Copyright  (C) 20132016 University of Twente 2017 Google Inc. 2019 Myrtle Software Ltd 

License  BSD2 (see the file LICENSE) 
Maintainer  Christiaan Baaij <christiaan.baaij@gmail.com> 
Safe Haskell  Unsafe 
Language  Haskell2010 
Extensions 

This module defines the explicitly clocked counterparts of the functions defined in Clash.Prelude.
Synopsis
 mealy :: (KnownDomain dom, NFDataX s) => Clock dom > Reset dom > Enable dom > (s > i > (s, o)) > s > Signal dom i > Signal dom o
 mealyB :: (KnownDomain dom, NFDataX s, Bundle i, Bundle o) => Clock dom > Reset dom > Enable dom > (s > i > (s, o)) > s > Unbundled dom i > Unbundled dom o
 moore :: (KnownDomain dom, NFDataX s) => Clock dom > Reset dom > Enable dom > (s > i > s) > (s > o) > s > Signal dom i > Signal dom o
 mooreB :: (KnownDomain dom, NFDataX s, Bundle i, Bundle o) => Clock dom > Reset dom > Enable dom > (s > i > s) > (s > o) > s > Unbundled dom i > Unbundled dom o
 registerB :: (KnownDomain dom, NFDataX a, Bundle a) => Clock dom > Reset dom > Enable dom > a > Unbundled dom a > Unbundled dom a
 dualFlipFlopSynchronizer :: (NFDataX a, KnownDomain dom1, KnownDomain dom2) => Clock dom1 > Clock dom2 > Reset dom2 > Enable dom2 > a > Signal dom1 a > Signal dom2 a
 asyncFIFOSynchronizer :: (KnownDomain wdom, KnownDomain rdom, 2 <= addrSize) => SNat addrSize > Clock wdom > Clock rdom > Reset wdom > Reset rdom > Enable wdom > Enable rdom > Signal rdom Bool > Signal wdom (Maybe a) > (Signal rdom a, Signal rdom Bool, Signal wdom Bool)
 asyncRom :: (KnownNat n, Enum addr) => Vec n a > addr > a
 asyncRomPow2 :: KnownNat n => Vec (2 ^ n) a > Unsigned n > a
 rom :: (KnownDomain dom, KnownNat n, NFDataX a, Enum addr) => Clock dom > Enable dom > Vec n a > Signal dom addr > Signal dom a
 romPow2 :: (KnownDomain dom, KnownNat n, NFDataX a) => Clock dom > Enable dom > Vec (2 ^ n) a > Signal dom (Unsigned n) > Signal dom a
 asyncRomFile :: (KnownNat m, Enum addr) => SNat n > FilePath > addr > BitVector m
 asyncRomFilePow2 :: forall n m. (KnownNat m, KnownNat n) => FilePath > Unsigned n > BitVector m
 romFile :: (KnownNat m, Enum addr, KnownDomain dom) => Clock dom > Enable dom > SNat n > FilePath > Signal dom addr > Signal dom (BitVector m)
 romFilePow2 :: forall dom n m. (KnownNat m, KnownNat n, KnownDomain dom) => Clock dom > Enable dom > FilePath > Signal dom (Unsigned n) > Signal dom (BitVector m)
 asyncRam :: (Enum addr, HasCallStack, KnownDomain wdom, KnownDomain rdom) => Clock wdom > Clock rdom > Enable wdom > SNat n > Signal rdom addr > Signal wdom (Maybe (addr, a)) > Signal rdom a
 asyncRamPow2 :: forall wdom rdom n a. (KnownNat n, HasCallStack, KnownDomain wdom, KnownDomain rdom) => Clock wdom > Clock rdom > Enable wdom > Signal rdom (Unsigned n) > Signal wdom (Maybe (Unsigned n, a)) > Signal rdom a
 blockRam :: (KnownDomain dom, HasCallStack, NFDataX a, Enum addr) => Clock dom > Enable dom > Vec n a > Signal dom addr > Signal dom (Maybe (addr, a)) > Signal dom a
 blockRamPow2 :: (KnownDomain dom, HasCallStack, NFDataX a, KnownNat n) => Clock dom > Enable dom > Vec (2 ^ n) a > Signal dom (Unsigned n) > Signal dom (Maybe (Unsigned n, a)) > Signal dom a
 blockRamU :: forall n dom a r addr. (KnownDomain dom, HasCallStack, NFDataX a, Enum addr, 1 <= n) => Clock dom > Reset dom > Enable dom > ResetStrategy r > SNat n > (Index n > a) > Signal dom addr > Signal dom (Maybe (addr, a)) > Signal dom a
 blockRam1 :: forall n dom a r addr. (KnownDomain dom, HasCallStack, NFDataX a, Enum addr, 1 <= n) => Clock dom > Reset dom > Enable dom > ResetStrategy r > SNat n > a > Signal dom addr > Signal dom (Maybe (addr, a)) > Signal dom a
 data ResetStrategy (r :: Bool) where
 blockRamFile :: (KnownDomain dom, KnownNat m, Enum addr, HasCallStack) => Clock dom > Enable dom > SNat n > FilePath > Signal dom addr > Signal dom (Maybe (addr, BitVector m)) > Signal dom (BitVector m)
 blockRamFilePow2 :: forall dom n m. (KnownDomain dom, KnownNat m, KnownNat n, HasCallStack) => Clock dom > Enable dom > FilePath > Signal dom (Unsigned n) > Signal dom (Maybe (Unsigned n, BitVector m)) > Signal dom (BitVector m)
 readNew :: (KnownDomain dom, NFDataX a, Eq addr) => Clock dom > Reset dom > Enable dom > (Signal dom addr > Signal dom (Maybe (addr, a)) > Signal dom a) > Signal dom addr > Signal dom (Maybe (addr, a)) > Signal dom a
 window :: (KnownNat n, KnownDomain dom, NFDataX a, Default a) => Clock dom > Reset dom > Enable dom > Signal dom a > Vec (n + 1) (Signal dom a)
 windowD :: (KnownNat n, NFDataX a, Default a, KnownDomain dom) => Clock dom > Reset dom > Enable dom > Signal dom a > Vec (n + 1) (Signal dom a)
 isRising :: (KnownDomain dom, NFDataX a, Bounded a, Eq a) => Clock dom > Reset dom > Enable dom > a > Signal dom a > Signal dom Bool
 isFalling :: (KnownDomain dom, NFDataX a, Bounded a, Eq a) => Clock dom > Reset dom > Enable dom > a > Signal dom a > Signal dom Bool
 riseEvery :: forall dom n. KnownDomain dom => Clock dom > Reset dom > Enable dom > SNat n > Signal dom Bool
 oscillate :: forall dom n. KnownDomain dom => Clock dom > Reset dom > Enable dom > Bool > SNat n > Signal dom Bool
 assert :: (KnownDomain dom, Eq a, ShowX a) => Clock dom > Reset dom > String > Signal dom a > Signal dom a > Signal dom b > Signal dom b
 stimuliGenerator :: forall l dom a. (KnownNat l, KnownDomain dom) => Clock dom > Reset dom > Vec l a > Signal dom a
 outputVerifier' :: forall l a dom. (KnownNat l, KnownDomain dom, Eq a, ShowX a) => Clock dom > Reset dom > Vec l a > Signal dom a > Signal dom Bool
 traceSignal1 :: (BitPack a, NFDataX a, Typeable a) => String > Signal dom a > Signal dom a
 traceVecSignal1 :: (KnownNat n, BitPack a, NFDataX a, Typeable a) => String > Signal dom (Vec (n + 1) a) > Signal dom (Vec (n + 1) a)
 traceSignal :: forall dom a. (KnownDomain dom, BitPack a, NFDataX a, Typeable a) => String > Signal dom a > Signal dom a
 traceVecSignal :: forall dom a n. (KnownDomain dom, KnownNat n, BitPack a, NFDataX a, Typeable a) => String > Signal dom (Vec (n + 1) a) > Signal dom (Vec (n + 1) a)
 dumpVCD :: NFDataX a => (Int, Int) > Signal dom a > [String] > IO (Either String Text)
 module Clash.Explicit.Reset
 module Clash.Explicit.Signal
 module Clash.Explicit.Signal.Delayed
 module Clash.Sized.BitVector
 module Clash.Prelude.BitIndex
 module Clash.Prelude.BitReduction
 module Clash.Sized.Signed
 module Clash.Sized.Unsigned
 module Clash.Sized.Index
 module Clash.Sized.Fixed
 data Vec :: Nat > Type > Type where
 foldl :: (b > a > b) > b > Vec n a > b
 foldr :: (a > b > b) > b > Vec n a > b
 map :: (a > b) > Vec n a > Vec n b
 bv2v :: KnownNat n => BitVector n > Vec n Bit
 data VCons (a :: Type) (f :: TyFun Nat Type) :: Type
 traverse# :: forall a f b n. Applicative f => (a > f b) > Vec n a > f (Vec n b)
 singleton :: a > Vec 1 a
 head :: Vec (n + 1) a > a
 tail :: Vec (n + 1) a > Vec n a
 last :: Vec (n + 1) a > a
 init :: Vec (n + 1) a > Vec n a
 shiftInAt0 :: KnownNat n => Vec n a > Vec m a > (Vec n a, Vec m a)
 shiftInAtN :: KnownNat m => Vec n a > Vec m a > (Vec n a, Vec m a)
 (+>>) :: KnownNat n => a > Vec n a > Vec n a
 (<<+) :: Vec n a > a > Vec n a
