together with the new vector.

>>> mapAccumR (\acc x -> (acc + x,acc + 1)) 0 (1 :> 2 :> 3 :> 4 :> Nil)
(10,<10,8,5,1>)

"mapAccumR f acc xs" corresponds to the following circuit layout:

zip :: Vec n a -> Vec n b -> Vec n (a, b) Source #

zip takes two vectors and returns a vector of corresponding pairs.

>>> zip (1:>2:>3:>4:>Nil) (4:>3:>2:>1:>Nil)
<(1,4),(2,3),(3,2),(4,1)>

zip3 :: Vec n a -> Vec n b -> Vec n c -> Vec n (a, b, c) Source #

zip3 takes three vectors and returns a vector of corresponding triplets.

>>> zip3 (1:>2:>3:>4:>Nil) (4:>3:>2:>1:>Nil) (5:>6:>7:>8:>Nil)
<(1,4,5),(2,3,6),(3,2,7),(4,1,8)>

zip4 :: Vec n a -> Vec n b -> Vec n c -> Vec n d -> Vec n (a, b, c, d) Source #

zip4 takes four vectors and returns a list of quadruples, analogous to zip.

zip5 :: Vec n a -> Vec n b -> Vec n c -> Vec n d -> Vec n e -> Vec n (a, b, c, d, e) Source #

zip5 takes five vectors and returns a list of five-tuples, analogous to zip.

zip6 :: Vec n a -> Vec n b -> Vec n c -> Vec n d -> Vec n e -> Vec n f -> Vec n (a, b, c, d, e, f) Source #

zip6 takes six vectors and returns a list of six-tuples, analogous to zip.

zip7 :: Vec n a -> Vec n b -> Vec n c -> Vec n d -> Vec n e -> Vec n f -> Vec n g -> Vec n (a, b, c, d, e, f, g) Source #

zip7 takes seven vectors and returns a list of seven-tuples, analogous to zip.

unzip :: Vec n (a, b) -> (Vec n a, Vec n b) Source #

unzip transforms a vector of pairs into a vector of first components and a vector of second components.

>>> unzip ((1,4):>(2,3):>(3,2):>(4,1):>Nil)
(<1,2,3,4>,<4,3,2,1>)

unzip3 :: Vec n (a, b, c) -> (Vec n a, Vec n b, Vec n c) Source #

unzip3 transforms a vector of triplets into a vector of first components, a vector of second components, and a vector of third components.

>>> unzip3 ((1,4,5):>(2,3,6):>(3,2,7):>(4,1,8):>Nil)
(<1,2,3,4>,<4,3,2,1>,<5,6,7,8>)

unzip4 :: Vec n (a, b, c, d) -> (Vec n a, Vec n b, Vec n c, Vec n d) Source #

unzip4 takes a vector of quadruples and returns four vectors, analogous to unzip.

unzip5 :: Vec n (a, b, c, d, e) -> (Vec n a, Vec n b, Vec n c, Vec n d, Vec n e) Source #

unzip5 takes a vector of five-tuples and returns five vectors, analogous to unzip.

unzip6 :: Vec n (a, b, c, d, e, f) -> (Vec n a, Vec n b, Vec n c, Vec n d, Vec n e, Vec n f) Source #

unzip6 takes a vector of six-tuples and returns six vectors, analogous to unzip.

unzip7 :: Vec n (a, b, c, d, e, f, g) -> (Vec n a, Vec n b, Vec n c, Vec n d, Vec n e, Vec n f, Vec n g) Source #

unzip7 takes a vector of seven-tuples and returns seven vectors, analogous to unzip.

(!!) :: (KnownNat n, Enum i) => Vec n a -> i -> a Source #

"xs !! n" returns the n'th element of xs.

NB: vector elements have an ASCENDING subscript starting from 0 and ending at length - 1.

>>> (1:>2:>3:>4:>5:>Nil) !! 4
5
>>> (1:>2:>3:>4:>5:>Nil) !! (length (1:>2:>3:>4:>5:>Nil) - 1)
5
>>> (1:>2:>3:>4:>5:>Nil) !! 1
2
>>> (1:>2:>3:>4:>5:>Nil) !! 14
*** Exception: Clash.Sized.Vector.(!!): index 14 is larger than maximum index 4
...

length :: KnownNat n => Vec n a -> Int Source #

The length of a Vector as an Int value.

>>> length (6 :> 7 :> 8 :> Nil)
3

replace :: (KnownNat n, Enum i) => i -> a -> Vec n a -> Vec n a Source #

"replace n a xs" returns the vector xs where the n'th element is replaced by a.

NB: vector elements have an ASCENDING subscript starting from 0 and ending at length - 1.

>>> replace 3 7 (1:>2:>3:>4:>5:>Nil)
<1,2,3,7,5>
>>> replace 0 7 (1:>2:>3:>4:>5:>Nil)
<7,2,3,4,5>
>>> replace 9 7 (1:>2:>3:>4:>5:>Nil)
<1,2,3,4,*** Exception: Clash.Sized.Vector.replace: index 9 is larger than maximum index 4
...

take :: SNat m -> Vec (m + n) a -> Vec m a Source #

"take n xs" returns the n-length prefix of xs.

>>> take (SNat :: SNat 3) (1:>2:>3:>4:>5:>Nil)
<1,2,3>
>>> take d3               (1:>2:>3:>4:>5:>Nil)
<1,2,3>
>>> take d0               (1:>2:>Nil)
<>

# 1446 "srcClashSized/Vector.hs" >>> take d4 (1:>2:>Nil) BLANKLINE interactive:... • Couldn't match type ‘4 + n0’ with ‘2’ Expected type: Vec (4 + n0) a Actual type: Vec (1 + 1) a The type variable ‘n0’ is ambiguous • In the second argument of ‘take’, namely ‘(1 :> 2 :> Nil)’ In the expression: take d4 (1 :> 2 :> Nil) In an equation for ‘it’: it = take d4 (1 :> 2 :> Nil)

takeI :: KnownNat m => Vec (m + n) a -> Vec m a Source #

"takeI xs" returns the prefix of xs as demanded by the context.

>>> takeI (1:>2:>3:>4:>5:>Nil) :: Vec 2 Int
<1,2>

drop :: SNat m -> Vec (m + n) a -> Vec n a Source #

"drop n xs" returns the suffix of xs after the first n elements.

>>> drop (SNat :: SNat 3) (1:>2:>3:>4:>5:>Nil)
<4,5>
>>> drop d3               (1:>2:>3:>4:>5:>Nil)
<4,5>
>>> drop d0               (1:>2:>Nil)
<1,2>
>>> drop d4               (1:>2:>Nil)

<interactive>:...: error:
    • Couldn't match...type ‘4 + n0...
      The type variable ‘n0’ is ambiguous
    • In the first argument of ‘print’, namely ‘it’
      In a stmt of an interactive GHCi command: print it

dropI :: KnownNat m => Vec (m + n) a -> Vec n a Source #

"dropI xs" returns the suffix of xs as demanded by the context.

>>> dropI (1:>2:>3:>4:>5:>Nil) :: Vec 2 Int
<4,5>

at :: SNat m -> Vec (m + (n + 1)) a -> a Source #

"at n xs" returns n'th element of xs

NB: vector elements have an ASCENDING subscript starting from 0 and ending at length - 1.

>>> at (SNat :: SNat 1) (1:>2:>3:>4:>5:>Nil)
2
>>> at d1               (1:>2:>3:>4:>5:>Nil)
2

select :: CmpNat (i + s) (s * n) ~ 'GT => SNat f -> SNat s -> SNat n -> Vec (f + i) a -> Vec n a Source #

"select f s n xs" selects n elements with step-size s and offset f from xs.

>>> select (SNat :: SNat 1) (SNat :: SNat 2) (SNat :: SNat 3) (1:>2:>3:>4:>5:>6:>7:>8:>Nil)
<2,4,6>
>>> select d1 d2 d3 (1:>2:>3:>4:>5:>6:>7:>8:>Nil)
<2,4,6>

selectI :: (CmpNat (i + s) (s * n) ~ 'GT, KnownNat n) => SNat f -> SNat s -> Vec (f + i) a -> Vec n a Source #

"selectI f s xs" selects as many elements as demanded by the context with step-size s and offset f from xs.

>>> selectI d1 d2 (1:>2:>3:>4:>5:>6:>7:>8:>Nil) :: Vec 2 Int
<2,4>

replicate :: SNat n -> a -> Vec n a Source #

"replicate n a" returns a vector that has n copies of a.

>>> replicate (SNat :: SNat 3) 6
<6,6,6>
>>> replicate d3 6
<6,6,6>

repeat :: KnownNat n => a -> Vec n a Source #

"repeat a" creates a vector with as many copies of a as demanded by the context.

>>> repeat 6 :: Vec 5 Int
<6,6,6,6,6>

iterate :: SNat n -> (a -> a) -> a -> Vec n a Source #

"iterate n f x" returns a vector starting with x followed by n repeated applications of f to x.

iterate (SNat :: SNat 4) f x == (x :> f x :> f (f x) :> f (f (f x)) :> Nil)
iterate d4 f x               == (x :> f x :> f (f x) :> f (f (f x)) :> Nil)
>>> iterate d4 (+1) 1
<1,2,3,4>

"iterate n f z" corresponds to the following circuit layout:

iterateI :: forall n a. KnownNat n => (a -> a) -> a -> Vec n a Source #

"iterate f x" returns a vector starting with x followed by n repeated applications of f to x, where n is determined by the context.

iterateI f x :: Vec 3 a == (x :> f x :> f (f x) :> Nil)
>>> iterateI (+1) 1 :: Vec 3 Int
<1,2,3>

"iterateI f z" corresponds to the following circuit layout:

unfoldr :: SNat n -> (s -> (a, s)) -> s -> Vec n a Source #

"'unfoldr n f s" builds a vector of length n from a seed value s, where every element a is created by successive calls of f on s. Unlike unfoldr from Data.List the generating function f cannot dictate the length of the resulting vector, it must be statically known.

a simple use of unfoldr:

>>> unfoldr d10 (\s -> (s,s-1)) 10
<10,9,8,7,6,5,4,3,2,1>

unfoldrI :: KnownNat n => (s -> (a, s)) -> s -> Vec n a Source #

"'unfoldr f s" builds a vector from a seed value s, where every element a is created by successive calls of f on s; the length of the vector is inferred from the context. Unlike unfoldr from Data.List the generating function f cannot dictate the length of the resulting vector, it must be statically known.

a simple use of unfoldrI:

>>> unfoldrI (\s -> (s,s-1)) 10 :: Vec 10 Int
<10,9,8,7,6,5,4,3,2,1>

generate :: SNat n -> (a -> a) -> a -> Vec n a Source #

"generate n f x" returns a vector with n repeated applications of f to x.

generate (SNat :: SNat 4) f x == (f x :> f (f x) :> f (f (f x)) :> f (f (f (f x))) :> Nil)
generate d4 f x               == (f x :> f (f x) :> f (f (f x)) :> f (f (f (f x))) :> Nil)
>>> generate d4 (+1) 1
<2,3,4,5>

"generate n f z" corresponds to the following circuit layout:

generateI :: KnownNat n => (a -> a) -> a -> Vec n a Source #

"generateI f x" returns a vector with n repeated applications of f to x, where n is determined by the context.

generateI f x :: Vec 3 a == (f x :> f (f x) :> f (f (f x)) :> Nil)
>>> generateI (+1) 1 :: Vec 3 Int
<2,3,4>

"generateI f z" corresponds to the following circuit layout:

transpose :: KnownNat n => Vec m (Vec n a) -> Vec n (Vec m a) Source #

Transpose a matrix: go from row-major to column-major

>>> let xss = (1:>2:>Nil):>(3:>4:>Nil):>(5:>6:>Nil):>Nil
>>> xss
<<1,2>,<3,4>,<5,6>>
>>> transpose xss
<<1,3,5>,<2,4,6>>

stencil1d Source #

Arguments

:: KnownNat n 
=> SNat (stX + 1)

Windows length stX, at least size 1

-> (Vec (stX + 1) a -> b)

The stencil (function)

-> Vec ((stX + n) + 1) a 
-> Vec (n + 1) b 

1-dimensional stencil computations

"stencil1d stX f xs", where xs has stX + n elements, applies the stencil computation f on: n + 1 overlapping (1D) windows of length stX, drawn from xs. The resulting vector has n + 1 elements.