 shiftOutFrom0 :: (Default a, KnownNat m) => SNat m > Vec (m + n) a > (Vec (m + n) a, Vec m a)
 shiftOutFromN :: (Default a, KnownNat n) => SNat m > Vec (m + n) a > (Vec (m + n) a, Vec m a)
 (++) :: Vec n a > Vec m a > Vec (n + m) a
 splitAt :: SNat m > Vec (m + n) a > (Vec m a, Vec n a)
 splitAtI :: KnownNat m => Vec (m + n) a > (Vec m a, Vec n a)
 concat :: Vec n (Vec m a) > Vec (n * m) a
 concatMap :: (a > Vec m b) > Vec n a > Vec (n * m) b
 unconcat :: KnownNat n => SNat m > Vec (n * m) a > Vec n (Vec m a)
 unconcatI :: (KnownNat n, KnownNat m) => Vec (n * m) a > Vec n (Vec m a)
 merge :: KnownNat n => Vec n a > Vec n a > Vec (2 * n) a
 reverse :: Vec n a > Vec n a
 imap :: forall n a b. KnownNat n => (Index n > a > b) > Vec n a > Vec n b
 izipWith :: KnownNat n => (Index n > a > b > c) > Vec n a > Vec n b > Vec n c
 ifoldr :: KnownNat n => (Index n > a > b > b) > b > Vec n a > b
 ifoldl :: KnownNat n => (a > Index n > b > a) > a > Vec n b > a
 indices :: KnownNat n => SNat n > Vec n (Index n)
 indicesI :: KnownNat n => Vec n (Index n)
 findIndex :: KnownNat n => (a > Bool) > Vec n a > Maybe (Index n)
 elemIndex :: (KnownNat n, Eq a) => a > Vec n a > Maybe (Index n)
 zipWith :: (a > b > c) > Vec n a > Vec n b > Vec n c
 zipWith3 :: (a > b > c > d) > Vec n a > Vec n b > Vec n c > Vec n d
 zipWith4 :: (a > b > c > d > e) > Vec n a > Vec n b > Vec n c > Vec n d > Vec n e
 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
 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
 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
 foldr1 :: (a > a > a) > Vec (n + 1) a > a
 foldl1 :: (a > a > a) > Vec (n + 1) a > a
 fold :: forall n a. (a > a > a) > Vec (n + 1) a > a
 scanl :: (b > a > b) > b > Vec n a > Vec (n + 1) b
 postscanl :: (b > a > b) > b > Vec n a > Vec n b
 scanr :: (a > b > b) > b > Vec n a > Vec (n + 1) b
 postscanr :: (a > b > b) > b > Vec n a > Vec n b
 mapAccumL :: (acc > x > (acc, y)) > acc > Vec n x > (acc, Vec n y)
 mapAccumR :: (acc > x > (acc, y)) > acc > Vec n x > (acc, Vec n y)
 zip :: Vec n a > Vec n b > Vec n (a, b)
 zip3 :: Vec n a > Vec n b > Vec n c > Vec n (a, b, c)
 zip4 :: Vec n a > Vec n b > Vec n c > Vec n d > Vec n (a, b, c, d)
 zip5 :: Vec n a > Vec n b > Vec n c > Vec n d > Vec n e > Vec n (a, b, c, d, e)
 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)
 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)
 unzip :: Vec n (a, b) > (Vec n a, Vec n b)
 unzip3 :: Vec n (a, b, c) > (Vec n a, Vec n b, Vec n c)
 unzip4 :: Vec n (a, b, c, d) > (Vec n a, Vec n b, Vec n c, Vec n d)
 unzip5 :: Vec n (a, b, c, d, e) > (Vec n a, Vec n b, Vec n c, Vec n d, Vec n e)
 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)
 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)
 (!!) :: (KnownNat n, Enum i) => Vec n a > i > a
 length :: KnownNat n => Vec n a > Int
 replace :: (KnownNat n, Enum i) => i > a > Vec n a > Vec n a
 take :: SNat m > Vec (m + n) a > Vec m a
 takeI :: KnownNat m => Vec (m + n) a > Vec m a
 drop :: SNat m > Vec (m + n) a > Vec n a
 dropI :: KnownNat m => Vec (m + n) a > Vec n a
 at :: SNat m > Vec (m + (n + 1)) a > a
 select :: CmpNat (i + s) (s * n) ~ 'GT => SNat f > SNat s > SNat n > Vec (f + i) a > Vec n a
 selectI :: (CmpNat (i + s) (s * n) ~ 'GT, KnownNat n) => SNat f > SNat s > Vec (f + i) a > Vec n a
 replicate :: SNat n > a > Vec n a
 repeat :: KnownNat n => a > Vec n a
 iterate :: SNat n > (a > a) > a > Vec n a
 iterateI :: forall n a. KnownNat n => (a > a) > a > Vec n a
 unfoldr :: SNat n > (s > (a, s)) > s > Vec n a
 unfoldrI :: KnownNat n => (s > (a, s)) > s > Vec n a
 generate :: SNat n > (a > a) > a > Vec n a
 generateI :: KnownNat n => (a > a) > a > Vec n a
 transpose :: KnownNat n => Vec m (Vec n a) > Vec n (Vec m a)
 stencil1d :: KnownNat n => SNat (stX + 1) > (Vec (stX + 1) a > b) > Vec ((stX + n) + 1) a > Vec (n + 1) b
 stencil2d :: (KnownNat n, KnownNat m) => SNat (stY + 1) > SNat (stX + 1) > (Vec (stY + 1) (Vec (stX + 1) a) > b) > Vec ((stY + m) + 1) (Vec ((stX + n) + 1) a) > Vec (m + 1) (Vec (n + 1) b)
 windows1d :: KnownNat n => SNat (stX + 1) > Vec ((stX + n) + 1) a > Vec (n + 1) (Vec (stX + 1) a)
 windows2d :: (KnownNat n, KnownNat m) => SNat (stY + 1) > SNat (stX + 1) > Vec ((stY + m) + 1) (Vec ((stX + n) + 1) a) > Vec (m + 1) (Vec (n + 1) (Vec (stY + 1) (Vec (stX + 1) a)))
 permute :: (Enum i, KnownNat n, KnownNat m) => (a > a > a) > Vec n a > Vec m i > Vec (m + k) a > Vec n a
 backpermute :: (Enum i, KnownNat n) => Vec n a > Vec m i > Vec m a
 scatter :: (Enum i, KnownNat n, KnownNat m) => Vec n a > Vec m i > Vec (m + k) a > Vec n a
 gather :: (Enum i, KnownNat n) => Vec n a > Vec m i > Vec m a
 interleave :: (KnownNat n, KnownNat d) => SNat d > Vec (n * d) a > Vec (d * n) a
 rotateLeft :: (Enum i, KnownNat n) => Vec n a > i > Vec n a
 rotateRight :: (Enum i, KnownNat n) => Vec n a > i > Vec n a
 rotateLeftS :: KnownNat n => Vec n a > SNat d > Vec n a
 rotateRightS :: KnownNat n => Vec n a > SNat d > Vec n a
 toList :: Vec n a > [a]
 listToVecTH :: Lift a => [a] > ExpQ
 asNatProxy :: Vec n a > Proxy n
 lengthS :: KnownNat n => Vec n a > SNat n
 lazyV :: KnownNat n => Vec n a > Vec n a
 dfold :: forall p k a. KnownNat k => Proxy (p :: TyFun Nat Type > Type) > (forall l. SNat l > a > (p @@ l) > p @@ (l + 1)) > (p @@ 0) > Vec k a > p @@ k
 dtfold :: forall p k a. KnownNat k => Proxy (p :: TyFun Nat Type > Type) > (a > p @@ 0) > (forall l. SNat l > (p @@ l) > (p @@ l) > p @@ (l + 1)) > Vec (2 ^ k) a > p @@ k
 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
 smap :: forall k a b. KnownNat k => (forall l. SNat l > a > b) > Vec k a > Vec k b
 concatBitVector# :: forall n m. (KnownNat n, KnownNat m) => Vec n (BitVector m) > BitVector (n * m)
 unconcatBitVector# :: forall n m. (KnownNat n, KnownNat m) => BitVector (n * m) > Vec n (BitVector m)
 v2bv :: KnownNat n => Vec n Bit > BitVector n
 seqV :: KnownNat n => Vec n a > b > b
 forceV :: KnownNat n => Vec n a > Vec n a
 seqVX :: KnownNat n => Vec n a > b > b
 forceVX :: KnownNat n => Vec n a > Vec n a
 module Clash.Sized.RTree
 module Clash.Annotations.TopEntity
 class Generic a
 class Generic1 (f :: k > Type)
 module GHC.TypeLits
 module GHC.TypeLits.Extra
 module Clash.Promoted.Nat
 module Clash.Promoted.Nat.Literals
 module Clash.Promoted.Nat.TH
 module Clash.Promoted.Symbol
 class Lift (t :: TYPE r) where
 module Clash.Class.AutoReg
 class KnownNat (BitSize a) => BitPack a where
 packXWith :: KnownNat n => (a > BitVector n) > a > BitVector n
 bitCoerce :: (BitPack a, BitPack b, BitSize a ~ BitSize b) => a > b
 bitCoerceMap :: forall a b. (BitPack a, BitPack b, BitSize a ~ BitSize b) => (a > a) > b > b
 boolToBV :: KnownNat n => Bool > BitVector (n + 1)
 boolToBit :: Bool > Bit
 bitToBool :: Bit > Bool
 module Clash.Class.Exp
 module Clash.Class.Num
 module Clash.Class.Resize
 module Control.Applicative
 module Data.Bits
 module Data.Default.Class
 module Clash.XException
 module Clash.NamedTypes
 module Clash.Magic
 module Clash.HaskellPrelude
Creating synchronous sequential circuits
:: (KnownDomain dom, NFDataX s)  
=> Clock dom 

> Reset dom  
> Enable dom  Global enable 
> (s > i > (s, o))  Transfer function in mealy machine form: 
> 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
import qualified Data.List as L macT :: Int  Current state > (Int,Int)  Input > (Int,Int)  (Updated state, output) macT s (x,y) = (s',s) where s' = x * y + s mac ::KnownDomain
dom =>Clock
dom >Reset
dom >Enable
dom >Signal
dom (Int, Int) >Signal
dom Int mac clk rst en =mealy
clk rst en macT 0
>>>
simulate (mac systemClockGen systemResetGen enableGen) [(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 ::KnownDomain
dom =>Clock
dom >Reset
dom >Enable
dom > (Signal
dom Int,Signal
dom Int) > (Signal
dom Int,Signal
dom Int) >Signal
dom Int dualMac clk rst en (a,b) (x,y) = s1 + s2 where s1 =mealy
clk rst en mac 0 (bundle
(a,x)) s2 =mealy
clk rst en mac 0 (bundle
(b,y))
:: (KnownDomain dom, NFDataX s, Bundle i, Bundle o)  
=> Clock dom  
> Reset dom  
> Enable dom  
> (s > i > (s, o))  Transfer function in mealy machine form: 
> 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 Bundle
ing
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 clk rst en a b c = (b1,b2,i2) where (i1,b1) =unbundle
(mealy clk rst en f 0 (bundle
(a,b))) (i2,b2) =unbundle
(mealy clk rst en f 3 (bundle
(c,i1)))
Using mealyB
however we can write:
g clk rst en a b c = (b1,b2,i2) where (i1,b1) =mealyB
clk rst en f 0 (a,b) (i2,b2) =mealyB
clk rst en f 3 (c,i1)
:: (KnownDomain dom, NFDataX s)  
=> Clock dom 