>>> let xs = (1:>2:>3:>4:>5:>6:>Nil)
>>> :t xs
xs :: Num a => Vec 6 a
>>> :t stencil1d d2 sum xs
stencil1d d2 sum xs :: Num b => Vec 5 b
>>> stencil1d d2 sum xs
<3,5,7,9,11>

stencil2d Source #

Arguments

:: (KnownNat n, KnownNat m) 
=> SNat (stY + 1)

Window hight stY, at least size 1

-> SNat (stX + 1)

Window width stX, at least size 1

-> (Vec (stY + 1) (Vec (stX + 1) a) -> b)

The stencil (function)

-> Vec ((stY + m) + 1) (Vec ((stX + n) + 1) a) 
-> Vec (m + 1) (Vec (n + 1) b) 

2-dimensional stencil computations

"stencil2d stY stX f xss", where xss is a matrix of stY + m rows of stX + n elements, applies the stencil computation f on: (m + 1) * (n + 1) overlapping (2D) windows of stY rows of stX elements, drawn from xss. The result matrix has m + 1 rows of n + 1 elements.

>>> let xss = ((1:>2:>3:>4:>Nil):>(5:>6:>7:>8:>Nil):>(9:>10:>11:>12:>Nil):>(13:>14:>15:>16:>Nil):>Nil)
>>> :t xss
xss :: Num a => Vec 4 (Vec 4 a)
>>> :t stencil2d d2 d2 (sum . map sum) xss
stencil2d d2 d2 (sum . map sum) xss :: Num b => Vec 3 (Vec 3 b)
>>> stencil2d d2 d2 (sum . map sum) xss
<<14,18,22>,<30,34,38>,<46,50,54>>

windows1d Source #

Arguments

:: KnownNat n 
=> SNat (stX + 1)

Length of the window, at least size 1

-> Vec ((stX + n) + 1) a 
-> Vec (n + 1) (Vec (stX + 1) a) 

"windows1d stX xs", where the vector xs has stX + n elements, returns a vector of n + 1 overlapping (1D) windows of xs of length stX.

>>> let xs = (1:>2:>3:>4:>5:>6:>Nil)
>>> :t xs
xs :: Num a => Vec 6 a
>>> :t windows1d d2 xs
windows1d d2 xs :: Num a => Vec 5 (Vec 2 a)
>>> windows1d d2 xs
<<1,2>,<2,3>,<3,4>,<4,5>,<5,6>>

windows2d Source #

Arguments

:: (KnownNat n, KnownNat m) 
=> SNat (stY + 1)

Window hight stY, at least size 1

-> SNat (stX + 1)

Window width stX, at least size 1

-> Vec ((stY + m) + 1) (Vec ((stX + n) + 1) a) 
-> Vec (m + 1) (Vec (n + 1) (Vec (stY + 1) (Vec (stX + 1) a))) 

"windows2d stY stX xss", where matrix xss has stY + m rows of stX + n, returns a matrix of m+1 rows of n+1 elements. The elements of this new matrix are the overlapping (2D) windows of xss, where every window has stY rows of stX elements.

>>> let xss = ((1:>2:>3:>4:>Nil):>(5:>6:>7:>8:>Nil):>(9:>10:>11:>12:>Nil):>(13:>14:>15:>16:>Nil):>Nil)
>>> :t xss
xss :: Num a => Vec 4 (Vec 4 a)
>>> :t windows2d d2 d2 xss
windows2d d2 d2 xss :: Num a => Vec 3 (Vec 3 (Vec 2 (Vec 2 a)))
>>> windows2d d2 d2 xss
<<<<1,2>,<5,6>>,<<2,3>,<6,7>>,<<3,4>,<7,8>>>,<<<5,6>,<9,10>>,<<6,7>,<10,11>>,<<7,8>,<11,12>>>,<<<9,10>,<13,14>>,<<10,11>,<14,15>>,<<11,12>,<15,16>>>>

permute Source #

Arguments

:: (Enum i, KnownNat n, KnownNat m) 
=> (a -> a -> a)

Combination function, f

-> Vec n a

Default values, def

-> Vec m i

Index mapping, is

-> Vec (m + k) a

Vector to be permuted, xs

-> Vec n a 

Forward permutation specified by an index mapping, ix. The result vector is initialized by the given defaults, def, and an further values that are permuted into the result are added to the current value using the given combination function, f.

The combination function must be associative and commutative.

backpermute Source #

Arguments

:: (Enum i, KnownNat n) 
=> Vec n a

Source vector, xs

-> Vec m i

Index mapping, is

-> Vec m a 

Backwards permutation specified by an index mapping, is, from the destination vector specifying which element of the source vector xs to read.

"backpermute xs is" is equivalent to "map (xs !!) is".

For example:

>>> let input = 1:>9:>6:>4:>4:>2:>0:>1:>2:>Nil
>>> let from  = 1:>3:>7:>2:>5:>3:>Nil
>>> backpermute input from
<9,4,1,6,2,4>

scatter Source #

Arguments

:: (Enum i, KnownNat n, KnownNat m) 
=> Vec n a

Default values, def

-> Vec m i

Index mapping, is

-> Vec (m + k) a

Vector to be scattered, xs

-> Vec n a 

Copy elements from the source vector, xs, to the destination vector according to an index mapping is. This is a forward permute operation where a to vector encodes an input to output index mapping. Output elements for indices that are not mapped assume the value in the default vector def.

For example:

>>> let defVec = 0:>0:>0:>0:>0:>0:>0:>0:>0:>Nil
>>> let to = 1:>3:>7:>2:>5:>8:>Nil
>>> let input = 1:>9:>6:>4:>4:>2:>5:>Nil
>>> scatter defVec to input
<0,1,4,9,0,4,0,6,2>

NB: If the same index appears in the index mapping more than once, the latest mapping is chosen.

gather Source #

Arguments

:: (Enum i, KnownNat n) 
=> Vec n a

Source vector, xs

-> Vec m i

Index mapping, is

-> Vec m a 

Backwards permutation specified by an index mapping, is, from the destination vector specifying which element of the source vector xs to read.

"gather xs is" is equivalent to "map (xs !!) is".

For example:

>>> let input = 1:>9:>6:>4:>4:>2:>0:>1:>2:>Nil
>>> let from  = 1:>3:>7:>2:>5:>3:>Nil
>>> gather input from
<9,4,1,6,2,4>

interleave Source #

Arguments

:: (KnownNat n, KnownNat d) 
=> SNat d

Interleave step, d

-> Vec (n * d) a 
-> Vec (d * n) a 

"interleave d xs" creates a vector:

<x_0,x_d,x_(2d),...,x_1,x_(d+1),x_(2d+1),...,x_(d-1),x_(2d-1),x_(3d-1)>
>>> let xs = 1 :> 2 :> 3 :> 4 :> 5 :> 6 :> 7 :> 8 :> 9 :> Nil
>>> interleave d3 xs
<1,4,7,2,5,8,3,6,9>

rotateLeft :: (Enum i, KnownNat n) => Vec n a -> i -> Vec n a Source #

Dynamically rotate a Vector to the left:

>>> let xs = 1 :> 2 :> 3 :> 4 :> Nil
>>> rotateLeft xs 1
<2,3,4,1>
>>> rotateLeft xs 2
<3,4,1,2>
>>> rotateLeft xs (-1)
<4,1,2,3>

NB: use rotateLeftS if you want to rotate left by a static amount.

rotateRight :: (Enum i, KnownNat n) => Vec n a -> i -> Vec n a Source #

Dynamically rotate a Vector to the right:

>>> let xs = 1 :> 2 :> 3 :> 4 :> Nil
>>> rotateRight xs 1
<4,1,2,3>
>>> rotateRight xs 2
<3,4,1,2>
>>> rotateRight xs (-1)
<2,3,4,1>

NB: use rotateRightS if you want to rotate right by a static amount.

rotateLeftS :: KnownNat n => Vec n a -> SNat d -> Vec n a Source #

Statically rotate a Vector to the left:

>>> let xs = 1 :> 2 :> 3 :> 4 :> Nil
>>> rotateLeftS xs d1
<2,3,4,1>

NB: use rotateLeft if you want to rotate left by a dynamic amount.

rotateRightS :: KnownNat n => Vec n a -> SNat d -> Vec n a Source #

Statically rotate a Vector to the right:

>>> let xs = 1 :> 2 :> 3 :> 4 :> Nil
>>> rotateRightS xs d1
<4,1,2,3>

NB: use rotateRight if you want to rotate right by a dynamic amount.

toList :: Vec n a -> [a] Source #

Convert a vector to a list.

>>> toList (1:>2:>3:>Nil)
[1,2,3]

listToVecTH :: Lift a => [a] -> ExpQ Source #

Create a vector literal from a list literal.

$(listToVecTH [1::Signed 8,2,3,4,5]) == (8:>2:>3:>4:>5:>Nil) :: Vec 5 (Signed 8)
>>> [1 :: Signed 8,2,3,4,5]
[1,2,3,4,5]
>>> $(listToVecTH [1::Signed 8,2,3,4,5])
<1,2,3,4,5>

asNatProxy :: Vec n a -> Proxy n Source #

Vector as a Proxy for Nat

lengthS :: KnownNat n => Vec n a -> SNat n Source #

Length of a Vector as an SNat value

lazyV :: KnownNat n => Vec n a -> Vec n a Source #

What you should use when your vector functions are too strict in their arguments.

For example:

-- Bubble sort for 1 iteration
sortV xs = map fst sorted :< (snd (last sorted))
 where
   lefts  = head xs :> map snd (init sorted)
   rights = tail xs
   sorted = zipWith compareSwapL lefts rights

-- Compare and swap
compareSwapL a b = if a < b then (a,b)
                            else (b,a)

Will not terminate because zipWith is too strict in its second argument.

In this case, adding lazyV on zipWiths second argument:

sortVL xs = map fst sorted :< (snd (last sorted))
 where
   lefts  = head xs :> map snd (init sorted)
   rights = tail xs
   sorted = zipWith compareSwapL (lazyV lefts) rights

Results in a successful computation:

>>> sortVL (4 :> 1 :> 2 :> 3 :> Nil)
<1,2,3,4>

NB: There is also a solution using flip, but it slightly obfuscates the meaning of the code:

sortV_flip xs = map fst sorted :< (snd (last sorted))
 where
   lefts  = head xs :> map snd (init sorted)
   rights = tail xs
   sorted = zipWith (flip compareSwapL) rights lefts
>>> sortV_flip (4 :> 1 :> 2 :> 3 :> Nil)
<1,2,3,4>

dfold Source #

Arguments

:: forall p k a. KnownNat k 
=> Proxy (p :: TyFun Nat Type -> Type)

The motive

-> (forall l. SNat l -> a -> (p @@ l) -> p @@ (l + 1))

Function to fold.

NB: The SNat l is not the index (see (!!)) to the element a. SNat l is the number of elements that occur to the right of a.

-> (p @@ 0)

Initial element

-> Vec k a

Vector to fold over

-> p @@ k 

A dependently typed fold.

Using lists, we can define append (a.k.a. Data.List.++) in terms of Data.List.foldr:

>>> import qualified Data.List
>>> let append xs ys = Data.List.foldr (:) ys xs
>>> append [1,2] [3,4]
[1,2,3,4]

However, when we try to do the same for Vec, by defining append' in terms of Clash.Sized.Vector.foldr:

append' xs ys = foldr (:>) ys xs

we get a type error:

>>> let append' xs ys = foldr (:>) ys xs

<interactive>:...
    • Occurs check: cannot construct the infinite type: ... ~ ... + 1
      Expected type: a -> Vec ... a -> Vec ... a
        Actual type: a -> Vec ... a -> Vec (... + 1) a
    • In the first argument of ‘foldr’, namely ‘(:>)’
      In the expression: foldr (:>) ys xs
      In an equation for ‘append'’: append' xs ys = foldr (:>) ys xs
    • Relevant bindings include
        ys :: Vec ... a (bound at ...)
        append' :: Vec n a -> Vec ... a -> Vec ... a
          (bound at ...)

The reason is that the type of foldr is:

>>> :t foldr
foldr :: (a -> b -> b) -> b -> Vec n a -> b

While the type of (:>) is:

>>> :t (:>)
(:>) :: a -> Vec n a -> Vec (n + 1) a

We thus need a fold function that can handle the growing vector type: dfold. Compared to foldr, dfold takes an extra parameter, called the motive, that allows the folded function to have an argument and result type that depends on the current length of the vector. Using dfold, we can now correctly define append':

import Data.Singletons
import Data.Proxy

data Append (m :: Nat) (a :: *) (f :: TyFun Nat *) :: *
type instance Apply (Append m a) l = Vec (l + m) a

append' xs ys = dfold (Proxy :: Proxy (Append m a)) (const (:>)) ys xs

We now see that append' has the appropriate type:

>>> :t append'
append' :: KnownNat k => Vec k a -> Vec m a -> Vec (k + m) a

And that it works:

>>> append' (1 :> 2 :> Nil) (3 :> 4 :> Nil)
<1,2,3,4>

NB: "dfold m f z xs" creates a linear structure, which has a depth, or delay, of O(length xs). Look at dtfold for a dependently typed fold that produces a structure with a depth of O(log_2(length xs)).

dtfold Source #

Arguments

:: forall p k a. KnownNat k 
=> Proxy (p :: TyFun Nat Type -> Type)

The motive

-> (a -> p @@ 0)

Function to apply to every element

-> (forall l. SNat l -> (p @@ l) -> (p @@ l) -> p @@ (l + 1))

Function to combine results.

NB: The SNat l indicates the depth/height of the node in the tree that is created by applying this function. The leafs of the tree have depth/height 0, and the root of the tree has height k.

-> Vec (2 ^ k) a

Vector to fold over.

NB: Must have a length that is a power of 2.

-> p @@ k 

A combination of dfold and fold: a dependently typed fold that reduces a vector in a tree-like structure.

As an example of when you might want to use dtfold we will build a population counter: a circuit that counts the number of bits set to '1' in a BitVector. Given a vector of n bits, we only need we need a data type that can represent the number n: Index (n+1). Index k has a range of [0 .. k-1] (using ceil(log2(k)) bits), hence we need Index n+1. As an initial attempt we will use sum, because it gives a nice (log2(n)) tree-structure of adders:

populationCount :: (KnownNat (n+1), KnownNat (n+2))
                => BitVector (n+1) -> Index (n+2)
populationCount = sum . map fromIntegral . bv2v

The "problem" with this description is that all adders have the same bit-width, i.e. all adders are of the type:

(+) :: Index (n+2) -> Index (n+2) -> Index (n+2).

This is a "problem" because we could have a more efficient structure: one where each layer of adders is precisely wide enough to count the number of bits at that layer. That is, at height d we want the adder to be of type:

Index ((2^d)+1) -> Index ((2^d)+1) -> Index ((2^(d+1))+1)

We have such an adder in the form of the add function, as defined in the instance ExtendingNum instance of Index. However, we cannot simply use fold to create a tree-structure of addes:

# 2231 "srcClashSized/Vector.hs" >>> :{ let populationCount' :: (KnownNat (n+1), KnownNat (n+2)) => BitVector (n+1) -> Index (n+2) populationCount' = fold add . map fromIntegral . bv2v :} BLANKLINE interactive:... • Couldn't match type ‘((n + 2) + (n + 2)) - 1’ with ‘n + 2’ Expected type: Index (n + 2) -> Index (n + 2) -> Index (n + 2) Actual type: Index (n + 2) -> Index (n + 2) -> AResult (Index (n + 2)) (Index (n + 2)) • In the first argument of ‘fold’, namely ‘add’ In the first argument of ‘(.)’, namely ‘fold add’ In the expression: fold add . map fromIntegral . bv2v • Relevant bindings include populationCount' :: BitVector (n + 1) -> Index (n + 2) (bound at ...)

because fold expects a function of type "a -> a -> a", i.e. a function where the arguments and result all have exactly the same type.

In order to accommodate the type of our add, where the result is larger than the arguments, we must use a dependently typed fold in the form of dtfold:

{-# LANGUAGE UndecidableInstances #-}
import Data.Singletons
import Data.Proxy

data IIndex (f :: TyFun Nat *) :: *
type instance Apply IIndex l = Index ((2^l)+1)

populationCount' :: (KnownNat k, KnownNat (2^k))
                 => BitVector (2^k) -> Index ((2^k)+1)
populationCount' bv = dtfold (Proxy @IIndex)
                             fromIntegral
                             (\_ x y -> add x y)
                             (bv2v bv)

And we can test that it works:

>>> :t populationCount' (7 :: BitVector 16)
populationCount' (7 :: BitVector 16) :: Index 17
>>> populationCount' (7 :: BitVector 16)
3

Some final remarks:

  • By using dtfold instead of fold, we had to restrict our BitVector argument to have bit-width that is a power of 2.
  • Even though our original populationCount function specified a structure where all adders had the same width. Most VHDL/(System)Verilog synthesis tools will create a more efficient circuit, i.e. one where the adders have an increasing bit-width for every layer, from the VHDL/(System)Verilog produced by the Clash compiler.

NB: The depth, or delay, of the structure produced by "dtfold m f g xs" is O(log_2(length xs)).

vfold :: forall k a b. KnownNat k => (forall l. SNat l -> a -> Vec l b -> Vec (l + 1) b) -> Vec k a -> Vec k b Source #

Specialised version of dfold that builds a triangular computational structure.

Example:

compareSwap a b = if a > b then (a,b) else (b,a)
insert y xs     = let (y',xs') = mapAccumL compareSwap y xs in xs' :< y'
insertionSort   = vfold (const insert)

Builds a triangular structure of compare and swaps to sort a row.

>>> insertionSort (7 :> 3 :> 9 :> 1 :> Nil)
<1,3,7,9>

The circuit layout of insertionSort, build using vfold, is:

smap :: forall k a b. KnownNat k => (forall l. SNat l -> a -> b) -> Vec k a -> Vec k b Source #

Apply a function to every element of a vector and the element's position (as an SNat value) in the vector.

>>> let rotateMatrix = smap (flip rotateRightS)
>>> let xss = (1:>2:>3:>Nil):>(1:>2:>3:>Nil):>(1:>2:>3:>Nil):>Nil
>>> xss
<<1,2,3>,<1,2,3>,<1,2,3>>
>>> rotateMatrix xss
<<1,2,3>,<3,1,2>,<2,3,1>>

concatBitVector# :: forall n m. (KnownNat n, KnownNat m) => Vec n (BitVector m) -> BitVector (n * m) Source #

unconcatBitVector# :: forall n m. (KnownNat n, KnownNat m) => BitVector (n * m) -> Vec n (BitVector m) Source #

v2bv :: KnownNat n => Vec n Bit -> BitVector n Source #

Convert a Vec of Bits to a BitVector.

>>> let x = (0:>0:>0:>1:>0:>0:>1:>0:>Nil) :: Vec 8 Bit
>>> x
<0,0,0,1,0,0,1,0>
>>> v2bv x
0001_0010

seqV :: KnownNat n => Vec n a -> b -> b infixr 0 Source #

Evaluate all elements of a vector to WHNF, returning the second argument

forceV :: KnownNat n => Vec n a -> Vec n a Source #

Evaluate all elements of a vector to WHNF

seqVX :: KnownNat n => Vec n a -> b -> b infixr 0 Source #

Evaluate all elements of a vector to WHNF, returning the second argument. Does not propagate XExceptions.

forceVX :: KnownNat n => Vec n a -> Vec n a Source #

Evaluate all elements of a vector to WHNF. Does not propagate XExceptions.

Perfect depth trees

Annotations

Generics type-classes

class Generic a #

Representable types of kind *. This class is derivable in GHC with the DeriveGeneric flag on.

A Generic instance must satisfy the following laws:

from . toid
to . fromid

Minimal complete definition

from, to

Instances

Instances details
Generic Bool

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep Bool :: Type -> Type #

Methods

from :: Bool -> Rep Bool x #

to :: Rep Bool x -> Bool #

Generic Ordering

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep Ordering :: Type -> Type #

Methods

from :: Ordering -> Rep Ordering x #

to :: Rep Ordering x -> Ordering #

Generic Exp 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Exp :: Type -> Type #

Methods

from :: Exp -> Rep Exp x #

to :: Rep Exp x -> Exp #

Generic Match 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Match :: Type -> Type #

Methods

from :: Match -> Rep Match x #

to :: Rep Match x -> Match #

Generic Clause 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Clause :: Type -> Type #

Methods

from :: Clause -> Rep Clause x #

to :: Rep Clause x -> Clause #

Generic Pat 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Pat :: Type -> Type #

Methods

from :: Pat -> Rep Pat x #

to :: Rep Pat x -> Pat #

Generic Type 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Type :: Type -> Type #

Methods

from :: Type -> Rep Type x #

to :: Rep Type x -> Type #

Generic Dec 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Dec :: Type -> Type #

Methods

from :: Dec -> Rep Dec x #

to :: Rep Dec x -> Dec #

Generic Name 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Name :: Type -> Type #

Methods

from :: Name -> Rep Name x #

to :: Rep Name x -> Name #

Generic FunDep 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep FunDep :: Type -> Type #

Methods

from :: FunDep -> Rep FunDep x #

to :: Rep FunDep x -> FunDep #

Generic InjectivityAnn 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep InjectivityAnn :: Type -> Type #

Generic Overlap 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Overlap :: Type -> Type #

Methods

from :: Overlap -> Rep Overlap x #

to :: Rep Overlap x -> Overlap #

Generic ()

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep () :: Type -> Type #

Methods

from :: () -> Rep () x #

to :: Rep () x -> () #

Generic Version

Since: base-4.9.0.0

Instance details

Defined in Data.Version

Associated Types

type Rep Version :: Type -> Type #

Methods

from :: Version -> Rep Version x #

to :: Rep Version x -> Version #

Generic Void

Since: base-4.8.0.0

Instance details

Defined in Data.Void

Associated Types

type Rep Void :: Type -> Type #

Methods

from :: Void -> Rep Void x #

to :: Rep Void x -> Void #

Generic ExitCode 
Instance details

Defined in GHC.IO.Exception

Associated Types

type Rep ExitCode :: Type -> Type #

Methods

from :: ExitCode -> Rep ExitCode x #

to :: Rep ExitCode x -> ExitCode #

Generic All

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep All :: Type -> Type #

Methods

from :: All -> Rep All x #

to :: Rep All x -> All #

Generic Any

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep Any :: Type -> Type #

Methods

from :: Any -> Rep Any x #

to :: Rep Any x -> Any #

Generic Fixity

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep Fixity :: Type -> Type #

Methods

from :: Fixity -> Rep Fixity x #

to :: Rep Fixity x -> Fixity #

Generic Associativity

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep Associativity :: Type -> Type #