> Reset dom  
> Enable dom  
> (s > i > s)  Transfer function in moore machine form: 
> (s > o)  Output function in moore machine form: 
> 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,Int)  Updated state macT s (x,y) = x * y + s mac ::KnownDomain
dom =>Clock
dom >Reset
dom >Enable
dom >Signal
dom (Int, Int) >Signal
dom Int mac clk rst en =moore
clk rst en macT id 0
>>>
simulate (mac systemClockGen systemResetGen enableGen) [(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 ::KnownDomain
dom =>Clock
dom >Reset
dom >Enable
dom > (Signal
dom Int,Signal
dom Int) > (Signal
dom Int,Signal
dom Int) >Signal
dom Int dualMac clk rst en (a,b) (x,y) = s1 + s2 where s1 =moore
clk rst en mac id 0 (bundle
(a,x)) s2 =moore
clk rst en mac id 0 (bundle
(b,y))
:: (KnownDomain dom, NFDataX s, Bundle i, Bundle o)  
=> Clock dom  
> Reset dom  
> Enable dom  
> (s > i > s)  Transfer function in moore machine form:

> (s > o)  Output function in moore machine form:

> 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 Bundle
ing
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 clk rst en a b c = (b1,b2,i2) where (i1,b1) =unbundle
(moore clk rst en t o 0 (bundle
(a,b))) (i2,b2) =unbundle
(moore clk rst en t o 3 (bundle
(c,i1)))
Using mooreB
however we can write:
g clk rst en a b c = (b1,b2,i2) where (i1,b1) =mooreB
clk rst en t o 0 (a,b) (i2,b2) =mooreB
clk rst en t o 3 (c,i1)
registerB :: (KnownDomain dom, NFDataX a, Bundle a) => Clock dom > Reset dom > Enable dom > a > Unbundled dom a > Unbundled dom a Source #
Create a register
function for producttype like signals (e.g.
(
)Signal
a, Signal
b)
rP :: Clock dom > Reset dom > Enable dom > (Signal
dom Int,Signal
dom Int) > (Signal
dom Int,Signal
dom Int) rP clk rst en =registerB
clk rst en (8,8)
>>>
simulateB (rP systemClockGen systemResetGen enableGen) [(1,1),(1,1),(2,2),(3,3)] :: [(Int,Int)]
[(8,8),(8,8),(1,1),(2,2),(3,3)... ...
Synchronizer circuits for safe clock domain crossings
dualFlipFlopSynchronizer Source #
:: (NFDataX a, KnownDomain dom1, KnownDomain dom2)  
=> Clock dom1 

> Clock dom2 

> Reset dom2 

> Enable dom2 

> a  Initial value of the two synchronization registers 
> Signal dom1 a  Incoming data 
> Signal dom2 a  Outgoing, synchronized, data 
Synchronizer based on two sequentially connected flipflops.
 NB: This synchronizer can be used for bitsynchronization.
NB: Although this synchronizer does reduce metastability, it does not guarantee the proper synchronization of a whole word. For example, given that the output is sampled twice as fast as the input is running, and we have two samples in the input stream that look like:
[0111,1000]
But the circuit driving the input stream has a longer propagation delay on msb compared to the lsbs. What can happen is an output stream that looks like this:
[0111,0111,0000,1000]
Where the levelchange of the msb was not captured, but the level change of the lsbs were.
If you want to have safe wordsynchronization use
asyncFIFOSynchronizer
.
asyncFIFOSynchronizer Source #
:: (KnownDomain wdom, KnownDomain rdom, 2 <= addrSize)  
=> SNat addrSize  Size of the internally used addresses, the FIFO contains 
> Clock wdom 

> Clock rdom 

> Reset wdom  
> Reset rdom  
> Enable wdom  
> Enable rdom  
> Signal rdom Bool  Read request 
> Signal wdom (Maybe a)  Element to insert 
> (Signal rdom a, Signal rdom Bool, Signal wdom Bool)  (Oldest element in the FIFO, 
Synchronizer implemented as a FIFO around an asynchronous RAM. Based on the design described in Clash.Tutorial, which is itself based on the design described in http://www.sunburstdesign.com/papers/CummingsSNUG2002SJ_FIFO1.pdf.
NB: This synchronizer can be used for wordsynchronization.
ROMs
:: (KnownNat n, Enum addr)  
=> Vec n a  ROM content NB: must be a constant 
> addr  Read address 
> a  The value of the ROM at address 
An asynchronous/combinational ROM with space for n
elements
Additional helpful information:
 See Clash.Sized.Fixed and Clash.Prelude.BlockRam for ideas on how to use ROMs and RAMs
:: KnownNat n  
=> Vec (2 ^ n) a  ROM content NB: must be a constant 
> Unsigned n  Read address 
> a  The value of the ROM at address 
An asynchronous/combinational ROM with space for 2^n
elements
Additional helpful information:
 See Clash.Sized.Fixed and Clash.Prelude.BlockRam for ideas on how to use ROMs and RAMs
:: (KnownDomain dom, KnownNat n, NFDataX a, Enum addr)  
=> Clock dom 