Generic SourceUnpackedness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep SourceUnpackedness :: Type -> Type #

Generic SourceStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep SourceStrictness :: Type -> Type #

Generic DecidedStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep DecidedStrictness :: Type -> Type #

Generic ConstructorInfo 
Instance details

Defined in Language.Haskell.TH.Datatype

Associated Types

type Rep ConstructorInfo :: Type -> Type #

Generic DatatypeVariant 
Instance details

Defined in Language.Haskell.TH.Datatype

Associated Types

type Rep DatatypeVariant :: Type -> Type #

Generic Extension 
Instance details

Defined in GHC.LanguageExtensions.Type

Associated Types

type Rep Extension :: Type -> Type #

Generic ForeignSrcLang 
Instance details

Defined in GHC.ForeignSrcLang.Type

Associated Types

type Rep ForeignSrcLang :: Type -> Type #

Generic Half 
Instance details

Defined in Numeric.Half.Internal

Associated Types

type Rep Half :: Type -> Type #

Methods

from :: Half -> Rep Half x #

to :: Rep Half x -> Half #

Generic Boxed 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep Boxed :: Type -> Type #

Methods

from :: Boxed -> Rep Boxed x #

to :: Rep Boxed x -> Boxed #

Generic Tool 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep Tool :: Type -> Type #

Methods

from :: Tool -> Rep Tool x #

to :: Rep Tool x -> Tool #

Generic SrcLoc 
Instance details

Defined in Language.Haskell.Exts.SrcLoc

Associated Types

type Rep SrcLoc :: Type -> Type #

Methods

from :: SrcLoc -> Rep SrcLoc x #

to :: Rep SrcLoc x -> SrcLoc #

Generic SrcSpan 
Instance details

Defined in Language.Haskell.Exts.SrcLoc

Associated Types

type Rep SrcSpan :: Type -> Type #

Methods

from :: SrcSpan -> Rep SrcSpan x #

to :: Rep SrcSpan x -> SrcSpan #

Generic SrcSpanInfo 
Instance details

Defined in Language.Haskell.Exts.SrcLoc

Associated Types

type Rep SrcSpanInfo :: Type -> Type #

Generic Mode 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Associated Types

type Rep Mode :: Type -> Type #

Methods

from :: Mode -> Rep Mode x #

to :: Rep Mode x -> Mode #

Generic Style 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Associated Types

type Rep Style :: Type -> Type #

Methods

from :: Style -> Rep Style x #

to :: Rep Style x -> Style #

Generic Stmt 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Stmt :: Type -> Type #

Methods

from :: Stmt -> Rep Stmt x #

to :: Rep Stmt x -> Stmt #

Generic ModName 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep ModName :: Type -> Type #

Methods

from :: ModName -> Rep ModName x #

to :: Rep ModName x -> ModName #

Generic Phases 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Phases :: Type -> Type #

Methods

from :: Phases -> Rep Phases x #

to :: Rep Phases x -> Phases #

Generic RuleBndr 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep RuleBndr :: Type -> Type #

Methods

from :: RuleBndr -> Rep RuleBndr x #

to :: Rep RuleBndr x -> RuleBndr #

Generic Pragma 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Pragma :: Type -> Type #

Methods

from :: Pragma -> Rep Pragma x #

to :: Rep Pragma x -> Pragma #

Generic DerivClause 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep DerivClause :: Type -> Type #

Generic DerivStrategy 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep DerivStrategy :: Type -> Type #

Generic TySynEqn 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep TySynEqn :: Type -> Type #

Methods

from :: TySynEqn -> Rep TySynEqn x #

to :: Rep TySynEqn x -> TySynEqn #

Generic Fixity 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Fixity :: Type -> Type #

Methods

from :: Fixity -> Rep Fixity x #

to :: Rep Fixity x -> Fixity #

Generic Info 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Info :: Type -> Type #

Methods

from :: Info -> Rep Info x #

to :: Rep Info x -> Info #

Generic Con 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Con :: Type -> Type #

Methods

from :: Con -> Rep Con x #

to :: Rep Con x -> Con #

Generic TyVarBndr 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep TyVarBndr :: Type -> Type #

Generic Doc 
Instance details

Defined in Text.PrettyPrint.HughesPJ

Associated Types

type Rep Doc :: Type -> Type #

Methods

from :: Doc -> Rep Doc x #

to :: Rep Doc x -> Doc #

Generic TextDetails 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Associated Types

type Rep TextDetails :: Type -> Type #

Generic PkgName 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep PkgName :: Type -> Type #

Methods

from :: PkgName -> Rep PkgName x #

to :: Rep PkgName x -> PkgName #

Generic Module 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Module :: Type -> Type #

Methods

from :: Module -> Rep Module x #

to :: Rep Module x -> Module #

Generic OccName 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep OccName :: Type -> Type #

Methods

from :: OccName -> Rep OccName x #

to :: Rep OccName x -> OccName #

Generic NameFlavour 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep NameFlavour :: Type -> Type #

Generic NameSpace 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep NameSpace :: Type -> Type #

Generic Loc 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Loc :: Type -> Type #

Methods

from :: Loc -> Rep Loc x #

to :: Rep Loc x -> Loc #

Generic ModuleInfo 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep ModuleInfo :: Type -> Type #

Generic FixityDirection 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep FixityDirection :: Type -> Type #

Generic Lit 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Lit :: Type -> Type #

Methods

from :: Lit -> Rep Lit x #

to :: Rep Lit x -> Lit #

Generic Bytes 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Bytes :: Type -> Type #

Methods

from :: Bytes -> Rep Bytes x #

to :: Rep Bytes x -> Bytes #

Generic Body 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Body :: Type -> Type #

Methods

from :: Body -> Rep Body x #

to :: Rep Body x -> Body #

Generic Guard 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Guard :: Type -> Type #

Methods

from :: Guard -> Rep Guard x #

to :: Rep Guard x -> Guard #

Generic Range 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Range :: Type -> Type #

Methods

from :: Range -> Rep Range x #

to :: Rep Range x -> Range #

Generic TypeFamilyHead 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep TypeFamilyHead :: Type -> Type #

Generic Foreign 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Foreign :: Type -> Type #

Methods

from :: Foreign -> Rep Foreign x #

to :: Rep Foreign x -> Foreign #

Generic Callconv 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Callconv :: Type -> Type #

Methods

from :: Callconv -> Rep Callconv x #

to :: Rep Callconv x -> Callconv #

Generic Safety 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Safety :: Type -> Type #

Methods

from :: Safety -> Rep Safety x #

to :: Rep Safety x -> Safety #

Generic Inline 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Inline :: Type -> Type #

Methods

from :: Inline -> Rep Inline x #

to :: Rep Inline x -> Inline #

Generic RuleMatch 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep RuleMatch :: Type -> Type #

Generic AnnTarget 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep AnnTarget :: Type -> Type #

Generic SourceUnpackedness 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep SourceUnpackedness :: Type -> Type #

Generic SourceStrictness 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep SourceStrictness :: Type -> Type #

Generic DecidedStrictness 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep DecidedStrictness :: Type -> Type #

Generic Bang 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Bang :: Type -> Type #

Methods

from :: Bang -> Rep Bang x #

to :: Rep Bang x -> Bang #

Generic PatSynDir 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep PatSynDir :: Type -> Type #

Generic PatSynArgs 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep PatSynArgs :: Type -> Type #

Generic FamilyResultSig 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep FamilyResultSig :: Type -> Type #

Generic TyLit 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep TyLit :: Type -> Type #

Methods

from :: TyLit -> Rep TyLit x #

to :: Rep TyLit x -> TyLit #

Generic Role 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep Role :: Type -> Type #

Methods

from :: Role -> Rep Role x #

to :: Rep Role x -> Role #

Generic AnnLookup 
Instance details

Defined in Language.Haskell.TH.Syntax

Associated Types

type Rep AnnLookup :: Type -> Type #

Generic ConType 
Instance details

Defined in TextShow.Generic

Associated Types

type Rep ConType :: Type -> Type #

Methods

from :: ConType -> Rep ConType x #

to :: Rep ConType x -> ConType #

Generic Options 
Instance details

Defined in TextShow.Options

Associated Types

type Rep Options :: Type -> Type #

Methods

from :: Options -> Rep Options x #

to :: Rep Options x -> Options #

Generic GenTextMethods 
Instance details

Defined in TextShow.Options

Associated Types

type Rep GenTextMethods :: Type -> Type #

Generic DatatypeInfo 
Instance details

Defined in Language.Haskell.TH.Datatype

Associated Types

type Rep DatatypeInfo :: Type -> Type #

Generic ConstructorVariant 
Instance details

Defined in Language.Haskell.TH.Datatype

Associated Types

type Rep ConstructorVariant :: Type -> Type #

Generic FieldStrictness 
Instance details

Defined in Language.Haskell.TH.Datatype

Associated Types

type Rep FieldStrictness :: Type -> Type #

Generic Unpackedness 
Instance details

Defined in Language.Haskell.TH.Datatype

Associated Types

type Rep Unpackedness :: Type -> Type #

Generic Strictness 
Instance details

Defined in Language.Haskell.TH.Datatype

Associated Types

type Rep Strictness :: Type -> Type #

Generic Specificity 
Instance details

Defined in Language.Haskell.TH.Datatype.TyVarBndr

Associated Types

type Rep Specificity :: Type -> Type #

Generic DTypeArg 
Instance details

Defined in Language.Haskell.TH.Desugar.Core

Associated Types

type Rep DTypeArg :: Type -> Type #

Methods

from :: DTypeArg -> Rep DTypeArg x #

to :: Rep DTypeArg x -> DTypeArg #

Generic DFunArgs 
Instance details

Defined in Language.Haskell.TH.Desugar.Core

Associated Types

type Rep DFunArgs :: Type -> Type #

Methods

from :: DFunArgs -> Rep DFunArgs x #

to :: Rep DFunArgs x -> DFunArgs #

Generic DVisFunArg 
Instance details

Defined in Language.Haskell.TH.Desugar.Core

Associated Types

type Rep DVisFunArg :: Type -> Type #

Generic DExp 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DExp :: Type -> Type #

Methods

from :: DExp -> Rep DExp x #

to :: Rep DExp x -> DExp #

Generic DPat 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DPat :: Type -> Type #

Methods

from :: DPat -> Rep DPat x #

to :: Rep DPat x -> DPat #

Generic DType 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DType :: Type -> Type #

Methods

from :: DType -> Rep DType x #

to :: Rep DType x -> DType #

Generic DTyVarBndr 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DTyVarBndr :: Type -> Type #

Generic DMatch 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DMatch :: Type -> Type #

Methods

from :: DMatch -> Rep DMatch x #

to :: Rep DMatch x -> DMatch #

Generic DClause 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DClause :: Type -> Type #

Methods

from :: DClause -> Rep DClause x #

to :: Rep DClause x -> DClause #

Generic DLetDec 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DLetDec :: Type -> Type #

Methods

from :: DLetDec -> Rep DLetDec x #

to :: Rep DLetDec x -> DLetDec #

Generic NewOrData 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep NewOrData :: Type -> Type #

Generic DDec 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DDec :: Type -> Type #

Methods

from :: DDec -> Rep DDec x #

to :: Rep DDec x -> DDec #

Generic DPatSynDir 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DPatSynDir :: Type -> Type #

Generic DTypeFamilyHead 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DTypeFamilyHead :: Type -> Type #

Generic DFamilyResultSig 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DFamilyResultSig :: Type -> Type #

Generic DCon 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DCon :: Type -> Type #

Methods

from :: DCon -> Rep DCon x #

to :: Rep DCon x -> DCon #

Generic DConFields 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DConFields :: Type -> Type #

Generic DForeign 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DForeign :: Type -> Type #

Methods

from :: DForeign -> Rep DForeign x #

to :: Rep DForeign x -> DForeign #

Generic DPragma 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DPragma :: Type -> Type #

Methods

from :: DPragma -> Rep DPragma x #

to :: Rep DPragma x -> DPragma #

Generic DRuleBndr 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DRuleBndr :: Type -> Type #

Generic DTySynEqn 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DTySynEqn :: Type -> Type #

Generic DInfo 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DInfo :: Type -> Type #

Methods

from :: DInfo -> Rep DInfo x #

to :: Rep DInfo x -> DInfo #

Generic DDerivClause 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DDerivClause :: Type -> Type #

Generic DDerivStrategy 
Instance details

Defined in Language.Haskell.TH.Desugar.AST

Associated Types

type Rep DDerivStrategy :: Type -> Type #

Generic ConstrRepr Source # 
Instance details

Defined in Clash.Annotations.BitRepresentation

Associated Types

type Rep ConstrRepr :: Type -> Type #

Generic DataReprAnn Source # 
Instance details

Defined in Clash.Annotations.BitRepresentation

Associated Types

type Rep DataReprAnn :: Type -> Type #

Generic ConstrRepr' Source # 
Instance details

Defined in Clash.Annotations.BitRepresentation.Internal

Associated Types

type Rep ConstrRepr' :: Type -> Type #

Generic DataRepr' Source # 
Instance details

Defined in Clash.Annotations.BitRepresentation.Internal

Associated Types

type Rep DataRepr' :: Type -> Type #

Generic Type' Source # 
Instance details

Defined in Clash.Annotations.BitRepresentation.Internal

Associated Types

type Rep Type' :: Type -> Type #

Methods

from :: Type' -> Rep Type' x #

to :: Rep Type' x -> Type' #

Generic PrimitiveWarning Source # 
Instance details

Defined in Clash.Annotations.Primitive

Associated Types

type Rep PrimitiveWarning :: Type -> Type #

Generic Primitive Source # 
Instance details

Defined in Clash.Annotations.Primitive

Associated Types

type Rep Primitive :: Type -> Type #

Generic HDL Source # 
Instance details

Defined in Clash.Annotations.Primitive

Associated Types

type Rep HDL :: Type -> Type #

Methods

from :: HDL -> Rep HDL x #

to :: Rep HDL x -> HDL #

Generic Bit Source # 
Instance details

Defined in Clash.Sized.Internal.BitVector

Associated Types

type Rep Bit :: Type -> Type #

Methods

from :: Bit -> Rep Bit x #

to :: Rep Bit x -> Bit #

Generic InitBehavior Source # 
Instance details

Defined in Clash.Signal.Internal

Associated Types

type Rep InitBehavior :: Type -> Type #

Generic ResetPolarity Source # 
Instance details

Defined in Clash.Signal.Internal

Associated Types

type Rep ResetPolarity :: Type -> Type #

Generic ResetKind Source # 
Instance details

Defined in Clash.Signal.Internal

Associated Types

type Rep ResetKind :: Type -> Type #

Generic ActiveEdge Source # 
Instance details

Defined in Clash.Signal.Internal

Associated Types

type Rep ActiveEdge :: Type -> Type #

Generic PortName Source # 
Instance details

Defined in Clash.Annotations.TopEntity

Associated Types

type Rep PortName :: Type -> Type #

Methods

from :: PortName -> Rep PortName x #

to :: Rep PortName x -> PortName #

Generic TopEntity Source # 
Instance details

Defined in Clash.Annotations.TopEntity

Associated Types

type Rep TopEntity :: Type -> Type #

Generic [a]

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep [a] :: Type -> Type #

Methods

from :: [a] -> Rep [a] x #

to :: Rep [a] x -> [a] #

Generic (Maybe a)

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (Maybe a) :: Type -> Type #

Methods

from :: Maybe a -> Rep (Maybe a) x #

to :: Rep (Maybe a) x -> Maybe a #

Generic (Par1 p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (Par1 p) :: Type -> Type #

Methods

from :: Par1 p -> Rep (Par1 p) x #

to :: Rep (Par1 p) x -> Par1 p #

Generic (Complex a)

Since: base-4.9.0.0

Instance details

Defined in Data.Complex

Associated Types

type Rep (Complex a) :: Type -> Type #

Methods

from :: Complex a -> Rep (Complex a) x #

to :: Rep (Complex a) x -> Complex a #

Generic (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Associated Types

type Rep (Min a) :: Type -> Type #

Methods

from :: Min a -> Rep (Min a) x #

to :: Rep (Min a) x -> Min a #

Generic (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Associated Types

type Rep (Max a) :: Type -> Type #

Methods

from :: Max a -> Rep (Max a) x #

to :: Rep (Max a) x -> Max a #

Generic (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Associated Types

type Rep (First a) :: Type -> Type #

Methods

from :: First a -> Rep (First a) x #

to :: Rep (First a) x -> First a #

Generic (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Associated Types

type Rep (Last a) :: Type -> Type #

Methods

from :: Last a -> Rep (Last a) x #

to :: Rep (Last a) x -> Last a #

Generic (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Associated Types

type Rep (WrappedMonoid m) :: Type -> Type #

Generic (Option a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Associated Types

type Rep (Option a) :: Type -> Type #

Methods

from :: Option a -> Rep (Option a) x #

to :: Rep (Option a) x -> Option a #

Generic (ZipList a)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Associated Types

type Rep (ZipList a) :: Type -> Type #

Methods

from :: ZipList a -> Rep (ZipList a) x #

to :: Rep (ZipList a) x -> ZipList a #

Generic (Identity a)

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Associated Types

type Rep (Identity a) :: Type -> Type #

Methods

from :: Identity a -> Rep (Identity a) x #

to :: Rep (Identity a) x -> Identity a #

Generic (First a)

Since: base-4.7.0.0

Instance details

Defined in Data.Monoid

Associated Types

type Rep (First a) :: Type -> Type #

Methods

from :: First a -> Rep (First a) x #

to :: Rep (First a) x -> First a #

Generic (Last a)

Since: base-4.7.0.0

Instance details

Defined in Data.Monoid

Associated Types

type Rep (Last a) :: Type -> Type #

Methods

from :: Last a -> Rep (Last a) x #

to :: Rep (Last a) x -> Last a #

Generic (Dual a)

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Dual a) :: Type -> Type #

Methods

from :: Dual a -> Rep (Dual a) x #

to :: Rep (Dual a) x -> Dual a #

Generic (Endo a)

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Endo a) :: Type -> Type #

Methods

from :: Endo a -> Rep (Endo a) x #

to :: Rep (Endo a) x -> Endo a #

Generic (Sum a)

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Sum a) :: Type -> Type #

Methods

from :: Sum a -> Rep (Sum a) x #

to :: Rep (Sum a) x -> Sum a #

Generic (Product a)

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Product a) :: Type -> Type #

Methods

from :: Product a -> Rep (Product a) x #

to :: Rep (Product a) x -> Product a #

Generic (Down a)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (Down a) :: Type -> Type #

Methods

from :: Down a -> Rep (Down a) x #

to :: Rep (Down a) x -> Down a #

Generic (NonEmpty a)

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (NonEmpty a) :: Type -> Type #

Methods

from :: NonEmpty a -> Rep (NonEmpty a) x #

to :: Rep (NonEmpty a) x -> NonEmpty a #

Generic (Tree a)

Since: containers-0.5.8

Instance details

Defined in Data.Tree

Associated Types

type Rep (Tree a) :: Type -> Type #

Methods

from :: Tree a -> Rep (Tree a) x #

to :: Rep (Tree a) x -> Tree a #

Generic (FingerTree a)

Since: containers-0.6.1

Instance details

Defined in Data.Sequence.Internal

Associated Types

type Rep (FingerTree a) :: Type -> Type #

Methods

from :: FingerTree a -> Rep (FingerTree a) x #

to :: Rep (FingerTree a) x -> FingerTree a #

Generic (Digit a)

Since: containers-0.6.1

Instance details

Defined in Data.Sequence.Internal

Associated Types

type Rep (Digit a) :: Type -> Type #

Methods

from :: Digit a -> Rep (Digit a) x #

to :: Rep (Digit a) x -> Digit a #

Generic (Node a)

Since: containers-0.6.1

Instance details

Defined in Data.Sequence.Internal

Associated Types

type Rep (Node a) :: Type -> Type #

Methods

from :: Node a -> Rep (Node a) x #

to :: Rep (Node a) x -> Node a #

Generic (Elem a)

Since: containers-0.6.1

Instance details

Defined in Data.Sequence.Internal

Associated Types

type Rep (Elem a) :: Type -> Type #

Methods

from :: Elem a -> Rep (Elem a) x #

to :: Rep (Elem a) x -> Elem a #

Generic (ViewL a)

Since: containers-0.5.8

Instance details

Defined in Data.Sequence.Internal

Associated Types

type Rep (ViewL a) :: Type -> Type #

Methods

from :: ViewL a -> Rep (ViewL a) x #

to :: Rep (ViewL a) x -> ViewL a #

Generic (ViewR a)

Since: containers-0.5.8

Instance details

Defined in Data.Sequence.Internal

Associated Types

type Rep (ViewR a) :: Type -> Type #

Methods

from :: ViewR a -> Rep (ViewR a) x #

to :: Rep (ViewR a) x -> ViewR a #

Generic (Fix f) 
Instance details

Defined in Data.Fix

Associated Types

type Rep (Fix f) :: Type -> Type #

Methods

from :: Fix f -> Rep (Fix f) x #

to :: Rep (Fix f) x -> Fix f #

Generic (ModuleName l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (ModuleName l) :: Type -> Type #

Methods

from :: ModuleName l -> Rep (ModuleName l) x #

to :: Rep (ModuleName l) x -> ModuleName l #

Generic (SpecialCon l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (SpecialCon l) :: Type -> Type #

Methods

from :: SpecialCon l -> Rep (SpecialCon l) x #

to :: Rep (SpecialCon l) x -> SpecialCon l #

Generic (QName l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (QName l) :: Type -> Type #

Methods

from :: QName l -> Rep (QName l) x #

to :: Rep (QName l) x -> QName l #

Generic (Name l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Name l) :: Type -> Type #

Methods

from :: Name l -> Rep (Name l) x #

to :: Rep (Name l) x -> Name l #

Generic (IPName l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (IPName l) :: Type -> Type #

Methods

from :: IPName l -> Rep (IPName l) x #

to :: Rep (IPName l) x -> IPName l #

Generic (QOp l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (QOp l) :: Type -> Type #

Methods

from :: QOp l -> Rep (QOp l) x #

to :: Rep (QOp l) x -> QOp l #

Generic (Op l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Op l) :: Type -> Type #

Methods

from :: Op l -> Rep (Op l) x #

to :: Rep (Op l) x -> Op l #

Generic (CName l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (CName l) :: Type -> Type #

Methods

from :: CName l -> Rep (CName l) x #

to :: Rep (CName l) x -> CName l #

Generic (Module l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Module l) :: Type -> Type #