> Enable dom  Global enable 
> Vec n a  ROM content NB: must be a constant 
> Signal dom addr  Read address 
> Signal dom a  The value of the ROM at address 
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:
 See Clash.Sized.Fixed and Clash.Explicit.BlockRam for ideas on how to use ROMs and RAMs
:: (KnownDomain dom, KnownNat n, NFDataX a)  
=> Clock dom 

> Enable dom  Global enable 
> Vec (2 ^ n) a  ROM content NB: must be a constant 
> Signal dom (Unsigned n)  Read address 
> Signal dom a  The value of the ROM at address 
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:
 See Clash.Sized.Fixed and Clash.Explicit.BlockRam for ideas on how to use ROMs and RAMs
ROMs initialized with a data file
:: (KnownNat m, Enum addr)  
=> SNat n  Size of the ROM 
> FilePath  File describing the content of the ROM 
> addr  Read address 
> BitVector m  The value of the ROM at address 
An asynchronous/combinational ROM with space for n
elements
NB: This function might not work for specific combinations of codegeneration backends and hardware targets. Please check the support table below:
 VHDL  Verilog  SystemVerilog  ===============+==========+==========+===============+ Altera/Quartus  Broken  Works  Works  Xilinx/ISE  Works  Works  Works  ASIC  Untested  Untested  Untested  ===============+==========+==========+===============+
Additional helpful information:
 See Clash.Prelude.ROM.File for more information on how to instantiate a ROM with the contents of a data file.
 See Clash.Sized.Fixed for ideas on how to create your own data files.
When you notice that
asyncRomFile
is significantly slowing down your simulation, give it a monomorphic type signature. So instead of leaving the type to be inferred:myRomData = asyncRomFile d512 "memory.bin"
or giving it a polymorphic type signature:
myRomData :: Enum addr => addr > BitVector 16 myRomData = asyncRomFile d512 "memory.bin"
you should give it a monomorphic type signature:
myRomData :: Unsigned 9 > BitVector 16 myRomData = asyncRomFile d512 "memory.bin"
:: forall n m. (KnownNat m, KnownNat n)  
=> FilePath  File describing the content of the ROM 
> Unsigned n  Read address 
> BitVector m  The value of the ROM at address 
An asynchronous/combinational ROM with space for 2^n
elements
NB: This function might not work for specific combinations of codegeneration backends and hardware targets. Please check the support table below:
 VHDL  Verilog  SystemVerilog  ===============+==========+==========+===============+ Altera/Quartus  Broken  Works  Works  Xilinx/ISE  Works  Works  Works  ASIC  Untested  Untested  Untested  ===============+==========+==========+===============+
Additional helpful information:
 See Clash.Prelude.ROM.File for more information on how to instantiate a ROM with the contents of a data file.
 See Clash.Sized.Fixed for ideas on how to create your own data files.
When you notice that
asyncRomFilePow2
is significantly slowing down your simulation, give it a monomorphic type signature. So instead of leaving the type to be inferred:myRomData = asyncRomFilePow2 "memory.bin"
you should give it a monomorphic type signature:
myRomData :: Unsigned 9 > BitVector 16 myRomData = asyncRomFilePow2 "memory.bin"
:: (KnownNat m, Enum addr, KnownDomain dom)  
=> Clock dom 

> Enable dom  Global enable 
> SNat n  Size of the ROM 
> FilePath  File describing the content of the ROM 
> Signal dom addr  Read address 
> Signal dom (BitVector m)  The value of the ROM at address 
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
NB: This function might not work for specific combinations of codegeneration backends and hardware targets. Please check the support table below:
 VHDL  Verilog  SystemVerilog  ===============+==========+==========+===============+ Altera/Quartus  Broken  Works  Works  Xilinx/ISE  Works  Works  Works  ASIC  Untested  Untested  Untested  ===============+==========+==========+===============+
Additional helpful information:
 See Clash.Explicit.ROM.File for more information on how to instantiate a ROM with the contents of a data file.
 See Clash.Sized.Fixed for ideas on how to create your own data files.
:: forall dom n m. (KnownNat m, KnownNat n, KnownDomain dom)  
=> Clock dom 

> Enable dom  Global enable 
> FilePath  File describing the content of the ROM 
> Signal dom (Unsigned n)  Read address 
> Signal dom (BitVector m)  The value of the ROM at address 
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
NB: This function might not work for specific combinations of codegeneration backends and hardware targets. Please check the support table below:
 VHDL  Verilog  SystemVerilog  ===============+==========+==========+===============+ Altera/Quartus  Broken  Works  Works  Xilinx/ISE  Works  Works  Works  ASIC  Untested  Untested  Untested  ===============+==========+==========+===============+
Additional helpful information:
 See Clash.Explicit.ROM.File for more information on how to instantiate a ROM with the contents of a data file.
 See Clash.Sized.Fixed for ideas on how to create your own data files.
RAM primitives with a combinational read port
:: (Enum addr, HasCallStack, KnownDomain wdom, KnownDomain rdom)  
=> Clock wdom 

> Clock rdom 

> Enable wdom  Global enable 
> SNat n  Size 
> Signal rdom addr  Read address 
> Signal wdom (Maybe (addr, a))  (write address 
> Signal rdom a  Value of the 
Create a RAM with space for n
elements
 NB: Initial content of the RAM is
undefined
Additional helpful information:
 See Clash.Explicit.BlockRam for more information on how to use a RAM.
:: forall wdom rdom n a. (KnownNat n, HasCallStack, KnownDomain wdom, KnownDomain rdom)  
=> Clock wdom 

> Clock rdom 

> Enable wdom  Global enable 
> Signal rdom (Unsigned n)  Read address 
> Signal wdom (Maybe (Unsigned n, a))  (write address 
> Signal rdom a  Value of the 
Create a RAM with space for 2^n
elements
 NB: Initial content of the RAM is
undefined
Additional helpful information:
 See Clash.Prelude.BlockRam for more information on how to use a RAM.
BlockRAM primitives
:: (KnownDomain dom, HasCallStack, NFDataX a, Enum addr)  
=> Clock dom 