Methods

from :: Module l -> Rep (Module l) x #

to :: Rep (Module l) x -> Module l #

Generic (ModuleHead l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (ModuleHead l) :: Type -> Type #

Methods

from :: ModuleHead l -> Rep (ModuleHead l) x #

to :: Rep (ModuleHead l) x -> ModuleHead l #

Generic (ExportSpecList l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (ExportSpecList l) :: Type -> Type #

Generic (ExportSpec l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (ExportSpec l) :: Type -> Type #

Methods

from :: ExportSpec l -> Rep (ExportSpec l) x #

to :: Rep (ExportSpec l) x -> ExportSpec l #

Generic (EWildcard l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (EWildcard l) :: Type -> Type #

Methods

from :: EWildcard l -> Rep (EWildcard l) x #

to :: Rep (EWildcard l) x -> EWildcard l #

Generic (Namespace l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Namespace l) :: Type -> Type #

Methods

from :: Namespace l -> Rep (Namespace l) x #

to :: Rep (Namespace l) x -> Namespace l #

Generic (ImportDecl l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (ImportDecl l) :: Type -> Type #

Methods

from :: ImportDecl l -> Rep (ImportDecl l) x #

to :: Rep (ImportDecl l) x -> ImportDecl l #

Generic (ImportSpecList l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (ImportSpecList l) :: Type -> Type #

Generic (ImportSpec l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (ImportSpec l) :: Type -> Type #

Methods

from :: ImportSpec l -> Rep (ImportSpec l) x #

to :: Rep (ImportSpec l) x -> ImportSpec l #

Generic (Assoc l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Assoc l) :: Type -> Type #

Methods

from :: Assoc l -> Rep (Assoc l) x #

to :: Rep (Assoc l) x -> Assoc l #

Generic (Decl l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Decl l) :: Type -> Type #

Methods

from :: Decl l -> Rep (Decl l) x #

to :: Rep (Decl l) x -> Decl l #

Generic (PatternSynDirection l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (PatternSynDirection l) :: Type -> Type #

Generic (TypeEqn l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (TypeEqn l) :: Type -> Type #

Methods

from :: TypeEqn l -> Rep (TypeEqn l) x #

to :: Rep (TypeEqn l) x -> TypeEqn l #

Generic (Annotation l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Annotation l) :: Type -> Type #

Methods

from :: Annotation l -> Rep (Annotation l) x #

to :: Rep (Annotation l) x -> Annotation l #

Generic (BooleanFormula l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (BooleanFormula l) :: Type -> Type #

Generic (Role l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Role l) :: Type -> Type #

Methods

from :: Role l -> Rep (Role l) x #

to :: Rep (Role l) x -> Role l #

Generic (DataOrNew l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (DataOrNew l) :: Type -> Type #

Methods

from :: DataOrNew l -> Rep (DataOrNew l) x #

to :: Rep (DataOrNew l) x -> DataOrNew l #

Generic (InjectivityInfo l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (InjectivityInfo l) :: Type -> Type #

Generic (ResultSig l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (ResultSig l) :: Type -> Type #

Methods

from :: ResultSig l -> Rep (ResultSig l) x #

to :: Rep (ResultSig l) x -> ResultSig l #

Generic (DeclHead l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (DeclHead l) :: Type -> Type #

Methods

from :: DeclHead l -> Rep (DeclHead l) x #

to :: Rep (DeclHead l) x -> DeclHead l #

Generic (InstRule l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (InstRule l) :: Type -> Type #

Methods

from :: InstRule l -> Rep (InstRule l) x #

to :: Rep (InstRule l) x -> InstRule l #

Generic (InstHead l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (InstHead l) :: Type -> Type #

Methods

from :: InstHead l -> Rep (InstHead l) x #

to :: Rep (InstHead l) x -> InstHead l #

Generic (Deriving l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Deriving l) :: Type -> Type #

Methods

from :: Deriving l -> Rep (Deriving l) x #

to :: Rep (Deriving l) x -> Deriving l #

Generic (DerivStrategy l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (DerivStrategy l) :: Type -> Type #

Generic (Binds l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Binds l) :: Type -> Type #

Methods

from :: Binds l -> Rep (Binds l) x #

to :: Rep (Binds l) x -> Binds l #

Generic (IPBind l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (IPBind l) :: Type -> Type #

Methods

from :: IPBind l -> Rep (IPBind l) x #

to :: Rep (IPBind l) x -> IPBind l #

Generic (Match l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Match l) :: Type -> Type #

Methods

from :: Match l -> Rep (Match l) x #

to :: Rep (Match l) x -> Match l #

Generic (QualConDecl l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (QualConDecl l) :: Type -> Type #

Methods

from :: QualConDecl l -> Rep (QualConDecl l) x #

to :: Rep (QualConDecl l) x -> QualConDecl l #

Generic (ConDecl l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (ConDecl l) :: Type -> Type #

Methods

from :: ConDecl l -> Rep (ConDecl l) x #

to :: Rep (ConDecl l) x -> ConDecl l #

Generic (FieldDecl l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (FieldDecl l) :: Type -> Type #

Methods

from :: FieldDecl l -> Rep (FieldDecl l) x #

to :: Rep (FieldDecl l) x -> FieldDecl l #

Generic (GadtDecl l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (GadtDecl l) :: Type -> Type #

Methods

from :: GadtDecl l -> Rep (GadtDecl l) x #

to :: Rep (GadtDecl l) x -> GadtDecl l #

Generic (ClassDecl l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (ClassDecl l) :: Type -> Type #

Methods

from :: ClassDecl l -> Rep (ClassDecl l) x #

to :: Rep (ClassDecl l) x -> ClassDecl l #

Generic (InstDecl l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (InstDecl l) :: Type -> Type #

Methods

from :: InstDecl l -> Rep (InstDecl l) x #

to :: Rep (InstDecl l) x -> InstDecl l #

Generic (BangType l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (BangType l) :: Type -> Type #

Methods

from :: BangType l -> Rep (BangType l) x #

to :: Rep (BangType l) x -> BangType l #

Generic (Unpackedness l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Unpackedness l) :: Type -> Type #

Methods

from :: Unpackedness l -> Rep (Unpackedness l) x #

to :: Rep (Unpackedness l) x -> Unpackedness l #

Generic (Rhs l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Rhs l) :: Type -> Type #

Methods

from :: Rhs l -> Rep (Rhs l) x #

to :: Rep (Rhs l) x -> Rhs l #

Generic (GuardedRhs l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (GuardedRhs l) :: Type -> Type #

Methods

from :: GuardedRhs l -> Rep (GuardedRhs l) x #

to :: Rep (GuardedRhs l) x -> GuardedRhs l #

Generic (Type l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Type l) :: Type -> Type #

Methods

from :: Type l -> Rep (Type l) x #

to :: Rep (Type l) x -> Type l #

Generic (MaybePromotedName l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (MaybePromotedName l) :: Type -> Type #

Generic (Promoted l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Promoted l) :: Type -> Type #

Methods

from :: Promoted l -> Rep (Promoted l) x #

to :: Rep (Promoted l) x -> Promoted l #

Generic (TyVarBind l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (TyVarBind l) :: Type -> Type #

Methods

from :: TyVarBind l -> Rep (TyVarBind l) x #

to :: Rep (TyVarBind l) x -> TyVarBind l #

Generic (FunDep l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (FunDep l) :: Type -> Type #

Methods

from :: FunDep l -> Rep (FunDep l) x #

to :: Rep (FunDep l) x -> FunDep l #

Generic (Context l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Context l) :: Type -> Type #

Methods

from :: Context l -> Rep (Context l) x #

to :: Rep (Context l) x -> Context l #

Generic (Asst l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Asst l) :: Type -> Type #

Methods

from :: Asst l -> Rep (Asst l) x #

to :: Rep (Asst l) x -> Asst l #

Generic (Literal l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Literal l) :: Type -> Type #

Methods

from :: Literal l -> Rep (Literal l) x #

to :: Rep (Literal l) x -> Literal l #

Generic (Sign l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Sign l) :: Type -> Type #

Methods

from :: Sign l -> Rep (Sign l) x #

to :: Rep (Sign l) x -> Sign l #

Generic (Exp l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Exp l) :: Type -> Type #

Methods

from :: Exp l -> Rep (Exp l) x #

to :: Rep (Exp l) x -> Exp l #

Generic (XName l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (XName l) :: Type -> Type #

Methods

from :: XName l -> Rep (XName l) x #

to :: Rep (XName l) x -> XName l #

Generic (XAttr l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (XAttr l) :: Type -> Type #

Methods

from :: XAttr l -> Rep (XAttr l) x #

to :: Rep (XAttr l) x -> XAttr l #

Generic (Bracket l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Bracket l) :: Type -> Type #

Methods

from :: Bracket l -> Rep (Bracket l) x #

to :: Rep (Bracket l) x -> Bracket l #

Generic (Splice l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Splice l) :: Type -> Type #

Methods

from :: Splice l -> Rep (Splice l) x #

to :: Rep (Splice l) x -> Splice l #

Generic (Safety l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Safety l) :: Type -> Type #

Methods

from :: Safety l -> Rep (Safety l) x #

to :: Rep (Safety l) x -> Safety l #

Generic (CallConv l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (CallConv l) :: Type -> Type #

Methods

from :: CallConv l -> Rep (CallConv l) x #

to :: Rep (CallConv l) x -> CallConv l #

Generic (ModulePragma l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (ModulePragma l) :: Type -> Type #

Methods

from :: ModulePragma l -> Rep (ModulePragma l) x #

to :: Rep (ModulePragma l) x -> ModulePragma l #

Generic (Overlap l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Overlap l) :: Type -> Type #

Methods

from :: Overlap l -> Rep (Overlap l) x #

to :: Rep (Overlap l) x -> Overlap l #

Generic (Activation l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Activation l) :: Type -> Type #

Methods

from :: Activation l -> Rep (Activation l) x #

to :: Rep (Activation l) x -> Activation l #

Generic (Rule l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Rule l) :: Type -> Type #

Methods

from :: Rule l -> Rep (Rule l) x #

to :: Rep (Rule l) x -> Rule l #

Generic (RuleVar l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (RuleVar l) :: Type -> Type #

Methods

from :: RuleVar l -> Rep (RuleVar l) x #

to :: Rep (RuleVar l) x -> RuleVar l #

Generic (WarningText l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (WarningText l) :: Type -> Type #

Methods

from :: WarningText l -> Rep (WarningText l) x #

to :: Rep (WarningText l) x -> WarningText l #

Generic (Pat l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Pat l) :: Type -> Type #

Methods

from :: Pat l -> Rep (Pat l) x #

to :: Rep (Pat l) x -> Pat l #

Generic (PXAttr l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (PXAttr l) :: Type -> Type #

Methods

from :: PXAttr l -> Rep (PXAttr l) x #

to :: Rep (PXAttr l) x -> PXAttr l #

Generic (RPatOp l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (RPatOp l) :: Type -> Type #

Methods

from :: RPatOp l -> Rep (RPatOp l) x #

to :: Rep (RPatOp l) x -> RPatOp l #

Generic (RPat l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (RPat l) :: Type -> Type #

Methods

from :: RPat l -> Rep (RPat l) x #

to :: Rep (RPat l) x -> RPat l #

Generic (PatField l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (PatField l) :: Type -> Type #

Methods

from :: PatField l -> Rep (PatField l) x #

to :: Rep (PatField l) x -> PatField l #

Generic (Stmt l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Stmt l) :: Type -> Type #

Methods

from :: Stmt l -> Rep (Stmt l) x #

to :: Rep (Stmt l) x -> Stmt l #

Generic (QualStmt l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (QualStmt l) :: Type -> Type #