> Enable dom  Global enable 
> Vec n a  Initial content of the BRAM, also determines the size, NB: MUST be a constant. 
> Signal dom addr  Read address 
> Signal dom (Maybe (addr, a))  (write address 
> Signal dom a  Value of the 
Create a blockRAM with space for n
elements
 NB: Read value is delayed by 1 cycle
 NB: Initial output value is undefined
bram40 ::Clock
dom >Enable
dom >Signal
dom (Unsigned
6) >Signal
dom (Maybe (Unsigned
6,Bit
)) >Signal
domBit
bram40 clk en =blockRam
clk en (replicate
d40 1)
Additional helpful information:
 See Clash.Explicit.BlockRam for more information on how to use a Block RAM.
 Use the adapter
readNew
for obtaining writebeforeread semantics like this:
.readNew
clk rst (blockRam
clk inits) rd wrM
:: (KnownDomain dom, HasCallStack, NFDataX a, KnownNat n)  
=> Clock dom 

> Enable dom  Global enable 
> Vec (2 ^ n) a  Initial content of the BRAM, also
determines the size, NB: MUST be a constant. 
> Signal dom (Unsigned n)  Read address 
> Signal dom (Maybe (Unsigned n, a))  (Write address 
> Signal dom a  Value of the 
Create a blockRAM with space for 2^n
elements
 NB: Read value is delayed by 1 cycle
 NB: Initial output value is undefined
bram32 ::Clock
dom >Enable
dom >Signal
dom (Unsigned
5) >Signal
dom (Maybe (Unsigned
5,Bit
)) >Signal
domBit
bram32 clk en =blockRamPow2
clk en (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 writebeforeread semantics like this:
.readNew
clk rst (blockRamPow2
clk inits) rd wrM
:: forall n dom a r addr. (KnownDomain dom, HasCallStack, NFDataX a, Enum addr, 1 <= n)  
=> Clock dom 

> Reset dom 

> Enable dom  Global enable 
> ResetStrategy r  Whether to clear BRAM on asserted reset ( 
> SNat n  Number of elements in BRAM 
> (Index n > a)  If applicable (see first argument), reset BRAM using this function. 
> Signal dom addr  Read address 
> Signal dom (Maybe (addr, a))  (write address 
> Signal dom a  Value of the 
Version of blockram that has no default values set. May be cleared to a arbitrary state using a reset function.
:: forall n dom a r addr. (KnownDomain dom, HasCallStack, NFDataX a, Enum addr, 1 <= n)  
=> Clock dom 

> Reset dom 

> Enable dom  Global enable 
> ResetStrategy r  Whether to clear BRAM on asserted reset ( 
> SNat n  Number of elements in BRAM 
> a  Initial content of the BRAM (replicated n times) 
> Signal dom addr  Read address 
> Signal dom (Maybe (addr, a))  (write address 
> Signal dom a  Value of the 
Version of blockram that is initialized with the same value on all memory positions.
data ResetStrategy (r :: Bool) where Source #
BlockRAM primitives initialized with a data file
:: (KnownDomain dom, KnownNat m, Enum addr, HasCallStack)  
=> Clock dom 

> Enable dom  Global enable 
> SNat n  Size of the blockRAM 
> FilePath  File describing the initial content of the blockRAM 
> Signal dom addr  Read address 
> Signal dom (Maybe (addr, BitVector m))  (write address 
> Signal dom (BitVector m)  Value of the 
Create a blockRAM with space for n
elements
 NB: Read value is delayed by 1 cycle
 NB: Initial output value is
undefined
NB: This function might not work for specific combinations of codegeneration backends and hardware targets. Please check the support table below:
 VHDL  Verilog  SystemVerilog  ===============+==========+==========+===============+ Altera/Quartus  Broken  Works  Works  Xilinx/ISE  Works  Works  Works  ASIC  Untested  Untested  Untested  ===============+==========+==========+===============+
Additional helpful information:
 See Clash.Explicit.BlockRam for more information on how to use a Block RAM.
 Use the adapter
readNew
for obtaining writebeforeread semantics like this:
.readNew
clk rst en (blockRamFile
clk en size file) rd wrM  See Clash.Explicit.BlockRam.File for more information on how to instantiate a Block RAM with the contents of a data file.
 See Clash.Sized.Fixed for ideas on how to create your own data files.
:: forall dom n m. (KnownDomain dom, KnownNat m, KnownNat n, HasCallStack)  
=> Clock dom 

> Enable dom  Global enable 
> FilePath  File describing the initial content of the blockRAM 
> Signal dom (Unsigned n)  Read address 
> Signal dom (Maybe (Unsigned n, BitVector m))  (write address 
> Signal dom (BitVector m)  Value of the 
Create a blockRAM with space for 2^n
elements
 NB: Read value is delayed by 1 cycle
 NB: Initial output value is
undefined
NB: This function might not work for specific combinations of codegeneration backends and hardware targets. Please check the support table below:
 VHDL  Verilog  SystemVerilog  ===============+==========+==========+===============+ Altera/Quartus  Broken  Works  Works  Xilinx/ISE  Works  Works  Works  ASIC  Untested  Untested  Untested  ===============+==========+==========+===============+
Additional helpful information:
 See Clash.Prelude.BlockRam for more information on how to use a Block RAM.
 Use the adapter
readNew
for obtaining writebeforeread semantics like this:
.readNew
clk rst en (blockRamFilePow2' clk en file) rd wrM  See Clash.Explicit.BlockRam.File for more information on how to instantiate a Block RAM with the contents of a data file.
 See Clash.Explicit.Fixed for ideas on how to create your own data files.
BlockRAM read/write conflict resolution
:: (KnownDomain dom, NFDataX a, Eq addr)  
=> Clock dom  
> Reset dom  
> Enable dom  
> (Signal dom addr > Signal dom (Maybe (addr, a)) > Signal dom a)  The 
> Signal dom addr  Read address 
> Signal dom (Maybe (addr, a))  (Write address 
> Signal dom a  Value of the 
Create readafterwrite blockRAM from a readbeforewrite one
Utility functions
:: (KnownNat n, KnownDomain dom, NFDataX a, Default a)  
=> Clock dom  Clock to the incoming signal is synchronized 
> Reset dom  
> Enable dom  
> Signal dom a  Signal to create a window over 
> Vec (n + 1) (Signal dom a)  Window of at least size 1 
Give a window over a Signal
@ window4
:: (KnownNat n, NFDataX a, Default a, KnownDomain dom)  
=> Clock dom  Clock to which the incoming signal is synchronized 
> Reset dom  
> Enable dom  
> Signal dom a  Signal to create a window over 
> Vec (n + 1) (Signal dom a)  Window of at least size 1 
Give a delayed window over a Signal
windowD3 :: KnownDomain dom > Clock dom > Enable dom > Reset dom >Signal
dom Int >Vec
3 (Signal
dom Int) windowD3 =windowD
>>>
simulateB (windowD3 systemClockGen resetGen enableGen) [1::Int,1,2,3,4] :: [Vec 3 Int]
[<0,0,0>,<0,0,0>,<1,0,0>,<2,1,0>,<3,2,1>,<4,3,2>... ...
riseEvery :: forall dom n. KnownDomain dom => Clock dom > Reset dom > Enable dom > SNat n > Signal dom Bool Source #
oscillate :: forall dom n. KnownDomain dom => Clock dom > Reset dom > Enable dom > Bool > SNat n > Signal dom Bool Source #
Oscillate a
for a given number of cycles, given the starting state.Bool
Testbench functions
:: (KnownDomain dom, Eq a, ShowX a)  
=> Clock dom  
> Reset dom  
> String  Additional message 
> Signal dom a  Checked value 
> Signal dom a  Expected value 
> Signal dom b  Return value 
> Signal dom b 
Compares the first two Signal
s for equality and logs a warning when they
are not equal. The second Signal
is considered the expected value. This
function simply returns the third Signal
unaltered as its result. This
function is used by outputVerifier
.
NB: This function can be used in synthesizable designs.
:: forall l dom a. (KnownNat l, KnownDomain dom)  
=> Clock dom  Clock to which to synchronize the output signal 
> Reset dom  
> Vec l a  Samples to generate 
> Signal dom a  Signal of given samples 
Example:
testInput :: KnownDomain dom => Clock dom > Reset dom >Signal
dom Int testInput clk rst =stimuliGenerator
clk rst $(listToVecTH
[(1::Int),3..21])
>>>
sampleN 14 (testInput systemClockGen resetGen)
[1,1,3,5,7,9,11,13,15,17,19,21,21,21]
:: forall l a dom. (KnownNat l, KnownDomain dom, Eq a, ShowX a)  
=> Clock dom  Clock to which the testbench is synchronized to 
> Reset dom  Reset line of testbench 
> Vec l a  Samples to compare with 
> Signal dom a  Signal to verify 
> Signal dom Bool  Indicator that all samples are verified 
Same as outputVerifier
but used in cases where the testbench domain and
the domain of the circuit under test are the same.
Tracing
Simple
:: (BitPack a, NFDataX a, Typeable a)  
=> String  Name of signal in the VCD output 
> Signal dom a  Signal to trace 
> Signal dom a 
Trace a single signal. Will emit an error if a signal with the same name was previously registered.
NB associates the traced signal with a clock period of 1, which
results in incorrect VCD files when working with circuits that have
multiple clocks. Use traceSignal
when working with circuits that have
multiple clocks.
:: (KnownNat n, BitPack a, NFDataX a, Typeable a)  
=> String  Name of signal in debugging output. Will be appended by _0, _1, ..., _n. 
> Signal dom (Vec (n + 1) a)  Signal to trace 
> Signal dom (Vec (n + 1) a) 
Trace a single vector signal: each element in the vector will show up as a different trace. If the trace name already exists, this function will emit an error.
NB associates the traced signal with a clock period of 1, which
results in incorrect VCD files when working with circuits that have
multiple clocks. Use traceSignal
when working with circuits that have
multiple clocks.
Tracing in a multiclock environment
:: forall dom a. (KnownDomain dom, BitPack a, NFDataX a, Typeable a)  
=> String  Name of signal in the VCD output 
> Signal dom a  Signal to trace 
> Signal dom a 
Trace a single signal. Will emit an error if a signal with the same name was previously registered.
NB Works correctly when creating VCD files from traced signal in
multiclock circuits. However traceSignal1
might be more convenient to
use when the domain of your circuit is polymorphic.
:: forall dom a n. (KnownDomain dom, KnownNat n, BitPack a, NFDataX a, Typeable a)  
=> String  Name of signal in debugging output. Will be appended by _0, _1, ..., _n. 
> Signal dom (Vec (n + 1) a)  Signal to trace 
> Signal dom (Vec (n + 1) a) 
Trace a single vector signal: each element in the vector will show up as a different trace. If the trace name already exists, this function will emit an error.
NB Works correctly when creating VCD files from traced signal in
multiclock circuits. However traceSignal1
might be more convinient to
use when the domain of your circuit is polymorphic.
VCD dump functions
:: NFDataX a  
=> (Int, Int)  (offset, number of samples) 
> Signal dom a  (One of) the outputs of the circuit containing the traces 
> [String]  The names of the traces you definitely want to be dumped in the VCD file 
> IO (Either String Text) 
Produce a fourstate VCD (Value Change Dump) according to IEEE 1364{1995,2001}. This function fails if a trace name contains either nonprintable or nonVCD characters.
Due to lazy evaluation, the created VCD files might not contain all the traces you were expecting. You therefore have to provide a list of names you definately want to be dumped in the VCD file.
For example:
vcd < dumpVCD (0, 100) cntrOut ["main", "sub"]
Evaluates cntrOut long enough in order for to guarantee that the main
,
and sub
traces end up in the generated VCD file.
Exported modules
Synchronous signals
module Clash.Explicit.Reset
module Clash.Explicit.Signal
Datatypes
Bit vectors
module Clash.Sized.BitVector
module Clash.Prelude.BitIndex
module Clash.Prelude.BitReduction
Arbitrarywidth numbers
module Clash.Sized.Signed
module Clash.Sized.Unsigned
module Clash.Sized.Index
Fixed point numbers
module Clash.Sized.Fixed
Fixed size vectors
data Vec :: Nat > Type > Type where Source #
Fixed size vectors.
pattern (:<) :: Vec n a > a > Vec (n + 1) a infixl 5  Add an element to the tail of a vector.
Can be used as a pattern:
Also in conjunctions with (

pattern (:>) :: a > Vec n a > Vec (n + 1) a infixr 5  Add an element to the head of a vector.
Can be used as a pattern:
Also in conjunctions with (

Instances
Lift a => Lift (Vec n a :: Type) Source #  
Functor (Vec n) Source #  
KnownNat n => Applicative (Vec n) Source #  
(KnownNat n, 1 <= n) => Foldable (Vec n) Source #  
Defined in Clash.Sized.Vector 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 # elem :: Eq a => a > Vec n a > Bool # maximum :: Ord a => Vec n a > a # minimum :: Ord a => Vec n a > a #  
(KnownNat n, 1 <= n) => Traversable (Vec n) Source #  
(KnownNat n, Eq a) => Eq (Vec n a) Source #  
(KnownNat n, Typeable a, Data a) => Data (Vec n a) Source #  
Defined in Clash.Sized.Vector 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 #  
Show a => Show (Vec n a) Source #  
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 n1 in the Rep (Vec n a) definition. We'll have to wait for things like https://ryanglscott.github.io/2018/02/11/howtoderivegenericforsomegadts/ before we can work around this limitation 
(KnownNat n, Semigroup a) => Semigroup (Vec n a) Source #  
(KnownNat n, Monoid a) => Monoid (Vec n a) Source #  
(KnownNat n, Arbitrary a) => Arbitrary (Vec n a) Source #  
CoArbitrary a => CoArbitrary (Vec n a) Source #  
Defined in Clash.Sized.Vector coarbitrary :: Vec n a > Gen b > Gen b #  
(Default a, KnownNat n) => Default (Vec n a) Source #  
Defined in Clash.Sized.Vector  
NFData a => NFData (Vec n a) Source #  
Defined in Clash.Sized.Vector  
KnownNat n => Ixed (Vec n a) Source #  
Defined in Clash.Sized.Vector  
(NFDataX a, KnownNat n) => NFDataX (Vec n a) Source #  
Defined in Clash.Sized.Vector  
ShowX a => ShowX (Vec n a) Source #  
(KnownNat n, BitPack a) => BitPack (Vec n a) Source #  
KnownNat n => Bundle (Vec n a) Source #  
KnownNat n => Bundle (Vec n a) Source #  
Defined in Clash.Signal.Delayed.Bundle  
(KnownNat n, AutoReg a) => AutoReg (Vec n a) Source #  
Defined in Clash.Class.AutoReg.Internal  
(LockStep en a, KnownNat n) => LockStep (Vec n en) (Vec n a) Source #  
type Unbundled t d (Vec n a) Source #  
Defined in Clash.Signal.Delayed.Bundle  
type HasDomain dom (Vec n a) Source #  
Defined in Clash.Class.HasDomain.HasSpecificDomain  
type TryDomain t (Vec n a) Source #  
Defined in Clash.Class.HasDomain.HasSingleDomain  
type Unbundled t (Vec n a) Source #  
Defined in Clash.Signal.Bundle  
type Rep (Vec n a) Source #  
Defined in Clash.Sized.Vector type Rep (Vec n a) = D1 ('MetaData "Vec" "Clash.Data.Vector" "clashprelude" '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 #  
Defined in Clash.Sized.Vector  
type IxValue (Vec n a) Source #  
Defined in Clash.Sized.Vector  
type BitSize (Vec n a) Source #  
Defined in Clash.Sized.Vector 
foldl :: (b > a > b) > b > Vec n a > b Source #
foldl
, applied to a binary operator, a starting value (typically
the leftidentity 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)
8.333333333333333e3
"foldl
f z xs
" corresponds to the following circuit layout:
NB: "
produces a linear structure, which has a depth, or
delay, of O(foldl
f z xs"
). Use length
xsfold
if your binary operator f
is
associative, as "
produces a structure with a depth of
O(log_2(fold
f xs"
)).length
xs
foldr :: (a > b > b) > b > Vec n a > b Source #
foldr
, applied to a binary operator, a starting value (typically
the rightidentity 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: "
produces a linear structure, which has a depth, or
delay, of O(foldr
f z xs"
). Use length
xsfold
if your binary operator f
is
associative, as "
produces a structure with a depth of
O(log_2(fold
f xs"
)).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:
data VCons (a :: Type) (f :: TyFun Nat Type) :: Type Source #
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
:: 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>)
:: 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
<>
:: (Default a, KnownNat m)  
=> SNat m 

> 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>)
:: (Default a, KnownNat n)  
=> SNat m 

> 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>
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.
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 nonempty 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: "
produces a linear structure, which has a depth,
or delay, of O(foldr1
f z xs"
). Use length
xsfold
if your binary operator f
is
associative, as "
produces a structure with a depth of
O(log_2(fold
f xs"
)).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 nonempty 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)
8.333333333333333e3
"foldl1
f xs
" corresponds to the following circuit layout:
NB: "
produces a linear structure, which has a depth,
or delay, of O(foldl1
f z xs"
). Use length
xsfold
if your binary operator f
is
associative, as "
produces a structure with a depth of
O(log_2(fold
f xs"
)).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 treelike
structure. The depth, or delay, of the structure produced by
"
", is hence fold
f xsO(log_2(
, and not
length
xs))O(
.length
xs)
NB: The binary operator "f
" in "
" must be associative.fold
f xs
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
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
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)>
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 #
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 #
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>)
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 #
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 #
(!!) :: (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 ...
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 nlength 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>
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 stepsize 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 stepsize 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:
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,s1)) 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,s1)) 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:
transpose :: KnownNat n => Vec m (Vec n a) > Vec n (Vec m a) Source #
Transpose a matrix: go from rowmajor to columnmajor
>>>
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>>
:: 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 
1dimensional 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>
:: (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) 
2dimensional 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>>
:: 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>>
:: (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>>>>
:: (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.
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>
:: (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.
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
d xs
" creates a vector:
<x_0,x_d,x_(2d),...,x_1,x_(d+1),x_(2d+1),...,x_(d1),x_(2d1),x_(3d1)>
>>>
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 Vec
tor 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 Vec
tor 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 Vec
tor 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 Vec
tor 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.
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>
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 zipWith
s 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>
:: 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 
> (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 instanceApply
(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: "
" creates a linear structure, which has a depth,
or delay, of O(dfold
m f z xs
). Look at length
xsdtfold
for a dependently typed
fold that produces a structure with a depth of O(log_2(
)).length
xs
:: 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 
> 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 treelike 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 .. k1]
(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)
)
treestructure 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 bitwidth, 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 treestructure of
add
es:
# 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 instanceApply
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 offold
, we had to restrict ourBitVector
argument to have bitwidth 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 bitwidth for every layer, from the VHDL/(System)Verilog produced by the Clash compiler.
NB: The depth, or delay, of the structure produced by
"
" is O(log_2(dtfold
m f g xs
)).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 #
seqV :: KnownNat n => Vec n a > b > b infixr 0 Source #
Evaluate all elements of a vector to WHNF, returning the second argument
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 XException
s.
forceVX :: KnownNat n => Vec n a > Vec n a Source #
Evaluate all elements of a vector to WHNF. Does not propagate
XException
s.
Perfect depth trees
module Clash.Sized.RTree
Annotations
module Clash.Annotations.TopEntity
Generics typeclasses
Representable types of kind *
.
This class is derivable in GHC with the DeriveGeneric
flag on.
A Generic
instance must satisfy the following laws:
from
.to
≡id
to
.from
≡id