Methods

from :: QualStmt l -> Rep (QualStmt l) x #

to :: Rep (QualStmt l) x -> QualStmt l #

Generic (FieldUpdate l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (FieldUpdate l) :: Type -> Type #

Methods

from :: FieldUpdate l -> Rep (FieldUpdate l) x #

to :: Rep (FieldUpdate l) x -> FieldUpdate l #

Generic (Alt l) 
Instance details

Defined in Language.Haskell.Exts.Syntax

Associated Types

type Rep (Alt l) :: Type -> Type #

Methods

from :: Alt l -> Rep (Alt l) x #

to :: Rep (Alt l) x -> Alt l #

Generic (Loc a) 
Instance details

Defined in Language.Haskell.Exts.SrcLoc

Associated Types

type Rep (Loc a) :: Type -> Type #

Methods

from :: Loc a -> Rep (Loc a) x #

to :: Rep (Loc a) x -> Loc a #

Generic (Doc a) 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Associated Types

type Rep (Doc a) :: Type -> Type #

Methods

from :: Doc a -> Rep (Doc a) x #

to :: Rep (Doc a) x -> Doc a #

Generic (Maybe a) 
Instance details

Defined in Data.Strict.Maybe

Associated Types

type Rep (Maybe a) :: Type -> Type #

Methods

from :: Maybe a -> Rep (Maybe a) x #

to :: Rep (Maybe a) x -> Maybe a #

Generic (FromGeneric a) 
Instance details

Defined in TextShow.Generic

Associated Types

type Rep (FromGeneric a) :: Type -> Type #

Methods

from :: FromGeneric a -> Rep (FromGeneric a) x #

to :: Rep (FromGeneric a) x -> FromGeneric a #

Generic (FromStringShow a) 
Instance details

Defined in TextShow.FromStringTextShow

Associated Types

type Rep (FromStringShow a) :: Type -> Type #

Generic (FromTextShow a) 
Instance details

Defined in TextShow.FromStringTextShow

Associated Types

type Rep (FromTextShow a) :: Type -> Type #

Methods

from :: FromTextShow a -> Rep (FromTextShow a) x #

to :: Rep (FromTextShow a) x -> FromTextShow a #

Generic (PrimitiveGuard a) Source # 
Instance details

Defined in Clash.Annotations.Primitive

Associated Types

type Rep (PrimitiveGuard a) :: Type -> Type #

Generic (BitVector n) Source # 
Instance details

Defined in Clash.Sized.Internal.BitVector

Associated Types

type Rep (BitVector n) :: Type -> Type #

Methods

from :: BitVector n -> Rep (BitVector n) x #

to :: Rep (BitVector n) x -> BitVector n #

Generic (Index n) Source # 
Instance details

Defined in Clash.Sized.Internal.Index

Associated Types

type Rep (Index n) :: Type -> Type #

Methods

from :: Index n -> Rep (Index n) x #

to :: Rep (Index n) x -> Index n #

Generic (Unsigned n) Source # 
Instance details

Defined in Clash.Sized.Internal.Unsigned

Associated Types

type Rep (Unsigned n) :: Type -> Type #

Methods

from :: Unsigned n -> Rep (Unsigned n) x #

to :: Rep (Unsigned n) x -> Unsigned n #

Generic (Signed n) Source # 
Instance details

Defined in Clash.Sized.Internal.Signed

Associated Types

type Rep (Signed n) :: Type -> Type #

Methods

from :: Signed n -> Rep (Signed n) x #

to :: Rep (Signed n) x -> Signed n #

Generic (Either a b)

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (Either a b) :: Type -> Type #

Methods

from :: Either a b -> Rep (Either a b) x #

to :: Rep (Either a b) x -> Either a b #

Generic (V1 p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (V1 p) :: Type -> Type #

Methods

from :: V1 p -> Rep (V1 p) x #

to :: Rep (V1 p) x -> V1 p #

Generic (U1 p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (U1 p) :: Type -> Type #

Methods

from :: U1 p -> Rep (U1 p) x #

to :: Rep (U1 p) x -> U1 p #

Generic (a, b)

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (a, b) :: Type -> Type #

Methods

from :: (a, b) -> Rep (a, b) x #

to :: Rep (a, b) x -> (a, b) #

Generic (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Associated Types

type Rep (Arg a b) :: Type -> Type #

Methods

from :: Arg a b -> Rep (Arg a b) x #

to :: Rep (Arg a b) x -> Arg a b #

Generic (WrappedMonad m a)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Associated Types

type Rep (WrappedMonad m a) :: Type -> Type #

Methods

from :: WrappedMonad m a -> Rep (WrappedMonad m a) x #

to :: Rep (WrappedMonad m a) x -> WrappedMonad m a #

Generic (Proxy t)

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (Proxy t) :: Type -> Type #

Methods

from :: Proxy t -> Rep (Proxy t) x #

to :: Rep (Proxy t) x -> Proxy t #

Generic (Cofree f a) 
Instance details

Defined in Control.Comonad.Cofree

Associated Types

type Rep (Cofree f a) :: Type -> Type #

Methods

from :: Cofree f a -> Rep (Cofree f a) x #

to :: Rep (Cofree f a) x -> Cofree f a #

Generic (Free f a) 
Instance details

Defined in Control.Monad.Free

Associated Types

type Rep (Free f a) :: Type -> Type #

Methods

from :: Free f a -> Rep (Free f a) x #

to :: Rep (Free f a) x -> Free f a #

Generic (ListF a b) 
Instance details

Defined in Data.Functor.Base

Associated Types

type Rep (ListF a b) :: Type -> Type #

Methods

from :: ListF a b -> Rep (ListF a b) x #

to :: Rep (ListF a b) x -> ListF a b #

Generic (NonEmptyF a b) 
Instance details

Defined in Data.Functor.Base

Associated Types

type Rep (NonEmptyF a b) :: Type -> Type #

Methods

from :: NonEmptyF a b -> Rep (NonEmptyF a b) x #

to :: Rep (NonEmptyF a b) x -> NonEmptyF a b #

Generic (TreeF a b) 
Instance details

Defined in Data.Functor.Base

Associated Types

type Rep (TreeF a b) :: Type -> Type #

Methods

from :: TreeF a b -> Rep (TreeF a b) x #

to :: Rep (TreeF a b) x -> TreeF a b #

Generic (Pair a b) 
Instance details

Defined in Data.Strict.Tuple

Associated Types

type Rep (Pair a b) :: Type -> Type #

Methods

from :: Pair a b -> Rep (Pair a b) x #

to :: Rep (Pair a b) x -> Pair a b #

Generic (These a b) 
Instance details

Defined in Data.Strict.These

Associated Types

type Rep (These a b) :: Type -> Type #

Methods

from :: These a b -> Rep (These a b) x #

to :: Rep (These a b) x -> These a b #

Generic (Either a b) 
Instance details

Defined in Data.Strict.Either

Associated Types

type Rep (Either a b) :: Type -> Type #

Methods

from :: Either a b -> Rep (Either a b) x #

to :: Rep (Either a b) x -> Either a b #

Generic (These a b) 
Instance details

Defined in Data.These

Associated Types

type Rep (These a b) :: Type -> Type #

Methods

from :: These a b -> Rep (These a b) x #

to :: Rep (These a b) x -> These a b #

KnownNat n => Generic (Vec n a) Source #

In many cases, this Generic instance only allows generic functions/instances over vectors of at least size 1, due to the n-1 in the Rep (Vec n a) definition.

We'll have to wait for things like https://ryanglscott.github.io/2018/02/11/how-to-derive-generic-for-some-gadts/ before we can work around this limitation

Instance details

Defined in Clash.Sized.Vector

Associated Types

type Rep (Vec n a) :: Type -> Type #

Methods

from :: Vec n a -> Rep (Vec n a) x #

to :: Rep (Vec n a) x -> Vec n a #

Generic (Rec1 f p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (Rec1 f p) :: Type -> Type #

Methods

from :: Rec1 f p -> Rep (Rec1 f p) x #

to :: Rep (Rec1 f p) x -> Rec1 f p #

Generic (URec (Ptr ()) p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec (Ptr ()) p) :: Type -> Type #

Methods

from :: URec (Ptr ()) p -> Rep (URec (Ptr ()) p) x #

to :: Rep (URec (Ptr ()) p) x -> URec (Ptr ()) p #

Generic (URec Char p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Char p) :: Type -> Type #

Methods

from :: URec Char p -> Rep (URec Char p) x #

to :: Rep (URec Char p) x -> URec Char p #

Generic (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Double p) :: Type -> Type #

Methods

from :: URec Double p -> Rep (URec Double p) x #

to :: Rep (URec Double p) x -> URec Double p #

Generic (URec Float p) 
Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Float p) :: Type -> Type #

Methods

from :: URec Float p -> Rep (URec Float p) x #

to :: Rep (URec Float p) x -> URec Float p #

Generic (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Int p) :: Type -> Type #

Methods

from :: URec Int p -> Rep (URec Int p) x #

to :: Rep (URec Int p) x -> URec Int p #

Generic (URec Word p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Word p) :: Type -> Type #

Methods

from :: URec Word p -> Rep (URec Word p) x #

to :: Rep (URec Word p) x -> URec Word p #

Generic (a, b, c)

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (a, b, c) :: Type -> Type #

Methods

from :: (a, b, c) -> Rep (a, b, c) x #

to :: Rep (a, b, c) x -> (a, b, c) #

Generic (Kleisli m a b)

Since: base-4.14.0.0

Instance details

Defined in Control.Arrow

Associated Types

type Rep (Kleisli m a b) :: Type -> Type #

Methods

from :: Kleisli m a b -> Rep (Kleisli m a b) x #

to :: Rep (Kleisli m a b) x -> Kleisli m a b #

Generic (WrappedArrow a b c)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Associated Types

type Rep (WrappedArrow a b c) :: Type -> Type #

Methods

from :: WrappedArrow a b c -> Rep (WrappedArrow a b c) x #

to :: Rep (WrappedArrow a b c) x -> WrappedArrow a b c #

Generic (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Associated Types

type Rep (Const a b) :: Type -> Type #

Methods

from :: Const a b -> Rep (Const a b) x #

to :: Rep (Const a b) x -> Const a b #

Generic (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Associated Types

type Rep (Ap f a) :: Type -> Type #

Methods

from :: Ap f a -> Rep (Ap f a) x #

to :: Rep (Ap f a) x -> Ap f a #

Generic (Alt f a)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Alt f a) :: Type -> Type #

Methods

from :: Alt f a -> Rep (Alt f a) x #

to :: Rep (Alt f a) x -> Alt f a #

Generic (Join p a) 
Instance details

Defined in Data.Bifunctor.Join

Associated Types

type Rep (Join p a) :: Type -> Type #

Methods

from :: Join p a -> Rep (Join p a) x #

to :: Rep (Join p a) x -> Join p a #

Generic (Fix p a) 
Instance details

Defined in Data.Bifunctor.Fix

Associated Types

type Rep (Fix p a) :: Type -> Type #

Methods

from :: Fix p a -> Rep (Fix p a) x #

to :: Rep (Fix p a) x -> Fix p a #

Generic (FreeF f a b) 
Instance details

Defined in Control.Monad.Trans.Free

Associated Types

type Rep (FreeF f a b) :: Type -> Type #

Methods

from :: FreeF f a b -> Rep (FreeF f a b) x #

to :: Rep (FreeF f a b) x -> FreeF f a b #

Generic (CofreeF f a b) 
Instance details

Defined in Control.Comonad.Trans.Cofree

Associated Types

type Rep (CofreeF f a b) :: Type -> Type #

Methods

from :: CofreeF f a b -> Rep (CofreeF f a b) x #

to :: Rep (CofreeF f a b) x -> CofreeF f a b #

Generic (Tagged s b) 
Instance details

Defined in Data.Tagged

Associated Types

type Rep (Tagged s b) :: Type -> Type #

Methods

from :: Tagged s b -> Rep (Tagged s b) x #

to :: Rep (Tagged s b) x -> Tagged s b #

Generic (FromGeneric1 f a) 
Instance details

Defined in TextShow.Generic

Associated Types

type Rep (FromGeneric1 f a) :: Type -> Type #

Methods

from :: FromGeneric1 f a -> Rep (FromGeneric1 f a) x #

to :: Rep (FromGeneric1 f a) x -> FromGeneric1 f a #

Generic (FromStringShow1 f a) 
Instance details

Defined in TextShow.FromStringTextShow

Associated Types

type Rep (FromStringShow1 f a) :: Type -> Type #

Methods

from :: FromStringShow1 f a -> Rep (FromStringShow1 f a) x #

to :: Rep (FromStringShow1 f a) x -> FromStringShow1 f a #

Generic (FromTextShow1 f a) 
Instance details

Defined in TextShow.FromStringTextShow

Associated Types

type Rep (FromTextShow1 f a) :: Type -> Type #

Methods

from :: FromTextShow1 f a -> Rep (FromTextShow1 f a) x #

to :: Rep (FromTextShow1 f a) x -> FromTextShow1 f a #

Generic (K1 i c p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (K1 i c p) :: Type -> Type #

Methods

from :: K1 i c p -> Rep (K1 i c p) x #

to :: Rep (K1 i c p) x -> K1 i c p #

Generic ((f :+: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep ((f :+: g) p) :: Type -> Type #

Methods

from :: (f :+: g) p -> Rep ((f :+: g) p) x #

to :: Rep ((f :+: g) p) x -> (f :+: g) p #

Generic ((f :*: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep ((f :*: g) p) :: Type -> Type #

Methods

from :: (f :*: g) p -> Rep ((f :*: g) p) x #

to :: Rep ((f :*: g) p) x -> (f :*: g) p #

Generic (a, b, c, d)

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (a, b, c, d) :: Type -> Type #

Methods

from :: (a, b, c, d) -> Rep (a, b, c, d) x #

to :: Rep (a, b, c, d) x -> (a, b, c, d) #

Generic (Product f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Associated Types

type Rep (Product f g a) :: Type -> Type #

Methods

from :: Product f g a -> Rep (Product f g a) x #

to :: Rep (Product f g a) x -> Product f g a #

Generic (Sum f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Sum

Associated Types

type Rep (Sum f g a) :: Type -> Type #

Methods

from :: Sum f g a -> Rep (Sum f g a) x #

to :: Rep (Sum f g a) x -> Sum f g a #

Generic (M1 i c f p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (M1 i c f p) :: Type -> Type #

Methods

from :: M1 i c f p -> Rep (M1 i c f p) x #

to :: Rep (M1 i c f p) x -> M1 i c f p #

Generic ((f :.: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep ((f :.: g) p) :: Type -> Type #

Methods

from :: (f :.: g) p -> Rep ((f :.: g) p) x #

to :: Rep ((f :.: g) p) x -> (f :.: g) p #

Generic (a, b, c, d, e)

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (a, b, c, d, e) :: Type -> Type #

Methods

from :: (a, b, c, d, e) -> Rep (a, b, c, d, e) x #

to :: Rep (a, b, c, d, e) x -> (a, b, c, d, e) #

Generic (Compose f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Associated Types

type Rep (Compose f g a) :: Type -> Type #

Methods

from :: Compose f g a -> Rep (Compose f g a) x #

to :: Rep (Compose f g a) x -> Compose f g a #

Generic (WrappedBifunctor p a b) 
Instance details

Defined in Data.Bifunctor.Wrapped

Associated Types

type Rep (WrappedBifunctor p a b) :: Type -> Type #

Methods

from :: WrappedBifunctor p a b -> Rep (WrappedBifunctor p a b) x #

to :: Rep (WrappedBifunctor p a b) x -> WrappedBifunctor p a b #

Generic (Joker g a b) 
Instance details

Defined in Data.Bifunctor.Joker

Associated Types

type Rep (Joker g a b) :: Type -> Type #

Methods

from :: Joker g a b -> Rep (Joker g a b) x #

to :: Rep (Joker g a b) x -> Joker g a b #

Generic (Flip p a b) 
Instance details

Defined in Data.Bifunctor.Flip

Associated Types

type Rep (Flip p a b) :: Type -> Type #

Methods

from :: Flip p a b -> Rep (Flip p a b) x #

to :: Rep (Flip p a b) x -> Flip p a b #

Generic (Clown f a b) 
Instance details

Defined in Data.Bifunctor.Clown

Associated Types

type Rep (Clown f a b) :: Type -> Type #

Methods

from :: Clown f a b -> Rep (Clown f a b) x #

to :: Rep (Clown f a b) x -> Clown f a b #

Generic (FromStringShow2 f a b) 
Instance details

Defined in TextShow.FromStringTextShow

Associated Types

type Rep (FromStringShow2 f a b) :: Type -> Type #

Methods

from :: FromStringShow2 f a b -> Rep (FromStringShow2 f a b) x #

to :: Rep (FromStringShow2 f a b) x -> FromStringShow2 f a b #

Generic (FromTextShow2 f a b) 
Instance details

Defined in TextShow.FromStringTextShow

Associated Types

type Rep (FromTextShow2 f a b) :: Type -> Type #

Methods

from :: FromTextShow2 f a b -> Rep (FromTextShow2 f a b) x #

to :: Rep (FromTextShow2 f a b) x -> FromTextShow2 f a b #

Generic (a, b, c, d, e, f)

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (a, b, c, d, e, f) :: Type -> Type #

Methods

from :: (a, b, c, d, e, f) -> Rep (a, b, c, d, e, f) x #

to :: Rep (a, b, c, d, e, f) x -> (a, b, c, d, e, f) #

Generic (Sum p q a b) 
Instance details

Defined in Data.Bifunctor.Sum

Associated Types

type Rep (Sum p q a b) :: Type -> Type #

Methods

from :: Sum p q a b -> Rep (Sum p q a b) x #

to :: Rep (Sum p q a b) x -> Sum p q a b #

Generic (Product f g a b) 
Instance details

Defined in Data.Bifunctor.Product

Associated Types

type Rep (Product f g a b) :: Type -> Type #

Methods

from :: Product f g a b -> Rep (Product f g a b) x #

to :: Rep (Product f g a b) x -> Product f g a b #

Generic (a, b, c, d, e, f, g)

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (a, b, c, d, e, f, g) :: Type -> Type #

Methods

from :: (a, b, c, d, e, f, g) -> Rep (a, b, c, d, e, f, g) x #

to :: Rep (a, b, c, d, e, f, g) x -> (a, b, c, d, e, f, g) #

Generic (Tannen f p a b) 
Instance details

Defined in Data.Bifunctor.Tannen

Associated Types

type Rep (Tannen f p a b) :: Type -> Type #

Methods

from :: Tannen f p a b -> Rep (Tannen f p a b) x #

to :: Rep (Tannen f p a b) x -> Tannen f p a b #

Generic (Biff p f g a b) 
Instance details

Defined in Data.Bifunctor.Biff

Associated Types

type Rep (Biff p f g a b) :: Type -> Type #

Methods

from :: Biff p f g a b -> Rep (Biff p f g a b) x #

to :: Rep (Biff p f g a b) x -> Biff p f g a b #

class Generic1 (f :: k -> Type) #

Representable types of kind * -> * (or kind k -> *, when PolyKinds is enabled). This class is derivable in GHC with the DeriveGeneric flag on.

A Generic1 instance must satisfy the following laws:

from1 . to1id
to1 . from1id

Minimal complete definition

from1, to1

Instances

Instances details
Generic1 (V1 :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 V1 :: k -> Type #

Methods

from1 :: forall (a :: k0). V1 a -> Rep1 V1 a #

to1 :: forall (a :: k0). Rep1 V1 a -> V1 a #

Generic1 (U1 :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 U1 :: k -> Type #

Methods

from1 :: forall (a :: k0). U1 a -> Rep1 U1 a #

to1 :: forall (a :: k0). Rep1 U1 a -> U1 a #

Generic1 (Proxy :: k -> Type)

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 Proxy :: k -> Type #

Methods

from1 :: forall (a :: k0). Proxy a -> Rep1 Proxy a #

to1 :: forall (a :: k0). Rep1 Proxy a -> Proxy a #

Generic1 (FromTextShow1 f :: k -> Type) 
Instance details

Defined in TextShow.FromStringTextShow

Associated Types

type Rep1 (FromTextShow1 f) :: k -> Type #

Methods

from1 :: forall (a :: k0). FromTextShow1 f a -> Rep1 (FromTextShow1 f) a #

to1 :: forall (a :: k0). Rep1 (FromTextShow1 f) a -> FromTextShow1 f a #

Generic1 (FromStringShow1 f :: k -> Type) 
Instance details

Defined in TextShow.FromStringTextShow

Associated Types

type Rep1 (FromStringShow1 f) :: k -> Type #

Methods

from1 :: forall (a :: k0). FromStringShow1 f a -> Rep1 (FromStringShow1 f) a #

to1 :: forall (a :: k0). Rep1 (FromStringShow1 f) a -> FromStringShow1 f a #

Generic1 (FromGeneric1 f :: k -> Type) 
Instance details

Defined in TextShow.Generic

Associated Types

type Rep1 (FromGeneric1 f) :: k -> Type #

Methods

from1 :: forall (a :: k0). FromGeneric1 f a -> Rep1 (FromGeneric1 f) a #

to1 :: forall (a :: k0). Rep1 (FromGeneric1 f) a -> FromGeneric1 f a #

Generic1 (Alt f :: k -> Type)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 (Alt f) :: k -> Type #

Methods

from1 :: forall (a :: k0). Alt f a -> Rep1 (Alt f) a #

to1 :: forall (a :: k0). Rep1 (Alt f) a -> Alt f a #

Generic1 (Ap f :: k -> Type)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Associated Types

type Rep1 (Ap f) :: k -> Type #

Methods

from1 :: forall (a :: k0). Ap f a -> Rep1 (Ap f) a #

to1 :: forall (a :: k0). Rep1 (Ap f) a -> Ap f a #

Generic1 (Const a :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Associated Types

type Rep1 (Const a) :: k -> Type #

Methods

from1 :: forall (a0 :: k0). Const a a0 -> Rep1 (Const a) a0 #

to1 :: forall (a0 :: k0). Rep1 (Const a) a0 -> Const a a0 #

Generic1 (URec (Ptr ()) :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec (Ptr ())) :: k -> Type #

Methods

from1 :: forall (a :: k0). URec (Ptr ()) a -> Rep1 (URec (Ptr ())) a #

to1 :: forall (a :: k0). Rep1 (URec (Ptr ())) a -> URec (Ptr ()) a #

Generic1 (URec Char :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec Char) :: k -> Type #

Methods

from1 :: forall (a :: k0). URec Char a -> Rep1 (URec Char) a #

to1 :: forall (a :: k0). Rep1 (URec Char) a -> URec Char a #

Generic1 (URec Double :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec Double) :: k -> Type #

Methods

from1 :: forall (a :: k0). URec Double a -> Rep1 (URec Double) a #

to1 :: forall (a :: k0). Rep1 (URec Double) a -> URec Double a #

Generic1 (URec Float :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec <